Abstract:
An optical amplifier device comprising an input/output section that inputs incident light and outputs emission light; a polarized light splitting section that causes a polarized light component of the incident light input from the input/output section to branch, and outputs first polarization mode light having a first polarization and second polarization mode light having a second polarization different from the first polarization; a polarization converting section that receives the first polarization mode light, converts the first polarization to the second polarization, and outputs first polarization converted light; and an optical amplifying section that amplifies the first polarization converted light input to one end of a waveguide, outputs the resulting amplified first polarization converted light from another end of the waveguide, amplifies the second polarization mode light input to the other end of the waveguide, and outputs the resulting amplified second polarization mode light from the one end of the waveguide.

Description:
The contents of the following patent applications are incorporated herein by reference:
         No. 2011-196389 filed in Japan on Sep. 8, 2011, and   No. PCT/JP2012-005326 filed on Aug. 24, 2012.       

    
    
     BACKGROUND 
     1. Technical Field 
     The present invention relates to an optical amplifier device. 
     2. Related Art 
     An optical amplifier device is known that uses a polarization diversity circuit to split input light into TE polarized light and TM polarized light, keep the TE polarized light as-is, convert the TM polarized light into TE polarized light, and input the TE polarized light resulting from the conversion into an SOA (Semiconductor Optical Amplifier), such as shown in Non-Patent Document 1. 
     Non-Patent Document 1: K. Morito and S. Tanaka, “Record High Saturation Power (+22 dBm) and Low Noise FIG. 5.7dB) Polarization-Insensitive SOA Module”, IEEE PHOTONICS TECHNOLOGY LETTERS, 17, 6, 1298-1300, (2005) 
     The gain of the light in the SOA differs for the TE polarized light and the TM polarized light. With an optical amplifier device that uses a polarity diversity circuit, the TM polarized light is converted into TE polarized light and then input to the SOA. As a result, the difference in optical gain caused by the polarization direction can be decreased. However, the gain of the SOA also depends on the intensity of the light input to the SOA. Therefore, in the polarity diversity circuit, if there is a difference between the intensity of the light that is input to the SOA after being converted from TM polarized light to TE polarized light and the intensity of the light input to the SOA as the split TE polarized light, there is also a difference in gain between these two lights. 
     The difference in gain caused by the polarization direction is referred to as PDG (Polarized Dependent Gain). When the polarization direction of signal light input to an optical amplifier device changes randomly, PDG occurs and there is fluctuation in the intensity of the light output from the optical amplifier device, which causes signal error. Accordingly, in order to reduce the signal error, it is necessary to decrease the PDG. 
     SUMMARY 
     Therefore, it is an object of an aspect of the innovations herein to provide an optical amplifier device, which is capable of overcoming the above drawbacks accompanying the related art. The above and other objects can be achieved by combinations described in the claims. According to a first aspect of the present invention, provided is an optical amplifier device comprising an input/output section that inputs incident light and outputs emission light; a polarized light splitting section that causes a polarized light component of the incident light input from the input/output section to branch, and outputs first polarization mode light having a first polarization and second polarization mode light having a second polarization that is different from the first polarization; a polarization converting section into which is input the first polarization mode light, the polarization section converting the first polarization to the second polarization and outputting first polarization converted light; and an optical amplifying section that amplifies the first polarization converted light input to one end of a waveguide, outputs the resulting amplified first polarization converted light from another end of the waveguide, amplifies the second polarization mode light input to the other end of the waveguide, and outputs the resulting amplified second polarization mode light from the one end of the waveguide. An absolute value of a change in gain per unit intensity of the light input to the optical amplifying section is no greater than 0.16 dB/dBm. The optical amplifying section includes an active layer that propagates the first polarization converted light and the second polarization mode light, and an electrode that injects carriers into the active layer. With Γ representing a confinement coefficient that is a ratio between light confined in the active layer and light in the optical amplifying section and L representing length of the electrode in micrometers, the expression Γ×L&lt;1500% μm is satisfied. 
