Abstract:
A semiconductor optical device includes a waveguide layer and a reflecting multi-layer film. The waveguide layer includes two cladding layers and an active layer sandwiched between the two cladding layers. The reflecting multi-layer film including multiple layers is on at least one of a pair of opposing end faces of the waveguide layer. A summation Σn i d i  of products n i d i  of refractive indexes n i  and thicknesses d i  of the layers denoted i in the reflecting multi-layer film, and a wavelength λ 0  of light guided through the waveguide layer satisfies a relationship, Σn i d i &gt;λ 0 /4. A first wavelength bandwidth Δλ is wider than a second wavelength bandwidth ΔΛ. Δλ is a wavelength range including the wavelength λ 0  in which a reflectance R of the reflecting multi-layer film is not higher than +2.0% from reflectance R at the wavelength λ 0 . ΔΛ is a wavelength range including the wavelength λ 0  in which a reflectance R′ of a hypothetical layer is not higher than +2.0% from a hypothetical reflectance R′ at the wavelength λ 0  of a hypothetical layer having a thickness of 5λ 0 /(4n f ), a refractive index n f , on the at least one of opposing end faces, and satisfying a relationship, R′=((n c −n f   2 )/(n c +n f   2 )) 2 , where n c  denotes an effective refractive index of the waveguide layer.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a semiconductor optical device such as a semiconductor laser device used as a light source for optical information processing, a signal for optical communication, an excitation light source of a fiber amplifier, or the like, a semiconductor amplifier for amplifying an optical signal, or an optical modulator for modulating an optical signal. 
     2. Description of the Background Art 
     An end face, including a waveguide layer, of a semiconductor laser device or a semiconductor optical device, such as an optical modulator, is generally coated with a reflecting film. When a reflecting film having a refractive index n 1  on the end face portion of the semiconductor element has a film thickness d equal to an odd integer multiple of λ/(4n 1 ), the reflectance of the reflecting film becomes a minimum value. In addition, when a coating having a refractive index which is a square root of a refractive index n c  of a laminated element is on a waveguide layer at the end face portion is, an antireflecting film is obtained. For example, the reference of I. Ladany, et al., “Scandium oxide antireflection coatings for superluminescent LEDs”, Appl. Opt. Vol. 25, No. 4, pp. 472-473, (1986), describes a semiconductor laser with an antireflection film on the end face. 
     Wavelength dependence of reflectance of a reflecting film (refractive index n 1 =1.449) including films of various thicknesses in a laminated element (effective refractive index n c =3.37), including a waveguide layer of an end face portion of a semiconductor optical device, will be considered. In this case, the reflectance is set to be the minimum value at a setting wavelength λ=980 nm. When the reflectance is the minimum value, the thickness is an odd integer multiple of λ/(4n 1 ). If the single-layer reflecting film has a thickness of λ/(4n i ) and if the single-layer reflecting film has a thickness of 5λ/(4n 1 ), it is understood that a flat portion near a minimal value of the reflectance in the single-layer reflecting film having the thickness of λ/(4n 1 ) is larger than that in the single-layer reflecting film having the thickness of 5λ/(4n 1 ). 
     When a thickness d of the reflecting film on the end face portion of the semiconductor optical device is increased an odd-number of times λ/(4n 1 ), a wavelength band of a low-reflectance area near the minimal value of the reflectance becomes narrow, and a semiconductor laser characteristic disadvantageously varies singificantly due to the wavelength dependence of the reflectance of the reflecting film. 
     Typically, the single-layer reflecting film having a thickness of d 1 =λ/(4n 1 ) has a minimal reflectance of 4% at a wavelength λ of 980 nm. In this case, the reflectance in the range of a wavelength of 848 nm to a wavelength of 1161 nm ranges from a minimal value of 4.0% to 6.0%. The continuous wavelength band in the range of 4.0% to 6.0% is 313 nm. Meanwhile, the single-layer reflecting film having a thickness of d 1 =5λ/(4n 1 ) has a minimal reflectance of 4% at a wavelength λ of 980 nm. In this case, the reflectance in the range of a wavelength of 951 nm to a wavelength of 1011 nm ranges from a minimal value of 4.0% to 6.0%. The first continuous wavelength band in the range of 4.0% to 6.0% is 60 nm narrower than that of the single-layer reflecting film having a thickness of d 1 =λ/(4n 1 ). Then, a first reference value is obtained by dividing the wavelength band by the predetermined wavelength of 980 nm is about 0.061. Also, the reflectance in the range of a wavelength of 949 nm to a wavelength of 1013 nm ranges from a minimal value of 4.0% to 6.5%. The first continuous wavelength band in the range of 4.0% to 6.5% is 64 nm. Then, a second reference value is obtained by dividing the wavelength band by the predetermined wavelength of 980 nm is about 0.065. 
     SUMMARY OF THE INVENTION 
     Therefore, it is an object of the present invention to provide a semiconductor optical device including a reflecting film having a low reflectance over a wide wavelength band. 
     A semiconductor optical device includes a waveguide layer and a reflecting multi-layer film. The waveguide layer includes two cladding layers and an active layer sandwiched between the two cladding layers. The reflecting multi-layer film is formed on at least one of a pair of opposing end faces of the waveguide layer. A summation Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the reflecting multi-layer film, and a wavelength λ 0  of light guided through the waveguide layer satisfies a relationship, Σn i d i &gt;λ 0 /4. A first wavelength bandwidth Δλ is wider than a second wavelength bandwidth ΔΛ. The Δλ is a wavelength range including the wavelength λ 0  in which a hypothetical reflectance R(λ) at a wavelength λ is not higher than +2.0% from reflectance R(λ 0 ) at the wavelength λ 0 . The ΔΛ is a wavelength range including the wavelength λ 0  in which a hypothetical reflectance R′(λ) at a wavelength λ is not higher than +2.0% from a hypothetical reflectance R′(λ 0 ) at the wavelength λ 0  of a hypothetical layer having a thickness of 5λ 0 /(4n f ) of a refractive index n f  formed on the at least one of opposing end faces satisfies a relationship, R(λ 0 )=((n c −n f   2 )/(n c +n f   2 )) 2 . The n c  denotes an effective refractive index of the waveguide layer. 
     The Σn i d i  preferably satisfies the relationship Σn i d i &gt;5λ 0 /4. In this manner, the thickness of the reflecting film can be made more large. A value Δλ/λ 0  obtained by dividing the wavelength bandwidth Δλ by the wavelength λ 0  is preferably 0.070 or more, more preferably 0.090 or more, and still more preferably 0.10 or more. When the wavelength bandwidth Δλ of a low reflectance is large, the wavelength dependence of the reflectance is small. For this reason, a change in characteristic can be suppressed even though the wavelength of waveguide light changes. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will become readily understood from the following description of preferred embodiments thereof made with reference to the accompanying drawings, in which like parts are designated by like reference numeral and in which: 
         FIG. 1  is a graph of a complex plane of an amplitude reflectance by complex number expression; 
         FIG. 2  is a schematic sectional view of the structure of a semiconductor optical device having an hypothetical reflecting film on an end face; 
         FIG. 3  is a schematic sectional view of the structure of a semiconductor optical device according to the present invention when the hypothetical reflecting film in  FIG. 2  is replaced with a two-layer film; 
         FIG. 4  is a schematic sectional view of the structure of a semiconductor optical device according to the present invention when the hypothetical reflecting film in  FIG. 2  is replaced with a four-layer film; 
         FIG. 5  is a schematic sectional view of the structure of the end face portion of a semiconductor optical device according to the first embodiment of the present invention; 
         FIG. 6  is a graph of a waveguide dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of the semiconductor optical device according to the first embodiment of the present invention; 
         FIG. 7  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of a semiconductor optical device according to the second embodiment of the present invention; 
         FIG. 8  is a graph of a wavelength dependence of a reflectance in an hypothetical reflecting film formed on an end face portion; 
         FIG. 9  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the third embodiment of the present invention; 
         FIG. 10  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fourth embodiment of the present invention; 
         FIG. 11  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifth embodiment of the present invention; 
         FIG. 12  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixth embodiment of the present invention; 
         FIG. 13  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventh embodiment of the present invention; 
         FIG. 14  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighth embodiment of the present invention; 
         FIG. 15  is a schematic sectional view of the structure of an end face portion of a semiconductor optical device according to the ninth embodiment of the present invention; 
         FIG. 16  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of the semiconductor optical device according to the ninth embodiment of the present invention; 
         FIG. 17  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the tenth embodiment of the present invention; 
         FIG. 18  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eleventh embodiment of the present invention; 
         FIG. 19  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twelfth embodiment of the present invention; 
         FIG. 20  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirteenth embodiment of the present invention; 
         FIG. 21  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fourteenth embodiment of the present invention; 
         FIG. 22  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifteenth embodiment of the present invention; 
         FIG. 23  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixteenth embodiment of the present invention; 
         FIG. 24  is a schematic sectional view of the structure of an end face portion of a semiconductor optical device according to the seventeenth embodiment of the present invention; 
         FIG. 25  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of the semiconductor optical device according to the seventeenth embodiment of the present invention; 
         FIG. 26  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of the semiconductor optical device according to the eighteenth embodiment of the present invention; 
         FIG. 27  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the nineteenth embodiment of the present invention; 
         FIG. 28  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twentieth embodiment of the present invention; 
         FIG. 29  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twenty-first embodiment of the present invention; 
         FIG. 30  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twenty-second embodiment of the present invention; 
         FIG. 31  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twenty-third embodiment of the present invention; 
         FIG. 32  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twenty-fourth embodiment of the present invention; 
         FIG. 33  is a schematic sectional view of the structure of an end face portion of a semiconductor optical device according to the twenty-fifth embodiment of the present invention; 
         FIG. 34  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of the semiconductor optical device according to the twenty-fifth embodiment of the present invention; 
         FIG. 35  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of the semiconductor optical device according to the twenty-sixth embodiment of the present invention; 
         FIG. 36  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twenty-seventh embodiment of the present invention; 
         FIG. 37  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twenty-eighth embodiment of the present invention; 
         FIG. 38  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the twenty-ninth embodiment of the present invention; 
         FIG. 39  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirtieth embodiment of the present invention; 
         FIG. 40  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirty-first embodiment of the present invention; 
         FIG. 41  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirty-second embodiment of the present invention; 
         FIG. 42  is a schematic sectional view of the structure of an end face portion of a semiconductor optical device according to the thirty-third embodiment of the present invention; 
         FIG. 43  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of the semiconductor optical device according to the thirty-third embodiment of the present invention; 
         FIG. 44  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on the end face portion of the semiconductor optical device according to the thirty-fourth embodiment of the present invention; 
         FIG. 45  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirty-fifth embodiment of the present invention; 
         FIG. 46  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirty-sixth embodiment of the present invention; 
         FIG. 47  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirty-seventh embodiment of the present invention; 
         FIG. 48  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirty-eighth embodiment of the present invention; 
         FIG. 49  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the thirty-ninth embodiment of the present invention; 
         FIG. 50  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fortieth embodiment of the present invention; 
         FIG. 51  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-first embodiment of the present invention; 
         FIG. 52  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-second embodiment of the present invention; 
         FIG. 53  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-third embodiment of the present invention; 
         FIG. 54  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-fourth embodiment of the present invention; 
         FIG. 55  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-fifth embodiment of the present invention; 
         FIG. 56  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-sixth embodiment of the present invention; 
         FIG. 57  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-seventh embodiment of the present invention; 
         FIG. 58  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-eighth embodiment of the present invention; 
         FIG. 59  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the forty-ninth embodiment of the present invention; 
         FIG. 60  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fiftieth embodiment of the present invention; 
         FIG. 61  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-first embodiment of the present invention; 
         FIG. 62  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-second embodiment of the present invention; 
         FIG. 63  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-third embodiment of the present invention; 
         FIG. 64  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-fourth embodiment of the present invention; 
         FIG. 65  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-fifth embodiment of the present invention; 
         FIG. 66  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-sixth embodiment of the present invention; 
         FIG. 67  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-seventh embodiment of the present invention; 
         FIG. 68  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-eighth embodiment of the present invention; 
         FIG. 69  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the fifty-ninth embodiment of the present invention; 
         FIG. 70  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixtieth embodiment of the present invention; 
         FIG. 71  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-first embodiment of the present invention; 
         FIG. 72  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-second embodiment of the present invention; 
         FIG. 73  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-third embodiment of the present invention; 
         FIG. 74  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-fourth embodiment of the present invention; 
         FIG. 75  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-fifth embodiment of the present invention; 
         FIG. 76  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-sixth embodiment of the present invention; 
         FIG. 77  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-seventh embodiment of the present invention; 
         FIG. 78  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-eighth embodiment of the present invention; 
         FIG. 79  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the sixty-ninth embodiment of the present invention; 
         FIG. 80  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventieth embodiment of the present invention; 
         FIG. 81  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-first embodiment of the present invention; 
         FIG. 82  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-second embodiment of the present invention; 
         FIG. 83  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-third embodiment of the present invention; 
         FIG. 84  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-fourth embodiment of the present invention; 
         FIG. 85  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-fifth embodiment of the present invention; 
         FIG. 86  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-sixth embodiment of the present invention; 
         FIG. 87  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-seventh embodiment of the present invention; 
         FIG. 88  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-eighth embodiment of the present invention; 
         FIG. 89  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the seventy-ninth embodiment of the present invention; 
         FIG. 90  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eightieth embodiment of the present invention; 
         FIG. 91  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-first embodiment of the present invention; 
         FIG. 92  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-second embodiment of the present invention; 
         FIG. 93  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-third embodiment of the present invention; 
         FIG. 94  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-fourth embodiment of the present invention; 
         FIG. 95  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-fifth embodiment of the present invention; 
         FIG. 96  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-sixth embodiment of the present invention; 
         FIG. 97  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-seventh embodiment of the present invention; 
         FIG. 98  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-eighth embodiment of the present invention; 
         FIG. 99  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the eighty-ninth embodiment of the present invention; 
         FIG. 100  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninetieth embodiment of the present invention; 
         FIG. 101  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-first embodiment of the present invention; 
         FIG. 102  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-second embodiment of the present invention; 
         FIG. 103  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-third embodiment of the present invention; 
         FIG. 104  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-fourth embodiment of the present invention; 
         FIG. 105  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-fifth embodiment of the present invention; 
         FIG. 106  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-sixth embodiment of the present invention; 
         FIG. 107  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-seventh embodiment of the present invention; 
         FIG. 108  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-eighth embodiment of the present invention; 
         FIG. 109  is a schematic sectional view of the structure of an end face portion of a semiconductor optical device according to the ninety-ninth embodiment of the present invention; 
         FIG. 110  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the ninety-ninth embodiment of the present invention; 
         FIG. 111  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 100th embodiment of the present invention; 
         FIG. 112  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 101st embodiment of the present invention; 
         FIG. 113  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 102nd embodiment of the present invention; 
         FIG. 114  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 103rd embodiment of the present invention; 
         FIG. 115  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 104th embodiment of the present invention; 
         FIG. 116  is a schematic sectional view of the structure of an end face portion of a semiconductor optical device according to the 105th embodiment of the present invention; 
         FIG. 117  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 105th embodiment of the present invention; 
         FIG. 118  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 106th embodiment of the present invention; 
         FIG. 119  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 107th embodiment of the present invention; 
         FIG. 120  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 108th embodiment of the present invention; 
         FIG. 121  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 109th embodiment of the present invention; and 
         FIG. 122  is a graph of a wavelength dependence of a reflectance on a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to the 110th embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Semiconductor optical devices according to embodiments of the present invention will be described below with reference to the accompanying drawings. The same reference numerals as in the drawings denote the same parts in the drawings. 
     Calculation of a reflectance of a reflecting multi-layer film formed on an end face portion of a semiconductor optical device according to an embodiment of the present invention will be described below with reference to  FIGS. 1  to  5 .  FIG. 1  is a graph of a complex plane of an amplitude reflectance r which is expressed by a complex number.  FIG. 2  is a schematic sectional view of a single-layer reflecting film on an end face portion of a semiconductor optical device.  FIG. 3  is a schematic sectional view obtained when a two-layer reflecting film is formed in place of the single-layer reflecting film in FIG.  2 .  FIG. 4  is a schematic sectional view obtained when a four-layer reflecting film is formed in place of the single-layer reflecting film in FIG.  2 .  FIG. 5  is a schematic sectional view obtained when a seven-layer reflecting film is formed in place of the single-layer reflecting film. The amplitude reflectance r which is expressed as a complex number and which is related to light having a wavelength λ is expressed by the following equation (1), and can be indicated on the graph of the complex plane in FIG.  1 .
 
 r=r   r (λ)+ ir   i (λ)  (1)
 
Reference symbol i denotes an imaginary unit (i=(−1) 1/2 ), reference symbol r r (λ) denotes a real part, and reference symbol r i (λ) denotes an imaginary part. A general reflectance is the square of the amplitude reflectance. The case in which the reflectance is zero corresponds to the case in which the real part and the imaginary part of the amplitude reflectance are zero as expressed in the following equations (2a) and (2b). These relational expressions are solved to make it possible to obtain a condition for making the reflectance zero.
 
 r   r (λ)=0  (2a)
 
 r   i (λ)=0  (2b)
 
     On the other hand, in order to calculate a reflectance which is not zero, amplitude reflectance at respective points on a circumference on the complex plane in FIG.  1 . For this reason, the conditional expressions described above are not uniquely determined. Therefore, an hypothetical reflecting film from which a desired reflectance with reference to a wavelength λ of guided light will be considered.  FIG. 2  is a schematic sectional view of an hypothetical reflecting film obtained by forming a single-layer reflecting film  1  on an end face of a waveguide layer  10  of the semiconductor optical device. The single-layer reflecting film  1  faces a free space  5  such as the atmosphere. A condition for minimizing the amplitude reflectance r of the single-layer reflecting film  1  is expressed by the following equation (3) by using the wavelength λ of light guided through the waveguide layer  10  of the semiconductor optical device, a refractive index n f  of the single-layer reflecting film  1 , and a film thickness d f . 
               d   f     =       λ     4   ⁢           ⁢     n   f         ⁢     (       2   ⁢   m     +   1     )               (   3   )             
 
where m=0, 1, 2, 3, or the like which is 0 or a positive integer.
 
