Abstract:
An optical element has a small reflection loss of light on a boundary surface between a photonic crystal and the normal medium. The optical element includes: a normal medium region having a first refractive index; a photonic crystal region having a refractive index which is changed periodically depending upon a position thereof, the photonic crystal region having as an averaged refractive index a second refractive index different from the first refractive index; and an intermediate region interposed between the normal medium region and the photonic crystal region, the intermediate region having a refractive index which is gradually changed from the first refractive index to the second refractive index.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The present invention generally relates to an optical element. More specifically,the present invention is directed to an optical element with employment of photonic crystals, refractive indexes of which are changed periodically, depending upon positions thereof.  
           [0003]    2. Description of a Related Art  
           [0004]    Very recently, photonic crystals have been effectively developed, which represent peculier dispersion characteristics, as compared with the conventional optical crystals. Thus, these photonic crystals are strongly expected to be applied to various sorts of optical elements such as optical modulation elements, optical deflection element, and switching elements. Since a photonic crystal is structured in such a manner that within a first material, second materials whose refractive index is different from that of the first material are arranged at an interval corresponding to a wavelength of light, this photonic crystal owns such a characteristic that the refractive index thereof is changed periodically, depending upon the positions of this photonic crystal.  
           [0005]    The above-described characteristic represented by such a photonic crystal is described in detail, for instance, in the publication “Superprism phenomena in photonic crystals” written by H. Kosaka et al., in Physical Review B Vol. 58, No. 16, Oct. 15, 1998.  
           [0006]    However, in the conventional optical elements with employment of the above-described photonic crystals, there are large optical reflection losses occurred in boundary surfaces between the photonic crystals and the normal media, which constitutes a problem to be solved, and also which has been revealed by the extensive analyses made by inventors of the present invention.  
         SUMMARY OF THE INVENTION  
         [0007]    The present invention has been made to solve the above-explained problem and therefore, has an object to provide an optical element having a small light reflection loss produced in a boundary surface between a photonic crystal and the normal medium.  
           [0008]    To achieve the above-described object, an optical element according to one aspect of the present invention includes: a normal medium region having a first refractive index; a photonic crystal region having a refractive index which is changed periodically depending upon a position thereof, the photonic crystal region having as an averaged refractive index a second refractive index different from the first refractive index; and an intermediate region interposed between the normal medium region and the photonic crystal region, the intermediate region having a refractive index which is gradually changed from the first refractive index to the second refractive index.  
           [0009]    In accordance with the present invention, since the refractive index in the intermediate region is gradually changed from the first refractive index to the second refractive index, a mismatching problem of an impedance occurred between the normal medium region and the photonic crystal region can be gradually solved in the intermediate region. As a result, a reflection loss of light occurred in a boundary surface between the photonic crystal region and the normal medium region can be suppressed. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]    [0010]FIG. 1 is a plan view indicating a general structure of an optical element;  
         [0011]    [0011]FIG. 2 represents a photonic band diagram for explaining such a case where light is propagated into the photonic crystal region as shown in FIG. 1 in parallel to the plane of this drawing, and a plane of polarization of this light is located in parallel to the plane of this drawing;  
         [0012]    [0012]FIG. 3 is a diagram illustratively showing a first Brillouin zone of the photonic crystal as shown in FIG. 1 which is sliced at a specific normalized frequency;  
         [0013]    [0013]FIG. 4 is a graphic representation graphically showing a relationship among a normalized frequency, a transmittance, and a reflectance in a case where light belonging to a propagation band of the photonic crystal region as shown in FIG. 1 is propagated through this propagation band;  
         [0014]    [0014]FIG. 5 is a plan view indicating a structural of an optical element according to a first embodiment of the present invention;  
         [0015]    [0015]FIG. 6 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while an aspect ratio in an intermediate region indicated in FIG. 5 is set to one;  
         [0016]    [0016]FIG. 7 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to two;  
         [0017]    [0017]FIG. 8 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to three;  
         [0018]    [0018]FIG. 9 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to four;  
         [0019]    [0019]FIG. 10 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to five;  
         [0020]    [0020]FIG. 11 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to six;  
         [0021]    [0021]FIG. 12 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to seven;  
         [0022]    [0022]FIG. 13 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to eight;  
         [0023]    [0023]FIG. 14 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to nine;  
         [0024]    [0024]FIG. 15 is a diagram representing a relationship among a normalized frequency, a transmittance, and a reflectance in such a case where the light belonging to the propagation band of the photonic crystal region as shown in FIG. 5 is propagated through this propagation band while the aspect ratio in the intermediate region indicated in FIG. 5 is set to ten;  
         [0025]    [0025]FIG. 16 is a plan view indicating a structure of an optical element according to a second embodiment of the present invention; and  
         [0026]    [0026]FIG. 17 is a plan view showing a structure of an optical element according to a third embodiment of the present invention. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0027]    Referring now to drawings, various preferred embodiments of the present invention will be described in detail. It should be understood that the same reference numerals will be employed as those for indicating the same, or similar structural elements, and therefore, explanations thereof are omitted. It should also be noted that since the below-mentioned various numeral values employed in the respective embodiments correspond to typical values, the present invention is not limited to those typical numeral values, but may be applied to other values within the technical scope of the present invention.  