     The summary clause does not necessarily describe all necessary features of the embodiments of the present invention. The present invention may also be a sub-combination of the features described above. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an overhead schematic view of an optical amplifier device according to a first embodiment of the present invention. 
         FIG. 2  shows the error rate characteristic for an SOA and EDFA used in a booster amplifier. 
         FIG. 3  is a schematic enlarged view of the inclined waveguide of the optical amplifier device according to the first embodiment. 
         FIG. 4  is a schematic cross-sectional view of the quartz waveguide and the quartz waveguide of the optical amplifier device according to the first embodiment. 
         FIG. 5  is a schematic cross-sectional view of the U-turn waveguide of the optical amplifier device according to the first embodiment. 
         FIG. 6  is a schematic cross-sectional view of an SOA according to the first embodiment that is included in the optical amplifier device according to the first embodiment. 
         FIG. 7A  shows the relationship between the gain and the intensity of the light input to the SOA according to the first embodiment, when the confinement coefficient is changed. 
         FIG. 7B  shows the relationship between the non-linearity of the gain and the confinement coefficient in the SOA according to the first embodiment, when the intensity of the input light is 0 dB. 
         FIG. 8A  shows the relationship between the gain and the intensity of the light input to the SOA according to the first embodiment, when the mesa width is changed. 
         FIG. 8B  shows the relationship between the non-linearity of the gain and the mesa width in the SOA according to the first embodiment, when the intensity of the input light is 0 dB. 
         FIG. 9A  shows the relationship between the gain and the intensity of the light input to the SOA according to the first embodiment, when the SOA length is changed. 
         FIG. 9B  shows the relationship between the non-linearity of the gain and the SOA length in the SOA according to the first embodiment, when the intensity of the input light is 0 dB. 
         FIG. 10  is a schematic cross-sectional view of an SOA according to a second embodiment of the present invention. 
         FIG. 11  is a schematic overhead view of the SOA according to a third embodiment of the present invention. 
         FIG. 12  is a schematic cross-sectional view of the gain clamping waveguide in the SOA according to the third embodiment. 
         FIG. 13  is a schematic cross-sectional view of the optical waveguide in the SOA according to a fourth embodiment of the present invention. 
         FIG. 14  is a schematic cross-sectional view of the gain clamping waveguide of the SOA according to the fourth embodiment. 
         FIG. 15  is a schematic overhead view of an SOA according to a fifth embodiment of the present invention. 
         FIG. 16  is a schematic overhead view of an SOA according to a sixth embodiment of the present invention. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Hereinafter, some embodiments of the present invention will be described. The embodiments do not limit the invention according to the claims, and all the combinations of the features described in the embodiments are not necessarily essential to means provided by aspects of the invention. 
       FIG. 1  is an overhead schematic view of an optical amplifier device  100  according to a first embodiment of the present invention. The optical amplifier device  100  includes a circulator  102 , an optical amplifier device  100 , a PLC-PBS chip (Planar Lightwave Circuit-Polarity Beam Splitter chip)  110 , and an SOA-COS  140  (Semiconductor Optical Amplifier-Chip On Submount). The waveguide of the PLC-PBS chip  110  and the waveguide of the SOA-COS  140  are coupled to each other. The optical amplifier device  100  is an SOA-PLC hybrid-type integrated polarity diversity circuit. 
     The circulator  102  inputs incident light and outputs emission light. The incident light input to the optical amplifier device  100  from the input IN is propagated in the input port  112  by the circulator  102 . The incident light is non-polarized light. The emission light propagated to the circulator  102  from the output port  114  is output from the output OUT by the circulator  102 . 
     The PLC-PBS chip  110  includes an MZI  124  (Mach-Zehnder Interferometer), a quartz waveguide  126 , a quartz waveguide  127 , a slit  130 , a half-wave plate  132 , a quartz waveguide  144 , a quartz waveguide  145 , and an inclined waveguide  146 . The MZI  124  includes an input port  112 , an output port  114 , a coupler  116 , a pair of heaters  122 , a TM output port  118 , and a TE output port  120 . 
