Patent Publication Number: US-2002001325-A1

Title: Semiconductor laser device with optical waveguide exhibiting high kink output

Description:
BACKGROUND OF THE INVENTION  
       [0001] 1. Field of the Invention  
       [0002] The present invention relates to a semiconductor laser device, and more particularly to a semiconductor laser device with an optical waveguide exhibiting a high kink output.  
       [0003] 2. Description of the Related Art  
       [0004] The semiconductor laser device shows a non-linearity on variation of optical output versus injection current, namely the non-linearity of output-current characteristic. Such a non-linearity will be referred to as “kink”. An output, where kink appears, will be referred to as “kink output”. When the kink appears, a near field pattern may be deformed or translated, whereby a coupling coefficient is reduced. The kink effect reduces the coupling coefficient, even a high coupling coefficient is needed for obtaining a high output.  
       [0005] A conventional semiconductor laser device, which has a self-aligned structure for emitting a laser beam of 0.98 micrometers wavelength, is disclosed in Japanese laid-open patent publication No.  10-200201.  The device has an n-AlGaAs current blocking layer, which varies an aluminum-compositional ratio in layer-thickness direction for optimizing the kink output. As the aluminum-compositional ratio is reduced, a difference in equivalent refractive index or effective refractive index is reduced, whereby the kink output is increased. The reduction in such a compositional ratio deteriorates device characteristics under high temperature. An optimum aluminum-compositional index is 0.39, where the kink output is 250 mW at an operating temperature of 25° C. A further increase in the kink output from 250 mW is, however, advantageous for the advanced laser device.  
       [0006] In the above circumstances, the development of a novel semiconductor laser device having an improved optical waveguide structure, which makes the device free from the above problems, is desirable.  
       SUMMARY OF THE INVENTION  
       [0007] Accordingly, it is an object of the present invention to provide a novel semiconductor laser device having an improved optical waveguide structure in a manner that avoid the problems of the prior art.  
       [0008] It is a further object of the present invention to provide a novel semiconductor laser device having an improved optical waveguide structure, allowing the device to show high kink output.  
       [0009] It is another object of the present invention to provide a novel a semiconductor laser device having at least an active layer and an optical waveguide region, which includes at least a part of the active layer, wherein Δ gain /Γ is at least 85 [cm −1 /%], where Δ gain  [cm −1 ] is a difference in gain between a zero-order fundamental mode and a one-order high-order mode in a lateral transverse mode of the optical waveguide, and Γ [%] is a total optical confinement rate of the at least part of the active layer in the zero-order fundamental mode.  
       [0010] These objects and other objects, features and advantages of the present invention will be apparent from the following description of preferred embodiments. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0011] Preferred embodiments according to the present invention will be described in detail with reference to the accompanying drawings.  
     [0012]FIG. 1 is a fragmentary cross sectional elevation view of a semiconductor laser device having an improved optical waveguide structure and a separate confinement hetero-structure active layer in accordance with the present invention.  
     [0013]FIG. 2 is a fragmentary cross sectional elevation view of a semiconductor laser device with an improved optical waveguide structure in combination with a diagram illustrative of a refractive index profile in an optical waveguide region of a stripe-shaped plan region in a first embodiment in accordance with the present invention.  
     [0014]FIG. 3 is a fragmentary cross sectional elevation view of a semiconductor laser device with an improved optical waveguide structure in combination with a diagram illustrative of a refractive index profile in an optical waveguide region of a stripe-shaped plan region in a second embodiment in accordance with the present invention.  
     [0015]FIG. 4 is a fragmentary cross sectional elevation view of a semiconductor laser device with an improved optical waveguide structure in combination with a diagram illustrative of a refractive index profile in an optical waveguide region of a stripe-shaped plan region in a third embodiment in accordance with the present invention.  
     [0016]FIG. 5 is a fragmentary cross sectional elevation view of a semiconductor laser device with a conventional optical waveguide structure in combination with a diagram illustrative of a refractive index profile in an optical waveguide region of a stripe-shaped plan region in a comparative example 1.  
     [0017]FIG. 6 is a fragmentary cross sectional elevation view of a semiconductor laser device with a conventional optical waveguide structure in combination with a diagram illustrative of a refractive index profile in an optical waveguide region of a stripe-shaped plan region in a comparative example 2.  
     [0018]FIG. 7 is a diagram illustrative of kink output versus Δ gain /Γ of the semiconductor laser devices in the first to third embodiments and the comparative examples 1 and 2.  
     [0019]FIG. 8 is a diagram illustrative of kink output versus Δ gain , transformed from FIG. 7, wherein a lateral axis is translated from Δ gain /Γ to Δ gain  . 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
     [0020] A first aspect of the present invention is a semiconductor laser device having at least an active layer and an optical waveguide region, which includes at least a part of the active layer, wherein Δ gain /Γ is at least 85 [cm −1/ %], where Δ gain  [cm −1 ] is a difference in gain between a zero-order fundamental mode and a one-order high-order mode in a lateral transverse mode of the optical waveguide, and Γ[%] is a total optical confinement rate of the at least part of the active layer in the zero-order fundamental mode.  
     [0021] If only the mode gain difference Δ gain  is increased, then it is uncertain that the kink output is increased. If both the mode gain difference Δ gain  and the optical confinement rate Γ are increased, then the kink output is not increased. If the mode gain difference Δ gain  is increased and the optical confinement rate Γ is decreased, then the kink output is increased. Accordingly, in order to obtain an increased kink output, it is essential that Δ gain /Γ is increased.  
     [0022] In this specification, the zero-order mode is defined to be fundamental mode, and the one-order mode is defined to be high-order mode. Namely, the zero-order mode as the fundamental mode will, hereinafter, be referred to as “zero-order fundamental mode”, and the one-order mode as the high-order mode will, hereinafter, be referred to as “one-order high-order mode”.  
     [0023] At least one active layer may comprises plural active layers, and the Γ [%] is a total sum of individual optical confinement rates of the plural active layers. Each of the plural active layers in the optical waveguide region has an individual optical confinement rate. If the device has plural active layers such as multiple quantum well layers, then the Γ [%] is the total sum of individual optical confinement rates of the plural active layers.  
     [0024] The plural active layers may comprise multiple quantum well layers, and the at least part of each of the multiple quantum well layers has an optical confinement rate of at most 0.5% in the zero-order fundamental mode.  
     [0025] At least one active layer may have a separate confinement hetero-structure, and the Γ [%] is an optical confinement rate of the at least part of the separate confinement hetero-structure.  
     [0026] For obtaining the high Δ gain /Γ of at least 85 [cm −1 /%], the optical waveguide region may have a symmetrical refractive index profile with reference to the at least one active layer in a vertical direction to interfaces of the at least one active layer. Alternatively, the optical waveguide region may have an asymmetrical refractive index profile with reference to the at least one active layer in a vertical direction to interfaces of the at least one active layer In the asymmetrical refractive index profile, for obtaining the Δ gain /Γ of at least 85 [cm 31 1 /%], the device may have an n-side region and a p-side region, which are separated by the at least one active layer, and the asymmetrical refractive index profile is that the n-side region is higher than the p-side region in an integrated value of a refractive index in the vertical direction.  
     [0027] At least a cladding region may optically be provided adjacent to at least one interface of the at least one active layer, and wherein the at least cladding region comprises a plural-layered structure, which includes at least an optical confinement layer. The plural-layered structure comprises plural cladding layers different in refractive index. The layer higher in refractive index serves as the optical confinement layer. Adjustment to variations in refractive index among the plural cladding layers adjusts the lateral transverse mode in the at least one active layer, thereby obtaining the increased value of the mode gain difference Δ gain.    
     [0028] The cladding region may optionally comprise p-side and n-side cladding regions adjacent to opposite surfaces of the at least one active layer, and the p-side and n-side cladding regions comprise first and second plural-layered structures respectively, and each of the first and second plural-layered structures includes at least an optical confinement layer. The first plural-layered structure comprise a first set of plural cladding layers different in refractive index, The layer higher in refractive index serves as the optical confinement layer. The second plural-layered structure compnse a second set of other plural cladding layers different in refractive index. The layer higher in refractive index serves as the optical confinement layer. Adjustment to variations in refractive index among the plural cladding layers adjusts the lateral transverse mode in the at least one active layer, thereby obtaining the increased value of the mode gain difference Δ gain . Both a uniform adjustment or different adjustments to the first and second plural-layered structures may be possible for obtaining the high Δ gain Γ. Notwithstanding, different adjustments to the first and second plural-layered structures are preferable.  
     [0029] At least one active layer and the p-side and n-side cladding regions may have a symmetrical refractive index profile with reference to the at least one active layer in a vertical direction to the interfaces of the at least one active layer for obtaining the high Δ gain /Γ.  