     The minimum value of the amplitude reflectance r of the hypothetical film is expressed by the following equation (4). 
             r   =         n   c     -     n   f   2           n   c     +     n   f   2                 (   4   )             
 
     A reflectance R is expressed by |r| 2  with reference to the amplitude reflectance r. More specifically, R=((n c −n f   2 )/(n c +n f   2 )) 2  is satisfied. Therefore, in order to satisfy reflectance R=4%, when an effective refractive index n c  of the waveguide layer of the semiconductor optical device satisfies n c =3.37, the above equation is solved, 2.248 or 1.499 is obtained as the refractive index n f  of the single-layer reflecting film  1 . However, in general, a single-layer film having such a refractive index is hardly obtained. Therefore, it will be considered that the hypothetical reflecting film is replaced with a reflecting multi-layer film. 
     A reflectance obtained when a two-layer reflecting film is arranged in place of the single-layer reflecting film will be considered.  FIG. 3  is a schematic sectional view obtained when the two-layer reflecting film is used on the end face portion in place of the hypothetical reflecting film. A consideration result by the present inventors will be described below with reference to a condition for setting a minimal value of the reflectance of the two-layer reflecting film. It is assumed that phase shifts of the first-layer film  1  and the second-layer film  2  constituting the two-layer reflecting film are represented by φ 1  and φ 2 , respectively. In this case, the phase shifts are defined by the following equations (5) and (6): 
               ϕ   1     =         2   ⁢           ⁢   π     λ     ⁢     n   1     ⁢     d   1               (   5   )                 ϕ   2     =         2   ⁢           ⁢   π     λ     ⁢     n   2     ⁢     d   2               (   6   )             
 
     In this case, an amplitude reflectance r expressed by a complex number is given by the following equation (7): 
             r   =         Re   ⁢           ⁢   1     +     i   ⁢           ⁢   Im   ⁢           ⁢   1           Re   ⁢   2     +     i   ⁢           ⁢   Im   ⁢           ⁢   2                 (   7   )             
 
     where i is an imaginary unit, Re 1  and Re 2  are real parts of the numerator and the denominator, and Im 1  and Im 2  are imaginary parts of the numerator and the denominator. 
     In the equation (7), the real parts Re 1  and Re 2  and the imaginary parts Im 1  and Im 2  of the numerator and the denominator are expressed as described in the following equations (8a) to (8d): 
               Re   ⁢           ⁢   1     =         (       n   c     -   1     )     ⁢   cos   ⁢           ⁢     ϕ   1     ⁢   cos   ⁢           ⁢     ϕ   2       +       (         n   1       n   2       -         n   2     ⁢     n   c         n   1         )     ⁢   sin   ⁢           ⁢     ϕ   1     ⁢   sin   ⁢           ⁢     ϕ   2                 (     8   ⁢   a     )                 Im   ⁢           ⁢   1     =     -     {         (         n   c       n   2       -     n   2       )     ⁢   cos   ⁢           ⁢     ϕ   1     ⁢   sin   ⁢           ⁢     ϕ   2       +       (         n   c       n   1       -     n   1       )     ⁢   sin   ⁢           ⁢     ϕ   1     ⁢   cos   ⁢           ⁢     ϕ   2         }               (     8   ⁢   b     )                 Re   ⁢           ⁢   2     =         (       n   c     +   1     )     ⁢   cos   ⁢           ⁢     ϕ   1     ⁢   cos   ⁢           ⁢     ϕ   2       -       (           n   2     ⁢     n   c         n   1       +       n   1       n   2         )     ⁢   sin   ⁢           ⁢     ϕ   1     ⁢   sin   ⁢           ⁢     ϕ   2                 (     8   ⁢   c     )                 Im   ⁢           ⁢   2     =     -     {         (         n   c       n   2       +     n   2       )     ⁢   cos   ⁢           ⁢     ϕ   1     ⁢   sin   ⁢           ⁢     ϕ   2       +       (         n   c       n   1       +     n   1       )     ⁢   sin   ⁢           ⁢     ϕ   1     ⁢   cos   ⁢           ⁢     ϕ   2         }               (     8   ⁢   d     )             
 
     The reflectance R is expressed as |r| 2  by using the amplitude reflectance r. Thickness d 1  and d 2  may be determined such that the amplitude reflectance expressed by the equation (7) is equal to the amplitude reflectance of the hypothetical reflecting film expressed by the equation (4). 
       FIG. 4  is a schematic sectional view obtained when a four-layer reflecting film is formed on the end face portion in place of the single-layer reflecting film. A condition for making the reflectance of the four-layer reflecting film equal to the reflectance of the hypothetical single-layer film at a setting wavelength will be considered. In the four-layer reflecting film, the amplitude reflectance is expressed by the following equation (9). 
             r   =           (       m   11     +     m   12       )     ⁢     n   c       -     (       m   21     +     m   22       )             (       m   11     +     m   12       )     ⁢     n   c       +     (       m   21     +     m   22       )                 (   9   )               
     where m ij  (i, j=1 or 2) is expressed by the following equation (10): 
                     (           m   11           m   12               m   21           m   22           )     =       ⁢     (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1                   -           ⁢   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             )                     ⁢       (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2                   -           ⁢   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             )     ×                     ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1                   -           ⁢   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             )                     ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2                   -           ⁢   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             )                   (   10   )             
 
     where A and B are parameters representing contributing rates of respective two-layer films (pair) when a film thickness Ad 1  of a first-layer reflecting film  1 , a film thickness Ad 2  of a second-layer film  2 , a film thickness Bd 1  of a third-layer film  3 , and a film thickness Bd 2  of a fourth-layer film  4  are given. 
       FIG. 5  is a schematic sectional view obtained when a seven-layer reflecting film  20  is formed on an end face portion of a waveguide layer  10 . A condition for setting the reflectance of the seven-layer reflecting film  20  to be equal to the reflectance of the hypothetical film will be considered. In the seven-layer reflecting film  20 , an amplitude reflectance is expressed by the following equation (11) as in the four-layer reflecting film. 
             r   =           (       m   11     +     m   12       )     ⁢     n   c       -     (       m   21     +     m   22       )             (       m   11     +     m   12       )     ⁢     n   c       +     (       m   21     +     m   22       )                 (   11   )               
     where m ij  (i, j=1 or 2) is expressed by the following equation (12): 
                     (           m   11           m   12               m   21           m   22           )     =       ⁢       (           cos   ⁢           ⁢   O   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   O   ⁢           ⁢     ϕ   2                   -           ⁢   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   O   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   O   ⁢           ⁢     ϕ   2             )     ×                     ⁢     (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1                   -           ⁢   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             )     ⁢                       ⁢       (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2                   -           ⁢   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             )     ×                     ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1                   -           ⁢   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             )                     ⁢       (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2                   -           ⁢   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             )     ×                     ⁢     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1                   -           ⁢   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             )                     ⁢     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2                   -           ⁢   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             )                   (   12   )             
 
     where O, A, B, and C are parameters representing contributing rates of respective two-layer films (pair) when a film thickness Od 2  of a first-layer film  11 , a film thickness Ad 1  of a second-layer film  12 , a film thickness Ad 2  of a third-layer film  13 , a film thickness Bd 1  of a fourth-layer film  14 , a film thickness Bd 2  of a fifth-layer film  15 , a film thickness Cd 1  of a sixth-layer film  16 , and a film thickness Cd 2  of a seventh-layer film  17  are given. 
     First Embodiment 
     A semiconductor optical device according to the first embodiment of the present invention will be described below with reference to  FIGS. 5 and 6 .  FIG. 5  is a schematic sectional view obtained when a seven-layer reflective film is formed in place of a single-layer reflecting film. This semiconductor optical device is, for example, a semiconductor laser device, an optical modulator, an optical switch, or the like. In this semiconductor optical device, a reflecting multi-layer film having a low reflectance over a wide wavelength band centering around a predetermined wavelength is formed on an end face portion of a waveguide layer through which light is guided. In this manner, when the reflecting multi-layer film having the low reflectance is formed, noise or the like generated by the so-called reflected can be reduced in, e.g., a semiconductor laser device. In an optical modulator and an optical switch, a signal can be transmitted with a low loss. Since this reflecting multi-layer film has a low reflectance over the wide wavelength band, A wavelength dependence of a reflection characteristic can be suppressed even though an oscillation wavelength or a center wavelength of a signal changes. 
     The seven-layer reflecting film  20  formed on the end face portion of the semiconductor optical device will be described below with reference to FIG.  5 .  FIG. 5  is a schematic sectional view of the configuration of the seven-layer reflecting film  20  formed on the end face portion of the semiconductor optical device. In this semiconductor optical device, on an end face portion of a waveguide layer  10  (equivalent refractive index n c =3.37), a first-layer film  11  (refractive index n 2 =1.62 and a film thickness Od 2 ) made of aluminum oxide, a second-layer film  12  (refractive index n 1 =2.057 and a film thickness Ad 1 ) made of tantalum oxide, a third-layer film  13  (refractive index n 2 =1.62 and a film thickness Ad 2 ) made of aluminum oxide, a fourth-layer film  14  (refractive index n 1 =2.057 and a film thickness Bd 1 ) made of tantalum oxide, a fifth-layer film  15  (refractive index n 1 =1.62 and a film thickness Bd 2 ) made of aluminum oxide, a sixth-layer film  16  (refractive index n 1 =2.057 and a film thickness Cd 1 ) made of tantalum oxide, and a seventh-layer film  17  (refractive index n 2 =1.62 and a film thickness Cd 2 ) made of aluminum oxide are sequentially stacked. The seventh-layer film  17  is in contact with a free space  5  such as the atmosphere. 
     The reflection characteristic of the seven-layer reflecting film  20  formed on the end face portion of the semiconductor optical device will be described below. A setting reflectance R(λ 0 ) is set at 2% when a setting wavelength λ 0 =980 nm. When the parameters are given by O=0.2, A=2.2, B=2.0, and C=2.0, and when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.45844 and φ 2 =1.14932, a reflectance of 2% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =22.13 nm/76.47 nm/234.44 nm/69.52 nm/221.31 nm/69.52 nm/221.31 nm. The total thickness (d total =Σd 1 ) of the film is 923.7 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1590.57 nm which is very large, i.e., about 6.49 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. More specifically, the film thickness is larger than the 5/4 wavelength of the predetermined wavelength 980 nm of guided light. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 6  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  20 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In this case, about +1% of the set reference is a target reflectance. In this seven-layer reflecting film, a flat portion having about 3% of the target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 968 nm to a wavelength of 1210 nm ranges from a minimal value of 1.3% to 4.0%. With reference to the reflectance of 2.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 242 nm. A value obtained by dividing the wavelength band by the predetermined wavelength λ 0  (=980 nm) is about 0.246. 
     Meanwhile, it is assumed that a hypothetical single reflecting film having a thickness of 5λ/(4n 1 ) has a minimal reflectance of 4% at a wavelength λ of 980 nm. It should be noted that the effective refractive index n c =3.37, and the refractive index n 1 =1.449. In this case, the reflectance in the range of a wavelength of 951 nm to a wavelength of 1011 nm ranges from a minimal value of 4.0% to 6.0%. The continuous wavelength band in the range of 4.0% to 6.0% is 60 nm. An reference index of continuous wavelength band is obtained by dividing the wavelength band by the predetermined wavelength of 980 nm is about 0.061. 
     Then, as compared to the reference index, the value of 0.246 is larger than the reference index of 0.061 in the hypothetical single reflecting film. Therefore, as described above, it is understood that, although the seven-layer reflecting film has a film thickness which is larger than the 5/4 wavelength of the predetermined wavelength of 980 nm of the guided light, the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Second Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the second embodiment of the present invention will be described below with reference to FIG.  7 .  FIG. 7  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The semiconductor optical device has the same multi-layer film configuration as that of the semiconductor optical device according to the first embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 2.0% when the setting wavelength λ 0  is 879 nm. When the parameters are given by O=0.2, A=2.2, B=2.0, and C=2.0, when the phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxidea are given by φ 1 =0.45844 and φ 2 =1.14932, a reflectance of 2% is obtained at a wavelength of 879 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =19.85 nm/68.59 nm/218.35 nm/62.36 nm/198.50 nm/62.36 nm/198.50 nm. The total thickness (d total =Σd i ) of the film is 828.51 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1426.66 nm which is very large, i.e., about 5.82 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 7  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 861 nm to a wavelength of 1098 nm ranges from a minimal value of 1.3% to 4.0%. In this case, the flat portion centering around a predetermined wavelength of 980 nm of guided light can be obtained. With reference to the reflectance of 2.0% at the setting wavelength 879 nm, a continuous wavelength bandwidth Δλ in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 237 nm. A value obtained by dividing the wavelength band by the setting wavelength of 879 nm is about 0.270, and is larger than 0.061 in the hypothetical reflecting film. Therefore, as described above, it is understood that, although the seven-layer reflecting film has a film thickness which is larger than the 5/4 wavelength of the predetermined wavelength of 980 nm of the guided light, the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. Here, the “predetermined wavelength” means the wavelength of light guided through a waveguide layer. In this case, light having a wavelength of 980 nm is used. On the other hand, the “setting wavelength” means a wavelength which is set such that the predetermined wavelength is almost set at the center of the flat portion having the low reflection. 
     The widths of the wavelength bands each having a reflectance of +2.0% with reference to a minimal reflectance in the seven-layer reflecting film and the hypothetical reflecting film will be compared and considered. The minimal reflectance of the seven-layer reflecting film is 1.3%. For this reason, a wavelength range in which a reflectance of +2.0% is obtained with reference to the minimal reflectance, i.e., a range in which a reflectance of 3.3% or less is obtained is from a wavelength 866 nm to 1089 nm. More specifically, the wavelength band is 223 nm. On the other hand, in order to realize the equal minimal reflectance by an hypothetical reflecting film, since an effective refractive index n c =3.37 is satisfied, a refractive index n f  of the single-layer film may be set at 1.637 or 2.058. For example,  FIG. 8  shows a wavelength dependence of an hypothetical reflecting film having a refractive index n f =1.637 and a film thickness d=5λ/(4n f ). A range in which a reflectance is lower than the minimal reflectance +2.0% with reference to the minimal reflectance of 1.3% of the hypothetical reflecting film is from a wavelength of 952 nm to a wavelength of 1009 nm. More specifically, the wavelength band is 57 nm. Therefore, a wavelength band of a low reflectance in the seven-layer reflecting film is considerably wider than that in the hypothetical reflecting film having a thickness of d=5λ/(4n f ). 
     Third Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the third embodiment of the present invention will be described below with reference to FIG.  9 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.2, A=2.4, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.518834 and φ 2 =0.789695, a reflectance of 3.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =15.21 nm/94.42 nm/182.47 nm/78.68 nm/152.06 nm/78.68 nm/152.06 nm. The total thickness (d total =Σd i ) of the film is 753.58 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1330.83 nm which is very large, i.e., about 5.43 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 9  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 841 nm to a wavelength of 1014 nm ranges from 2.5% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 173 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.177, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fourth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fourth embodiment will be described below with reference to FIG.  9 . This semiconductor optical device is different from the semiconductor optical device according to the third embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =1035 nm. Parameters are given by O=0.2, A=2.4, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.518834 and φ 2 =0.789695, a reflectance of 3% is obtained at a wavelength of 1035 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =16.06 nm/99.72 nm/192.72 nm/83.10 nm/160.60 nm/83.10 nm/160.60 nm. The total thickness (d total =Σd i ) of the film is 795.9 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1405.57 nm which is very large, i.e., about 5.43 times a ¼ wavelength (=258.75 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 10  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 888 nm to a wavelength of 1071 nm ranges from 2.5% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 1035 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 183 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1035 nm is about 0.177, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fifth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fifth embodiment of the present invention will be described below with reference to FIG.  11 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.15, A=2.5, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.52082 and φ 2 =0.767337, a reflectance of 4.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =11.08 nm/98.73 nm/184.70 nm/78.98 nm/147.76 nm/78.98 nm/147.76 nm. The total thickness (d total =Σd i ) of the film is 747.99 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1323.92 nm which is very large, i.e., about 5.40 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 11  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 834 nm to a wavelength of 1012 nm ranges from 3.5% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 178 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.182, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Sixth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the sixth embodiment will be described below with reference to FIG.  12 . This semiconductor optical device is different from the semiconductor optical device according to the fifth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelengths =1040 nm. Parameters are given by O=0.15, A=2.5, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.52082 and φ 2 =0.767337, a reflectance of 4% is obtained at a wavelength of 1040 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =11.76 nm/104.77 nm/196.00 nm/83.82 nm/156.80 nm/83.82 nm/156.80 nm. The total thickness (d total =Σd i ) of the film is 793.77 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1404.95 nm which is very large, i.e., about 5.73 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 12  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 885 nm to a wavelength of 1074 nm ranges from 3.5% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 1040 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 189 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1040 nm is about 0.1827, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Seventh Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the seventh embodiment of the present invention will be described below with reference to FIG.  13 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.15, A=2.5, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.541022 and φ 2 =0.741397, a reflectance of 5.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =10.71 nm/102.56 nm/178.45 nm/82.05 nm/142.76 nm/82.05 nm/142.76 nm. The total thickness (d total =Σd i ) of the film is 741.34 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1391.41 nm which is very large, i.e., about 5.38 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 13  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 843 nm to a wavelength of 1013 nm ranges from 4.6% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 170 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.173, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Eighth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the eighth embodiment will be described below with reference to FIG.  14 . This semiconductor optical device is different from the semiconductor optical device according to the third embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =1035 nm. Parameters are given by O=0.15, A=2.5, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.541022 and φ 2 =0.741397, a reflectance of 5% is obtained at a wavelength of 1035 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =11.31 nm/108.31 nm/188.47 nm/86.65 nm/150.77 nm/86.65 nm/150.77 nm. The total thickness (d total =Σd i ) of the film is 782.93 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1391.41 nm which is very large, i.e., about 5.68 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 14  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 890 nm to a wavelength of 1070 nm ranges from 4.6% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 1035 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 170 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1035 nm is about 0.164, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Ninth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the ninth embodiment will be described below with reference to  FIGS. 15 and 16 .  FIG. 15  is a schematic sectional view of a configuration in which a seven-layer reflecting film  30  using a tantalum oxide film as a first-layer film is formed as a reflecting film on an end face portion of the semiconductor optical device. This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that tantalum oxide 21/aluminum oxide 22/tantalum oxide 23/aluminum oxide 24/tantalum oxide 25/aluminum oxide 26/tantalum oxide 27 are sequentially stacked from the waveguide layer  10  side and the first-layer film  21  on the waveguide layer  10  side made of tantalum oxide. More specifically, in the seven-layer reflecting film  30 , from the waveguide layer  10  side, a first-layer film  21  (refractive index n 2 =2.037 and film thickness Od 2 ) made of tantalum oxide, a second-layer film  22  (refractive index n 1 =1.62 and film thickness Ad 1 ) made of aluminum oxide, a third-layer film  23  (refractive index n 2 =2.037 and film thickness Ad 2 ) made of tantalum oxide, a fourth-layer film  24  (refractive index n 1 =1.62 and film thickness Bd 1 ) made of aluminum oxide, a fifth-layer film  25  (refractive index n 2 =2.037 and film thickness Bd 2 ) made of tantalum oxide, a sixth-layer film  26  (refractive index n 1 =1.62 and film thickness Cd 1 ) made of aluminum oxide, and a seventh-layer film  27  (refractive index n 2 =2.037 and film thickness Cd 2 ) made of tantalum oxide. The semiconductor optical device is equal to the semiconductor optical device according to the first embodiment in that films made of aluminum oxide and tantalum oxide are alternately stacked. 
     In the seven-layer reflecting film  30  on the end face portion of the semiconductor optical device, a setting reflectance R(λ 0 ) is set to be 2.0% at a setting wavelength λ 0 =980 nm. In this case, when parameters are given by O=1.15, A=1.82, B=1.97, and C=2.06, and when phase shifts φ 1  and φ 2  of aluminum oxide and tantalum oxide are given by φ 1 =0.645821 and φ 2 =1.452041, a reflectance of 2% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =126.62 nm/1 13.17 nm/200.38 nm/122.49 nm/216.90 nm/128.09 nm/226.81 nm. The total thickness (d total =Σd i ) of the film is 1134.46 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 2174.63 nm which is very large, i.e., about 8.88 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 16  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  30 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 996 nm to a wavelength of 1119 nm ranges from 1.5% to 4.0%. With reference to the reflectance of 2.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 157 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.160, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Tenth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the tenth embodiment will be described below with reference to FIG.  17 . This semiconductor optical device is different from the semiconductor optical device according to the ninth embodiment in that a setting reflectance R(λ 0 ) is 2.0% at a setting wavelength λ 0 =908 nm. Parameters are given by O=1.15, A=1.82, B=1.97, and C=2.06 In addition, when phase shifts φ 1  and φ 2  of aluminum oxide and tantalum oxide are given by φ 1 =0.645821 and φ 2 =1.452041, a reflectance of 2.0% is obtained at a wavelength of 908 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =117.31 nm/104.85 nm/185.66 nm/113.49 nm/200.96 nm/118.68 nm/210.14 nm. The total thickness (d total =Σd i ) of the film is 1051.09 nm. A sum Σn i d i  of products n i d i  of refractive index n and film thickness d i  of a layer denoted with i in the seven films is 2014.81 nm which is very large, i.e., about 8.22 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 17  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 924 nm to a wavelength of 1037 nm ranges from 1.5% to 4.0%. With reference to the reflectance of 2.0% at the setting wavelength 908 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 145 nm. A value obtained by dividing the wavelength band by the setting wavelength of 908 nm is about 0.160, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Eleventh Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the eleventh embodiment will be described below with reference to FIG.  18 . This semiconductor optical device is different from the semiconductor optical device according to the ninth embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=1.15, A=1.82, B=1.97, and C=2.06. In addition, when phase shifts φ 1  and φ 2  of aluminum oxide and tantalum oxide are given by φ 1 =0.893399 and φ 2 =1.26984, a reflectance of 3.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =110.73 nm/156.55 nm/175.24 nm/169.45 nm/189.68 nm/177.19 nm/198.35 nm. The total thickness (d total =Σd i ) of the film is 1177.19 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 2201.59 nm which is very large, i.e., about 8.99 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 18  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 4% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 962 nm to a wavelength of 1053 nm ranges from 2.6% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 91 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.093, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Twelfth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the twelfth embodiment will be described below with reference to FIG.  19 . This semiconductor optical device is different from the semiconductor optical device according to the eleventh embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =913 nm. Parameters are given by O=1.15, A=1.82, B=1.97, and C=2.06. In addition, when phase shifts φ 1  and φ 2  of aluminum oxide and tantalum oxide are given by φ 1 =0.893399 and φ 2 =1.26984, a reflectance of 3.0% is obtained at a wavelength of 953 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =103.16 nm/145.85 nm/163.26 nm/157.87 nm/176.72 nm/165.08 nm/184.79 nm. The total thickness (d total =Σd i ) of the film is 1096.73 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 2140.93 nm which is very large, i.e., about 8.74 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 19  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 4% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 962 nm to a wavelength of 1053 nm ranges from 2.6% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 953 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 89 nm. A value obtained by dividing the wavelength band by the setting wavelength of 953 nm is about 0.093, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Thirteenth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the thirteenth embodiment will be described below with reference to FIG.  20 . This semiconductor optical device is different from the semiconductor optical device according to the ninth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=1.09, A=1.80, B=1.98, and C=2.05. In addition, when phase shifts φ 1  and φ 2  of aluminum oxide and tantalum oxide are given by φ 1 =0.922613 and φ 2 =1.26872, a reflectance of 4.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =104.86 nm/159.89 nm/173.16 nm/175.88 nm/190.48 nm/182.99 nm/198.17 nm. The total thickness (d total =Σd i ) of the film is 1185.43 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 2211.73 nm which is very large, i.e., about 9.03 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 20  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 890 nm to a wavelength of 980 nm ranges from 3.7% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 190 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.093, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fourteenth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fourteenth embodiment will be described below with reference to FIG.  21 . This semiconductor optical device is different from the semiconductor optical device according to the thirteenth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =912 nm. Parameters are given by O=1.09, A=1.80, B=1.98, and C=2.05. In addition, when phase shifts φ 1  and φ 2  of aluminum oxide and tantalum oxide are given by φ 1 =0.922613 and φ 2 =1.26872, a reflectance of 4.0% is obtained at a wavelength of 912 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =97.58 nm/148.80 nm/161.15 nm/163.68 nm/177.26 nm/170.29 nm/184.42 nm. The total thickness (d total =Σd 1 ) of the film is 1103.18 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 2059.26 nm which is very large, i.e., about 8.41 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 21  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 891 nm to a wavelength of 1069 nm ranges from 3.7% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 912 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 178 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1035 nm is about 0.195, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fifteenth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fifteenth embodiment will be described below with reference to FIG.  22 . This semiconductor optical device is different from the semiconductor optical device according to the ninth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =912 nm. Parameters are given by O=1.13, A=1.76, B=1.98, and C=2.06. In addition, when phase shifts φ 1  and φ 2  of aluminum oxide and tantalum oxide are given by φ 1 =1.0252 and φ 2 =1.18958, a reflectance of 5.0% is obtained at a wavelength of 912 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =101.93 nm/173.72 nm/158.75 nm/195.44 nm/178.60 nm/203.33 nm/185.81 nm. The total thickness (d total =Σd i ) of the film is 1103.18 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 2213.24 nm which is very large, i.e., about 9.03 times a 114 wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 22  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. With reference to the reflectance of 5.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 190 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.194, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Sixteenth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the sixteenth embodiment will be described below with reference to FIG.  23 . This semiconductor optical device is different from the semiconductor optical device according to the fifteenth embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =910 nm. Parameters are given by O=1.13, A=1.76, B=1.98, and C=2.06. In addition, when phase shifts φ 1  and φ 2  of aluminum oxide and tantalum oxide are given by φ 1 =1.0252 and φ 2 =1.18958, a reflectance of 5.0% is obtained at a wavelength of 910 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =94.65 nm/161.31 nm/147.41 nm/181.48 nm/165.84 nm/188.81 nm/172.54 nm. The total thickness (d total =Σd i ) of the film is 1112.04 nm. A sum Σn i d i  of products n i d i  of refractive index n and film thickness d i  of a layer denoted with i in the seven films is 2055.16 nm which is very large, i.e., about 8.39 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 23  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 891 nm to a wavelength of 1068 nm ranges from 4.7% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 910 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 177 nm. A value obtained by dividing the wavelength band by the setting wavelength of 910 nm is about 0.195, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical elements according to the first embodiment to the sixteenth embodiment are shown in Table 1. In Table 1, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands Δλ in which the reflectance falls within the range from −1.0 to +2.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
                                                                                 TABLE 1                   Characteristic of Reflecting Multi-layer Film                    Setting       Summation Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.0 to 2.0 of R(λ 0 )   Δλ/λ 0                      1   Seven films   980 nm   1.3%   1590.57 nm   242 nm   242/980 = 0.246               2.0%       6.49 times       2   Seven films   879 nm   1.3%   1426.66 nm   237 nm   237/879 = 0.270               2.0%       5.82 times       3   Seven films   980 nm   2.5%   1330.83 nm   173 nm   173/980 = 0.177               3.0%       5.43 times       4   Seven films   1035 nm    2.5%   1405.57 nm   183 nm   183/1035 = 0.177               3.0%       5.74 times       5   Seven films   980 nm   3.5%   1323.92 nm   178 nm   178/980 = 0.182               4.0%       5.40 times       6   Seven films   1040 nm    3.5%   1405.95 nm   189 nm   189/1040 = 0.182               4.0%       5.73 times       7   Seven films   980 nm   4.6%   1391.41 nm   170 nm   170/980 = 0.173               5.0%       5.38 times       8   Seven films   1035 nm    4.6%   1391.41 nm   170 nm   170/1035 = 0.164               5.0%       5.68 times       9   Seven films   980 nm   1.5%   2174.63 nm   157 nm   157/980 = 0.160               2.0%       8.88 times       10   Seven films   908 nm   1.5%   2014.81 nm   145 nm   145/908 = 0.160               2.0%       8.22 times       11   Seven films   980 nm   2.6%   2201.59 nm    91 nm    91/980 = 0.093               3.0%       8.99 times       12   Seven films   953 nm   2.6%   2140.93 nm    89 nm    89/953 = 0.093               3.0%       8.74 times       13   Seven films   980 nm   3.7%   2211.73 nm   190 nm   190/980 = 0.194               4.0%       9.03 times       14   Seven films   912 nm   3.7%   2059.26 nm   178 nm   178/912 = 0.195               4.0%       8.41 times       15   Seven films   980 nm   4.7%   2213.24 nm   190 nm   190/980 = 0.194               5.0%       9.03 times       16   Seven films   910 nm   4.7%   2055.16 nm   177 nm   177/910 = 0.195               5.0%       8.39 times                    
Seventeenth Embodiment
 