     A pair of the heaters  122  are arranged respectively on the two arms of the MZI  124 , and are coupled to the input port  112  and the output port  114  via the coupler  116 . Furthermore, the heaters  122  are coupled to the TM output port  118  and the TE output port  120  on the opposite side of the input port  112  and the output port  114 , via a coupler  116 . 
     The quartz waveguide  126  coupled to the TM output port  118  is coupled to the quartz waveguide  144  via the half-wave plate  132 . The half-wave plate  132  is formed in the slit  130  and provided between the quartz waveguide  126  and the quartz waveguide  144 . The TM polarized light is converted into TE polarized light by the half-wave plate  132 . The quartz waveguide  144  is coupled to the inclined waveguide  146 . The quartz waveguide  127  coupled to the TE output port  120  is coupled to the quartz waveguide  145  via the slit  130 . The quartz waveguide  145  is coupled to the inclined waveguide  146 . The quartz waveguide  144 , the quartz waveguide  145 , and the inclined waveguide  146  have an embedded mesa structure. 
     The MZI  124  has a phase difference of ΔΦ between the two arms. Birefringence occurs in the MZI  124 , and the TE polarized light and the TM polarized light each have a different ΔΦ. With ΔΦ TE  representing the phase difference of the TE polarized light and ΔΦ TM  representing the phase difference of the TM polarized light, the expression |ΔΦ TE −ΔΦ TM |=(2π/λ)B·L can be defined. Here, λ is the wavelength, B is the birefringence index of the MZI  124 , and L is the length of the arms of the MZI  124 . When |ΔΦ TE −ΔΦ TM |=(2π+1)π, where n is an integer, the non-polarized incident light input to the MZI  124  from the circulator  102  has its polarized component split by the MZI  124 . As a result, the MZI  124  splits light into the TE polarized light and the TM polarized light, which is orthogonal to the TE polarized light. The TE polarized light is output to the TE output port  120  and the TM polarized light is output to a separate TM output port  118 . The TM polarized light output from the TM output port  118  is converted into TE polarized light by the half-wave plate  132 . 
     The SOA-COS  140  includes a silicon bench  142  and an SOA chip  148 . The SOA chip  148  is mounted on the silicon bench  142 . The mounting on the silicon bench  142  may be solder mounting. The SOA chip  148  includes a semiconductor optical waveguide  150 , two SOAs  154 , and a U-turn waveguide  152 . The inclined waveguide  146  is formed between the quartz waveguide  144  and the semiconductor optical waveguide  150 , and is at an angle relative to the quartz waveguide  144 . 
     A portion of the semiconductor optical waveguide  150  on the SOA  154  side is formed to be parallel with the quartz waveguide  144 . A portion of the semiconductor optical waveguide  150  on the inclined waveguide  146  side is formed to be at an angle relative to another position of the semiconductor optical waveguide  150 . One end of the semiconductor optical waveguide  150  is coupled to the SOAs  154 . The ends of the two SOAs  154  that are opposite the ends connected to the semiconductor optical waveguides  150  are coupled to a U-turn waveguide  152  formed as an arc shape. In other words, the two SOAs  154  are coupled to each other via the semiconductor U-turn waveguide  152 . The U-turn waveguide  152  has a high mesa configuration obtained by etching a semiconductor core on a waveguide side. 
     Since the U-turn waveguide  152  forms a U-turn portion with an arc shape, the end of the semiconductor optical waveguide  150  opposite the SOAs  154  is formed in the same area as the SOA chip  148 . Therefore, the size of the SOA-COS  140  can be decreased. The U-turn waveguide  152  has a high mesa structure, and therefore the light confinement strength is high and light loss due to bending can be restricted, even if the curvature radius of the U-turn waveguide  152  is 125 μm, for example. As a result, the optical amplification characteristic and noise characteristic can both be improved. 
     The TE polarized light output from the quartz waveguide  126  and converted by the half-wave plate  132  is input to the half-wave plate  132  side end of the waveguide of the SOA-COS  140 . In other words, the light that has been converted to TE polarized light by the half-wave plate  132  is input to the semiconductor optical waveguide  150  on the half-wave plate  132  side via the quartz waveguide  144  and the inclined waveguide  146 . The TE polarized light input to the quartz waveguide  144  on the half-wave plate  132  side is amplified by the two SOAs  154 , and output from the other end of the waveguide of the SOA-COS  140 , which is opposite the input end. 