     [0030] At least one active layer and the p-side and n-side cladding regions may have an asymmetrical refractive index profile with reference to the at least one active layer in a vertical direction to the interfaces of the at least one active layer for obtaining the high Δ gain /Γ.  
     [0031] In the above case of the asymmetrical refractive index profile, the asymmetrical refractive index profile may be that the n-side cladding region is higher than the p-side cladding region in an integrated value of a refractive index in the vertical direction for obtaining the high Δ gain /Γ.  
     [0032] The device may have a ridged waveguide structure, and a partial region of the at least one active layer is included in the optical waveguide region.  
     [0033] Further, current blocking layers may optionally be provided in both sides of the ridged waveguide structure.  
     [0034] The device may optionally have a self-aligned structure, and a partial region of the active layer may be included in the optical waveguide region.  
     [0035] The device may optionally have current confinement layers in both sides of the at least one active layer, and substantially all regions of the active layer may be included in the optical waveguide region.  
     [0036] The device further may optionally have a bottom cladding region under the at least one active layer; a top cladding region over the at least one active layer, and the top cladding region having a stripe-shaped region, which defines the optical waveguide region; and current blocking layers adjacent to both sides of the stripe-shaped region.  
     [0037] In the above case, the optical waveguide region may be a ridge-type optical waveguide.  
     [0038] In the above case, the optical waveguide region may be a self-aligned structure optical waveguide.  
     [0039] In the above case, the bottom cladding region may optionally have a first multi-layered structure comprising plural layers different in reflexive index, and the top cladding region may optionally have a second multi-layered structure comprising other plural layers different in reflexive index.  
     [0040] In accordance with the present invention, Δ gain /Γ is an important factor for the kink output. The optical waveguide is designed so that Δ gain /Γ is high, for example, at least 85 [cm −1 /%], where Δgain [cm 31 1 ] is a gain difference between a zero-order fundamental mode and a one-order high-order mode in a lateral transverse mode of the optical waveguide, and Γ[%] is a total optical confinement rate of the at least part of the active layer in the zero-order fundamental mode. If the laser device has a single active layer, then the total optical confinement rate is an optical confinement rate of the part of the single active layer in the optical waveguide region. If the laser device has plural active layers, then the total optical confinement rate is the sum of individual optical confinement rates of the parts of the plural active layers in the optical waveguide region.  
     [0041] The present inventor could first discover that Δ gain /Γ is the important factor for the kink output. Before the present invention was invented, it had been known that the mode gain difference Δ gain  is one factor for the kink output. The present inventor could first confirm that the kink output depends on not only the mode gain difference Δ gain  but also the optical confinement rate Γ. If the optical confinement rate Γ is large, such a large Γ cancels the effect of the large modc gain difference Δ gain . If the mode gain difference Δgain is large and the optical confinement rate Γ is small, then the large kink output is obtained.  
     [0042] In order to increase Δ gain /Γ, various design measures are available. For example, a multi-layered structure of the cladding layer and an asymmetrical optical waveguide structure may be effective. If the cladding layer comprises compositionally different plural layers, then a highest refractive index layer serves as an optical confinement layer in the cladding layer. The optical confinement rate of the optical confinement layer is made different between inside and outside of the optical waveguide region, for accurately adjusting the lateral transverse mode of the active layer so as to increase the mode gain difference Δ gain .  
     [0043] The above feature of the present invention is more effective if applied to preferable structures that the top cladding region has a stripe-shaped selected region, both sides of which are adjacent to current blocking layers for current confinement into the stripe-shaped selected region. A ridge-shaped optical waveguide structure and a self-aligned optical waveguide structure are typical examples of the above structures. The ridge-shaped optical waveguide structure has a ridge-shaped top cladding layer or a mesa-structurcd top cladding layer. The stripe-shaped selected region of the top cladding layer defines the optical waveguide region.  
     [0044] In the above preferable structures, the active layer extends entirely over a substrate. Namely, the active layer extends not only inside of the optical waveguide region but also outside thereof. The top cladding layer having the stripe-shaped region is provided over the active layer. A longitudinal direction of the stripe-shaped region is parallel to a light-propagating direction of the optical waveguide. Since the current blocking layers extend both sides of the stripe-shaped region, an injection current is confined to tlhe stripe-shaped region by the current blocking layers.  
     [0045] The device may further comprises: a bottom cladding region under the at least one active layer, the bottom cladding region comprising a first plural-layered structure different in refractive index and including at least a first optical confinement cladding layer having a higher refractive index ; and a top cladding region over the at least one active layer, the top cladding region also having a ridge structure having a stripe-shape region which defines the optical waveguide region, and the top cladding region comprising a second plural-layered structure different in refractive index and including at least a second optical confinement cladding layer having a higher refractive index, and the second optical confinement cladding layer selectively extending in the ridge structure, wherein an inside of the optical waveguide region has a symmetrical refractive index profile with reference to the at least one active layer in a vertical direction to surfaces of the at least one active layer, whilst an outside of the optical waveguide region has an asymmetrical refractive index profile with reference to the at least one active layer in the vertical direction.  
     [0046] Current blocking layers may be provided adjacent to both sides of the ridge structure.  
     [0047] The device may further comprise: a bottom cladding region under the at least one active layer, the bottom cladding region comprising a first plural-layered structure different in refractive index and including at least a first optical confinement cladding layer having a higher refractive index; and a top cladding region over the at least one active layer, the top cladding region also having a ridge structure having a stripe-shape region which defines the optical waveguide region, and the top cladding region comprising a second plural-layered structure different in refractive index and including at least a second optical confinement cladding layer having a higher refractive index, and the second optical confinement cladding layer selectively extending in the ridge structure, wherein an inside of the optical waveguide region has a symmetrical optical confinement rate profile with reference to the at least one active layer in a vertical direction to surfaces of the at least one active layer, whilst an outside of the optical waveguide region has an asymmetrical optical confinement rate profile with reference to the at least one active layer in the vertical direction, and wherein the inside of the optical waveguide region is higher than the outside of the optical waveguide region in an optical confinement rate of the at least one active layer.  
     [0048] A second aspect of the present invention is a semiconductor laser device, which comprises: at least an active layer; a bottom cladding region under the at least one active layer, the bottom cladding region comprising a first plural-layered structure different in refractive index and including at least a first optical confinement cladding layer having a higher refractive index; and a top cladding region over the at least one active layer, the top cladding region also having a ridge structure having a stripe-shape region which defines an optical waveguide region, and the top cladding region comprising a second plural-layered structure different in refractive index and including at least a second optical confinement cladding layer having a higher refractive index, and the second optical confinement cladding layer selectively extending in the ridge structure, wherein an inside of the optical waveguide region has a symmetrical refractive index profile with reference to the at least one active layer in a vertical direction to surfaces of the at least one active layer, whilst an outside of the optical waveguide region has an asymmetrical refractive index profile with reference to the at least one active layer in the vertical direction. A third aspect of the present invention is a semiconductor laser device, which comprises: at least an active layer; a bottom cladding region under the at least one active layer, the bottom cladding region comprising a first plural-layered structure different in refractive index and including at least a first optical confinement cladding layer having a higher refractive index ; and a top cladding region over the at least one active layer, the top cladding region also having a ridge structure having a stripe-shape region which defines an optical waveguide region, and the top cladding region comprising a second plural-layered structure different in refractive index and including at least a second optical confinement cladding layer having a higher refractive index, and the second optical confinement cladding layer selectively extending in the ridge structure, wherein an inside of the optical waveguide region has a symmetrical optical confinement rate profile with reference to the at least one active layer in a vertical direction to surfaces of the at least one active layer, whilst an outside of the optical waveguide region has an asymmetrical optical confinement rate profile with reference to the at least one active layer in the vertical direction, and wherein the inside of the optical waveguide region is higher than the outside of the optical waveguide region in an optical confinement rate of the at least one active layer.  
     [0049] The above described present invention provides the following advantages. Not only the optical confinement but also the current confinement are realized, whereby a highly stable lateral transverse mode is also realized. Further, it is easy to control the refractive index of the optical waveguide.  
     [0050] As described above, the active layer extends entirely over the substrate, although the stripe-shaped selected region of the top cladding layer defines the optical waveguide region. It is possible that the active region outside the optical waveguide region receives carrier injections by carrier diffusion and lateral leakage of injection current.  
     [0051] If the injection current is large for high output, then it is possible that a gain be caused in the outside of the stripe-shaped selected region or the optical waveguide region, particularly adjacent regions to the stripe-shaped selected region or the optical waveguide region. This means increasing the width of the effective optical waveguide region which generates the gain, whereby a high-order mode gain may also be increased, resulting in promoting the kink.  