     A semiconductor optical device having a six-layer reflecting film according to the seventeenth embodiment of the present invention will be described below with reference to  FIGS. 24 and 25 .  FIG. 24  is a schematic sectional view of a configuration obtained when a six-layer reflecting film  40  is formed in place of a single-layer reflecting film as a reflecting film on an end face portion of the semiconductor optical element. The semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that the reflecting multi-layer film includes the six-layer reflecting film  40 . A condition for setting the reflectance of the six-layer reflecting film  40  to be equal to the reflectance of the hypothetical film will be considered. Also in the six-layer reflecting film  40 , as in the seven-layer reflecting film, an amplitude reflectance is expressed by the following equation (13): 
             r   =           (       m   11     +     m   12       )     ⁢     n   c       -     (       m   21     +     m   22       )             (       m   11     +     m   12       )     ⁢     n   c       +     (       m   21     +     m   22       )                 (   13   )             
 
     where m ij  (i and j are 1 or 2) is expressed by the following equation (14): 
               (           m   11           m   12               m   21           m   22           )     =       (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             )     ×     
     ⁢           ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             )     ×     
     ⁢           ⁢     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             )               (   14   )             
 
     where A, B, and C are parameters representing contributing rates of respective two-layer films (pair) when a film thickness Ad 1  of a first-layer film  31 , a film thickness Ad 2  of a second-layer film  32 , a film thickness Bd 1  of a third-layer film  33 , a film thickness Bd 2  of a fourth-layer film  34 , a film thickness Cd 1  of a fifth-layer film  35 , and a film thickness Cd 2  of a sixth-layer film  36  are given. 
     A case in which the six-layer reflecting film  40  is formed on an end face portion of the semiconductor optical device will be described below.  FIG. 24  is a schematic sectional view of the configuration of the six-layer reflecting film  40  formed on the end face portion. In this semiconductor optical device, on an end face portion of a waveguide layer  10  (equivalent refractive index n c =3.37), the first-layer film  31  (refractive index n 1 =2.057 and a film thickness Ad 1 ) made of tantalum oxide, the second-layer film  32  (refractive index n 2 =1.62 and a film thickness Ad 2 ) made of aluminum oxide, the third-layer film  33  (refractive index n 1 =2.057 and a film thickness Bd 1 ) made of tantalum oxide, the fourth-layer film  34  (refractive index n 2 =1.62 and a film thickness Bd 2 ) made of aluminum oxide, the fifth-layer film  35  (refractive index n 1 =2.057 and a film thickness Cd 1 ) made of tantalum oxide, and the sixth-layer film  36  (refractive index n 2 =1.62 and a film thickness Cd 2 ) made of aluminum oxide are sequentially stacked. In addition, the six-layer reflecting film  40  is in contact with a free space  5  such as the air. 
     The reflection characteristic of the six-layer reflecting film  40  formed on the end face portion of the semiconductor optical device will be described below. A setting reflectance R(λ 0 ) is set at 2% when a setting wavelength λ 0 =980 nm. When the parameters are given by A=2.0, B=2.0, and C=2.0, and when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.792828 and φ 2 =0.715471, a reflectance of 2% is obtained. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =120.23 nm/137.77 nm/120.23 nm/137.77 nm/120.23 nm/137.77 nm. The total thickness (d total =Σd i ) of the film is 774.0 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1411.50 nm which is very large, i.e., about 5.76 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 25  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In this six-layer reflecting film, a flat portion having about 3% of the target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 877 nm to a wavelength of 1017 nm ranges from a minimal value of 1.4% to 4.0%. With reference to the reflectance of 2.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 140 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.143, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that, the six-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Eighteenth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the eighteenth embodiment of the present invention will be described below with reference to FIG.  26 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 2.0% at a setting wavelength λ 0 =1014 nm. Parameters are given by A=2.0, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.792828 and φ 2 =0.715471, a reflectance of 2.0% is obtained at a wavelength of 1014 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =124.40 nm/142.55 nm/124.40 nm/142.55 nm/124.40 nm/142.55 nm. The total thickness (d total =Σd i ) of the film is 800.85 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1460.47 nm which is very large, i.e., about 5.96 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 26  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 907 nm to a wavelength of 1053 nm ranges from 1.4% to 4.0%. With reference to the reflectance of 2.0% at the setting wavelength 1014 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 146 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1014 nm is about 0.144, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Nineteenth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the nineteenth embodiment of the present invention will be described below with reference to FIG.  27 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.94, B=1.90, and C=2.2. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.948585 and φ 2 =0.476939, a reflectance of 3.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =139.54 nm/89.08 nm/136.66 nm/87.25 nm/158.24 nm/101.02 nm. The total thickness (d total =Σd i ) of the film is 711.79 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1342.95 nm which is very large, i.e., about 5.48 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 27  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 4% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 806 nm to a wavelength of 1009 nm ranges from 2.3% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 203 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.207, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Twentieth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the twentieth embodiment of the present invention will be described below with reference to FIG.  28 . This semiconductor optical device is different from the semiconductor optical device according to the nineteenth embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =1052 nm. Parameters are given by A=1.94, B=1.90, and C=2.2. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.948585 and φ 2 =0.476939, a reflectance of 3.0% is obtained at a wavelength of 1052 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =150.64 nm/96.17 nm/147.54 nm/94.19 nm/170.83 nm/109.06 nm. The total thickness (d total =Σd i ) of the film is 768.43 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1449.81 nm which is very large, i.e., about 5.92 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 28  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 4% of a target reflectance over a wide wavelength band can be obtained. More specifically, the minimal reflectance is 2.3%. With reference to the reflectance of 3.0% at the setting wavelength 1052 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 218 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1052 nm is about 0.207, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Twenty-first Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the twenty-first embodiment of the present invention will be described below with reference to FIG.  29 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.94, B=1.90, and C=2.2. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.98561 and φ 2 =0.417545, a reflectance of 4.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =144.98 nm/77.99 nm/141.99 nm/76.38 nm/164.41 nm/188.44 nm. The total thickness (d total =Σd i ) of the film is 794.19 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1483.84 nm which is very large, i.e., about 6.06 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 29  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 791 nm to a wavelength of 1020 nm ranges from 3.3% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 229 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.234, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Twenty-second Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the twenty-second embodiment of the present invention will be described below with reference to FIG.  30 . This semiconductor optical device is different from the semiconductor optical device according to the twenty-first embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =1075 nm. Parameters are given by A=1.94, B=1.90, and C=2.2. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.98561 and φ 2 =0.417545, a reflectance of 4.0% is obtained at a wavelength of 1075 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =159.04 nm/85.55 nm/155.76 nm/83.79 nm/180.35 nm/97.02 nm. The total thickness (d total =Σd i ) of the film is 761.51 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1450.03 nm which is very large, i.e., about 5.92 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 30  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 854 nm to a wavelength of 1105 nm ranges from 3.3% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 1075 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 251 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1075 nm is about 0.233, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Twenty-third Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the twenty-third embodiment of the present invention will be described below with reference to FIG.  31 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=2.04, B=1.92, and C=2.2. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.93793 and φ 2 =0.433879, a reflectance of 5.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =145.08 nm/85.22 nm/136.55 nm/80.21 nm/156.46 nm/91.90 nm. The total thickness (d total =Σd i ) of the film is 695.42 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1318.03 nm which is very large, i.e., about 5.38 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 31  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 787 nm to a wavelength of 1009 nm ranges from 4.6% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 222 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.227, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Twenty-fourth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the twenty-fourth embodiment of the present invention will be described below with reference to FIG.  32 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =1069 nm. Parameters are given by A=2.04, B=1.92, and C=2.2. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.93793 and φ 2 =0.433879, a reflectance of 5.0% is obtained at a wavelength of 1069 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =158.26 nm/92.96 nm/148.95 nm/87.49 nm/170.67 nm/100.25 nm. The total thickness (d total =Σd i ) of the film is 758.58 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1437.73 nm which is very large, i.e., about 5.87 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 32  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 858 nm to a wavelength of 1101 nm ranges from 4.6% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 1069 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 243 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1069 nm is about 0.227, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical elements according to the seventeenth embodiment to the twenty-fourth embodiment are shown in Table 2. In Table 2, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands AA in which the reflectance falls within the range from −1.0 to +2.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
                                                   TABLE 2                   Characteristic of Multi-layer Reflecting Film                    Setting       Summation Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.0 to 2.0 of R(λ 0 )   Δλ/λ 0                 17   Six films    980 nm   1.4%   1411.50 nm   140 nm   140/980 = 0.143               2.0%       5.76 times       18   Six films   1014 nm   1.4%   1460.47 nm   146 nm   146/1014 = 0.144               2.0%       5.96 times       19   Six films    980 nm   2.3%   1342.95 nm   203 nm   203/980 = 0.207               3.0%       5.48 times       20   Six films   1014 nm   2.3%   1449.81 nm   218 nm   218/1014 = 0.207               3.0%       5.92 times       21   Six films    980 nm   3.3%   1483.84 nm   229 nm   229/980 = 0.234               4.0%       6.06 times       22   Six films   1075 nm   3.3%   1450.03 nm   251 nm   251/1075 = 0.233               4.0%       5.92 times       23   Six films    980 nm   4.6%   1318.03 nm   222 nm   222/980 = 0.227               5.0%       5.38 times       24   Six films   1069 nm   4.6%   1437.73 nm   243 nm   243/1069 = 0.164               5.0%       5.87 times                    
Twenty-fifth Embodiment
 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the twenty-fifth embodiment of the present invention will be described below with reference to  FIGS. 33 and 34 .  FIG. 33  is a schematic sectional view of a configuration obtained when a seven-layer reflecting film  50  including three types films is formed in place of a single-layer reflecting film as a reflecting film on an end face portion of the semiconductor optical device. This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that the reflecting multi-layer film is the seven-layer reflecting film  50  including the three types films. More specifically, the semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a first-layer film being in contact with a waveguide layer  10  is an aluminum nitride film  41 . These semiconductor optical devices are equal to each other in that tantalum oxide films and aluminum oxide films are alternately stacked from the second-layer films to the seventh-layer films. 
     A condition for setting the reflectance of the seven-layer reflecting film  50  including the films of three types to be equal to the reflectance of the hypothetical film will be considered. A case in which the film of the third type is used as the first-layer film being in contact with the waveguide layer  10  is considered here. A phase shift φ3 of the third film is expressed by the following equation (15). 
               ϕ   3     =         2   ⁢   π     λ     ⁢     n   3     ⁢     d   3               (   15   )             
 