     The TE polarized light output from the quartz waveguide  127  on the side where the half-wave plate  132  is not provided is input to the end of the waveguide of the SOA-COS  140  on the side where the half-wave plate  132  is not provided. In other words, the light output from the quartz waveguide  127  is input to the quartz waveguide  145 . The TE polarized light input to the quartz waveguide  145  is amplified by the two SOAs  154 , and output from one end of the waveguide of the SOA-COS  140  that is opposite the input end. In the manner described above, the SOA-COS  140  has bi-directional input in which light can be input from either end of the waveguide and amplified light is output from whichever end this light was not input to. 
     In the SOA-COS  140 , the absolute value of the change in gain per unit intensity of the light input thereto, within an intensity range of the light input to the SOA-COS  140 , is no greater than 0.16 dB/dBm. Here, the intensity range of the light input to the SOA-COS  140  may be greater than or equal to −30 dBm and less than or equal to 0 dBm. Furthermore, when the intensity of the input light increases by 1 dBm, the change in the gain per unit intensity of the input light is expressed by the increase value (dB) of the gain. In other words, with the intensity (dBm) of the input light on a horizontal axis and the gain (dB) on a vertical axis, the change in the gain per unit intensity of the input light corresponds to the slope in the graph. Furthermore, the change in the gain per unit intensity of the input light corresponds to a derivative value of an expression represented by a function of the gain (dB) and the intensity (dBm) of the input light. The PDG of the optical amplifier device  100  can be approximated by the expression PDG(dB)=ΔG(dB/dBm)×3(dBm). Here, ΔG is the absolute value of the change in gain per unit intensity (dB/dBm). 
     In the polarization diversity circuit, the gain is at a maximum when the intensity of the light in the TM output port  118  is equal to the intensity of the light in the TE output port  120 . At this time, the output light can be expressed by P out (dBm)={P in (dBm)−3}+{ΔG×3+G(dB)}+3(dB). Here, P out  and P in  are the total intensities obtained by combining the TE mode light intensity and the TM mode light intensity, for the output light and input light respectively. Furthermore, G is the gain for the input P in . The term {P in (dBm)−3}, which is the first term on the right side in the above expression, represents the intensity of the light input to each of the TE and TM ports. The input light is distributed uniformly between the TE and TM ports, which results in the term {P in (dBm)−3}. The term {ΔG×3+G(dB)}, which is the second term on the right side of the above expression, represents the gain provided by the TE and TM ports. The term 3(dB), which is the third term on the right side of the above expression, corresponds to doubling through the combination of the TE port and TM port of the circulator  102  by the output port, and the a value of 3(dB) is added in the above expression. On the other hand, the gain is at a minimum when the incident light is output to only one of the TM output port  118  and the TE output port  120 . At this time, the output can be expressed as P out (dBm)=P in (dBm)+G(dB). In the polarity diversity circuit, when the expression for the minimum gain is subtracted from the expression for the maximum gain, PDG is found to be ΔG×3(dB), and this is the same as the above expression of PDG(dB)=ΔG(dB/dBm)×3(dBm). In an SOA-COS  140  having significant non-linearity for the gain, the difference between a case of maximum gain and a case of minimum gain is the PDG. Accordingly, the PDG for polarity diversity is approximated in the manner described above. In other words, if the absolute value of the change in gain per unit intensity within the intensity range of the light input to the SOA-COS  140  is 0.16 dB/dBm or less, then the PDG is 0.5 dB or less. 