     [0052] In accordance with the present invention, however, the optical waveguide structure has the high value of Δ gain /Γ so that the kink output, which is the critical level for causing the kink effect, is high or increased, for the purpose of avoiding the kink effect, even if the injection current is large for high output. It is essential for the present invention that Δ gain /Γ is at least 85[cm −1 /%]. However, Δ gain /Γ is preferably 95 [cm −1 /%] or higher, and more preferably 100 [cm −1 /%] or higher.  
     [0053] In order to obtain the high Δ gain /Γ, it is necessary that the mode gain difference Δ gain  is increased and the optical confinement rate Γ is decreased. The decrease in the optical confinement rate Γ is, actually, however, limited by the lower limit of a slope rate. The decrease in the optical confinement rate Γ decreases the slope rate. An extensive decrease of the slope rate is not preferable. There is the lower limit of the slope rate. The optical confinement rate Γ is decided as low as possible but in consideration of the lower limit of the slope rate. It is, therefore, important that the optical waveguide structure is designed to obtain a large mode gain difference Δgain.  
     [0054] Available method for. designing the optical waveguide will subsequently be described by way of a ridged optical waveguide with reference to FIG. 1. A semiconductor laser device is provided over a substrate. The semiconductor laser device has an n-side bottom cladding region over the substrate, a separate confinement hetero-structure active layer over the n-side bottom cladding region, and a p-side top cladding region over the separate confinement heterostructure active layer.  
     [0055] The p-side top cladding region has a ridge, which extends on a stripe-shape region, which defines the optical waveguide region. The p-side top cladding region has a three-layered structure, which comprises first to third p-cladding layers. The first p-cladding layer has a low refractive index and extends directly in contact with an entire region of a top surface of the separate confinement hctero-structure active layer. The second p-cladding layer has a high refractive index and extends directly on a selected stripe-shaped region of a top surface of the first p-cladding layer. The third p-cladding layer has a low refractive index and extends directly on a top surface of the second p-cladding layer. Laminations of the second and third p-cladding layers form the ridge, which has the stripe-shaped region, which further defines the optical waveguide region.  
     [0056] The n-side bottom cladding region also has a three-layered structure, which comprises first to third n-cladding layers. The first n-cladding layer has a low refractive index and extends directly in contact with an entire region of a bottom surface of the separate confinement hetero-structure active layer. The second n-cladding layer has a high refractive index and extends directly in contact with an entire region of a bottom surface of the first n-cladding layer. The third n-cladding layer has a low refractive index and extends directly in contact with an entire region of a bottom surface of the second n-cladding layer and also directly in contact with an entire region of a top surface of the substrate.  
     [0057] The second p-claddinig layer having the high refractive index serves as a p-side optical confinement layer. The second n-cladding layer having the high refractive index serves as an n-side optical confinement layer The separate confinement hetero-structure active layer serves as a primary optical confinement layer. In the p-side region, the p-side optical confinement layer selectively extends on the stripe-shaped region, which defines the optical waveguide region. In the n-side region, the n-side optical confinement layer entirely extends not only inside of the optical wavegluide region but also outside thereof.  
     [0058] The first p-cladding layer and the first n-cladding layer may have the same thickness and the same refractive index as each other, The second p-cladding layer and the second n-cladding layer may have the same thickness and the same refractive index as each other.  
     [0059] Inside the optical waveguide region, the refractive index profile is symmetrical with reference to the separate confinement hetero-structure active layer in a thickness direction vertical to the interfaces of the layers. Inside the optical waveguide region, a light intensity profile is symmetrical with reference to the separate confinement hetero-structure active layer in the thickness direction. The light intensity is highest in the separate confinement hetero-structure active layer, and next higher in the p-side and n-side optical confinement layers, which comprise the second p-cladding layer and the second n-cladding layer. The light intensity profile has a highest or primary peak in the separate confinement hetero-structure active layer. The light intensity profile has valleys in the first p-cladding and n-cladding layers of the lower refractive index. The light intensity profile has secondary peaks in the p-side and n-side optical confinement layers of the higher refractive index, which comprise the second p-cladding layer and the second n-cladding layer. The secondary peaks are separated by the valleys from the highest or primary peak.  
     [0060] Outside the optical waveguide region, the p-side optical confinement layer is absent and the n-side optical confinement layer is present. Namely, outside the optical waveguide region, the refractive index profile is asymmetrical with reference to the separate confinement hetero-structure active layer in the thickness direction. The light intensity is highest in the n-side optical confinement layer or the second n-cladding layer, and next higher in the separate confinement hetero-structure active layer. The light intensity profile has a highest or primary peak in the n-side optical confinement layer or the second n-cladding layer. The light intensity profile has valleys in the first n-cladding layer of the lower refractive index. The light intensity profile has secondary peaks in the separate confinement hetero-structure active layer. In the p-side, the light intensity profile has no peak and a simply rapid drop. Outside the optical waveguide region, the peak of the light intensity profile is shifted toward the n-side because any optical confinement structure is absent.  
     [0061] The n-side optical confinement cladding layer is present not only inside of the optical waveguide region but also outside thereof. The p-side optical confinement cladding layer is selectively present only on the inside of the optical waveguide region but absent the outside of the optical waveguide region. The refractive index profile is quite different between the inside and outside of the optical waveguide region. Further, the light intensity profile is also quite different between the inside and outside of the optical waveguide region. Inside the optical waveguide region, the active layer has the primary or highest peak of the light intensity profile. Outside the optical waveguide region, the active layer has the secondary peak of the light intensity profile. The active layer has the higher light intensity inside the optical waveguide region and the lower light intensity outside the optical waveguide region. The active layer has a small or reduced gain outside the optical waveguide region, and has a large or increased gain inside the optical waveguide region. Generation of the kink is suppressed.  
     [0062] The above asymmetrical cladding layer structure controls the lateral transverse mode in the active layer, whereby the large mode gain difference Δ gain  can be obtained.  
     [0063] As described above, in order to obtain a large difference in light intensity between the inside and outside of the optical waveguide region, the above asymmetrical cladding layer structure is effective, This increases the freedom in design of the optical intensity profile in the active layer, and controls the lateral transverse mode in the active layer, whereby the large mode gain difference Δ gain  can be obtained.  
     [0064] An available method of analyzing both Δ gain  and Γ will subsequently be described, wherein Δ gain  is the gain difference between the zero-order fundamental mode and the one-order high-order mode in the lateral transverse mode, and Γ is the optical confinement rate of the active layer in the optical waveguide region in the zero-order fundamental mode.  
     [0065] The analysis of Δ gain  may be made by using the following rate equations (1), (2), (3) and (4) in consideration of non-radiative recombination, induced emission, carrier diffusion, and transverse leak current.  
                   J        (   x   )       qd     +     D            ∂   2          N        (   x   )           ∂     x   2             =       R        [     N        (   x   )       ]       +       g        [     N        (   x   )       ]            P        (   x   )                   (   1   )                 J        (   x   )       =     {           J   e           (          x        &lt;     W   /   2       )                 J   e         (     1   +            x        -     W   /   2       L       )     2             (          x        ≥     W   /   2       )                     (   2   )                       
 
     [0066] where “J” is the injection current density taking the transverse leak current into account, “q” is the unit charge of electron, “d” is the thickness of active layer, “D” is the diffusion coefficient, “N” is the carrier density, “P(x)” is the light intensity distribution, “Je” is the injection current density on the stripe-shaped region, “L” is a current broadening in the lateral direction, “W” is the width of the stripe-shaped region, R[N(x)] is the carrier life-time represented by the carrier density distribution function N(x), and “g” is the optical gain represented by the carrier density distribution function N(x). 
       R ( N ) =/τ+BN   2    . . . (3) 
       g ( N )=Γνζ ln ( N/N   0   . . . (4) 
     [0067] where “τ” is the time constant for the non-radiative recombination, “B” is the carrier recombination by spontaneous emission, “Γ” is the optical confinement rate of the active layer, “ν” is the group velocity of light, “ζ” is the differential gain, and “N 0 ” is the population inversion carrier density. The gain “g(N)” is represented by taking into account the effect of saturation upon a high current injection.  
     [0068] From the above equations, the distribution of the carrier density can be obtained. Based on this result, a gain/loss distribution is added to the refractive index distribution of the optical waveguide. A mode analysis to the optical waveguide is made to calculate a gain difference between the fundamental mode and the high-order mode. The gain difference varies depending on operational conditions such as injection current. It is, however, assumed that the optical output is 100 mW. The above individual parameters are D=10(cm 2 /s), τ=10(ns), B=1E-10 (cm 3 /s), ζ=1500 (cm- 1 ), NO=E18(cm- 3 ).  
     [0069] For the optical mode analysis, the approximately calculation method such as equivalent refractive index method is not so highly accurate analysis method. A two-dimensional mode analysis method such as finite element method or finite difference method is preferable for the highly accurate optical mode analysis. In this example, the finite difference method is used as the two-dimensional mode analysis method.  