         [0028]    [0028]FIG. 1 is a plan view schematically indicating a general-purpose structure of an optical element  100  constituted in such a manner that a photonic crystal region  102  is formed in a central portion of a substrate  101  made of a silicon material.  
         [0029]    In the photonic crystal region  102  as shown in FIG. 1, a plurality of cylindrical holes  103  are formed in five layers, and are arranged in a two-dimensional triangular lattice shape in such a way that these holes  103  are positioned perpendicular to a propagation direction of light. Air is filled with these holes  103 . In the first embodiment, while an effective refractive index of the substrate  101  is set to 3.065, in such a case where a wavelength of light of interest propagated in a vacuum atmosphere is equal to, for example, 1.55 μm, a radius R of one hole  103  is selected to be 0.387 μm, and also a pitch A of the arranged holes  103  is selected to be 0.93 μm.  
         [0030]    Such a photonic crystal region  102  is fabricated in such a manner that, for instance, after resist has been made on a portion over the substrate  101 , where the holes  103  are not formed, the resultant substrate  101  is treated by a dry etching process having a superior vertical characteristic.  
         [0031]    Light propagated through a photonic crystal is adversely influenced by a multiple scattering phenomenon caused by a periodic (cyclic or alternate) structure of this photonic crystal. This propagation characteristic may be explained with reference to a photonic band diagram which is similar to an electron band diagram in a semiconductor. For instance, in such a case where light is propagated through the photonic crystal region  102  as shown in FIG. 1 in parallel to a plane of this drawing, and further, a plane of polarization of this light is located in parallel to the plane of this drawing, such a photonic band diagram (reduced zone scheme) as shown in FIG. 2 is obtained. A photonic band diagram may give a relationship between a wave vector and a normalized frequency Ω=ω A/(2 π c) in an reciprocal lattice space. It should be noted that “ω” represents an angular frequency of light, “A” represents an arrangement pitch of holes, and “c” represents a light velocity in a vacuum atmosphere.  
         [0032]    Also, it should be understood that “Γ”, “M”, “K” given to an abscissa in FIG. 2 indicate specific wave vectors in a first Brillouin zone as shown in FIG. 3.  
         [0033]    As indicated in FIG. 2, there is such a normalized frequency band (namely, photonic band gap), in which light can not be propagated through a photonic crystal, within a photonic band. As a consequence, such light existing in a normalized frequency band lower than the photonic band gap or higher than the photonic band gap may be propagated through the photonic crystal. In FIG. 2, a normalized frequency band from 0.29 to 0.45 corresponds to the photonic band gap. Also, in a normalized frequency band (namely, a propagation band) from 0.45 to 0.80, there is such light propagated through the photonic crystal region  102  toward a minus direction of the Y-axis (namely, wave vectors of point “Γ” to point “M”).  
         [0034]    When an optical element is manufactured by utilizing a transmission characteristic of a photonic crystal with respect to light, losses of such light belonging to the propagation band of the photonic crystal become low in an ideal condition, which losses may occur when this light transmits through the photonic crystal. As a consequence, the inventors of the present invention calculated both a transmittance and a reflectance on the basis of intensity of light obtained from the following simulation. That is, Gaussian distribution pulse light belonging to the normalized frequency band from 0.5 to 0.75 as shown in FIG. 2 is propagated toward an arrow direction as shown in FIG. 1, and the intensity of the light is simulated at a position P which is just after the Gaussian distribution pulse light had been projected from the photonic crystal region  102 . Both the transmittance and a reflectance were calculated based upon the intensity of light obtained from a simulation. It should also be noted that this simulation has been carried out by employing the FDTD (finite difference time domain) method which is generally utilized in a numeral analysis of a photonic crystal.  