     When the polarization direction of the light incident to the optical amplifier device  100  changes randomly, the PDG causes the gain to change, and therefore errors are caused by a change in the intensity of the light emitted from the optical amplifier device  100 . If the PDG is 0.5 dB or lower, the effect is equivalent to that of other practical optical amplifiers, and this is a standard for what is allowable for use in optical transmission.  FIG. 2  shows the error characteristic when an SOA (Semiconductor Optical Amplifier) having a PDG of 0.5 dB is used in an optical amplifier (booster amplifier) for amplifying an input signal.  FIG. 2  shows the error rate for the SOA when put to the same use as an EDFA (Erbium Doped Fiber Amplifier) already used in a practical system. The intensity of the input to the SOA and EDFA is −2 dBm, and the output is set to 11 dBm. By inserting a variable attenuator downstream of the optical amplifier, the received intensity of the optical detected was changed and the error rate was measured. Based on  FIG. 2 , it was found that if the PDG of the SOA is 0.5 dB or less, then the same characteristics as the EDFA are realized. In other words, if the PDG is 0.5 dB or less, the back-to-back error rate characteristic occurring when light is not transmitted through the fiber has an error rate no greater than 10 −9 , and therefore data signals can be accurately transmitted. If this error rate is no greater than 10 −9 , after the conversion to an electrical signal, an error signal can be corrected by using an error correction code. The optical amplifier device  100  of the first embodiment, which is an SOA-PLC hybrid integrated polarization diversity circuit, includes an SOA-COS  140  in which the absolute value of the change in gain per unit intensity of the input light is 0.16 dB/dBm or less, and therefore the PDG is 0.5 dB or less and characteristics equivalent to those realized when using another practical optical amplifier can be obtained. 
     Here, the length of the optical path of the waveguide from one end of the waveguide of the SOA-COS  140  to one of the SOAs  154  is equal to the length of the optical path of the waveguide from the other end of the waveguide of the SOA-COS  140  to the other SOA  154 . In other words, the length of the semiconductor optical waveguide  150  on the side where the half-wave plate  132  is provided is equal to the length of the semiconductor optical waveguide  150  on the side where the half-wave plate  132  is not provided. Here, the length of the waveguide refers to the length of the waveguide in the direction of the light path. As a result, there is a reduced difference between the intensity of the light input to the SOA  154  from the semiconductor optical waveguide  150  on the side where the half-wave plate  132  is provided and the intensity of the light input to the SOA  154  from the semiconductor optical waveguide  150  on the side where the half-wave plate  132  is not provided. The gains of the SOAs  154  may differ according to the intensity of the input light. In the optical amplifier device  100 , since the difference in intensity of the lights input to the two SOAs  154  in each direction is small, the difference in the gain of the lights input tot eh SOAs  154  in each direction is also small. Accordingly, the gain fluctuation is restricted and the signal error can be decreased. 
     Furthermore, the total length of the quartz waveguide  144 , the inclined waveguide  146 , and the semiconductor optical waveguide  150  on the side where the half-wave plate  132  is provided may be equal to the total length of the quartz waveguide  145 , the inclined waveguide  146 , and the semiconductor optical waveguide  150  on the side where the half-wave plate  132  is not provided. As a result, the difference between the intensity of the TE polarized light input to the quartz waveguide  144  and the SOA  154  on the quartz waveguide  144  side and the intensity of the TE polarized light input to the quartz waveguide  145  and the SOA  154  on the quartz waveguide  145  side is further reduced. Accordingly, the difference in gain between the lights input to the SOAs  154  from each direction is further reduced, and the fluctuation in the gain can be restricted to reduce the signal error. 
       FIG. 3  is a schematic enlarged view of the inclined waveguide  146  of the optical amplifier device  100  according to the first embodiment.  FIG. 3  shows a portion of the inclined waveguide  146  side of the quartz waveguide  144  and a portion of the inclined waveguide  146  side of the semiconductor optical waveguide  150 . 
     The central axis  204  of the inclined waveguide  146  forms a prescribed angle θ 1  with respect to a straight line perpendicular to the bonding surface  208  between the SOA chip  148  and the PLC-PBS chip  110 . The central axis  202  of the quartz waveguide  144  is formed parallel to the straight line perpendicular to the bonding surface  208 , and the central axis  204  of the inclined waveguide  146  forms a prescribed angle θ 1  relative to the central axis  202  of the quartz waveguide  144 . As a result, the light input to the quartz waveguide  144  is incident to the bonding surface  208  at an angle. 