     [0070] If the optical waveguide is placed in a cut-off condition, under which the high-order mode is not generated, it is possible that the result of the optical mode analysis is not well converged. In this case, it may be possible to converge the result of the optical mode analysis by an available method such as widening the width of the stripe-shaped region. A highly accurate evaluation of the mode gain difference is difficult, but a relative evaluation between the modified structures for convergence of the solution is usable.  
     [0071] If there are plural active layers such as multiple quantum wells, the optical confinement rate may be calculated by simply summing individual optical confinement rates of individual active layers such as quantum wells.  
     [0072] Consequently, it is important for the present invention that Δ gain / Γ is high to obtain a high kink output.  
     [0073] A first embodiment according to the present invention will be described in detail with reference to FIG. 2. The semiconductor laser device has an n-GaAs substrate not illustrated, an n-cladding region, a self confinement hetero-structure active layer, a p-cladding region, and current blocking layers. The n-cladding region is provided over the n-GaAs substrate. The n-cladding region is in contact directly with an entire region of a top surface of the n-GaAs substrate. The self confinement hetero-structure active layer is provided over the n-cladding region. The self confinement hetero-structure active layer is in contact directly with an entire region of a top surface of the n-cladding region. The p-cladding region is provided over the self confinement hetero-structure active layer. The p-cladding region is in contact directly with an entire region of a top surface of the self confinement hetero-structure active layer. The p-cladding region further has a mesa-structure which extends on a stripe-shaped region. A width of the mesa-structure is 2.8 micrometers. The current blocking layers are provided in contact directly with both sloped side faces of the mesa-structure and with planarized surfaces outside the stripe-shaped region.  
     [0074] The n-cladding region has the following multi-layered structure, which varies refractive index in a thickness direction. An n-Al 0.35 G 0.65 As cladding layer 12 having a thickness of 1000 nanometers is provided in contact directly with an entire region of the top surface of the non-illustrated n-GaAs substrate. An n-Al 0.2 Ga 0.8 As cladding layer  13  having a thickness of 700 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.35 Ga 0.65 As cladding layer  12 . An n-Al 0.35 Ga 0.65 As cladding layer  14  having a thickness of 200 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As cladding layer  13 .  
     [0075] The n-Al 0.2 Ga 0.8 As cladding layer  13  is sandwiched between the n-AI 0.35 Ga 0.65 As cladding layers  12  and  14 , wherein the n-Al 0.2 Ga 0.8 As cladding layer  13  is higher in refractive index than the n-Al 0.35 Ga 0.65 As cladding layers  12  and  14 .  
     [0076] The self confinement hetero-structure active layer has the following multi-layered structure, which varies refractive index in a thickness direction. An n-Al 0.2 Ga 0.8 As layer  15  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the n-cladding region or the n-Al 0.35 (Ga 0.65 As cladding layer  14 . An Al 0.1 Ga 0.9 As layer  16  having a thickness of 40 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As layer  15 . A double quantum well active layer  17  of InGaAs quantum well layer having a thickness of 4.1 nanometers and GaAs potential barrier layer having a thickness of 5 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  16 . An Al 0.1 Ga 0.9 As layer  18  having a thickness of 40 nanometers is provided in contact directly with an entire region of the top surface of the double quantum well active layer  17 . A p-Al 0.2 Ga 0.8 gAs layer  19  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  18 .  
     [0077] The double quantum well active layer  17  is sandwiched between the Al 0.1 Ga 0.9 As layers  16  and  18 , wherein the double quantum well active layer  17  is higher in refractive index than the Al 0.1 Ga 0.9 As layers  16  and  18 . The laminations of the layers  16 ,  17  and  18  are disposed between the n-Al 0.2 Ga 0.8 As layer  15  and the p-Alhd  0 . 2 Ga 0.8 As layer  19 , wherein the Al 0.1 Ga 0.9 As layers  16  and  18  are higher in refractive index than the n-Al 0.2 Ga 0.8 As layer  15  and the p-Al 0.2 Ga 0.8 As layer  19 . The double quantum well active layer  17  is highest in refractive index. The Al 0.1 Ga 0.9 As layers  16  and  18  are second higher in refractive index. The n-Al 0.2 Ga 0.8 As layer  15  and the p-Al 0.2 Ga 0.8 As layer  19  are lower in refractive index but are the same level as the n-Al 0.2 Ga 0.8 As cladding layer  13  in the n-cladding region, wherein the n-Al 0.2 Ga 0.8 As cladding layer  13  is highest in refractive index in the n-cladding region.  
     [0078] The p-cladding region has the following multi-layered structure, which varies refractive index in a thickness direction, A p-Al 0.35 Ga 0.65 As cladding layer  20  having a thickness of 200 nanometers is provided in contact directly with an entire region of the top surface of the self confinement hetero-structure active layer or the p-Al 0.2 Ga 0.8 As layer  19 . A mesa-structure is selectively provided on a stripe-shaped region of a top surface of the p-Al 0.35 Ga 0.65 As cladding layer  20 . The stripe-shaped region defines the optical waveguide region. The mesa-structure comprises the following double-layered structure. A p-Al 0.2 Ga 0.8 As cladding layer  21  having a thickness of 700 nanometers is provided in contact directly with the stripe-shaped region of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  20 . The p-Al 0.2 Ga 0.8 As cladding layer  21  has a ridge-shape. A p-Al 0.35 Ga 0.65 As cladding layer  22  having a thickness of 1000 nanometers is provided in contact directly with a top surface of the p-Al 0.2 Ga 0.8 As cladding layer  21 . The p-Al 0.35 Ga 0.65 As cladding layer  22  has a ridge-shape.  
     [0079] Further, n-Al 0.35 Ga 0.65 As current blocking layers  23  are provided in contact directly with opposite side regions of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  20  and also in contact directly with sloped side faces of the mesa-structure, wherein the opposite side regions extend in opposite sides of the stripe-shaped region.  
     [0080] The p-Al 0.2 Ga 0.8 As cladding layer  21  is sandwiched between the p-Al 0.35 Ga 65 As cladding layers  20  and  22 , wherein the p-Al 0.2 Ga 0.8 As cladding layer  21  is higher in refractive index than the p-AI 0.35 Ga 0.65 As cladding layers  20  and  22 .  
     [0081] The refractive index profile in the optical waveguide region defined by the stripe-shaped region is symmetrical in the thickness direction as described below. The p-Al 0.35 Ga 0.65 As cladding layer  20  in the p-cladding region is identical in thickness and refractive index with the n-Al 0.35 Ga 0.65 As cladding layer  14  in the n-cladding region. The p-Al 0.2 Ga 0.8 As cladding layer  21  in the p-cladding region is identical in thickness and refractive index with the n-Al 0.2 Ga 0.8 As cladding layer  13  in the n-cladding region. The p-Al 0.35 Ga 0.65 As cladding layer  22  in the p-cladding region is identical in thickness and refractive index with the n-Al 0.35 Ga 0.65 As cladding layer  12  in the n-cladding region. The n-Al 0.2 Ga 0.8 As layer  15  and the p-Al 0.2 Ga 0.8 As layer  19  of the self-confinement hetero-structure active layer are identical with each other in thickness and refractive index, The Al 0.1 Ga 0.9 As layers  16  and  18  of the self-confinement hetero-structure active layer are identical with each other in thickness and refractive index.  
     [0082] The double quantum well active layer  17  is highest in refractive index. The Al 0.1 Ga 0.9 As layers  16  and  18  are second in refractive index.  
     [0083] The n-Al 0.2 Ga 0.8 As layer  15  and the p-Al 0.2 Ga 0.8 As layer  19  as well as the n-Al 0.2 Ga 0.8 As cladding layer  13  in the n-cladding region and the p-Al 0.2 Ga 0.8 As cladding layer  21  in the p-cladding region are third level in refractive index. The n-Al 0.35 Ga 0.65 As cladding layers  14  and  12  in the n-cladding region and the p-Al 0.35 Ga 0.65 As cladding layers  20  and  22  in the p-cladding region are lowest in refractive index.  
     [0084] Accordingly, inside the optical waveguide region defined by the stripe-shaped region, the refractive index profile is symmetrical with reference to the double quantum well active layer  17  in the thickness direction. Outside the optical waveguide region, however, the refractive index profile is asymmetrical with reference to the double quantum well active layer  17  in the thickness direction. As described above, the light intensity depends upon the refractive index. The light intensity profile also depends upon the refractive index profile.  