     Therefore, the amplitude reflectance of the seven-layer reflecting film  50  including the three types films is expressed by the following equation (16) like the amplitude reflectance of the seven-layer reflecting film and the six-layer reflecting film. 
             r   =           (       m   11     +     m   12       )     ⁢     n   c       -     (       m   21     +     m   22       )             (       m   11     +     m   12       )     ⁢     n   c       +     (       m   21     +     m   22       )                 (   16   )             
 
     where m ij  (i and j are 1 or 2) is expressed by the following equation (17): 
               (           m   11           m   12               m   21           m   22           )     =       (           cos   ⁢           ⁢     ϕ   3               -     i     n   3         ⁢   sin   ⁢           ⁢     ϕ   3                   -   i     ⁢           ⁢     n   3     ⁢   sin   ⁢           ⁢     ϕ   3             cos   ⁢           ⁢     ϕ   3             )     ×     (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             )     ×     
     ⁢           ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             )     ×     
     ⁢           ⁢     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             )               (   17   )             
 
     where A, B, and C represent contributing rates of respective two-layer films (pair) when a film thickness Ad 1  of a second-layer film  42 , a film thickness Ad 2  of a third-layer film  43 , a film thickness Bd 1  of a fourth-layer film  44 , a film thickness Bd 2  of a fifth-layer film  45 , a film thickness Cd 1  of a sixth-layer film  46 , and a film thickness Cd 2  of a seven-layer film  47  are given. 
     A case in which the seven-layer reflecting film  50  including the films of three types is formed on an end face portion of the semiconductor optical device will be described below.  FIG. 33  is a schematic sectional view of the configuration of the seven-layer reflecting film including the films of three types formed on the end face portion. In this semiconductor optical device, on an end face portion of the waveguide layer  10  (equivalent refractive index n c =3.37), a first-layer film  41  (refractive index n 3 =2.072 and a film thickness d 3 =50 nm) made of aluminum nitride (AlN), a second-layer film  42  (refractive index n 1 =2.057 and a film thickness Ad 1 ) made of tantalum oxide, a third-layer film  43  (refractive index n 2 =1.62 and a film thickness Ad 2 ) made of aluminum oxide, a fourth-layer film  44  (refractive index n 1 =2.057 and a film thickness Bd 1 ) made of tantalum oxide, a fifth-layer film  45  (refractive index n 2 =1.62 and a film thickness Bd 2 ) made of aluminum oxide, a sixth-layer film  46  (refractive index n 1 =2.057 and a film thickness Cd 1 ) made of tantalum oxide, and a seventh-layer film  47  (refractive index n 2 =1.62 and a film thickness Cd 2 ) made of aluminum oxide are stacked. In addition, the seven-layer reflecting film  50  is in contact with a free space  5  such as the air. 
     The thermal characteristic of the seven-layer reflecting film including the films of three types, i.e., the films made of aluminum nitride, tantalum oxide film, and aluminum oxide will be described below. The heat conductivity of the films of three types are about 1.8 W/(cm·K), about 0.1 W/(cm·K), and about 0.2 W/(cm·K), respectively. The aluminum nitride has the highest heat conductivity. For this reason, heat of the waveguide layer  10  can be rapidly radiated outside. 
     The reflecting characteristic of the seven-layer reflecting film  50  including the films of three types on the end face portion of the semiconductor optical device will be described below. A setting reflectance R(λ 0 ) is set to be 2.0% at a setting wavelength λ 0 =980 nm. When parameters are given by A=1.0, B=2.0, and C=2.0, and when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.23574 and φ 2 =0.727856, a reflectance of 2% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/93.7 nm/70.08 nm/187.40 nm/140.15 nm/187.40 nm/140.15 nm. The total thickness (d total =Σd i ) of the film is 868.88 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1634.92 nm which is very large, i.e., about 6.67 times a ¼ wavelength (=245 nm). For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 34  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 952 nm to a wavelength of 1194 nm ranges from 1.6% to 4.0%. With reference to the reflectance of 2.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 242 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.247, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Twenty-sixth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the twenty-sixth embodiment of the present invention will be described below with reference to FIG.  35 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the twenty-fifth embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 2.0% at a setting wavelength λ 0 =897 nm. Parameters are given by A=1.0, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.23574 and φ 2 =0.727856, a reflectance of 2.0% is obtained at a wavelength of 897 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50/83.26 nm/65.10 nm/166.52 nm/130.20 nm/166.52 nm/130.20 nm. The total thickness (d total =Σd i ) of the film is 791.8 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1487.24 nm which is very large, i.e., about 6.07 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 35  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 872 nm to a wavelength of 1086 nm ranges from 1.5% to 4.0%. With reference to the reflectance of 2.0% at the setting wavelength 897 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 214 nm. A value obtained by dividing the wavelength band by the setting wavelength of 897 nm is about 0.239, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Twenty-seventh Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the twenty-seventh embodiment of the present invention will be described below with reference to FIG.  36 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the twenty-fifth embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.0, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.20275 and φ 2 =0.765599, a reflectance of 3.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/91.20 nm/73.71 nm/182.40 nm/147.42 nm/182.40 nm/147.42 nm. The total thickness (d total =Σd i ) of the film is 874.55 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1638.64 nm which is very large, i.e., about 6.69 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 36  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 4% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 953 nm to a wavelength of 1195 nm ranges from 2.6% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 242 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.247, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Twenty-eighth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the twenty-eighth embodiment of the present invention will be described below with reference to FIG.  37 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the twenty-seventh embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the twenty-seventh embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =896 nm. Parameters are given by A=1.0, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.23574 and φ 2 =0.727856, a reflectance of 3.0% is obtained at a wavelength of 896 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/81.08 nm/68.15 nm/162.16 nm/136.31 nm/162.16 nm/136.31 nm. The total thickness (d total =Σd i ) of the film is 796.17 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1489.56 nm which is very large, i.e., about 6.08 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 37  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 4% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 872 nm to a wavelength of 1089 nm ranges from 2.5% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 896 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 217 nm. A value obtained by dividing the wavelength band by the setting wavelength of 896 nm is about 0.242, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Twenty-ninth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the twenty-ninth embodiment of the present invention will be described below with reference to FIG.  38 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the twenty-fifth embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.0, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.17459 and φ 2 =0.798874, a reflectance of 4.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/89.06 nm/76.91 nm/178.13 nm/153.83 nm/178.13 nm/153.83 nm. The total thickness (d total =Σd i ) of the film is 879.89 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1642.63 nm which is very large, i.e., about 6.70 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 38  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 953 nm to a wavelength of 1198 nm ranges from 3.6% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 245 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.250, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirtieth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the thirtieth embodiment of the present invention will be described below with reference to FIG.  39 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the twenty-ninth embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the twenty-ninth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =893 nm. Parameters are given by A=1.0, B=2.0, and C=2.0°. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.14262 and φ 2 =0.805876, a reflectance of 4.0% is obtained at a wavelength of 893 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/78.95 nm/70.70 nm/157.90 nm/141.40 nm/157.90 nm/141.40 nm. The total thickness (d total =Σd i ) of the film is 798.25 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1488.27 nm which is very large, i.e., about 6.07 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 39  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including three films made of materials different from each other. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 870 nm to a wavelength of 1090 nm ranges from 3.4% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 893 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 220 nm. A value obtained by dividing the wavelength band by the setting wavelength of 893 nm is about 0.246, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirty-first Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including three films made of materials different from each other according to the thirty-first embodiment of the present invention will be described below with reference to FIG.  40 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the twenty-fifth embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.0, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.14888 and φ 2 =0.829916, a reflectance of 5.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/87.11 nm/79.90 nm/174.23 nm/159.81 nm/174.23 nm/159.81 nm. The total thickness (d total =Σd i ) of the film is 885.09 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1646.79 nm which is very large, i.e., about 6.72 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 40  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including three films made of materials different from each other. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 952 nm to a wavelength of 1201 nm ranges from 4.6% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 249 nm. A value obtained by dividing the wavelength band by the setting wavelength of 897 nm is about 0.254, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirty-second Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including three films according to the thirty-second embodiment of the present invention will be described below with reference to FIG.  41 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the thirty-first embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the thirty-first embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =890 nm. Parameters are given by A=1.0, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.11792 and φ 2 =0.835299, a reflectance of 5.0% is obtained at a wavelength of 890 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/76.98 nm/73.04 nm/153.96 nm/146.07 nm/153.96 nm/146.07 nm. The total thickness (d total =Σd i ) of the film is 800.08 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1486.93 nm which is very large, i.e., about 6.07 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 41  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including three films made of materials different from each other. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 867 nm to a wavelength of 1093 nm ranges from 4.4% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 890 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 226 nm. A value obtained by dividing the wavelength band by the setting wavelength of 890 nm is about 0.254, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical elements according to the twenty-fifth embodiment to the thirty-second embodiment are shown in Table 3. In Table 3, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands Δλ in which the reflectance falls within the range from −1.0 to +2.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
                                                   TABLE 3                   Characteristic of Reflecting Multi-layer Film                    Setting       Summation Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.0 to 2.0 of R(λ 0 )   Δλ/λ 0                 25   Seven films   980 nm   1.6%   1634.92 nm   242 nm   242/980 = 0.247           (three types)   2.0%       6.67 times       26   Seven films   897 nm   1.5%   1487.24 nm   214 nm   214/897 = 0.239           (three types)   2.0%       6.07 times       27   Seven films   980 nm   2.6%   1638.64 nm   242 nm   242/980 = 0.247           (three types)   3.0%       6.69 times       28   Seven films   896 nm   2.5%   1489.56 nm   217 nm   217/896 = 0.242           (three types)   3.0%       6.08 times       29   Seven films   980 nm   3.6%   1642.63 nm   245 nm   245/980 = 0.250           (three types)   4.0%       6.70 times       30   Seven films   893 nm   3.4%   1488.27 nm   220 nm   220/893 = 0.246           (three types)   4.0%       6.07 times       31   Seven films   980 nm   4.6%   1646.79 nm   249 nm   249/980 = 0.254           (three types)   5.0%       5.38 times       32   Seven films   890 nm   4.4%   1486.93 nm   226 nm   226/890 = 0.254           (three types)   5.0%       6.07 times                    
Thirty-third Embodiment
 
     A semiconductor optical device having a nine-layer reflecting film according to the thirty-third embodiment of the present invention will be described below with reference to  FIGS. 42 and 43 .  FIG. 42  is a schematic sectional view of a configuration obtained when a nine-layer reflecting film  60  is formed in place of a single-layer reflecting film as a reflecting film on an end face portion of the semiconductor optical device. This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that the reflecting multi-layer film is the nine-layer reflecting film  60 . A condition for setting the reflectance of the nine-layer reflecting film  60  to be equal to the reflectance of the hypothetical film at a predetermined wavelength will be considered. The amplitude reflectance of the nine-layer reflecting film  60  is expressed by the following equation (18) like the amplitude reflectance of the four-layer reflecting film and the seven-layer reflecting film. 
             r   =           (       m   11     +     m   12       )     ⁢     n   c       -     (       m   21     +     m   22       )             (       m   11     +     m   12       )     ⁢     n   c       +     (       m   21     +     m   22       )                 (   18   )             
 
     where m ij  (i and j are 1 or 2) is expressed by the following equation (19): 
                 (           m   11           m   12               m   21           m   22           )     =       (           cos   ⁢           ⁢   O   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   O   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   O   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   O   ⁢           ⁢     ϕ   2             )     ×     (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             )     ×     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             )     ×     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             )     ×     (           cos   ⁢           ⁢   D   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   D   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   D   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   D   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   D   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   D   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   D   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   D   ⁢           ⁢     ϕ   2             )         ⁢                   (   19   )             
 