         [0035]    [0035]FIG. 4 graphically represents a relationship among the normalized frequency, the transmittance, and the reflectance, which are obtained in the above-explained calculation. In FIG. 4, a solid line indicates the transmittance, and a broken line indicates the reflectance. As shown in FIG. 4, although the light which belongs to the propagation region of the photonic crystal region  102  as shown in FIG. 1 is propagated through this photonic crystal region  102 , the transmittance is equal to −8 dB to −10 dB. Thus, intensity of the light measured after transmitting through the photonic crystal region  102  is dropped by appropriately 1 digit than intensity of the light measured before transmitting through it. Further, the reflectance of the light at the boundary surface of the photonic crystal region  102  is high, which light belongs to the propagation region of this photonic crystal region  102 . As a result, it is predicted that a reflection loss occurred at the boundary surface of the photonic crystal region  102  may constitute a main reason why the intensity of the light transmitting through this photonic crystal region  102  is lowered. Such a reflection loss is improper in the case where the transmission light belonging to the propagation region of the photonic crystal is utilized because the S/N ratio of the output signal would be deteriorated, and further, the high power of the light source should be required.  
         [0036]    In this photonic crystal region  102 , as also apparent from the area ratio, since the holes  103  are predominant, an averaged refractive index of the photonic crystal region  102  becomes lower than that of silicon. An averaged refractive index N AV  of such a photonic crystal region in which holes are arranged in a two-dimensional triangular lattice form is given in accordance with the following formula (1):  
               N   AV     =         N   1        π                   R   2       +       N   2          {           3     2          A   2       -     π                   R   2         }                 (   1   )                               
 
         [0037]    where:  
         [0038]    N 1  indicates a refractive index of a material filled into a hole, and  
         [0039]    N 2  indicates a refractive index of a background material.  
         [0040]    For instance, when the below-mentioned numerals are applied to the above-explained formula (1), the averaged refractive index N AV  is equal to 1.32. That is, N 1 =1, N 2 =3.065, A=0.93 μm, and R=0.387 μm. In this case, assuming now that the refractive index N of the material of the normal medium region is equal to 3.065, a ratio of this refractive index N to the averaged refractive index N AV  becomes 2.3, namely represents a large value. As a result, it is so conceived that even when such light belonging to the propagation band of the photonic crystal is employed, since a mismatching of impedance at a boundary surface between the photonic crystal and the normal medium is high, the light is strongly reflected from the boundary surface. Then, if the ratio of the refractive index N to the averaged refractive index N AV  becomes such a value larger than 2.3, then the light is further strongly reflected on the boundary surface between the photonic crystal and the normal medium.  
         [0041]    Under such a circumstance, the inventors of the present invention have tried to increase transmittances of light which belongs to the propagation region of the photonic crystal by interposing the below-mentioned intermediate region between the normal medium region and the photonic crystal region.  
         [0042]    [0042]FIG. 5 is a plan view schematically showing a structure of an optical element according to a first embodiment of the present invention.  
         [0043]    As indicated in this drawing, an optical element  10  is arranged in such a manner that a photonic crystal region  13  is formed at a central portion of a substrate  11  including silicon as a medium, and furthermore, an intermediate  14  is formed between a normal medium region  12  located at an upper portion of the substrate  11  and the photonic crystal region  13 .  
         [0044]    In the photonic crystal region  13 , a plurality of holes  15  having cylinder shapes are arranged in a two-dimensional triangular lattice shape, and these holes  15  are filled with air. On the other hand, in the intermediate region  14 , holes  16  having projection portions  17  are arranged at an regular interval along one lateral column (namely, plus direction of the X-axis). The projection portions  17  are tapered and have sharp edges toward the normal medium region  12 , and lower halves of the projection portions  17  are united to semi-cylindrical portions  18 . Similar to the photonic crystal region  13 , these holes  16  are filled with air.  
         [0045]    The inventors of the present invention measured both a transmittance and a reflectance of light belonging to the propagation band of the photonic crystal region  13  with respect to this photonic crystal region  13 , while an aspect ratio is changed. This aspect ratio is defined between a length B of the projection portions  17  of the holes  16  formed in the intermediate region  14  and a pitch A among these holes  15  formed in the photonic crystal region  13 . FIGS.  6 - 15  are graphic diagrams graphically showing relations among normalized frequencies, transmittances, and reflectances in the respective cases where the aspect ratios are selected to be one to ten. It should also be noted that in these graphic diagrams, a solid line indicates a transmittance, and a broken line indicates a reflectance. As shown in these graphic representations, the following fact can be seen. That is, when the aspect ratio is selected to be larger than, or equal to  3 , the transmittances of the light belonging to the propagation region of the photonic crystal with respect to this photonic crystal are increased over a wide portion of the propagation range (namely, a normalized frequency band from 0.5 to 0.75) of this photonic crystal. Thus, it may be apparent that the transmittance may be improved by 4 dB to 5 dB in an average value. In this case, it is so assumed that a ratio of an averaged refractive index of the intermediate region  14  to an averaged refractive index of the photonic crystal region  13  is selected to be smaller than 2.3.  