     [0085] Inside the optical waveguide region, a primary optical confinement is obtained in the self confinement hetero-structure active layer, which is highest in refractive index, and a secondary optical confinement is obtained both in the n-Al 0.2 Ga 0.8 As cladding layer  13 , which is higher in refractive index in the n-cladding region as well as in the p-Al 0.2 Ga 0.8 As cladding layer  21 , which is higher in refractive index in the p-cladding region. Therefore, inside the optical waveguide region, the light intensity profile is symmetrical with reference to the double quantum well active layer  17  in the thickness direction.  
     [0086] Outside the optical wavegLLide region, the primary optical confinement is obtained only in the n-Al 0.2 Ga 0.8 As cladding layer  13  in the n-cladding region, and the secondary optical confinement is obtained in the self confinement hetero-structure active layer Therefore, outside the optical waveguide region, the light intensity profile is asymmetrical with reference to the double quantum well active layer  17  in the thickness direction.  
     [0087] The semiconductor laser device has a buried ridge-shaped optical waveguide for emitting a laser beam of a wavelength at 0.98 micrometers. The mode gain difference and the optical confinement rate are calculated. Δ gain /Γ is 87.60[cm- −1 /%] which satisfies the requirement thatΔ gain /Γ is at least 85 [cm −1 /%]. The double quantum well active layer  17  has two quantum wells, cach of which has an optical confinement rate Γ at 0.394% in the fundamental mode. If a cavity length is 890 micrometers, then an average kink output is 285 mW, wherein the width of the stripe-shaped region is 2.8 micrometers.  
     [0088] A second embodiment according to the present invention will be described in detail with reference to FIG. 3. A main difference of this second embodiment from the first embodiment is as follows. The refractive index profile inside the optical waveguide region is asymmetrical with reference to the self confinement hetero-structure active layer in the thickness direction, wherein inside the optical waveguide region, the n-cladding region is higher in average refractive index than the p-cladding region having the mesa-structure. Namely, the light intensity profile inside the optical waveguide region is asymmetrical with reference to the self confinement hetero-structure active layer in the thickness direction, wherein inside the optical waveguide region, the n-cladding region is higher in average optical intensity than the p-cladding region having the mesa-structure.  
     [0089] A subordinate difference of this second embodiment from the first embodiment is as follows. The n-cladding region comprises a four-layered structure which includes not only a main optical confinement layer but also a subordinate optical confinement layer. The p-cladding region has the same structure as in the first embodiment. Namely, the p-cladding region has the mesa-structure and comprises the three-layered structure.  
     [0090] Another subordinate difference of this second embodiment from the first embodiment is as follows. The self confinement hetero-structure active layer includes a multiple quantum well structure in place of the above double quantum well structure.  
     [0091] The semiconductor laser device has an n-GaAs substrate not illustrated, an n-cladding region, a self confinement hetero-structure active layer including a multiple quantum well structure, a p-cladding region, and current blocking layers. The n-cladding region is provided over the n-GaAs substrate. The n-cladding region is in contact directly with an entire region of a top surface of the n-GaAs substrate. The self confinement hetero-structure active layer is provided over the n-cladding region, The self confinement hetero-structure active layer is in contact directly with an entire region of a top surface of the n-cladding region. The p-cladding region is provided over the self confinement hetero-structure active layer. The p-cladding region is in contact directly with an entire region of a top surface of the self confinement hetero-structure active layer. The p-cladding region further has a mesa-structure which extends on a stripe-shaped region. A width of the mesa-structure is 2.8 micrometers. The current blocking layers are provided in contact directly with both sloped side faces of the mesa-structure and with planarized surfaces outside the stripe-shaped region.  
     [0092] The n-cladding region. has the following multi-layered structure, which varies refractive index in a thickness direction. An n-Al 0.35 Ga 0.65 As cladding layer  24  having a thickness of 1000 nanometers is provided in contact directly with an entire region of the top surface of the non-illustrated n-GaAs substrate. An n-Al 0.2 Ga 0.8 As cladding layer  25  having a thickness of 800 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.35 Ga 0.65 As cladding layer  24 . An n-Al 0.15 Ga 0.85 As cladding layer  26  having a thickness of 350 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As cladding layer  25 . An n-Al 0.35 Ga 0.65 As cladding layer  27  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.15 Ga 0.85 As cladding layer  26 .  
     [0093] The laminations of the n-Al 0.2 Ga 0.8 As cladding layer  25  and the n-Al 0.15 Ga 0.85 As cladding layer  26  are sandwiched between the n-Al 0.35 Ga 0.65 As cladding layers  24  and  27 , wherein the n-Al 0.15 Ga0.85As cladding layer  26  and the n-Al 0.2 Ga 0.8 As cladding layer  25  are higher in refractive index than the n-Al 0.35 Ga 0.65 As cladding layers  24  and  27 . The n-Al 0.15 Ga 0.85 As cladding layer  26  is higher in refractive index than the n-Al 0.2 Ga 0.8 As cladding layer  25 .  
     [0094] The self confinement hetero-structure active layer has the following multi-layered structure, which varies refractive index in a thickness direction. An n-Al 0.2 Ga 0.8 As layer  28  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the n-cladding region or the n-Al 0.35 Ga 0.65 As cladding layer  27 . An Al 0.1 Ga 0.9 As layer  29  having a thickness of 60 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As layer  28 . A multiple quantum well active layer  30  of InGaAs quantum well layer having a thickness of 4.1 nanometers and GaAs potential barrier layer having a thickness of 5 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  29 . An Al 0.1 Ga 0.9 As layer  31  having a thickness of 60 nanometers is provided in contact directly with an entire region of the top surface of the multiple quantum well active layer  30 . A p-Al 0.2 Ga 0.8 As layer  32  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  31 .  
     [0095] The multiple quantum well active layer  30  is sandwiched between the Al 0.1 Ga 0.9 As layers  29  and  31 , wherein the multiple quantum well active layer  30  is higher in refractive index than the Al 0.1 Ga 0.9 As layers  29  and  31 . The laminations of the layers  29 ,  30  and  31  are disposed between the n-Al 0.2 Ga 0.8 As layer  28  and the p-Al 0.2 Ga 0.8 As layer  32 , wherein the Al 0.1 Ga 0.9 As layers  29  and  31  arc higher in refractive index than the n-Al 0.2 Ga 0.8 As layer  28  and the p-Al 0.2 Ga 0.8 As layer  32 . The multiple quantum well active layer  30  is highest in refractive index. The Al 0.1 Ga 0.9 As layers  29  and  31  are second higher in refractive index. The n-Al 0.2 Ga 0.8 As layer  28  and the p-Al 0.2 Ga 0.8 As layer  32  are lower in refractive index but are the same level as the n-Al 0.2 Ga 0.8 As cladding layer  25  in the n-cladding region, wherein the n-Al 0.2 Ga 0.8 As cladding layer  25  is second highest in refractive index in the n-cladding region.  
     [0096] The p-cladding region has the following multi-layered structure, which varies refractive index in a thickness direction. A p-Al 0.3.5 Ga 0.65 As cladding layer  33  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the self confinement hetero-structure active layer or the p-Al 0.2 Ga 0.8 As layer  32 . A mesa-structure is selectively provided on a stripe-shaped region of a top surface of the p-Al 0.35 Ga 0.65 As cladding layer  33 . The stripe-shaped region defines the optical waveguide region. The mesa-structure comprises the following double-layered structure. A p-Al 0.15 Ga 0.85 As cladding layer  34  having a thickness of 375 nanometers is provided in contact directly with the stripe-shaped region of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  33 . The p-Al 0.15 Ga 0.85 As cladding layer  34  has a ridge-shape. A p-Al 0.35 Ga 0.65 As cladding layer  35  having a thickness of 1000 nanometers is provided in contact directly with a top surface of the p-Al 0.15 Ga 0.85 As cladding layer  34 . The p-Al 0.35 Ga 0.65 As cladding layer  35  has a ridge-shape.  
     [0097] Further, n-AI 0.35 Ga 0.65 As current blocking layers  36  are provided in contact directly with opposite side regions of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  33  and also in contact directly with sloped side faces of the mesa-structure, wherein the opposite side regions extend in opposite sides of the stripe-shaped region.  
     [0098] The p-Al 0.15 Ga 0.85 As cladding layer  34  is sandwiched between the p-Al 0.35 Ga 0.85 As cladding layers  33  and  35 , wherein the p-Al 0.15 Ga 0.85 As cladding layer  34  is higher in refractive index than the p-Al 0.35 Ga 0.65 As cladding layers  33  and  35 .  