     where O, A, B, C and D are parameters representing contributing rates of respective two-layer films (pair) in a film thickness Od 2  of a first-layer film  51 , a film thickness Ad 1  of a second-layer film  52 , a film thickness Ad 2  of a third-layer film  63 , a film thickness Bd 1  of a fourth-layer film  54 , a film thickness Bd 2  of a fifth-layer film  55 , a film thickness Cd 1  of a sixth-layer film  56 , a film thickness Cd 2  of a seventh-layer film  57 , a film thickness Dd 1  of an eighth-layer film  58 , and a film thickness Dd 2  of a ninth-layer film  59  except for the first-layer film  51 . 
     A case in which the nine-layer reflecting film  60  is formed on an end face portion of the semiconductor optical device will be described below.  FIG. 42  is a schematic sectional view of the configuration of the nine-layer reflecting film formed on the end face portion. In this semiconductor optical device, on an end face portion of the waveguide layer  10  (equivalent refractive index n c =3.37), the first-layer film  51  (refractive index n 2 =1.62 and a film thickness Od 2 ) made of aluminum oxide, the second-layer film  52  (refractive index n 1 =2.057 and a film thickness Ad 1 ) made of tantalum oxide, the third-layer film  53  (refractive index n 2 =1.62 and a film thickness Ad 2 ) made of aluminum oxide, the fourth-layer film  54  (refractive index n 1 =2.057 and a film thickness Bd 1 ) made of tantalum oxide, the fifth-layer film  55  (refractive index n 2 =1.62 and a film thickness Bd 2 ) made of aluminum oxide, the sixth-layer film  56  (refractive index n 1 =2.057 and a film thickness Cd 1 ) made of tantalum oxide, the seventh-layer film  57  (refractive index n 2 =1.62 and a film thickness Cd 2 ) made of aluminum oxide, the eighth-layer film  58  (refractive index n 1 =2.057 and a film thickness Dd 1 ) made of tantalum oxide, the ninth-layer film  59  (refractive index n 2 =1.62 and a film thickness Dd 2 ) made of aluminum oxide are stacked. In addition, the nine-layer reflecting film  60  is in contact with a free space  5  such as the air. 
     The reflecting characteristic of the nine-layer reflecting film  60  on the end face portion of the semiconductor optical device will be described below. A setting reflectance R(λ 0 ) is set to be 2.0% at a setting wavelength λ 0 =980 nm. When parameters are given by O=0.2, A=2.7, B=2.0, C=2.0, and D=2.0, and when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.35769 and φ 2 =0.958077, a reflectance of 2% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =18.45 nm/73.23 nm/249.06 nm/54.24 nm/184.49 nm/54.24 nm/184.49 nm/54.24 nm/184.49 nm. The total thickness (d total =Σd i ) of the film is 1056.93 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1815.34 nm which is very large, i.e., about 7.41 times a ¼ wavelength (=245 nm) at a predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 43  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 877 nm to a wavelength of 1007 nm ranges from 1.6% to 4.0%. With reference to the reflectance of 2.0% at the predetermined wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 130 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.133, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirty-fourth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the thirty-fourth embodiment of the present invention will be described below with reference to FIG.  44 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the thirty-third embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 2.0% at a setting wavelength λ 0 =1020 nm. Parameters are given by O=0.2, A=2.7, B=2.0, C=2.0 and D=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.35769 and φ 2 =0.958077, a reflectance of 2.0% can be obtained at a wavelength of 1020 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =19.20 nm/76.22 nm/259.22 nm/56.46 nm/192.02 nm/56.46 nm/192.02 nm/56.46 nm/192.02 nm. The total thickness (d total =Σd i ) of the film is 1100.08 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1889.46 nm which is very large, i.e., about 7.71 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 44  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 3% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 912 nm to a wavelength of 1048 nm ranges from 1.6% to 4.0%. With reference to the reflectance of 2.0% at the setting wavelength 1020 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 1.0% to 4.0% is 136 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1020 nm is about 0.133, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirty-fifth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the thirty-fifth embodiment of the present invention will be described below with reference to FIG.  45 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the thirty-third embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.2, A=2.7, B=2.0, C=2.0 and D=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.377348 and φ 2 =0.935416, a reflectance of 3.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =18.01 nm/77.25 nm/243.16 nm/57.22 nm/180.12 nm/57.22 nm/180.12 nm/57.22 nm/180.12 nm. The total thickness (d total =Σd i ) of the film is 1050.44 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1810.49 nm which is very large, i.e., about 7.49 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 45  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 4% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 882 nm to a wavelength of 1007 nm ranges from 2.6% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 125 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.128, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirty-sixth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the thirty-sixth embodiment of the present invention will be described below with reference to FIG.  46 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the thirty-fifth embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the thirty-fifth embodiment in that a setting reflectance R(λ 0 ) is 3.0% at a setting wavelength λ 0 =1017 nm. Parameters are given by O=0.2, A=2.7, B=2.0, C=2.0 and D=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.377348 and φ 2 =0.935416, a reflectance of 3.0% can be obtained at a wavelength of 1017 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =18.69 nm/80.17 nm/252.35 nm/59.39 nm/186.92 nm/59.39 nm/186.92 nm/59.39 nm/186.92 nm. The total thickness (d total =Σd i ) of the film is 1090.14 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1878.92 nm which is very large, i.e., about 7.67 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 46  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 4% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 915 nm to a wavelength of 1045 nm ranges from 2.6% to 5.0%. With reference to the reflectance of 3.0% at the setting wavelength 1017 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 2.0% to 5.0% is 130 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1017 nm is about 0.128, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirty-seventh Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the thirty-seventh embodiment of the present invention will be described below with reference to FIG.  47 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the thirty-third embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.15, A=2.8, B=2.0, C=2.0 and D=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.38725 and φ 2 =0.911369, a reflectance of 4.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =13.16 nm/82.22 nm/245.69 nm/58.73 nm/175.49 nm/58.73 nm/175.49 nm/58.73 nm/175.49 nm. The total thickness (d total =Σd i ) of the film is 1043.73 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1803.77 nm which is very large, i.e., about 7.36 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 47  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 883 nm to a wavelength of 1006 nm ranges from 3.6% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 123 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.126, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirty-eighth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the thirty-eighth embodiment of the present invention will be described below with reference to FIG.  48 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the thirty-seventh embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the thirty-seventh embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =1017 nm. Parameters are given by O=0.15, A=2.8, B=2.0, C=2.0 and D=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.38725 and φ 2 =0.911369, a reflectance of 4.0% can be obtained at a wavelength of 1017 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =13.66 nm/85.32 nm/245.96 nm/60.94 nm/182.12 nm/60.94 nm/182.12 nm/60.94 nm/182.12 nm. The total thickness (d total =Σd i ) of the film is 1083.12 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1871.83 nm which is very large, i.e., about 7.64 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 48  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 5% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 916 nm to a wavelength of 1044 nm ranges from 3.6% to 6.0%. With reference to the reflectance of 4.0% at the setting wavelength 1017 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 3.0% to 6.0% is 128 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1017 nm is about 0.126, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Thirty-ninth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the thirty-ninth embodiment of the present invention will be described below with reference to FIG.  49 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the thirty-third embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.10, A=2.9, B=2.0, C=2.0 and D=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.397519 and φ 2 =0.886992, a reflectance of 5.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.54 nm/87.41 nm/247.66 nm/60.28 nm/170.80 nm/60.28 nm/170.80 nm/60.28 nm/170.80 nm. The total thickness (d total =Σd i ) of the film is 1036.85 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1801.04 nm which is very large, i.e., about 7.35 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 49  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 890 nm to a wavelength of 1006 nm ranges from 4.6% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 116 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.118, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Fortieth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the fortieth embodiment of the present invention will be described below with reference to FIG.  50 . This semiconductor optical device has the same configuration as that of the semiconductor optical device according to the thirty-ninth embodiment. However, the semiconductor optical device is different from the semiconductor optical device according to the thirty-ninth embodiment in that a setting reflectance R(λ 0 ) is 5.0% at a setting wavelength λ 0 =1013 nm. Parameters are given by O=0.10, A=2.9, B=2.0, C=2.0 and D=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.397519 and φ 2 =0.886992, a reflectance of 5.0% can be obtained at a wavelength of 1013 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.83 nm/90.35 nm/256.00 nm/62.31 nm/176.55 nm/62.31 nm/176.55 nm/62.31 nm/176.55 nm. The total thickness (d total =Σd i ) of the film is 1071.76 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1857.42 nm which is very large, i.e., about 7.58 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 50  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 6% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 920 nm to a wavelength of 1040 nm ranges from 4.6% to 7.0%. With reference to the reflectance of 5.0% at the setting wavelength 1013 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 4.0% to 7.0% is 120 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1013 nm is about 0.118, and is larger than 0.061 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical device according to the thirty-third embodiment to the fortieth embodiment are shown in Table 4. In Table 4, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands Δλ in which the reflectance falls within the range from −1.0 to +2.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
                                                   TABLE 4                   Characteristic of Reflecting Multi-layer Film                    Setting       Summation of Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.0 to 2.0 of R(λ 0 )   Δλ/λ 0                 33   nine films    980 nm   1.4%   1815.34 nm   130 nm   130/980 = 0.133               2.0%       7.41 times       34   nine films   1020 nm   1.4%   1889.46 nm   136 nm   136/1020 = 0.133               2.0%       7.71 times       35   nine films    980 nm   2.6%   1810.49 nm   125 nm   125/980 = 0.128               3.0%       7.49 times       36   nine films   1017 nm   2.6%   1878.92 nm   130 nm   130/1017 = 0.128               3.0%       7.67 times       37   nine films    980 nm   3.6%   1803.77 nm   123 nm   123/980 = 0.126               4.0%       7.36 times       38   nine films   1017 nm   3.6%   1871.83 nm   128 nm   128/1017 = 0.126               4.0%       7.64 times       39   nine films    980 nm   4.6%   1801.04 nm   116 nm   116/980 = 0.118               5.0%       7.35 times       40   nine films   1013 nm   4.6%   1857.42 nm   120 nm   120/1013 = 0.118               5.0%       7.58 times                    
Forty-first Embodiment
 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-first embodiment of the present invention will be described below with reference to FIG.  51 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.15, A=1.95, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.845348 and φ 2 =0.578286, a reflectance of 6.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =8.35 nm/124.99 nm/108.57 nm/128.20 nm/111.35 nm/128.20 nm/111.35 nm. The total thickness (d total =Σd i ) of the film is 721.01 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1334.70 nm which is very large, i.e., about 5.45 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 51  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 7% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 828 nm to a wavelength of 1009 nm ranges from 5.4% to 8.0%. With reference to the reflectance of 6.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 5.0% to 8.0% is 181 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.185, and is larger than 0.062 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Forty-second Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-second embodiment will be described below with reference to FIG.  52 . This semiconductor optical device is different from the semiconductor optical device according to the forty-first embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =1045 nm. Parameters are given by O=0.15, A=1.95, B=2.0, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.541022 and φ 2 =0.741397, a reflectance of 6% is obtained at a wavelength of 1045 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =8.91 nm/133.28 nm/115.77 nm/136.70 nm/118.74 nm/136.70 nm/118.74 nm. The total thickness (d total =Σd i ) of the film is 768.84 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1423.24 nm which is very large, i.e., about 5.81 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 52  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 7% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 883 nm to a wavelength of 1076 nm ranges from 5.4% to 8.0%. With reference to the reflectance of 6.0% at the setting wavelength 1045 nm, a continuous wavelength band in the range of −1.0% to +2.0%, i.e., 5.0% to 8.0% is 193 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1045 nm is about 0.185, and is larger than 0.062 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical device according to the forty-first embodiment to the forty-second embodiment are shown in Table 5. In Table 5, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands Δλ in which the reflectance falls within the range from −1.0 to +2.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
                                                   TABLE 5                   Characteristic of Reflecting Multi-layer Film                    Setting       Summation Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.0 to 2.0 of R(λ 0 )   Δλ/λ 0                 41   Seven films    980 nm   5.4%   1334.70 nm   181 nm   181/980 = 0.185               6.0%       5.45 times       42   Seven films   1045 nm   5.4%   1423.24 nm   193 nm   193/1045 = 0.185               6.0%       5.81 times                    
Forty-third Embodiment
 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-third embodiment of the present invention will be described below with reference to FIG.  53 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.20, A=1.97, B=2.35, and C=2.10. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.79703 and φ 2 =0.528684, a reflectance of 6.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =10.18 nm/119.06 nm/100.28 nm/145.02 nm/119.62 nm/126.91 nm/106.89 nm. The total thickness (d total =Σd i ) of the film is 727.96 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1350.16 nm which is very large, i.e., about 5.51 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 53  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 7% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 813 nm to a wavelength of 994 nm ranges from 5.0% to 7.0%. With reference to the reflectance of 6.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 4.5% to 7.0% is 181 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.185. 
     Meanwhile, it is assumed that a hypothetical single reflecting film having a thickness of 5λ/(4n 1 ) has a minimal reflectance of 4% at a wavelength λ of 980 nm. It should be noted that the effective refractive index n c =3.37, and the refractive index n 1 =1.449. In this case, the reflectance in the range of a wavelength of 949 nm to a wavelength of 1013 nm ranges from a minimal value of 4.0% to 6.5%. The continuous wavelength band in the range of 4.0% to 6.5% is 64 nm. An reference index of continuous wavelength band is obtained by dividing the wavelength band by the predetermined wavelength of 980 nm is about 0.065. 
     Then, as compared to the reference index, the value of 0.185 is larger than the reference index of 0.065 in the hypothetical single reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Forty-fourth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-fourth embodiment will be described below with reference to FIG.  54 . This semiconductor optical device is different from the semiconductor optical device according to the forty-third embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =1063 nm. Parameters are given by O=0.20, A=1.97, B=2.35, and C=2.10. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.79703 and φ 2 =0.528684, a reflectance of 6% is obtained at a wavelength of 1063 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =11.04 nm/129.14 nm/108.77 nm/154.05 nm/129.75 nm/137.66 nm/115.95 nm. The total thickness (d total =Σd i ) of the film is 786.36 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1457.82 nm which is very large, i.e., about 5.95 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 54  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 7% of a target reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 882 nm to a wavelength of 1078 nm ranges from 5.0% to 7.0%. With reference to the reflectance of 6.0% at the setting wavelength 1063 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 4.5% to 7.0% is 196 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1063 nm is about 0.184, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Forty-fifth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-fifth embodiment of the present invention will be described below with reference to FIG.  55 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 7.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.17, A=1.97, B=2.35, and C 2.05. In addition, when phase shifts φ 1  and cφ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.80763 and φ 2 =0.525803, a reflectance of 6.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =8.61 nm/120.64 nm/99.73 nm/143.91 nm/118.97 nm/125.54 nm/103.78 nm. The total thickness (d total =Σd i ) of the film is 721.18 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1338.78 nm which is very large, i.e., about 5.46 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 55  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 7% of a setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 797 nm to a wavelength of 993 nm ranges from 5.9% to 8.0%. With reference to the reflectance of 7.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 196 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.200, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Forty-sixth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-sixth embodiment will be described below with reference to FIG.  56 . This semiconductor optical device is different from the semiconductor optical device according to the forty-first embodiment in that a setting reflectance R(λ 0 ) is 7.0% at a setting wavelength λ 0 =1073 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.80763 and φ 2 =0.525803, a reflectance of 7% is obtained at a wavelength of 1073 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =9.42 nm/132.09 nm/109.19 nm/157.57 nm/130.26 nm/137.45 nm/113.63 nm. The total thickness (d total =Σd i ) of the film is 789.61 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1465.82 nm which is very large, i.e., about 5.98 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 56  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 7% of a setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 872 nm to a wavelength of 1088 nm ranges from 5.9% to 8.0%. With reference to the reflectance of 7.0% at the setting wavelength 1073 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 196 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1073 nm is about 0.183, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Forty-seventh Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-seventh embodiment of the present invention will be described below with reference to FIG.  57 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.17, A=1.97, B=2.35, and C=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.806965 and φ 2 =0.531203, a reflectance of 8.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =8.69 nm/120.54 nm/100.75 nm/143.79 nm/120.19 nm/122.38 nm/102.29 nm. The total thickness (d total =Σd i ) of the film is 718.63 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1333.17 nm which is very large, i.e., about 5.44 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 57  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 8% of a setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 786 nm to a wavelength of 994 nm ranges from 7.0% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 208 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.212, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Forty-eighth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-eighth embodiment will be described below with reference to FIG.  58 . This semiconductor optical device is different from the semiconductor optical device according to the forty-seventh embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =1079 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.806965 and φ 2 =0.531203, a reflectance of 8% is obtained at a wavelength of 1079 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =9.57 nm/132.72 nm/110.93 nm/158.32 nm/132.33 nm/134.74 nm/112.62 nm. The total thickness (d total =Σd i ) of the film is 791.23 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1467.86 nm which is very large, i.e., about 5.99 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 58  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 8% of a setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 866 nm to a wavelength of 1094 nm ranges from 7.0% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 1079 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 228 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1079 nm is about 0.211, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Forty-ninth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the forty-ninth embodiment of the present invention will be described below with reference to FIG.  59 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 9.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.20, A=2.05, B=2.40, and C=1.95. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.734549 and φ 2 =0.580342, a reflectance of 9.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =11.17 nm/114.18 nm/114.54 nm/133.67 nm/134.10 nm/108.61 nm/108.96 nm. The total thickness (d total =φd i ) of the film is 725.23 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1330.65 nm which is very large, i.e., about 5.43 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 59  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 9% of a setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 793 nm to a wavelength of 994 nm ranges from 8.1% to 10.0%. With reference to the reflectance of 9.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 7.5% to 10.0% is 202 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.206, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fiftieth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fiftieth embodiment will be described below with reference to FIG.  60 . This semiconductor optical device is different from the semiconductor optical device according to the forty-ninth embodiment in that a setting reflectance R(λ 0 ) is 9.0% at a setting wavelength λ 0 =1075 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.734549 and φ 2 =0.580342, a reflectance of 9% is obtained at a wavelength of 1075 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 1 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =12.26 nm/125.25 nm/125.65 nm/146.63 nm/147.10 nm/119.14 nm/119.52 nm. The total thickness (d total =Σd i ) of the film is 795.55 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1459.67 nm which is very large, i.e., about 5.96 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 60  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 9% of a setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 870 nm to a wavelength of 1090 nm ranges from 8.1% to 10.0%. With reference to the reflectance of 9.0% at the setting wavelength 1075 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 7.5% to 10.0% is 220 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1075 nm is about 0.205, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fifty-first Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fifty-first embodiment of the present invention will be described below with reference to FIG.  61 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 10.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.17, A=2.10, B=2.45, and C=1.95. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.729549 and φ 2 =0.56426, a reflectance of 10.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =9.24 nm/116.17 nm/114.09 nm/135.53 nm/133.10 nm/107.87 nm/105.94 nm. The total thickness (d total =Σd i ) of the film is 721.94 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1326.67 nm which is very large, i.e., about 5.41 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 61  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 10% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 773 nm to a wavelength of 994 nm ranges from 9.0% to 11.0%. With reference to the reflectance of 10.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 8.5% to 11.0% is 221 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.226, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fifty-second Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fifty-second embodiment will be described below with reference to FIG.  62 . This semiconductor optical device is different from the semiconductor optical device according to the fifty-first embodiment in that a setting reflectance R(λ 0 ) is 10.0% at a setting wavelength λ 0 =1087 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.729549 and φ 2 =0.564265, a reflectance of 10% is obtained at a wavelength of 1087 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =10.24 nm/128.85 nm/126.54 nm/150.33 nm/147.63 nm/1 19.65 nm/1 17.50 nm. The total thickness (d total =Σd i ) of the film is 800.74 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1471.49 nm which is very large, i.e., about 6.01 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 62  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 10% of a setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 857 nm to a wavelength of 1102 nm ranges from 9.0% to 11.0%. With reference to the reflectance of 10.0% at the setting wavelength 1087 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 8.5% to 11.0% is 245 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1087 nm is about 0.225, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fifty-third Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fifty-third embodiment of the present invention will be described below with reference to FIG.  63 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 11.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.20, A=2.20, B=2.55, and C=1.95. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.674425 and φ 2 =0.57230, a reflectance of 11.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =11.02 nm/112.50 nm/121.22 nm/130.40 nm/140.51 nm/99.72 nm/107.45 nm. The total thickness (d total =Σd i ) of the film is 722.82 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1320.69 nm which is very large, i.e., about 5.39 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 63  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 11% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 764 nm to a wavelength of 994 nm ranges from 10.2% to 12.0%. With reference to the reflectance of 11.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 9.5% to 12.0% is 230 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.235, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fifty-fourth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fifty-fourth embodiment will be described below with reference to FIG.  64 . This semiconductor optical device is different from the semiconductor optical device according to the fifty-third embodiment in that a setting reflectance R(λ 0 ) is 11.0% at a setting wavelength λ 0 =1092 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.674425 and φ 2 =0.572301, a reflectance of 11% is obtained at a wavelength of 1092 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =12.28 nm/125.36 nm/135.08 nm/145.31 nm/156.56 nm/111.12 nm/119.73 nm. The total thickness (d total =Σd i ) of the film is 805.44 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1471.66 nm which is very large, i.e., about 6.01 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 64  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 11% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 851 nm to a wavelength of 1108 nm ranges from 10.2% to 12.0%. With reference to the reflectance of 11.0% at the setting wavelength 1092 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 9.5% to 12.0% is 257 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1092 nm is about 0.235, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fifty-fifth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fifty-fifth embodiment of the present invention will be described below with reference to FIG.  65 . This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.20, A=2.35, B=2.65, and C=1.95. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.614143 and φ 2 =0.58198, a reflectance of 12.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =11.21 nm/109.43 nm/131.68 nm/123.40 nm/148.49 nm/90.81 nm/109.26 nm. The total thickness (d total =Σd i ) of the film is 724.28 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1314.76 nm which is very large, i.e., about 5.37 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 65  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 751 nm to a wavelength of 995 nm ranges from 10.9% to 13.0%. With reference to the reflectance of 120% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 244 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.249, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     Fifty-sixth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film according to the fifty-sixth embodiment will be described below with reference to FIG.  66 . This semiconductor optical device is different from the semiconductor optical device according to the fifty-fifth embodiment in that a setting reflectance R(φ 0 ) is 12.0% at a setting wavelength λ 0 =1100 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ1=0.614143 and φ 2 =0.581984, a reflectance of 7% is obtained at a wavelength of 1100 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =12.58 nm/122.83 nm/147.80 nm/138.51 nm/166.67 nm/101.93 nm/122.64 nm. The total thickness (d total =Σd i ) of the film is 812.96 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1475.74 nm which is very large, i.e., about 6.02 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 66  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 842 nm to a wavelength of 1117 nm ranges from 10.9% to 13.0%. With reference to the reflectance of 7.0% at the setting wavelength 1100 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 275 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1100 nm is about 0.250, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical device according to the forty-third embodiment to the fifty-sixth embodiment are shown in Table 6. In Table 6, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands Δλ in which the reflectance falls within the range from −1.5 to +1.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
                                                                                 TABLE 6                   Characteristic of Reflecting Multi-layer Film                    Setting       Summation Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.5 to 1.0 of R(λ 0 )   Δλ/λ 0                      43   Seven films    980 nm   5.0%   1350.16 nm   181 nm   181/980 = 0.185               6.0%       5.51 times       44   Seven films   1063 nm   5.0%   1457.82 nm   196 nm   196/1063 = 0.184               6.0%       5.95 times       45   Seven films    980 nm   5.9%   1338.78 nm   196 nm   196/980 = 0.200               7.0%       5.46 times       46   Seven films   1073 nm   5.9%   1465.82 nm   196 nm   196/1073 = 0.183               7.0%       5.98 times       47   Seven films    980 nm   7.0%   1333.17 nm   208 nm   208/980 = 0.212               8.0%       5.44 times       48   Seven films   1079 nm   7.0%   1467.86 nm   228 nm   228/1079 = 0.211               8.0%       5.99 times       49   Seven films    980 nm   8.1%   1330.65 nm   202 nm   202/980 = 0.206               9.0%       5.43 times       50   Seven films   1075 nm   8.1%   1459.67 nm   220 nm   220/1075 = 0.205               9.0%       5.96 times       51   Seven films    980 nm   9.0%   1326.67 nm   221 nm   221/980 = 0.226               10.0%        5.41 times       52   Seven films   1087 nm   9.0%   1471.49 nm   245 nm   245/1087 = 0.225               10.0%        6.01 times       53   Seven films    980 nm   10.2%   1320.69 nm   230 nm   230/980 = 0.235               11.0%        5.39 times       54   Seven films   1092 nm   10.2%   1471.66 nm   257 nm   257/1092 = 0.235               11.0%        6.01 times       55   Seven films    980 nm   10.9%   1314.76 nm   244 nm   244/980 = 0.249               12.0%        5.37 times       56   Seven films   1100 nm   10.9%   1475.74 nm   275 nm   275/1100 = 0.250               12.0%        6.02 times                    
Fifty-seventh Embodiment
 