         [0046]    In the first embodiment, since the holes  16  arranged in the intermediate region  14  are tapered toward the normal medium region  12 , the refractive index in the intermediate region  14  is gradually decreased from the refractive index of the normal medium region  12  to the averaged refractive index of the photonic crystal region  13 . As a result, the mismatching problem of the impedance occurred between the normal medium region  12  and the photonic crystal region  13  may be gradually solved in the intermediate region  14 , so that the reflection loss of the light produced at the boundary of the photonic crystal region  13  can be suppressed.  
         [0047]    As previously explained, when the ratio of the refractive index N of the normal medium region  12  to the averaged refractive index N AV  of the photonic crystal region  13  becomes larger than 2.3, the light is strongly reflected on the boundary surface between the normal medium region  12  and the photonic crystal region  13 . However, since the above-explained intermediate region  14  is newly provided, the reflection loss of the light occurred at the boundary surface of the photonic crystal region  13  can be suppressed similar to the above-explained embodiment.  
         [0048]    [0048]FIG. 16 is a plan view schematically showing a structure of an optical element  20  according to a second embodiment of the present invention.  
         [0049]    In an intermediate region  14  of an optical element  20 , a plurality of cylindrical-shaped holes  21  is arranged in a two-dimensional triangular lattice form in a pitch which is larger than that in a photonic crystal region  13 , and these holes  21  are filled with air.  
         [0050]    In the second embodiment, since the holes  21  having the same shapes as those of the hole  15  of the photonic crystal region  13  (as explained in the first embodiment) are arranged in the intermediate region  14  in lower density than that of the photonic crystal region  13 , a mismatching problem of an impedance between the normal medium region  12  and the photonic crystal region  13  may be gradually solved. As a result, a similar effect to that of the first embodiment can be achieved in accordance with the second embodiment.  
         [0051]    [0051]FIG. 17 is a plan view schematically showing a structure of an optical element  30  according to a third embodiment of the present invention.  
         [0052]    In an intermediate region  14  of an optical element  30 , a plurality of cylindrical-shaped holes  31  is arranged in a two-dimensional triangular lattice form in a pitch which is identical to that in a photonic crystal region  13 , and these holes  31  are filled with such a material as glass. This material owns a refractive index which is smaller than that of the material in the normal medium region  12  (for example, silicon) and which is larger than that of air.  
         [0053]    In the third embodiment, the material whose refractive index, which is smaller than that of the material for constituting the normal medium region  12  and which is larger than that of air, is filled into the holes  31  arranged in the same density as that of the photonic crystal region  13 . As a consequence, a mismatching problem of an impedance between the normal medium region  12  and the photonic crystal region  13  may be gradually solved. As a result, a similar effect to that of the first embodiment can be achieved in accordance with this third embodiment. Alternatively, such a material (for example, glass) may be filled into either the holes  16  or the holes  21  arranged in the intermediate region  14  according to the above-described first and second embodiments. In this alternative case, a similar effect may be achieved.  
         [0054]    In the first to third embodiments of the present invention, the arrangement form of the holes in the photonic crystal region is not limited to such a two-dimensional triangular lattice form as shown in FIG. 2, but also may be realized by other two-dimensionally periodic forms (for example, two-dimensional cube-lattice form), or three-dimensionally lattice forms. Even in the case where the holes are arranged in the above-described arrangement forms, since the first to third embodiments are applied thereto, similar effects may be achieved.  
         [0055]    Alternatively, in the case where the holes and the medium of the photonic crystal region employed in the first to third embodiments are constituted by any materials whose refractive indexes can be changed by an electric field, the optical elements may be used as an optical modulation element, an optical deflection element, or an optical switching element. In detail, while electrodes are mounted on the respective edge surfaces of the photonic crystal region of the optical element in such a manner that these electrodes are opposite to each other, since electric fields are applied among these electrodes so as to change the refractive index of the photonic crystal region, both intensity and a direction of the light which passes through this photonic crystal region may be changed. As a result, the modulation operation of the light, the deflection operation of the light, and the switching operation of the light may be carried out. It should also be noted that as a material whose refractive index may be changed by an electric field, for instance, lithium niobate may be employed.  
         [0056]    As previously described in detail, in accordance with the present invention, the reflection loss of the light occurred at the boundary surface between the photonic crystal and the normal medium can be suppressed, and thus, an optical element having the superior transmission characteristic can be provided.