     [0099] The refractive index profile in the optical waveguide region defined by the stripe-shaped region is symmetrical in the thickness direction as described below. The p-Al 0.35 Ga 0.65 As cladding layer  33  in the p-cladding region is identical in thickness and refractive index with the n-Al 0.35 Ga 0.65 As cladding layer  27  in the n-cladding region. The p-Al 0.15 Ga 0.85 As cladding layer  34  in the p-cladding region is identical in refractive index with the n-Al 0.15 Ga 0.65 As cladding layer  26  in the n-cladding region. The p-Al 0.35 Ga 0.65 As cladding layer  35  in the p-cladding region is identical in thickness and refractive index with the n-Al 0.35 Ga 0.65 As cladding layer  24  in the n-cladding region. The n-Al 0.2 Ga 0.8 As layer  28  and the p-Al 0.2 Ga 0.8 As layer  32  of the self-confinement hetero-structure active layer are identical with each other in thickness and refractive index. The Al 0.1 Ga 0.9 As layers  29  and  31  of the self-confinement hetero-structure active layer are identical with each other in thickness and refractive index. In the p-cladding region, the n-Al 0.2 Ga 0.8 As layer  25  has no corresponding layer in the n-cladding region. Namely, the presence of the n-Al 0.2 Ga 0.8 As layer  25  in the p-cladding region makes an asymmetrical refractive index profile, and causes that the n-cladding region is higher in averaged refractive index than the p-cladding layer.  
     [0100] The multiple quantum well active layer  30  is highest in refractive index. The Al 0.1 Ga 0.9 As layers  29  and  31  are second in refractive index. The n-Al 0.2 Ga 0.8 As layer  28  and the p-AI 0.2 Ga 0.8 As layer  32  as well as the n-Al 0.2 Ga 0.8 As cladding layer  25  in the n-cladding region and the p-Al 0.2 Ga 0.8 As cladding layer  34  in the p-cladding region are fourth level in refractive index, because the n-Al 0.15 Ga 0.85 As cladding layer  26  in the n-cladding region and the p-Al 0.15 Ga 0.85 As cladding layer  34  in the p-cladding region are third level in refractive index. The n-Al 0.35 Ga 0.65 As cladding layers  27  and  24  in the n-cladding region and the p-Al 0.35 Ga 0.65 As cladding layers  33  and  35  in the p-cladding region are lowest in refractive index. Accordingly, inside the optical waveguide region defined by the stripe-shaped region, the refractive index profile is asymmetrical with reference to the multiple quantum well active layer  30  in the thickness direction. Outside the optical waveguide region, the refractive index profile is also asymmetrical with reference to the multiple quantum well active layer  30  in the thickness direction. The presence of the n-Al 0.2 Ga 0.8 As layer  25  in the p-cladding region makes the asymmetrical refractive index profile, wherein the n-cladding region is higher in averaged refractive index than the p-cladding layer. As described above, the light intensity depends upon the refractive index. The light intensity profile also depends upon the refractive index profile.  
     [0101] Inside the optical waveguide region, a primary optical confinement is obtained in the self confinement hetero-structure active layer, which is highest in refractive index. A secondary optical confinement is obtained both in the n-Al 0.15 Ga 0.85 As cladding layer  26  in the n-cladding region and in the p-Al 0.15 Ga 0.85 As cladding layer  34  in the p-cladding region. A ternary optical confinement is obtained in the n-Al 0.2 Ga 0.8 As cladding layer  25 , which is higher in refractive index in the n-cladding region as well as in the n-Al 0.2 Ga 0.8 As layer  28  and the p-Al 0.2 Ga 0.8 As layer  32 . Therefore, inside the optical waveguide region, the light intensity profile is asymmetrical with reference to the multiple quantum well active layer  30  in the thickness direction, wherein the n-cladding region is higher in averaged light intensity than the p-cladding layer.  
     [0102] Outside the optical waveguide region, the primary optical confinement is obtained only in the n-Al 0.2 Ga 0.8 As cladding layer  25  in the n-cladding region, and the secondary optical confinement is obtained in the self confinement hetero-structure active layer. Therefore, outside the optical waveguide region, the light intensity profile is asymmetrical with reference to the multiple quantum well active layer  30  in the thickness direction.  
     [0103] The presence of the n-Al 0.2 Ga 0.8 As cladding layer  25  in the n-cladding region increases a difference in the optical confinement rate of the active layer between the optical waveguide region and the outside regions, resulting in an increased mode gain difference Δ  gain-    
     [0104] The semiconductor laser device has a buried ridge-shaped optical waveguide for omitting a laser beam of a wavelength at 0.98 micrometers. The mode gain difference and the optical confinement rate are calculated. Δ gain //Γ is 98.68[cm− 1 /%] which satisfies the requirement that Δ gain /Γ is at least 85 [cm− 1 /%]. The multiple quantum well active layer  30  has two quantum wells, each of which has an optical confinement rate Γ at 0.385% in the fundamental mode. If a cavity length is 890 micrometers, then an average kink output is 328 mW, wherein the width of the stripe-shaped region is 2.8 micrometers. If a cavity length is 1200 micrometers, then an average kink output is 346 mW, wherein the width of the stripe-shaped region is 2.8 micrometers.  
     [0105] A third embodiment according to the present invention will be described in detail with reference to FIG. 4. A main difference of this third embodiment from the second embodiment is as follows. The increase of the optical confmement rate in the n-cladding region increases the difference in the optical confinement rate in the active layer between the optical waveguide region and the outside regions, resulting in the increased mode gain difference. If, however, the optical confinement rate in the n-cladding region is excessively increased, then the influence of the optical confinement structure by the p-cladding region to the n-cladding region is increased. As a result, the light intensity profile in the n-cladding region is spread over the inside and outside of the optical waveguide region defined by the stripe-shaped region. This spreading causes that light intensity profile in the active layer is spread over the inside and outside of the optical waveguide region defined by the stripe-shaped region, resulting in influence of the gain in the peripheral portion of the stripe-shaped region. In this embodiment, the refractive index profile of the n-cladding region is adjusted to avoid the excess spread of the light intensity profile over not only inside but also outside the optical waveguide region defined in the stripe-shaped region.  
     [0106] The semiconductor laser device has an n-GaAs substrate not illustrated, an n-cladding region, a self confinement hetero-structure active layer including a multiple quantum well structure, a p-cladding region, and current blocking layers. The n-cladding region is provided over the n-GaAs substrate. The n-cladding region is in contact directly with an entire region of a top surface of the n-GaAs substrate. The self confinement hetero-structure active layer is provided over the n-cladding region. The self confinement hetero-structure active layer is in contact directly with an entire region of a top surface of the n-cladding region. The p-cladding region is provided over the self confinement hetero-structure active layer. The p-cladding region is in contact directly with an entire region of a top surface of the self confinement hetero-structure active layer. The p-cladding region further has a mesa-structure which extends on a stripe-shaped region, A width of the mesa-structure is 42 micrometers. The current blocking layers are provided in contact directly with both sloped side faces of the mesa-structure and with planarized surfaces outside the stripe-shaped region.  
     [0107] The n-cladding region has the following multi-layered structure, which varies refractive index in a thickness direction. An n-Al 0.35 Ga 0.65 As cladding layer  37  having a thickness of 1000 nanometers is provided in contact directly with an entire region of the top surface of the non-illustrated n-GaAs substrate. An n-Al 0.2 Ga 0.8 As cladding layer  38  having a thickness of 800 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.35 Ga 0.65 As cladding layer  37 . An n-Al 0.15 Ga 0.85 As cladding layer  39  having a thickness of 375 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As cladding layer  38 . An n-Al 0.2 Ga 0.8 As cladding layer  40  having a thickness of 50 nanomneters is provided in contact directly with an entire region of the top surface of the n-Al 0.15 Ga 0.85 As cladding layer  39 . An n-Al 0.35 Ga 0.65 As cladding layer  41 , having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As cladding layer  40 .  
     [0108] The n-Al 0.15 Ga 0.85 As cladding layer  39  is sandwiched between the n-Al 0.2 Ga 0.8 As cladding layers  38  and  40 , wherein the n-Al 0.15 Ga 0.85 As cladding layer  39  is higher in refractive index than. The laminations of the layers  38 ,  39  and  40  are disposed between the n-Al 0.35 ga 0.65 As cladding layers  37  and  41 , wherein the n-Al 0.15 Ga 0.85 As cladding layer  39  and the n-Al 0.2 Ga 0.8 As cladding layers  38  and  40  are higher in refractive index than the n-Al 0.35 Ga 0.65 As cladding layers  37  and  41 .  
     [0109] The presence of the n-AI 0.2 Ga 0.8 As cladding layer  40  avoids the excessive optical confinement in the n-cladding region. As a result, the light intensity profile in the n-cladding region does not any excessive spread over the inside and outside of the optical waveguide region defined by the stripe-shaped region. This non-excessive spreading does not cause that light intensity profile in the active layer is spread over the inside and outside of the optical waveguide region defined by the stripe-shaped region, resulting in a reduced influence of the gain in the peripheral portion of the stripe-shaped region In this embodiment, the presence of the n-Al 0.2 Ga 0.8 As cladding layer  40  avoids the excess spread of the light intensity profile over not only inside but also outside the optical waveguide region defined in the stripe-shaped region.  