     A semiconductor optical device having a six-layer reflecting film according to the fifty-seventh embodiment of the present invention will be described below with reference to FIG.  67 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.50, B=1.92, and C=2.2. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.16473 and φ 2 =0.715823, a reflectance of 6.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2  132.47 nm/103.38 nm/169.57 nm/132.32 nm/194.30 nm/151.62 nm. The total thickness (d total =Σd i ) of the film is 883.66 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1648.43 nm which is very large, i.e., about 6.73 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 67  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 6% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 966 nm to a wavelength of 1219 nm ranges from 5.0% to 7.0%. With reference to the reflectance of 6.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 4.5% to 7.0% is 253 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.258, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Fifty-eighth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the fifty-eighth embodiment of the present invention will be described below with reference to FIG.  68 . This semiconductor optical device is different from the semiconductor optical device according to the fifty-seventh embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =879 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.16473 and φ 2 =0.715823, a reflectance of 6.0% is obtained at a wavelength of 879 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =118.82 nm/92.72 nm/152.09 nm/118.69 nm/174.27 nm/136.00 nm. The total thickness (d total =Σd i ) of the film is 792.59 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1478.54 nm which is very large, i.e., about 6.03 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 68  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 6% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 866 nm to a wavelength of 1093 nm ranges from 5.0% to 7.0%. With reference to the reflectance of 6.0% at the setting wavelength 879 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 4.5% to 7.0% is 227 nm. A value obtained by dividing the wavelength band by the setting wavelength of 879 nm is about 0.258, and is larger than 0.0651 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Fifty-ninth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the fifty-ninth embodiment of the present invention will be described below with reference to FIG.  69 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 7.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.50, B=1.95, and C=2.20. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.13181 and φ 2 =0.744018, a reflectance of 7.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =128.73 nm/107.45 nm/167.35 nm/139.69 nm/188.80 nm/157.59 nm. The total thickness (d total =Σd i ) of the film is 889.61 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1653.06 nm which is very large, i.e., about 6.75 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 69  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 7% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 964 nm to a wavelength of 1219 nm ranges from 6.4% to 8.0%. With reference to the reflectance of 7.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 255 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.260, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixtieth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the sixtieth embodiment of the present invention will be described below with reference to FIG.  70 . This semiconductor optical device is different from the semiconductor optical device according to the fifty-ninth embodiment in that a setting reflectance R(λ 0 ) is 7.0% at a setting wavelength λ 0 =880 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.13181 and φ 2 =0.744018, a reflectance of 7.0% is obtained at a wavelength of 880 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =115.59 nm/96.49 nm/150.27 nm/125.43 nm/169.54 nm/141.51 nm. The total thickness (d total =Σd i ) of the film is 798.83 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1484.37 nm which is very large, i.e., about 6.06 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 70  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 7% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 866 nm to a wavelength of 1094 nm ranges from 6.4% to 8.0%. With reference to the reflectance of 7.0% at the setting wavelength 880 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 228 nm. A value obtained by dividing the wavelength band by the setting wavelength of 880 nm is about 0.259, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-first Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the sixty-first embodiment of the present invention will be described below with reference to FIG.  71 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.52, B=1.95, and C=2.20. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.09941 and φ 2 =0.769346, a reflectance of 8.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =126.71 nm/112.59 nm/162.56 nm/144.44 nm/183.40 nm/162.96 nm. The total thickness (d total =Σd i ) of the film is 892.66 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1652.67 nm which is very large, i.e., about 6.75 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 71  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 964 nm to a wavelength of 1223 nm ranges from 7.4% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 259 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.264, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-second Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the sixty-second embodiment of the present invention will be described below with reference to FIG.  72 . This semiconductor optical device is different from the semiconductor optical device according to the sixty-first embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =878 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.09941 and φ 2 =0.769346, a reflectance of 8.0% is obtained at a wavelength of 878 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =113.52 nm/100.87 nm/145.64 nm/129.41 nm/164.31 nm/146.00 nm. The total thickness (d total =Σd i ) of the film is 799.75 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1480.65 nm which is very large, i.e., about 6.04 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 72  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 864 nm to a wavelength of 1096 nm ranges from 7.4% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 878 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 232 nm. A value obtained by dividing the wavelength band by the setting wavelength of 878 nm is about 0.264, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-third Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the sixty-third embodiment of the present invention will be described below with reference to FIG.  73 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 9.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.55, B=1.97, and C=2.25. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.0677 and φ 2 =0.772496, a reflectance of 6.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =125.49 nm/115.28 nm/159.49 nm/146.52 nm/182.16 nm/167.34 nm. The total thickness (d total =Σd i ) of the film is 896.28 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1656.11 nm which is very large, i.e., about 6.76 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 73  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 9% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 963 nm to a wavelength of 1235 nm ranges from 8.4% to 10.0%. 
     With reference to the reflectance of 9.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 7.5% to 10.0% is 272 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.278, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-fourth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the sixty-fourth embodiment of the present invention will be described below with reference to FIG.  74 . This semiconductor optical device is different from the semiconductor optical device according to the sixty-third embodiment in that a setting reflectance R(λ 0 ) is 9.0% at a setting wavelength λ 0 =874 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.0677 and φ 2 =0.772496, a reflectance of 9.0% is obtained at a wavelength of 874 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =111.91 nm/102.81 nm/142.24 nm/130.67 nm/162.45 nm/149.24 nm. The total thickness (d total =Σd i ) of the film is 799.32 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1476.95 nm which is very large, i.e., about 6.03 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 74  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 9% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 859 nm to a wavelength of 1101 nm ranges from 8.4% to 10.0%. With reference to the reflectance of 9.0% at the setting wavelength 874 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 7.5% to 10.0% is 242 nm. A value obtained by dividing the wavelength band by the setting wavelength of 874 nm is about 0.244, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-fifth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the sixty-fifth embodiment of the present invention will be described below with reference to FIG.  75 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R (λ 0 ) is 10.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.60, B=2.02, and C=2.25. In addition, when phase shifts φ 1  and (φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.00317 and φ 2 =0.803388, a reflectance of 10.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =121.70 nm/123.76 nm/153.64 nm/156.25 nm/171.14 nm/174.04 nm. The total thickness (d total =Σd 1 ) of the film is 900.53 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1653.97 nm which is very large, i.e., about 6.75 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 75  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 10% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 963 nm to a wavelength of 1233 nm ranges from 9.5% to 11.0%. With reference to the reflectance of 10.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 8.5% to 12.0% is 270 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.276, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-sixth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the fifty-eighth embodiment of the present invention will be described below with reference to FIG.  76 . This semiconductor optical device is different from the semiconductor optical device according to the sixty-fifth embodiment in that a setting reflectance R(λ 0 ) is 10.0% at a setting wavelength λ 0 =874 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.0031 and φ 2 =0.803388, a reflectance of 10.0% is obtained at a wavelength of 874 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =108.53 nm/110.37 nm/137.02 nm/139.35 nm/152.63 nm/155.21 nm. The total thickness (d total =Σd i ) of the film is 803.11 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1475.04 nm which is very large, i.e., about 6.02 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 76  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 10% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 859 nm to a wavelength of 1100 nm ranges from 9.5% to 11.0%. With reference to the reflectance of 10.0% at the setting wavelength 874 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 8.5% to 11.0% is 241 nm. A value obtained by dividing the wavelength band by the setting wavelength of 874 nm is about 0.276, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-seventh Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the sixty-seventh embodiment of the present invention will be described below with reference to FIG.  77 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 11.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.65, B=2.05, and C=2.20. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by 4P1=0.931121 and φ 2 =0.862397, a reflectance of 11.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =116.49 nm/137.00 nm/144.73 nm/170.21 nm/155.33 nm/182.67 nm. The total thickness (d total =Σd i ) of the film is 906.43 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1650.45 nm which is very large, i.e., about 6.74 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 77  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 11% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 963 nm to a wavelength of 1233 nm ranges from 10.4% to 12.0%. With reference to the reflectance of 11.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 9.5% to 12.0% is 270 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.276, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-eighth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the Sixty-eighth embodiment of the present invention will be described below with reference to FIG.  78 . This semiconductor optical device is different from the semiconductor optical device according to the Sixty-seventh embodiment in that a setting reflectance R(λ 0 ) is 11.0% at a setting wavelength λ 0 =875 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.931121 and φ 2 =0.862397, a reflectance of 11.0% is obtained at a wavelength of 875 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =1104.01 nm/122.32 nm/129.23 nm/151.98 nm/138.68 nm/163.10 nm. The total thickness (d total =d) of the film is 809.32 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1473.63 nm which is very large, i.e., about 6.01 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 78  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 11% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 859 nm to a wavelength of 1100 nm ranges from 10.4% to 12.0%. With reference to the reflectance of 11.0% at the setting wavelength 875 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 9.5% to 12.0% is 241 nm. A value obtained by dividing the wavelength band by the setting wavelength of 875 nm is about 0.275, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Sixty-ninth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the sixty-ninth embodiment of the present invention will be described below with reference to FIG.  79 . This semiconductor optical device is different from the semiconductor optical device according to the seventeenth embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.70, B=2.07, and C=2.15. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.853386 and φ 2 =0.935812, a reflectance of 12.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =110.00 nm/153.17 nm/1 33.95 nm/186.51 nm/139.12 nm/193.71 nm. The total thickness (d total =Σd i ) of the film is 916.46 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1652.07 nm which is very large, i.e., about 6.74 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 79  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 961 nm to a wavelength of 1240 nm ranges from 11.5% to 13.0%. With reference to the reflectance of 12.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 279 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.285, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventieth Embodiment 
     A semiconductor optical device having a six-layer reflecting film according to the seventieth embodiment of the present invention will be described below with reference to FIG.  80 . This semiconductor optical device is different from the semiconductor optical device according to the sixty-ninth embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =873 nm. In addition, when phase shifts  41  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.853386 and φ 2 =0.935812, a reflectance of 12.0% is obtained at a wavelength of 873 nm. In this case, the film thickness of the layers of the six-layer reflecting film are given by Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =97.99 nm/136.45 nm/119.32 nm/166.14 nm/123.93 nm/172.56 nm. The total thickness (d total =Σd i ) of the film is 816.56 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the six films is 1471.67 nm which is very large, i.e., about 6.01 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 80  is a graph of a wavelength dependence of the reflectance of the six-layer reflecting film  40 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the six-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 856 nm to a wavelength of 1103 nm ranges from 11.5% to 13.0%. With reference to the reflectance of 12.0% at the setting wavelength 873 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 247 nm. A value obtained by dividing the wavelength band by the setting wavelength of 873 nm is about 0.283, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the six-layer reflecting film  40  has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical device according to the fifty-seventh embodiment to the seventieth embodiment are shown in Table 7. In Table 7, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands AA in which the reflectance falls within the range from −1.5 to +1.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
                                                                                 TABLE 7                   Characteristic of Multi-layer Reflecting Film                    Setting       Summation Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.5 to 1.0 of R(λ 0 )   Δλ/λ 0                      57   Six films   980 nm   5.0%   1648.43 nm   253 nm   253/980 = 0.258               6.0%       6.73 times       58   Six films   879 nm   5.0%   1478.54 nm   227 nm   227/879 = 0.258               6.0%       6.03 times       59   Six films   980 nm   6.4%   1653.06 nm   255 nm   255/980 = 0.260               7.0%       6.75 times       60   Six films   880 nm   6.4%   1484.37 nm   228 nm   228/880 = 0.259               7.0%       6.06 times       61   Six films   980 nm   7.4%   1652.67 nm   259 nm   259/980 = 0.264               8.0%       6.75 times       62   Six films   878 nm   7.4%   1480.65 nm   232 nm   232/878 = 0.264               8.0%       6.04 times       63   Six films   980 nm   8.4%   1656.11 nm   272 nm   272/980 = 0.278               9.0%       6.76 times       64   Six films   874 nm   8.4%   1476.95 nm   242 nm   242/874 = 0.244               9.0%       6.03 times       65   Six films   980 nm   9.5%   1653.97 nm   270 nm   270/980 = 0.276               10.0%        6.75 times       66   Six films   874 nm   9.5%   1475.04 nm   241 nm   241/874 = 0.276               10.0%        6.02 times       67   Six films   980 nm   10.4%   1650.45 nm   270 nm   270/980 = 0.276               11.0%        6.74 times       68   Six films   875 nm   10.4%   1473.63 nm   241 nm   241/875 = 0.275               11.0%        6.01 times       69   Six films   980 nm   11.5%   1652.07 nm   279 nm   279/980 = 0.285               12.0%        6.74 times       70   Six films   873 nm   11.5%   1471.67 nm   247 nm   247/873 = 0.283               12.0%        6.01 times                    
Seventy-first Embodiment
 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-first embodiment of the present invention will be described below with reference to FIG.  81 . This semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.05, B=2.00, and C=2.00. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.09082 and φ 2 =0.85958, a reflectance of 6.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/86.85 nm/86.90 nm/165.42 nm/165.52 nm/165.42 nm/165.52 nm. The total thickness (d total =d i ) of the film is 885.63 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1639.85 nm which is very large, i.e., about 6.69 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 81  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 6% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 965 nm to a wavelength of 1186 nm ranges from 5.4% to 7.0%. With reference to the reflectance of 6.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 4.5% to 7.0% is 221 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.226, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventy-second Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-second embodiment of the present invention will be described below with reference to FIG.  82 . This semiconductor optical device is different from the semiconductor optical device according to the seventy-first embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =889 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.05881 and φ 2 =0.86643, a reflectance of 6.0% is obtained at a wavelength of 889 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/76.47 nm/79.46 nm/145.66 nm/151.35 nm/145.66 nm/151.35 nm. The total thickness (d total =Σd i ) of the film is 799.95 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1479.24 nm which is very large, i.e., about 6.04 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 82  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 6% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 877 nm to a wavelength of 1081 nm ranges from 5.2% to 7.0%. With reference to the reflectance of 6.0% at the setting wavelength 889 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 4.5% to 7.0% is 204 nm. A value obtained by dividing the wavelength band by the setting wavelength of 889 nm is about 0.229, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventy-third Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-third embodiment of the present invention will be described below with reference to FIG.  83 . This semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 7.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.10, B=2.05, and C=2.00. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =1.01208 and φ 2 =0.89686, a reflectance of 7.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/84.41 nm/94.98 nm/157.32 nm/177.02 nm/143.48 nm/172.70 nm. The total thickness (d total =Σd i ) of the film is 879.91 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1636.96 nm which is very large, i.e., about 6.68 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 83  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 7% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 965 nm to a wavelength of 1194 nm ranges from 6.4% to 8.0%. With reference to the reflectance of 7.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 229 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.234, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventy-fourth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-fourth embodiment of the present invention will be described below with reference to FIG.  84 . This semiconductor optical device is different from the semiconductor optical device according to the seventy-third embodiment in that a setting reflectance R(λ 0 ) is 7.0% at a setting wavelength λ 0 =886 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.97974 and φ 2 =0.90431, a reflectance of 7.0% is obtained at a wavelength of 886 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/73.88 nm/86.59 nm/137.68 nm/161.37 nm/134.33 nm/157.43 nm. The total thickness (d total =Σd i ) of the film is 801.28 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1471.83 nm which is very large, i.e., about 6.01 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 84  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 7% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 874 nm to a wavelength of 1085 nm ranges from 6.0% to 8.0%. With reference to the reflectance of 7.0% at the setting wavelength 886 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 211 nm. A value obtained by dividing the wavelength band by the setting wavelength of 886 nm is about 0.238, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventy-fifth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-fifth embodiment of the present invention will be described below with reference to FIG.  85 . This semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.10, B=2.05, and C=2.00. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.991775 and φ 2 =0.923736, a reflectance of 8.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/82.72 nm/97.83 nm/154.16 nm/182.32 nm/150.40 nm/177.87 nm. The total thickness (d total =Σd i ) of the film is 895.3 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1642.23 nm which is very large, i.e., about 6.70 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 85  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 964 nm to a wavelength of 1204 nm ranges from 7.5% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 240 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.245, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventy-sixth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-sixth embodiment of the present invention will be described below with reference to FIG.  86 . This semiconductor optical device is different from the semiconductor optical device according to the seventy-fifth embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =881 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.958992 and φ 2 =0.930306, a reflectance of 8.0% is obtained at a wavelength of 881 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/71.91 nm/88.57 nm/134.01 nm/165.07 nm/130.74 nm/161.04 nm. The total thickness (d total =Σd i ) of the film is 801.34 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1467.89 nm which is very large, i.e., about 5.99 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 86  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 869 nm to a wavelength of 1090 nm ranges from 7.1% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 881 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 221 nm. A value obtained by dividing the wavelength band by the setting wavelength of 881 nm is about 0.251, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventy-seventh Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-seventh embodiment of the present invention will be described below with reference to FIG.  87 . This semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 9.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.15, B=2.10, and C=2.05. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.934834 and φ 2 =0.92769, a reflectance of 8.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/81.52 nm/102.72 nm/148.86 nm/187.57 nm/145.31 nm/183.10 nm. The total thickness (d total =Σd 1 ) of the film is 899.08 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1643.29 nm which is very large, i.e., about 6.71 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 87  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 9% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 965 nm to a wavelength of 1220 nm ranges from 8.4% to 10.0%. With reference to the reflectance of 9.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 7.5% to 10.0% is 255 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.260, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventy-eighth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-eighth embodiment of the present invention will be described below with reference to FIG.  88 . This semiconductor optical device is different from the semiconductor optical device according to the seventy-first embodiment in that a setting reflectance R(λ 0 ) is 9.0% at a setting wavelength λ 0 =874 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.900337 and φ 2 =0.935222, a reflectance of 9.0% is obtained at a wavelength of 874 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/70.02 nm/92.35 nm/127.86 nm/168.64 nm/124.81 nm/164.62 nm. The total thickness (d total =Σd i ) of the film is 798.3 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1456.86 nm which is very large, i.e., about 5.95 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 88  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 9% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 863 nm to a wavelength of 1096 nm ranges from 7.9% to 10.0%. With reference to the reflectance of 9.0% at the setting wavelength 874 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 7.5% to 10.0% is 233 nm. A value obtained by dividing the wavelength band by the setting wavelength of 874 nm is about 0.267, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Seventy-ninth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the seventy-ninth embodiment of the present invention will be described below with reference to FIG.  89 . This semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 10.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.15, B=2.10, and C=2.05. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.914148 and φ 2 =0.95535, a reflectance of 10.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/79.71 nm/105.78 nm/145.56 nm/193.16 nm/142.10 nm/188.56 nm. The total thickness (d total =Σd i ) of the film is 904.87 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1649.03 nm which is very large, i.e., about 6.73 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 89  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 10% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 963 nm to a wavelength of 1235 nm ranges from 9.6% to 11.0%. With reference to the reflectance of 10.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 8.5% to 11.0% is 272 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.278, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Eightieth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the eightieth embodiment of the present invention will be described below with reference to FIG.  90 . This semiconductor optical device is different from the semiconductor optical device according to the seventy-ninth embodiment in that a setting reflectance R(λ 0 ) is 10.0% at a setting wavelength λ 0 =868 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.879123 and φ 2 =0.96166, a reflectance of 10.0% is obtained at a wavelength of 868 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/67.90 nm/94.31 nm/123.99 nm/172.21 nm/121.03 nm/168.11 nm. The total thickness (d total =Σd i ) of the film is 797.55 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1451.38 nm which is very large, i.e., about 5.92 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 90  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 10% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 856 nm to a wavelength of 1102 nm ranges from 8.7% to 11.0%. With reference to the reflectance of 10.0% at the setting wavelength 868 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 8.5% to 11.0% is 246 nm. A value obtained by dividing the wavelength band by the setting wavelength of 868 nm is about 0.283, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Eighty-first Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the eighty-first embodiment of the present invention will be described below with reference to FIG.  91 . This semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 11.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.17, B=2.10, and C=2.05. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.881444 and φ 2 =0.983957, a reflectance of 11.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/78.20 nm/110.84 nm/140.35 nm/198.94 nm/1 37.01 nm/1 94.21 nm. The total thickness (d total =Σd i ) of the film is 909.55 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1651.45 nm which is very large, i.e., about 6.74 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 91  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 11% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 963 nm to a wavelength of 1254 nm ranges from 10.4% to 12.0%. With reference to the reflectance of 11.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 9.5% to 12.0% is 291 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.297, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Eighty-second Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the eighty-second embodiment of the present invention will be described below with reference to FIG.  92 . This semiconductor optical device is different from the semiconductor optical device according to the eighty-first embodiment in that a setting reflectance R(λ 0 ) is 11.0% at a setting wavelength λ 0 =862 nm. Parameters are given by A=1.15, B=2.10, and C=2.05. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.856738 and φ 2 =0.989623, a reflectance of 11.0% is obtained at a wavelength of 862 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/65.71 nm/96.38 nm/119.99 nm/176.00 nm/1 17.14 nm/1 71.81 nm. The total thickness (d total =Σd i ) of the film is 797.03 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1446.13 nm which is very large, i.e., about 5.90 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 92  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 11% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 850 nm to a wavelength of 1110 nm ranges from 9.5% to 12.0%. With reference to the reflectance of 11.0% at the setting wavelength 862 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 9.5% to 12.0% is 260 nm. A value obtained by dividing the wavelength band by the setting wavelength of 862 nm is about 0.302, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Eighty-third Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the eighty-third embodiment of the present invention will be described below with reference to FIG.  93 . This semiconductor optical device is different from the semiconductor optical device according to the twenty-fifth embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =980 nm. Parameters are given by A=1.22, B=2.13, and C=2.05. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.815005 and φ 2 =1.02518, a reflectance of 12.0% is obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/75.39 nm/120.42 nm/131.63 nm/210.24 nm/126.69 nm/1202.34 nm. The total thickness (d total =Σd i ) of the film is 916.71 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1653.50 nm which is very large, i.e., about 6.75 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 93  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 962 nm to a wavelength of 1275 nm ranges from 10.7% to 13.0%. With reference to the reflectance of 12.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 313 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.319, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     Eighty-fourth Embodiment 
     A semiconductor optical device having a seven-layer reflecting film including films of three types according to the eighty-fourth embodiment of the present invention will be described below with reference to FIG.  94 . This semiconductor optical device is different from the semiconductor optical device according to the eighty-third embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =853 nm. Parameters are given by A=1.13, B=2.10, and C=2.05. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.842465 and φ 2 =1.02038, a reflectance of 12.0% is obtained at a wavelength of 853 nm. In this case, the film thickness of the layers of the seven-layer reflecting film are given by d 3 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 =50 nm/62.83 nm/96.63 nm/116.76 nm/179.57 nm/113.98 nm/175.30 nm. The total thickness (d total =Σd i ) of the film is 795.07 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the seven films is 1438.90 nm which is very large, i.e., about 5.87 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 94  is a graph of a wavelength dependence of the reflectance of the seven-layer reflecting film  50  including the films of three types. The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the seven-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 838 nm to a wavelength of 1116 nm ranges from 10.6% to 13.0%. With reference to the reflectance of 12.0% at the setting wavelength 853 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 278 nm. A value obtained by dividing the wavelength band by the setting wavelength of 853 nm is about 0.326, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the seven-layer reflecting film  50  has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical device according to the seventy-first embodiment to the eighty-fourth embodiment are shown in Table 8. In Table 8, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands Δφ in which the reflectance falls within the range from −1.5 to +1.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
                                                   TABLE 8                   Characteristic of Reflecting Multi-layer Film                    Setting       Summation Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.5 to 1.0 of R(λ 0 )   Δλ/λ 0                 71   Seven films   980 nm   5.4%   1639.85 nm   221 nm   221/980 = 0.226           (three types)   6.0%       6.69 times       72   Seven films   889 nm   5.2%   1479.24 nm   204 nm   204/889 = 0.229           (three types)   6.0%       6.04 times       73   Seven films   980 nm   6.4%   1636.96 nm   229 nm   229/980 = 0.234           (three types)   7.0%       6.68 times       74   Seven films   886 nm   6.0%   1471.83 nm   211 nm   211/886 = 0.238           (three types)   7.0%       6.01 times       75   Seven films   980 nm   7.5%   1642.23 nm   240 nm   240/980 = 0.245           (three types)   8.0%       6.70 times       76   Seven films   881 nm   7.1%   1467.89 nm   221 nm   221/881 = 0.251           (three types)   8.0%       5.99 times       77   Seven films   980 nm   8.4%   1643.29 nm   255 nm   255/980 = 0.260           (three types)   9.0%       6.71 times       78   Seven films   874 nm   7.9%   1456.86 nm   233 nm   233/874 = 0.267           (three types)   9.0%       5.95 times       79   Seven films   980 nm   9.6%   1649.03 nm   272 nm   272/980 = 0.278           (three types)   10.0%        6.73 times       80   Seven films   868 nm   8.7%   1451.38 nm   246 nm   246/868 = 0.283           (three types)   10.0%        5.92 times       81   Seven films   980 nm   10.4%   1651.45 nm   291 nm   291/980 = 0.297           (three types)   11.0%        6.74 times       82   Seven films   862 nm   9.5%   1446.13 nm   260 nm   260/862 = 0.320           (three types)   11.0%        5.90 times       83   Seven films   980 nm   10.7%   1653.50 nm   313 nm   313/980 = 0.319           (three types)   12.0%        6.75 times       84   Seven films   853 nm   10.6%   1438.90 nm   278 nm   278/853 = 0.326           (three types)   12.0%        5.87 times                    
Eighty-fifth Embodiment
 