     The semiconductor optical waveguide  150  includes a wide portion  218 , an SSC  216  (Spot Size Converter), a bending portion  214 , and a narrow portion  212 . The central axis  206  of the SSC  216  and the wide portion  218  of the semiconductor optical waveguide  150  forms a prescribed angle θ 2  with respect to the straight line perpendicular to the bonding surface  208 . 
     With n 1  representing the refractive index of the inclined waveguide  146  and n 2  representing the refractive index of the semiconductor optical waveguide  150 , Snell&#39;s law can be used to determine θ 1  and θ 2  to fulfill the relationship n 1 sinθ 1 =n 2 sinθ 2 . The bonding surface  208  is coated with an antireflection coat  210 . Here, θ 1  is preferably from 5° to 9°, and θ 2  is preferably from 12° to 17°. 
     The semiconductor optical waveguide  150  can be bent at the bending portion  214  while maintaining the width of the narrow portion  212 . The portion of the semiconductor optical waveguide  150  not shown has the same width as the narrow portion  212  of the semiconductor optical waveguide  150 . The width of the waveguide refers to the width that is perpendicular to the optical path direction and within a plane parallel to the surface of the substrate on which the waveguide is formed. 
     The SSC  216  is an optical waveguide (width-flared SSC) with a tapered shape. Therefore, the mode field of the quartz waveguide  144  matches the mode field of the semiconductor optical waveguide  150 . The semiconductor optical waveguide  150  has a width that expands at the SSC  216  and is the same as the width of the inclined waveguide  146  at the wide portion  218 . 
     In the optical amplifier device  100  according to the first embodiment, the SSC  216  is formed in the SOA chip  148 , but the SSC  216  may be formed in the PLC-PBS chip  110  instead. Due to the SSC  216 , the coupling loss in the portion coupling with the waveguide can be decreased, thereby obtaining higher coupling efficiency. 
     The above describes the inclined waveguide  146  and the semiconductor optical waveguide  150  coupled to the quartz waveguide  144 , but the inclined waveguide  146  and the semiconductor optical waveguide  150  coupled to the quartz waveguide  145  are the same. 
       FIG. 4  is a schematic cross-sectional view of the quartz waveguide  144  and the quartz waveguide  145  of the optical amplifier device  100  according to the first embodiment. Specifically,  FIG. 4  is a schematic cross-sectional view over the line IV-IV of  FIG. 1 . A lower cladding layer  304  is formed on the PLC platform  302 . A core layer  306  is formed on a portion of the lower cladding layer  304 . The core layer  306  is formed of a quartz material, and serves as the quartz waveguide  144  and the quartz waveguide  145 . 
     An upper cladding layer  308  is formed on the core layer  306  and on the portion of the lower cladding layer  304  where the core layer  306  is not formed. In other words, the quartz waveguide  145  and the inclined waveguide  146  have an embedded mesa structure. The lower cladding layer  304  and the upper cladding layer  308  are formed of quartz material with a lower refractive index than the core layer  306 . The lower cladding layer  304  and the upper cladding layer  308  may be formed of the same material. The inclined waveguide  146  may include the same cross-sectional structure as the quartz waveguide  144  and the quartz waveguide  145 . 
       FIG. 5  is a schematic cross-sectional view of the U-turn waveguide  152  of the optical amplifier device  100  according to the first embodiment. Specifically,  FIG. 5  is a schematic cross-sectional view over the line V-V of  FIG. 1 . A semiconductor substrate  310  is formed on the silicon bench  142 . The semiconductor substrate  310  is formed of a compound semiconductor. A lower cladding layer  312  is formed on a portion of the semiconductor substrate  310 . A core layer  314  is formed on the lower cladding layer  312 . An upper cladding layer  316  is formed on the core layer  314 . The core layer  314  is formed of a compound semiconductor. The lower cladding layer  312  and the upper cladding layer  316  are formed of a compound semiconductor material with a lower refractive index than the core layer  314 . In other words, the U-turn waveguide  152  has a high mesa structure. The semiconductor substrate  310  may be formed of InP, the core layer  314  may be formed of GaAsP, and the lower cladding layer  312  and upper cladding layer  316  may be formed of InP, for example. 