     [0110] The self confinement hetero-structure active layer has the following multi-layered structure, which varies refractive index in a thickness direction. An n-Al 0.2 Ga 0.8 As layer  42  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the n-cladding region or the n-Al 0.35 Ga 0.65 As cladding layer  41 . An Al 0.1 Ga 0.9 As layer  43  having a thickness of 65 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As layer  42 . A multiple quantum well active layer  44  of InGaAs quantum well layer having a thickness of 4.1 nanometers and GaAs potential barrier layer having a thickness of 5 nanotneters is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  43 . An Al 0.1 Ga 0.9 As layer  45  having a thickness of 65 nanometers is provided in contact directly with an entire region of the top surface of the multiple quantum well active layer  44 . A p-Al 0.2 Ga 0.8 As layer  46  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  45 .  
     [0111] The multiple quantum well active layer  44  is sandwiched between the Al 0.1 Ga 0.9 As layers  43  and  45 , wherein the multiple quantum well active layer  44  is higher in refractive index than the Al 0.1 Ga 09 As layers  43  and  45 . The laminations of the layers  43 ,  44  and  45  are disposed between the n-Al 0.2 Ga 0.8 As layer  42  and the p-Al 0.2 Ga 0.8 As layer  46 , wherein the Al 0.1 Ga 0.9 As layers  43  and  45  are higher in refractive index than the n-Al 0.2 Ga 0.8 As layer  42  and the p-Al 0.2 Ga 0.8 As layer  46 . The multiple quantum well active layer  44  is highest in refractive index The Al 0.1 Ga 0.9 As layers  43  and  45  are second higher in refractive index. The n-Al 0.2 Ga 0.8 As layer  42  and the p-Al 0.2 Ga 0.8 As layer  46  are lower in refractive index but are the same level as the n-Al 0.2 Ga 0.8 As cladding layers  38  and  40  in the n-cladding region, wherein the n-Al 0.2 Ga 0.8 As cladding layers  38  and  40  are second highest in refractive index in the n-cladding region.  
     [0112] The p-cladding region has the following mnulti-layered structure, which varies refractive index in a thickness direction. A p-Al 0.35 Ga 0.65 As cladding layer  47  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the self confinement hetero-structure active layer or the p-Al 0.2 Ga 0.8 As layer  46 . A mesa-structure is selectively provided on a stripe-shaped region of a top surface of the p-A 0.35 Ga 0.65 As cladding layer  47 . The stripe-shaped region defines the optical waveguide region. The mesa-structure comprises the following double-layered structure. A p-Al 015 Ga 0.85 As cladding layer  48  having a thickness of 450 nanometers is provided in contact directly with the stripe-shaped region of the top surface of the p-A 1   0.35 Ga 0.65 As cladding layer  47 . The p-Al 0.15 Ga 0.85 As cladding layer  48  has a ridge-shape. A p-Al 0.35 Ga 0.65 As cladding layer  49  having a thickness of 1000 nanometers is provided in contact directly with a top surface of the p-Al 0.15 Ga 0.85 As cladding layer  48 . The p-Al 0.35 Ga 0.65 As cladding layer  49  has a ridge-shape.  
     [0113] Further, n-Al 0.35 Ga 0.65 As current blocking layers  50  are provided in contact directly with opposite side regions of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  47  and also in contact directly with sloped side faces of the mesa-structure, wherein the opposite side regions extend in opposite sides of the stripe-shaped region.  
     [0114] The p-Al 0.15 Ga 0.85 As cladding layer  48  is sandwiched between the p-Al 0.35 Ga 0.65 As cladding layers  47  and  49 , wherein the p-Al 0.15 Ga 0.85 As cladding layer  48  is higher in refractive index than the p-Al 0.35 Ga 0.65 As cladding layers  47  and  49 .  
     [0115] The refractive index profile in the optical wavegguide region defined by the stripe-shaped region is asymmetrical in the thickness S direction as described below. The p-Al 0.35 Ga 0.65 As cladding layer  47  in the p-cladding region is identical in thickness and refractive index with the n-Al 0.35 Ga 0.65 As cladding layer  41  in the n-cladding region. The p-Al 0.15 Ga 0.85 As cladding layer  48  in the p-cladding region is identical in refractive index with the n-Al 0.15 Ga 0.85 As cladding layer  39  in the n-cladding region. The p-Al 0.35 Ga 0.65 As cladding layer  49  in the p-cladding region is identical in thickness and refractive index with the n-Al 0.35 Ga 0.65 As cladding layer  37  in the n-cladding region. The n-Al 0.2 Ga 0.8 As layer  42  and the p-Al 0.2 Ga 0.8 As layer  46  of the self-confinement hetero-structure active layer are identical with each other in thickness and refractive index. The Al 0.1 Ga 0.9 As layers  43  and  45  of the self-confmement hetero-structure active layer are identical with each other in thickness and refractive index. In the p-cladding region, the n-Al 0.2 Ga 0.8 As layers  38  and  40  have no corresponding layer in the n-cladding region. Namely, the presence of the n-A 0.2 Ga 0.8 As layers  38  and  40  in the p-cladding region makes an asymtmetrical refractive index proflile, and causes that the n-cladding region is higher in averaged refractive index than the p-cladding layer.  
     [0116] The multiple quantum well active layer  44  is highest in refractive index. The Al 0.1 Ga 0.9 layers  43  and  45  are second in refractive index. The p-Al 0.15 Ga 0.85 As cladding layer  48  in the p-cladding region and the n-Al 0.15 Ga 0.85 As cladding layer  39  in the n-cladding region are third level in refractive index. The n-Al 0.2 Ga 0.8 As layer  42  and the p-Al 0.2 Ga 0.8 As layer  46  as well as the n-Al 0.2 Ga 0.8 As cladding layers  38  and  40  in the n-cladding region are fourth level in refractive index The n-Al 0.35 Ga 0.65 As cladding layers  41  and  37  in the n-cladding region and the p-Al 0.35 Ga 0.65 As cladding layers  47  and  49  in the p-cladding region are lowest in refractive index.  
     [0117] Accordingly, inside the optical waveguide region defined by the stripe-shaped region, the refractive index profile is asymmetrical with reference to the multiple quantum well active layer  44  in the thickness direction. Outside the optical waveguide region, the refractive index profile is also asymmetrical with reference to the multiple quantum well active layer  44  in the thickness direction. The presence of the n-Al 0.2 Ga 0.8 As layer  38  in the p-cladding region makes the asymmetrical refractive index profile, wherein the n-cladding region is higher in averaged refractive index than the p-cladding layer. As described above, the light intensity depends upon the refractive index. The light intensity profile also depends upon the refractive index profile,  
     [0118] Inside the optical waveguide region, a primary optical confinement is obtained in the self confinement hetero-structure active layer, which is highest in refractive indx. A secondary optical confinement is obtained both in the n-Al 0.15 Ga 0.85 As cladding layer  39  in the n-cladding region and in the p-Al 0.15 Ga 0.85 As cladding layer  48  in the p-cladding region. A ternary optical confinement is obtained in the n-Al 0.2 Ga 0.8 As cladding layers  38  and  40 , which are higher in refractive index in the n-cladding region as well as in the n-Al 0.2 Ga 0.8 As layer  42  and the p-Al 0.2 Ga 0.8 As layer  46 , Therefore, inside the optical waveguide region, the light intensity profile is asymmetrical with reference to the multiple quantum well active layer  44  in the thickness direction, wherein the n-cladding region is higher in averaged light intensity than the p-cladding layer.  
     [0119] Outside the optical waveguide region, the primary optical confinement is obtained only in the n-Al 0.2 Ga 0.8 As cladding layer  38  in the n-cladding region, and the secondary optical confinement is obtained in the self confinement hetero-structure active layer. Therefore, outside the aoptical waveguide region, the light intensity profile is asymmetrical with reference to the multiple quantum well active layer  44  in the thickness direction.  
     [0120] The presence of the n-Al 0.2 Ga 0.8 As cladding layers  38  and  40  in the n-cladding region increases a difference in the optical confinement rate of the active layer between the optical waveguide region and the outside regions, resulting in an increased mode gain difference Δ gain .  
     [0121] The. semiconductor laser device has a buried ridge-shaped optical waveguide for emitting a laser beam of a wavelength at 0.98 micrometers. The mode gain difference and the optical confinement rate are calculated. Δ gain /Γ is 100.42[cm −1 1/%] which satisfies the requirement that Δ   gain /Γ is at least 85 [cm −1 /%]. The multiple quantum well active layer  44  has two quantum wells, each of which has an optical confinement rate Γ at 0.362% in the fundamental mode. If a cavity length is 890 micrometers, then an average kink output is 289 mW, wherein the width of the stripe-shaped region is 42 micrometers. If a cavity length is 1200 micrometers, then an average kink output is 379 mW, wherein the width of the stripe-shaped region is 42 micrometers.  