     A semiconductor optical device having a nine-layer reflecting film according to the eighty-fifth embodiment of the present invention will be described below with reference to FIG.  95 . This semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.10, A=2.7, B=2.1, C=2.0 and D=2.0. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.429458 and φ 2 =0.889116, a reflectance of 6.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.56 nm/87.92 nm/231.13 nm/68.38 nm/179.77 nm/65.13 nm/171.21 nm/65.13 nm/171.21 nm. The total thickness (d total =Σd i ) of the film is 1048.44 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1823.70 nm which is very large, i.e., about 7.44 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 95  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 6% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 893 nm to a wavelength of 993 nm ranges from 5.1% to 7.0%. With reference to the reflectance of 6.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 4.5% to 7.0% is 100 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.102, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Eighty-sixth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the eighty-sixth embodiment of the present invention will be described below with reference to FIG.  96 . This semiconductor optical device is different from the semiconductor optical device according to the eighty-fifth embodiment in that a setting reflectance R(λ 0 ) is 6.0% at a setting wavelength λ 0 =1018 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.429458 and φ 2 =0.889116, a reflectance of 6.0% can be obtained at a wavelength of 1018 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.89 nm/91.33 nm/240.09 nm/71.04 nm/186.74 nm/67.65 nm/177.85 nm/67.65 nm/177.85 nm. The total thickness (d total =Σd i ) of the film is 1089.09 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1857.42 nm which is very large, i.e., about 7.73 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 96  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 6% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 928 nm to a wavelength of 1031 nm ranges from 5.1% to 7.0%. With reference to the reflectance of 6.0% at the setting wavelength 1018 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 4.5% to 7.0% is 103 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1018 nm is about 0.101, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Eighty-seventh Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the eighty-seventh embodiment of the present invention will be described below with reference to FIG.  97 . This semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 7.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.10, A=2.7, B=2.15, C=1.9 and D=1.9. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.413831 and φ 2 =0.91752, a reflectance of 7.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.83 nm/84.72 nm/238.51 nm/65.90 nm/185.51 nm/59.62 nm/167.84 nm/59.62 nm/167.84 nm. The total thickness (d total =Σd i ) of the film is 1038.39 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1800.12 nm which is very large, i.e., about 7.35 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 97  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 7% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 898 nm to a wavelength of 993 nm ranges from 6.3% to 8.0%. With reference to the reflectance of 7.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 95 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.097, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Eighty-eighth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the eighty-eighth embodiment of the present invention will be described below with reference to FIG.  98 . This semiconductor optical device is different from the semiconductor optical device according to the eighty-seventh embodiment in that a setting reflectance R(λ 0 ) is 7.0% at a setting wavelength λ 0 =1016 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.413831 and φ 2 =0.91752, a reflectance of 7.0% can be obtained at a wavelength of 1016 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 I/Dd 2 =9.16 nm/87.83 nm/247.27 nm/68.32 nm/192.32 nm/61.81 nm/174.01 nm/61.81 nm/174.01 nm. The total thickness (d total =Σd i ) of the film is 1076.54 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1866.25 nm which is very large, i.e., about 7.62 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 98  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 7% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 931 nm to a wavelength of 1029 nm ranges from 6.3% to 8.0%. With reference to the reflectance of 7.0% at the setting wavelength 1016 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 5.5% to 8.0% is 98 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1016 nm is about 0.096, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Eighty-ninth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the eighty-ninth embodiment of the present invention will be described below with reference to FIG.  99 . This semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(&gt;λ 0 ) is 8.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.10, A=2.70, B=2.10, C=2.05 and D=1.80. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.395103 and φ 2 =0.933593, a reflectance of 8.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.99 nm/80.89 nm/242.69 nm/62.91 nm/188.76 nm/61.42 nm/184.27 nm/53.93 nm/161.79 nm. The total thickness (d total =Σd i ) of the film is 1045.65 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1807.20 nm which is very large, i.e., about 7.38 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 99  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 886 nm to a wavelength of 991 nm ranges from 7.0% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 105 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.107, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninetieth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the ninetieth embodiment of the present invention will be described below with reference to FIG.  100 . This semiconductor optical device is different from the semiconductor optical device according to the eighty-ninth embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =1023 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.395103 and φ 2 =0.933593, a reflectance of 8.0% can be obtained at a wavelength of 1023 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =9.38 nm/84.44 nm/253.34 nm/65.67 nm/197.04 nm/64.11 nm/192.35 nm/56.29 nm/168.89 nm. The total thickness (d total =Σd i ) of the film is 1091.51 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1886.46 nm which is very large, i.e., about 7.70 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 100  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 925 nm to a wavelength of 1034 nm ranges from 7.0% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 1023 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 109 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1023 nm is about 0.107, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninety-first Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the ninety-first embodiment of the present invention will be described below with reference to FIG.  101 . This semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 9.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.10, A=2.70, B=2.10, C=2.15 and D=1.75. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.392646 and φ 2 =0.930741, a reflectance of 9.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.96 nm/80.39 nm/241.95 nm/62.52 nm/188.16 nm/64.01 nm/192.66 nm/52.10 nm/156.82 nm. The total thickness (d total =Σd i ) of the film is 1047.59 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1810.29 nm which is very large, i.e., about 7.39 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 101  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 9% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 872 nm to a wavelength of 990 nm ranges from 7.8% to 10.0%. With reference to the reflectance of 9.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 7.5% to 10.0% is 118 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.120, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninety-second Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the ninety-second embodiment of the present invention will be described below with reference to FIG.  102 . This semiconductor optical device is different from the semiconductor optical device according to the ninety-first embodiment in that a setting reflectance R(λ 0 ) is 9.0% at a setting wavelength λ 0 =1031 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.392646 and φ 2 =0.930741, a reflectance of 9.0% can be obtained at a wavelength of 1031 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =9.43 nm/84.57 nm/254.54 nm/65.78 nm/197.98 nm/67.34 nm/202.69 nm/54.81 nm/164.98 nm. The total thickness (d total =Σd i ) of the film is 1102.12 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1904.52 nm which is very large, i.e., about 7.77 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 102  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 9% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 918 nm to a wavelength of 1041 nm ranges from 7.8% to 10.0%. With reference to the reflectance of 9.0% at the setting wavelength 1031 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 7.5% to 10.0% is 123 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1031 nm is about 0.119, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninety-third Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the ninety-third embodiment of the present invention will be described below with reference to FIG.  103 . This semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 10.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.10, A=2.75, B=2.10, C=2.25 and D=1.75. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.394052 and φ 2 =0.907302, a reflectance of 10.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.74 nm/82.17 nm/240.22 nm/62.75 nm/183.44 nm/67.33 nm/196.55 nm/52.29 nm/152.87 nm. The total thickness (d total =Σd i ) of the film is 1046.36 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1810.50 nm which is very large, i.e., about 7.39 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 103  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 10% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 866 nm to a wavelength of 990 nm ranges from 8.7% to 11.0%. With reference to the reflectance of 10.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 8.5% to 11.0% is 124 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.127, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninety-fourth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the ninety-fourth embodiment of the present invention will be described below with reference to FIG.  104 . This semiconductor optical device is different from the semiconductor optical device according to the ninety-third embodiment in that a setting reflectance R(λ 0 ) is 10.0% at a setting wavelength λ 0 =1035 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.394052 and φ 2 =0.907302, a reflectance of 10.0% can be obtained at a wavelength of 1035 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =9.23 nm/86.78 nm/253.71 nm/66.27 nm/193.74 nm/71.00 nm/207.58 nm/55.22 nm/161.45 nm. The total thickness (d total =Σd i ) of the film is 1104.98 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1912.11 nm which is very large, i.e., about 7.80 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 104  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 10% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 914 nm to a wavelength of 1045 nm ranges from 8.7% to 11.0%. With reference to the reflectance of 10.0% at the setting wavelength 1035 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 8.5% to 11.0% is 131 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1035 nm is about 0.127, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninety-fifth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the ninety-fifth embodiment of the present invention will be described below with reference to FIG.  105 . This semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 11.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.10, A=2.80, B=2.10, C=2.35 and D=1.75. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.395641 and φ 2 =0.88414, a reflectance of 11.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.51 nm/84.00 nm/238.35 nm/63.00 nm/178.76 nm/70.50 nm/200.04 nm/52.50 nm/148.97 nm. The total thickness (d total =Σd i ) of the film is 1044.63 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1810.29 nm which is very large, i.e., about 7.39 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 105  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 11% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 856 nm to a wavelength of 990 nm ranges from 9.7% to 12.0%. With reference to the reflectance of 11.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 9.5% to 12.0% is 134 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.137, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninety-sixth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the nineth-sixth embodiment of the present invention will be described below with reference to FIG.  106 . This semiconductor optical device is different from the semiconductor optical device according to the ninety-fifth embodiment in that a setting reflectance R(λ 0 ) is 11.0% at a setting wavelength λ 0 =1040 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.395641 and φ 2 =0.88414, a reflectance of 11.0% can be obtained at a wavelength of 1040 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =9.03 nm/89.14 nm/252.94 nm/66.86 nm/189.71 nm/74.81 nm/212.29 nm/55.71 nm/158.09 nm. The total thickness (d total =Σd i ) of the film is 1108.58 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1921.11 nm which is very large, i.e., about 7.84 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 106  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 11% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 909 nm to a wavelength of 1050 nm ranges from 9.7% to 12.0%. With reference to the reflectance of 11.0% at the setting wavelength 1040 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 9.5% to 12.0% is 141 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1040 nm is about 0.136, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninety-seventh Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the ninety-seventh embodiment of the present invention will be described below with reference to FIG.  107 . This semiconductor optical device is different from the semiconductor optical device according to the thirty-third embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =980 nm. Parameters are given by O=0.10, A=2.85, B=2.10, C=2.42 and D=1.75. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.39697 and φ 2 =0.864124, a reflectance of 12.0% can be obtained at a wavelength of 980 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 I/Cd 2 /Dd 1 /Dd 2 =8.32 nm/85.79 nm/237.11 nm/63.21 nm/174.71 nm/72.84 nm/201.34 nm/52.68 nm/145.60 nm. The total thickness (d total =Σd i ) of the film is 1041.60 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1807.36 nm which is very large, i.e., about 7.38 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 107  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 852 nm to a wavelength of 990 nm ranges from 10.8% to 13.0%. With reference to the reflectance of 12.0% at the setting wavelength 980 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 138 nm. A value obtained by dividing the wavelength band by the setting wavelength of 980 nm is about 0.141, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     Ninety-eighth Embodiment 
     A semiconductor optical device having a nine-layer reflecting film according to the ninety-eighth embodiment of the present invention will be described below with reference to FIG.  108 . This semiconductor optical device is different from the semiconductor optical device according to the ninety-seventh embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =1043 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.39697 and φ 2 =0.864124, a reflectance of 12.0% can be obtained at a wavelength of 1043 nm. In this case, the film thickness of the layers of the nine-layer reflecting film are given by Od 2 /Ad 1 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =8.85 nm/91.30 nm/252.35 nm/67.27 nm/185.95 nm/77.53 nm/214.28 nm/56.06 nm/154.95 nm. The total thickness (d total =Σd i ) of the film is 1108.54 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the nine films is 1923.51 nm which is very large, i.e., about 7.85 times a ¼ wavelength (=245 nm) of the predetermined wavelength of 980 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 108  is a graph of a wavelength dependence of the reflectance of the nine-layer reflecting film  60 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the nine-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 907 nm to a wavelength of 1053 nm ranges from 10.8% to 13.0%. With reference to the reflectance of 12.0% at the setting wavelength 1043 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 146 nm. A value obtained by dividing the wavelength band by the setting wavelength of 1043 nm is about 0.140, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the nine-layer reflecting film  60  has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical device according to the eighty-fifth embodiment to the ninety-eighth embodiment are shown in Table 9. In Table 9, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (245 nm) of a predetermined wavelength 980 nm, band bands Δλ in which the reflectance falls within the range from −1.5 to +1.0% of R(λ 0 ), and ratio of Δλ/π 0  are shown. 
                                                                                 TABLE 9                   Characteristic of Reflecting Multi-layer Film                    Setting       Summation of Σnidi;   Band width Δλ               Configuration of   wavelength λ 0 ;       Ratio of Σnidi to 1/4   in which the reflectance       Embodiment   reflecting   Setting   Minimal   wave-length (245 nm) of   falls within the range   Ratio of       No.   multi-layer film   reflectance R(λ 0 )   reflectance   980 nm   from −1.5 to 1.0 of R(λ 0 )   Δλ/λ 0                      85   nine films    980 nm   5.1%   1823.70 nm   100 nm   100/980 = 0.102               6.0%       7.44 times       86   nine films   1018 nm   5.1%   1857.42 nm   103 nm   103/1018 = 0.101               6.0%       7.73 times       87   nine films    980 nm   6.3%   1800.12 nm   95 nm    95/980 = 0.097               7.0%       7.35 times       88   nine films   1016 nm   6.3%   1866.25 nm   98 nm    98/1016 = 0.096               7.0%       7.62 times       89   nine films    980 nm   7.0%   1807.20 nm   105 nm   105/980 = 0.107               8.0%       7.38 times       90   nine films   1023 nm   7.0%   1886.46 nm   109 nm   109/1023 = 0.107               8.0%       7.70 times       91   nine films    980 nm   7.8%   1810.29 nm   118 nm   118/980 = 0.120               9.0%       7.39 times       92   nine films   1031 nm   7.8%   1904.52 nm   123 nm   123/1031 = 0.119               9.0%       7.77 times       93   nine films    980 nm   8.7%   1810.50 nm   124 nm   124/980 = 0.127               10.0%        7.39 times       94   nine films   1035 nm   8.7%   1912.11 nm   131 nm   131/1035 = 0.127               10.0%        7.80 times       95   nine films    980 nm   9.7%   1810.29 nm   134 nm   134/980 = 0.137               11.0%        7.39 times       96   nine films   1040 nm   9.7%   1921.11 nm   141 nm   141/1040 = 0.136               11.0%        7.84 times       97   nine films    980 nm   10.8%   1807.36 nm   138 nm   138/980 = 0.141               12.0%        7.38 times       98   nine films   1043 nm   10.8%   1923.51 nm   146 nm   146/1043 = 0.140               12.0%        7.85 times                    
Ninety-ninth Embodiment
 
     A semiconductor optical device having a eight-layer reflecting film according to the ninety-ninth embodiment of the present invention will be described below with reference to  FIGS. 109 and 122 .  FIG. 109  is a schematic sectional view of a configuration obtained when a eight-layer reflecting film  70  is formed in place of a single-layer reflecting film as a reflecting film on an end face portion of the semiconductor optical device. This semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that the reflecting multi-layer film is the eight-layer reflecting film  70 . More specifically, the semiconductor optical device is different from the semiconductor optical device according to the first embodiment in that first-layer film being in contact with a waveguide layer  10  and second-layer film are respectively aluminum oxide layer and silicon oxide layer, and each film has a refractive index smaller than a square root of an effective refractive index n c  of the waveguide layer. It is noted that tantalum oxide films and silicon oxide films are alternately stacked from the third-layer film to the eight-layer film. 
     A condition for setting the reflectance of the eight-layer reflecting film  70  to be equal to the reflectance of the hypothetical film at a predetermined wavelength will be considered. A case in which the film of the third type is used as the first-layer film being in contact with the waveguide layer  10  is considered here. A phase shift φ 3  of the third film is expressed by the following equation (20). 
               ϕ   3     =         2   ⁢   π     λ     ⁢     n   3     ⁢     d   3               (   20   )             
 
     Therefore, the amplitude reflectance of the eight-layer reflecting film  70  is expressed by the following equation (21) like the amplitude reflectance of the seven-layers reflecting film. 
             r   =           (       m   11     +     m   12       )     ⁢     n   c       -     (       m   21     +     m   22       )             (       m   11     +     m   12       )     ⁢     n   c       +     (       m   21     +     m   22       )                 (   21   )             
 
     where m ij  (i and j are 1 or 2) is expressed by the following equation (22): 
                 (           m   11           m   12               m   21           m   22           )     =       (           cos   ⁢           ⁢     ϕ   3               -     i     n   3         ⁢   sin   ⁢           ⁢     ϕ   3                   -   i     ⁢           ⁢     n   3     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   3             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   A   ⁢           ⁢     ϕ   2             )     ×     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   B   ⁢           ⁢     ϕ   2             )     ×     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   C   ⁢           ⁢     ϕ   2             )     ×     (           cos   ⁢           ⁢   D   ⁢           ⁢     ϕ   1               -     i     n   1         ⁢   sin   ⁢           ⁢   D   ⁢           ⁢     ϕ   1                   -   i     ⁢           ⁢     n   1     ⁢   sin   ⁢           ⁢   D   ⁢           ⁢     ϕ   1             cos   ⁢           ⁢   D   ⁢           ⁢     ϕ   1             )     ⁢     (           cos   ⁢           ⁢   D   ⁢           ⁢     ϕ   2               -     i     n   2         ⁢   sin   ⁢           ⁢   D   ⁢           ⁢     ϕ   2                   -   i     ⁢           ⁢     n   2     ⁢   sin   ⁢           ⁢   D   ⁢           ⁢     ϕ   2             cos   ⁢           ⁢   D   ⁢           ⁢     ϕ   2             )         ⁢                   (   22   )             
 
     where A, B, C and D are parameters representing contributing rates of respective two-layer films (pair) in a film thickness Ad 2  of a second-layer film  72 , a film thickness Bd 1  of a third-layer film  73 , a film thickness Bd 2  of a fourth-layer film  74 , a film thickness Cd 1  of a fifth-layer film  75 , a film thickness Cd 2  of a sixth-layer film  76 , a film thickness Dd 1  of a seventh-layer film  77 , and a film thickness Dd 2  of an eighth-layer film  78 . It is noted that parameter “A” is contribution ratio for the second-layer film  72 . 
     A case in which the eight-layer reflecting film  70  is formed on an end face portion of the semiconductor optical device will be described below.  FIG. 109  is a schematic sectional view of the configuration of the eight-layer reflecting film formed on the end face portion. In this semiconductor optical device, on an end face portion of the waveguide layer  10  (equivalent refractive index n c =3.37), the first-layer film  71  (refractive index n 2 =1.636 and a film thickness d 3 =10 nm) made of aluminum oxide, the second-layer film  72  (refractive index n 1 =1.457 and a film thickness Ad 2 ) made of silicon oxide, the third-layer film  73  (refractive index n 1 =2.072 and a film thickness Bd 1 ) made of tantalum oxide, the fourth-layer film  74  (refractive index n 2 =1.457 and a film thickness Bd 2 ) made of silicon oxide, the fifth-layer film  75  (refractive index n 1 =2.072 and a film thickness Cd 1 ) made of tantalum oxide, the sixth-layer film  76  (refractive index n 2 =1.457 and a film thickness Cd 2 ) made of silicon oxide, the seventh-layer film  77  (refractive index n 1 =2.072 and a film thickness Dd 1 ) made of tantalum oxide, the eighth-layer film  78  (refractive index n 2 =1.457 and a film thickness Dd 2 ) made of silicon oxide, are stacked. In addition, the eight-layer reflecting film  70  is in contact with a free space  5  such as the air. 
     The reflecting characteristic of the eight-layer reflecting film  70  on the end face portion of the semiconductor optical device will be described below. A setting reflectance R(λ 0 ) is set to be 4.0% at a predetermined wavelength λ 0 =808 nm. When parameters are given by A=0.32, B=1.96, C=1.85, and D=2.00, and when phase shifts φ 1  and φ 2  of tantalum oxide and silicon oxide are given by  100   1 =0.356684 and φ 2 =1.26875, a reflectance of 4.0% is obtained at a wavelength of 808 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =10 nm/35.83 nm/43.39 nm/219.49 nm/40.95 nm/207.17 nm/44.27 nm/223.96 nm. The total thickness (d total =Σd i ) of the film is 825.06 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2108.54 nm which is very large, i.e., about 10.44 times a ¼ wavelength (=202 nm) at a predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 110  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  70 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 4% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 802 nm to a wavelength of 941 nm ranges from 2.6% to 5.0%. With reference to the reflectance of 4.0% at the predetermined wavelength 808 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 2.5% to 5.0% is 139 nm. A value obtained by dividing the wavelength band by the predetermined wavelength of 808 nm is about 0.172, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  70  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hunderedth embodiment of the present invention will be described below with reference to FIG.  111 . This semiconductor optical device is different from the semiconductor optical device according to the ninety-ninth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =744 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and silicon oxide are given by φ 1 =0.361744 and φ 2= 1.26093, a reflectance of 4.0% can be obtained at a wavelength of 744 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =10 nm/32.79 nm/40.31 nm/199.83 nm/38.25 nm/189.58 nm/41.35 nm/204.95 nm. The total thickness (d total =Σd i ) of the film is 757.06 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 1949.67 nm which is very large, i.e., about 9.65 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 111  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  70 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 4% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 738 nm to a wavelength of 869 nm ranges from 2.5% to 5.0%. With reference to the reflectance of 4.0% at the setting wavelength 744 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 2.5% to 5.0% is 131 nm. A value obtained by dividing the wavelength band by the setting wavelength of 744 nm is about 0.176, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  70  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-first Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hundredth-first embodiment of the present invention will be described below with reference to FIG.  112 . This semiconductor optical device is different from the semiconductor optical device according to the ninety-ninth embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =808 nm. Parameters are given by A=0.20, B=2.00, C=2.00 and D=2.00. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and silicon oxide are given by φ 1 =0.374385 and φ 2 =1.26121, a reflectance of 8.0% can be obtained at a wavelength of 808 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =10 nm/22.26 nm/46.47 nm/222.63 nm/46.47 nm/222.63 nm/46.47 nm/222.63 nm. The total thickness (d total =Σd i ) of the film is 839.56 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2177.34 nm which is very large, i.e., about 10.78 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 112  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  70 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 801 nm to a wavelength of 946 nm ranges from 6.6% to 9.0%. With reference to the reflectance of 8.0% at the predetermined wavelength 808 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 145 nm. A value obtained by dividing the wavelength band by the predetermined wavelength of 808 nm is about 0.179, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  70  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-second Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hunderedth-second embodiment of the present invention will be described below with reference to FIG.  113 . This semiconductor optical device is different from the semiconductor optical device according to the hundredth-first embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =753 nm. Parameter is given by A=0.19. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and silicon oxide are given by φ 1 =0.370822 and φ 2 =1.26896, a reflectance of 8.0% can be obtained at a wavelength of 753 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =10 nm/19.83 nm/42.90 nm/208.75 nm/42.90 nm/208.75 nm/42.90 nm/208.75 nm. The total thickness (d total =Σd i ) of the film is 784.78 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2024.36 nm which is very large, i.e., about 10.02 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 113  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  70 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 746 nm to a wavelength of 870 nm ranges from 6.7% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 753 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 124 nm. A value obtained by dividing the wavelength band by the setting wavelength of 753 nm is about 0.165, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  70  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-third Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hundredth-third embodiment of the present invention will be described below with reference to FIG.  114 . This semiconductor optical device is different from the semiconductor optical device according to the ninety-ninth embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a predetermined wavelength λ 0 =808 nm. Parameters are given by A=0.14, B=1.95, C=1.80 and D=2.00. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and silicon oxide are given by φ 1 =0.403695 and φ 2 =1.34024, a reflectance of 12.0% can be obtained at a wavelength of 808 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =10 nm/16.56 nm/48.86 nm/230.67 nm/45.10 nm/212.93 nm/50.11 nm/236.58 nm. The total thickness (d total =Σd i ) of the film is 850.81 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2264.47 nm which is very large, i.e., about 11.21 times a ¼ wavelength (−202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 114  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  70 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 801 nm to a wavelength of 1037 nm ranges from 10.7% to 13.0%. With reference to the reflectance of 12.0% at the predetermined wavelength 808 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 236 nm. A value obtained by dividing the wavelength band by the predetermined wavelength of 808 nm is about 0.292, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  70  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-fourth Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hunderedth-fourth embodiment of the present invention will be described below with reference to FIG.  115 . This semiconductor optical device is different from the semiconductor optical device according to the hundredth-third embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =706 nm. Parameter is given by B=1.93. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and silicon oxide are given by φ 1 =0.412469 and φ 2 =1.3303, a reflectance of 12.0% can be obtained at a wavelength of 706 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =10 nm/14.43 nm/43.90 nm/198.96 nm/40.56 nm/185.56 nm/45.06 nm/206.18 nm. The total thickness (d total =Σd i ) of the film is 744.24 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2005.83 nm which is very large, i.e., about 9.93 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 115  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  70 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 707 nm to a wavelength of 908 nm ranges from 10.9% to 13.0%. With reference to the reflectance of 12.0% at the setting wavelength 706 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 201 nm. A value obtained by dividing the wavelength band by the setting wavelength of 706 nm is about 0.285, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  70  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-fifth Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hundredth-fifth embodiment of the present invention will be described below with reference to  FIGS. 116 and 117 .  FIG. 116  is a schematic sectional view of a configuration obtained when a eight-layer reflecting film  80  is formed in place of a single-layer reflecting film as a reflecting film on an end face portion of the semiconductor optical device. This semiconductor optical device is different from the semiconductor optical device according to the ninety-ninth embodiment in that first-layer film being in contact with a waveguide layer  10  is silicon oxide layer and second-layer film, fourth-layer film, sixth-layer film, and eighth-layer film are aluminum oxide layers. 
     A case in which the eight-layer reflecting film  80  is formed on an end face portion of the semiconductor optical device will be described below.  FIG. 116  is a schematic sectional view of the configuration of the eight-layer reflecting film formed on the end face portion. In this semiconductor optical device, on an end face portion of the waveguide layer  10  (equivalent refractive index n c =3.37), the first-layer film  81  (refractive index n 2 =1.457 and a film thickness d 3 =5 nm) made of silicon oxide, the second-layer film  82  (refractive index n c =1.636 and a film thickness Ad 2 ) made of aluminum oxide, the third-layer film  83  (refractive index n 1 =2.072 and a film thickness Bd 1 ) made of tantalum oxide, the fourth-layer film  84  (refractive index n 2 =1.636 and a film thickness Bd 2 ) made of aluminum oxide, the fifth-layer film  85  (refractive index n 1 =2.072 and a film thickness Cd 1 ) made of tantalum oxide, the sixth-layer film  86  (refractive index n 2 =1.636 and a film thickness Cd 2 ) made of aluminum oxide, the seventh-layer film  87  (refractive index n 1 =2.072 and a film thickness Dd 1 ) made of tantalum oxide, the eighth-layer film  88  (refractive index n 2 =1.636 and a film thickness Dd 2 ) made of aluminum oxide, are stacked. In addition, the eight-layer reflecting film  80  is in contact with a free space  5  such as the air. 
     The reflecting characteristic of the eight-layer reflecting film  80  on the end face portion of the semiconductor optical device will be described below. A setting reflectance R(λ 0 ) is set to be 4.0% at a predetermined wavelength λ 0 =808 nm. When parameters are given by A=0.22, B=2.00, C=2.16, and D=2.00, and when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.44218 and φ 2 =1.18776, a reflectance of 4.0% is obtained at a wavelength of 808 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =5 nm/20.54 nm/54.89 nm/186.73 nm/59.28 nm/201.67 nm/54.89 nm/186.73 nm. The total thickness (d total =Σd i ) of the film is 769.73 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2355.68 nm which is very large, i.e., about 11.66 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 117  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  80 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 4% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 800 nm to a wavelength of 1032 nm ranges from 2.7% to 5.0%. With reference to the reflectance of 4.0% at the predetermined wavelength 808 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 2.5% to 5.0% is 232 nm. A value obtained by dividing the wavelength band by the predetermined wavelength of 808 nm is about 0.287, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  80  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-sixth Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hunderedth-sixth embodiment of the present invention will be described below with reference to FIG.  118 . This semiconductor optical device is different from the semiconductor optical device according to the hundredth-fifth embodiment in that a setting reflectance R(λ 0 ) is 4.0% at a setting wavelength λ 0 =716 nm. Parameter are given by A=0.17, B=1.93, C=2.24. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.455795 and φ 2 =1.15938, a reflectance of 4.0% can be obtained at a wavelength of 716 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =5 nm/13.73 nm/50.89 nm/163.94 nm/56.15 nm/180.89 nm/50.01 nm/161.11 nm. The total thickness (d total =Σd i ) of the film is 681.72 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2115.46 nm which is very large, i.e., about 10.47 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 118  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  80 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 4% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 709 nm to a wavelength of 906 nm ranges from 3.0% to 5.0%. With reference to the reflectance of 4.0% at the setting wavelength 716 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 2.5% to 5.0% is 197 nm. A value obtained by dividing the wavelength band by the setting wavelength of 716 nm is about 0.275, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  80  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-seventh Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hundredth-seventh embodiment of the present invention will be described below with reference to FIG.  119 . This semiconductor optical device is different from the semiconductor optical device according to the hundredth-fifth embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a predetermined wavelength λ 0 =808 nm. Parameters are given by A=0.20, B=2.00, C=2.60 and D=2.00. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by (i=0.703895 and φ 2 =0.563728, a reflectance of 8.0% can be obtained at a wavelength of 808 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =5 nm/8.86 nm/87.37 nm/88.62 nm/113.59 nm/115.21 nm/87.37 nm/88.62 nm. The total thickness (d total =Σd i ) of the film is 594.64 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2726.92 nm which is very large, i.e., about 13.50 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 119  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  80 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 647 nm to a wavelength of 819 nm ranges from 7.1% to 9.0%. With reference to the reflectance of 8.0% at the predetermined wavelength 808 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 172 nm. A value obtained by dividing the wavelength band by the predetermined wavelength of 808 nm is about 0.213, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  80  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-eight Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hunderedth-eighth embodiment of the present invention will be described below with reference to FIG.  120 . This semiconductor optical device is different from the semiconductor optical device according to the hundredth-seventh embodiment in that a setting reflectance R(λ 0 ) is 8.0% at a setting wavelength λ 0 =891 nm. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.707082 and φ 2 =0.56214, a reflectance of 8.0% can be obtained at a wavelength of 891 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =5 nm/9.75 nm/96.79 nm/97.45 nm/125.82 nm/126.69 nm/96.79 nm/97.45 nm. The total thickness (d total =Σd i ) of the film is 655.74 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 3016.09 nm which is very large, i.e., about 14.93 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 120  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  80 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 8% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 712 nm to a wavelength of 903 nm ranges from 7.0% to 9.0%. With reference to the reflectance of 8.0% at the setting wavelength 891 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 6.5% to 9.0% is 191 nm. A value obtained by dividing the wavelength band by the setting wavelength of 891 nm is about 0.214, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  80  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-ninth Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hundredth-ninth embodiment of the present invention will be described below with reference to FIG.  121 . This semiconductor optical device is different from the semiconductor optical device according to the hundredth-fifth embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a predetermined wavelength λ 0 =808 nm. Parameters are given by A=0.10, B=2.53, C 2.75 and D=2.00. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by (i=0.549712 and φ 2 =0.58774, a reflectance of 12.0% can be obtained at a wavelength of 808 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =5 nm/4.62 nm/86.32 nm/1 16.88 nm/93.82 nm/127.05 nm/68.24 nm/92.40 nm. The total thickness (d total =Σd i ) of the film is 594.33 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2352.26 nm which is very large, i.e., about 11.64 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 121  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  80 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 617 nm to a wavelength of 821 nm ranges from 10.6% to 13.0%. With reference to the reflectance of 12.0% at the predetermined wavelength 808 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 204 nm. A value obtained by dividing the wavelength band by the predetermined wavelength of 808 nm is about 0.252, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  80  has a flat portion having a low reflectance over a wide wavelength band. 
     Hundredth-tenth Embodiment 
     A semiconductor optical device having a eight-layer reflecting film according to the hunderedth-tenth embodiment of the present invention will be described below with reference to FIG.  122 . This semiconductor optical device is different from the semiconductor optical device according to the hundredth-ninth embodiment in that a setting reflectance R(λ 0 ) is 12.0% at a setting wavelength λ 0 =909 nm. Parameter is given by B=2.57. In addition, when phase shifts φ 1  and φ 2  of tantalum oxide and aluminum oxide are given by φ 1 =0.53932 and φ 2 =0.592482, a reflectance of 12.0% can be obtained at a wavelength of 909 nm. In this case, the film thickness of the layers of the eight-layer reflecting film are given by d 3 /Ad 2 /Bd 1 /Bd 2 /Cd 1 /Cd 2 /Dd 1 /Dd 2 =5 nm/5.24 nm/96.78 nm/134.65 nm/103.56 nm/144.08 nm/75.31 nm/104.79 nm. The total thickness (d total =Σd i ) of the film is 669.41 nm. A sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of a layer denoted with i in the eight films is 2618.82 nm which is very large, i.e., about 12.96 times a ¼ wavelength (=202 nm) of the predetermined wavelength of 808 nm. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. 
       FIG. 122  is a graph of a wavelength dependence of the reflectance of the eight-layer reflecting film  80 . The abscissa of the graph indicates a wavelength, and the ordinate denotes a reflectance. In the eight-layer reflecting film, a flat portion having about 12% of the setting reflectance over a wide wavelength band can be obtained. More specifically, the reflectance in the range of a wavelength of 693 nm to a wavelength of 923 nm ranges from 10.5% to 13.0%. With reference to the reflectance of 12.0% at the setting wavelength 909 nm, a continuous wavelength band in the range of −1.5% to +1.0%, i.e., 10.5% to 13.0% is 230 nm. A value obtained by dividing the wavelength band by the setting wavelength of 909 nm is about 0.253, and is larger than 0.065 in the hypothetical reflecting film. Therefore, it is understood that the eight-layer reflecting film  80  has a flat portion having a low reflectance over a wide wavelength band. 
     The characteristics of the reflecting multi-layer films of the semiconductor optical device according to the ninety-ninth embodiment to the hunderedth-tenth embodiment are shown in Table 10. In Table 10, as the characteristics of the reflecting multi-layer film, the configurations of the reflecting multi-layer film, setting wavelength λ 0  and setting reflectance R(λ 0 ), minimal reflectance, summation Σn i d i , ratio of Σn i d i  to ¼ wavelength (202 nm) of a predetermined wavelength 808 nm, band bands AA in which the reflectance falls within the range from −1.5 to +1.0% of R(λ 0 ), and ratio of Δλ/λ 0  are shown. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 10 
               
             
             
               
                   
               
               
                 Characteristic of Reflecting Multi-layer Film 
               
             
          
           
               
                   
                   
                 Setting 
                   
                 Summation of Σnidi; 
                 Band width Δλ 
                   
               
               
                   
                 Configuration of 
                 wavelength λ 0 ; 
                   
                 Ratio of Σnidi to 1/4 
                 in which the reflectance 
               
               
                 Embodiment 
                 reflecting 
                 Setting 
                 Minimal 
                 wave-length (202 nm) of 
                 falls within the range 
                 Ratio of 
               
               
                 No. 
                 multi-layer film 
                 reflectance R(λ 0 ) 
                 reflectance 
                 808 nm 
                 from −1.5 to 1.0 of R(λ 0 ) 
                 Δλ/λ 0   
               
               
                   
               
             
          
           
               
                 99 
                 eight films 
                 808 nm 
                 2.6% 
                 2108.54 nm 
                 139 nm 
                 139/808 = 0.172 
               
               
                   
                   
                 4.0% 
                   
                 10.44 times 
               
               
                 100 
                 eight films 
                 744 nm 
                 2.5% 
                 1949.67 nm 
                 131 nm 
                 131/744 = 0.101 
               
               
                   
                   
                 4.0% 
                   
                 9.65 times 
               
               
                 101 
                 eight films 
                 808 nm 
                 6.6% 
                 2177.34 nm 
                 145 nm 
                 145/808 = 0.179 
               
               
                   
                   
                 8.0% 
                   
                 10.78 times 
               
               
                 102 
                 eight films 
                 753 nm 
                 6.7% 
                 2024.36 nm 
                 124 nm 
                 124/753 = 0.165 
               
               
                   
                   
                 8.0% 
                   
                 10.02 times 
               
               
                 103 
                 eight films 
                 808 nm 
                 10.7% 
                 2264.47 nm 
                 236 nm 
                 236/808 = 0.292 
               
               
                   
                   
                 12.0%  
                   
                 11.21 times 
               
               
                 104 
                 eight films 
                 706 nm 
                 10.9% 
                 2005.83 nm 
                 201 nm 
                 201/706 = 0.285 
               
               
                   
                   
                 12.0%  
                   
                 9.93 times 
               
               
                 105 
                 eight films 
                 808 nm 
                 2.7% 
                 2355.68 nm 
                 232 nm 
                 232/808 = 0.287 
               
               
                   
                   
                 4.0% 
                   
                 11.66 times 
               
               
                 106 
                 eight films 
                 716 nm 
                 3.0% 
                 2115.46 nm 
                 197 nm 
                 197/716 = 0.275 
               
               
                   
                   
                 4.0% 
                   
                 10.47 times 
               
               
                 107 
                 eight films 
                 808 nm 
                 7.1% 
                 2726.92 nm 
                 172 nm 
                 172/808 = 0.213 
               
               
                   
                   
                 8.0% 
                   
                 13.50 times 
               
               
                 108 
                 eight films 
                 891 nm 
                 7.0% 
                 3016.09 nm 
                 191 nm 
                 191/891 = 0.214 
               
               
                   
                   
                 8.0% 
                   
                 14.93 times 
               
               
                 109 
                 eight films 
                 808 nm 
                 10.6% 
                 2352.26 nm 
                 204 nm 
                 204/808 = 0.252 
               
               
                   
                   
                 12.0%  
                   
                 11.64 times 
               
               
                 110 
                 eight films 
                 909 nm 
                 10.5% 
                 2618.82 nm 
                 230 nm 
                 230/909 = 0.253 
               
               
                   
                   
                 12.0%  
                   
                 12.96 times 
               
               
                   
               
             
          
         
       
     
     In the embodiments which describe the present invention, the seven-layers reflecting film, the six-layers reflecting film, the nine-layers reflecting film, and eight-layer reflecting film have been described as examples. The present invention is not limited to these embodiments. Other reflecting multi-layer films may be used as the reflecting multi-layer films described in the embodiments. The case in which the materials of three types are used has been described. However, even in a case in which materials of four or more types are used, when a phase condition is given in advance, films can be handled in the same manner as described above. It is noted that an aluminum nitride film having a thickness 50 nm, an aluminum oxide film having a thickness 10 nm, and a silicon oxide film having a thickness 5 nm are described as a third-type film. The third-type film and the thickness are not limited to the above examples. The parameters such as O, A, B, C, and D representing contribution of a two-layer film including a pair of films made of aluminum oxide and tantalum oxide are not limited to the values described in the above embodiments. In addition, the case in which a semiconductor laser device is used as a semiconductor optical device has been exemplified. However, the present invention is applied to not only the semiconductor laser device but also an optical device such as a semiconductor optical amplifier, a super luminescent, a diode, an optical modulator, or an optical switch. In addition, a wavelength is not limited to about 980 nm and 808 nm, and a wavelength in a visible region, a far infrared region, and an infrared region can also be applied. Furthermore, although a reflectance of about 2% to 12% has been described as a reflectance, the present invention can be applied to any other reflectance range. 
     According to the semiconductor optical device according to the present invention, a sum Σn i d i  of products n i d i  of refractive index n i  and film thickness d i  of layers of a reflecting multi-layer film is larger than a ¼ wavelength of, e.g., a predetermined wavelength of 980 nm of light guided through a waveguide layer. In addition, Σn i d i  of the reflecting multi-layer film is almost larger than a 5/4 wavelength of the guided light, and the thickness is very large. For this reason, a heat-radiation characteristic on the end face is improved, and the temperature of the end face can be suppressed from increasing. A value Δλ/λ obtained such that a continuous wavelength band Δλ in the range of a minimal value of a reflectance serving as a function of a wavelength to the minimal value +2.0% is divided by the wavelength λ is 0.062 or more. Therefore, although the film is very large in thickness, a wavelength band Δλ of a low reflectance becomes wide. 
     Although the present invention has been described in connection with the preferred embodiments thereof with reference to the accompanying drawings, it is to be noted that various changes and modifications are apparent to those skilled in the art. Such changes and modifications are to be understood as included within the scope of the present invention as defined by the appended claims, unless they depart therefrom.