     [0122] A comparative example 1 will be described with reference to FIG. 5. The semiconductor laser device of this comparative example 1 is identical in structure with the device of the above first embodiment, except for the compositional ratios and thicknesses of individual layers. An n-Al 0.35 Ga 0.65 As cladding layer  62  having a thickness of 1000 nanometers is provided in contact directly with an entire region of the top surface of the non-illustrated n-GaAs substrate. An n-Al 0.15 Ga 0.85 As cladding layer  63  having a thickness of 450 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.35 Ga 0.65 As cladding layer  62 , An n-Al 0.35 Ga 0.65 As cladding layer  64  having a thickness of 200 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.15 Ga 0.85 As cladding layer  63 .  
     [0123] The self confinement hetero-structure active layer has the following multi-layered structure, which varies refractive index in a thickness direction. An n-Al 0.2 Ga 0.8 As layer  65  having a thickness of 150 nanometers is provided in contact directly with an entire region of the top surface of the n-cladding region or the n-Al 0.35 Ga 0.65 As cladding layer  64 . An Al 0.1 Ga 0.9 As layer  66  having a thickness of 40 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As layer  65 . A double quantum well active layer  67  of InGaAs quantum well layer having a thickness of 4.1 nanometers and GaAs potential barrier layer having a thickness of 5 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  66 . An Al 0.1 Ga 0.9 As layer  68  having a thickness of 40 nanometers is provided in contact directly with an entire region of the top surface of the double quantum well active layer  67 . A p-Al 0.2 Ga 0.8 As layer  69  having a thickness of 150 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  68 .  
     [0124] The p-cladding region has the following multi-layered structure, which varies refractive index in a thickness direction. A p-Al 0.35 Ga 0.65 As cladding layer  70  having a thickness of 200 nanometers is provided in contact directly with an entire region of the top surface of the self confinement hetero-structure active layer or the p-Al 0.2 Ga 0.8 As layer  69 . A mesa-structure is selectively provided on a stripe-shaped region of a top surface of the p-Al 0.35 Ga 0.65 As cladding layer  70 . The stripe-shaped region defines the optical waveguide region. The mesa-structure comprises the following double-layered structure. A p-Al 0.15 Ga 0.85 As cladding layer  71  having a thickness of 400 nanometers is provided in contact directly with the stripe-shaped region of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  70 . The p-Al 0.15 Ga 0.85 As cladding layer  71  has a ridge-shape. A p-Al 0.35 Ga 0.65 As cladding layer  72  having a thickness of 1000 nanometers is provided in contact directly with a top surface of the p-Al 0.15 Ga 0.85 As cladding layer  71 . The p-Al 0.35 Ga 0.65 As cladding layer  72  has a ridge-shape.  
     [0125] Further, n-Al 0.35 Ga 0.65 As current blocking layers  73  are provided in contact directly with opposite side regions of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  70  and also in contact directly with sloped side faces of the mesa-structure, wherein the opposite side regions extend in opposite sides of the stripe-shaped region.  
     [0126] The semiconductor laser device has a buried ridge-shaped optical waveguide for emitting a laser beam of a wavelength at 0.98 micrometers. The mode gain difference and the optical confinement rate are calculated. Δ gain /Γ is 72.26[cm− 1 /%] which does not satisfy the requirement that Δ gain /Γ is at least 85 [cm− 1 /%]. An average kink output is 226 mW.  
     [0127] A comparative example 2 will be described with reference to FIG. 6. The semiconductor laser device of this comparative example 2 is identical in structure with the device of the above third embodiment, except for the compositional ratios and thicknesses of individual layers. An n-Al 0.35 Ga 0.65 As cladding layer  77  having a thickness of 1000 nanometers is provided in contact directly with an entire region of the top surface of the non-illustrated n-GaAs substrate. An n-Al 0.2 Ga 0.8 As cladding layer  78  having a thickness of 600 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.35 Ga 0.65 As cladding layer  77 . An n-Al 0.15 Ga 0.85 As cladding layer  79  having a thickness of 200 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As cladding layer  78 . An n-Al 0.2 Ga 0.8 As cladding layer  80  having a thickness of 700 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.15 Ga 0.85 As cladding layer  79 . An n-Al 0.35 Ga 0.65 As cladding layer  81  having a thickness of 70 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As cladding layer  80 .  
     [0128] The self confinement hetero-structure active layer has the following multi-layered structure, which varies refractive index in a thickness direction. An n-Al 0.2 Ga 0.8 As layer  82  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the n-cladding region or the n-Al 0.35 Ga 0.65 As cladding layer  81 . An Al 0.1 Ga 0.9 As layer  83  having a thickness of 65 nanometers is provided in contact directly with an entire region of the top surface of the n-Al 0.2 Ga 0.8 As layer  82 . A double quantum well active layer  84  of InGaAs quantum well layer having a thickness of 4.1 nanometers and GaAs potential barrier layer having a thickness of 5 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  83 . An Al 0.1 Ga 0.9 As layer  85  having a thickness of 65 nanometers is provided in contact directly with an entire region of the top surface of the double quantum well active layer  84 . A p-Al 0.2 Ga 0.8 As layer  86  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the Al 0.1 Ga 0.9 As layer  85 .  
     [0129] The p-cladding region has the following multi-layered structure, which varies refractive index in a thickness direction. A p-Al 0.35 Ga 0.65 As cladding layer  87  having a thickness of 100 nanometers is provided in contact directly with an entire region of the top surface of the self confinement hetero-structure active layer or the p-Al 0.2 Ga 0.8 As layer  86 . A mesa-structure is selectively provided on a stripe-shaped region of a top surface of the p-Al 0.35 Ga 0.65 As cladding layer  87 . The stripe-shaped region defines the optical waveguide region. The mesa-structure comprises the following double-layered structure. A p-Al 0.15 Ga 0.85 As cladding layer  88  having a thickness of 375 nanometers is provided in contact directly with the stripe-shaped region of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  87 . The p-Al 0.15 Ga 0.85 As cladding layer  88  has a ridge-shape. A p-Al 0.35 Ga 0.65 As cladding layer  89  having a thickness of 1000 nanometers is provided in contact directly with a top surface of the p-Al 0.15 Ga 0.85 As cladding layer  88 . The p-Al 0.35 Ga 0.65 AS cladding layer  89  has a ridge-shape.  
     [0130] Further, n-Al 0.35 Ga 0.65 As current blocking layers  90  are provided in contact directly with opposite side regions of the top surface of the p-Al 0.35 Ga 0.65 As cladding layer  87  and also in contact directly with sloped side faces of the mesa-structure, wherein the opposite side regions extend in opposite sides of the stripe-shaped region,  
     [0131] The semiconductor laser device has a buried ridge-shaped optical waveguide for emitting a laser beam of a wavelength at 0.98 micrometers. The mode gain difference and the optical confinement rate arc calculated. Δ gain /Γ is 61.66[cm− 1 /] which does not satisfy the requirement that Δ gain /Γ is at least 85 [cm− 1 /%]. An average kink output is 153 mW.  
     [0132] A relative relationship between Γ gain Γ and kink output will be described with reference to FIG. 7. The Δ gain /Γ and kink output has a strong and matured relative relationship with reference particularly to the examples 1 and 2 and the comparative examples 1 and 2 as well as the applicant&#39;s admitted prior art. The kink output is generally proportional to Δ gain /Γ. If Δ gain / Γ is 80[cm −1 /%], then the kink output is only 250 (mW). If a higher kink output than 250 (mW) is necessary, then it is necessary that Δ gain /Γ is at least 85[cm −1 /%].  
     [0133] With reference to FIG. 8, the mode gain difference Δ gain  and kink output has a weak and immature relative relationship. Namely, the kink output does not maturely depend on the mode gain difference Δ gain  only, and rather does maturely depend on Δ gain /Γ. If only the mode gain difference Δ gain  is increased, then it is uncertain that the kink output is increased. If both the mode gain difference Δ gain  and the optical confinement rate Γ are increased, then the kink output is not increased. If the mode gain difference Δ gain  is increased and the optical confinement rate Γ is decreased, then the kink output is increased. Accordingly, in order to obtain an increased kink output, it is essential that Δ gain /Γ is increased.  
     [0134] Although the invention has been described above in connection with several preferred embodiments therefor, it will be appreciated that those embodiments have been provided solely for illustrating the invention, and not in a limiting sense. Numerous modifications and substitutions of equivalent materials and techniques will be readily apparent to those skilled in the art after reading the present application, and all such modifications and substitutions are expressly understood to fall within the true scope and spirit of the appended claims.