     The curvature radius of the loop-back section provided in the optical waveguide can be made smaller when the difference between the specific refractive indexes of the core and the cladding is greater. Since the U-turn waveguide  152  has a high mesa structure, the difference between the specific refractive indexes of the core layer  314  and the air on both sides thereof becomes a high value of 30% to 40% or more, for example. Therefore, the curvature radius when viewed from above the U-turn waveguide  152  can be lowered to 125 μm, for example. In other words, compared to a case in which a loop-back structure including a U-turn optical waveguide is formed on a quartz PLC chip, forming a loop-back structure with a U-turn waveguide  152  that has a high mesa structure in the SOA-COS  140  enables the size of the SOA-COS  140  to be reduced. Accordingly, the size of the optical amplifier device  100  can be reduced. 
       FIG. 6  is a schematic cross-sectional view of an SOA  154  according to the first embodiment that is included in the optical amplifier device  100  according to the first embodiment, from a direction perpendicular to the waveguide direction. The SOA  154  is formed on the semiconductor substrate  310  mounted on the silicon bench  142 . The SOA  154  includes the semiconductor substrate  310 , a lower cladding layer  312 , an active layer  318 , a buried layer  320 , a current stopping layer  322 , an upper cladding layer  316 , a contact layer  324 , a passivation layer  328 , a p-side electrode  326 , and an n-side electrode  332 . 
     An n-side electrode  332  is formed on the rear surface of the semiconductor substrate  310 , and the n-side electrode  332  contacts the top of the silicon bench  142 . The semiconductor substrate  310  is formed of a compound semiconductor. The lower cladding layer  312  is formed on the semiconductor substrate  310 . The active layer  318  is formed on a portion of the lower cladding layer  312 . The active layer  318  has a multiquantum well structure formed by alternately layering a well layer and a barrier layer. For example, the active layer  318  may have a multiquantum well structure including five well layers, with each well layer having a thickness of 3.9 nm and each barrier layer having a thickness of 10 nm. The active layer  318  may be formed of GaInAsP, for example. 
     A portion of the lower cladding layer  312  in which the active layer  318  is not formed is removed, in the thickness direction of the lower cladding layer  312 . In other words, the lower cladding layer  312  is thicker in the region under the active layer  318  than in the region where the active layer  318  is not formed. In the region where the active layer  318  is not formed, a buried layer  320  is formed on the lower cladding layer  312 . The current stopping layer  322  is formed on the buried layer  320 . The buried layer  320  is formed of p-InP, for example. The current stopping layer  322  is formed of n-InP, for example. The upper cladding layer  316  is formed on the active layer  318  and the current stopping layer  322 . The top surface of the current stopping layer  322  protrudes beyond the top surface of the active layer  318 . In other words, the upper cladding layer  316  on the active layer  318  is thicker than the active layer  318  on the current stopping layer  322 . 
     The contact layer  324  is formed on the upper cladding layer  316 , above the active layer  318 . The passivation layer  328  is formed on the contact layer  324  and the upper cladding layer  316 . A portion of the passivation layer  328  on the contact layer  324  is removed, and the p-side electrode  326  is formed thereon. The p-side electrode  326  is formed from an opening in the passivation layer  328  onto the passivation layer  328 . In other words, the width of the p-side electrode  326  may be greater than the width of the active layer  318 . Here, the “width” refers to the length in a direction of the light path in the active layer  318  and a direction perpendicular to the direction of the thickness of the active layer  318 . An inverse distribution is formed by the carriers of the electrons and the holes introduced from the p-side electrode  326  and the n-side electrode  332 , and the light is amplified in the active layer  318 . 
       FIGS. 7A and 7B  show a relationship between the non-linearity of the gain and the confinement coefficient Γ of the SOA  154  according to the first embodiment. The confinement coefficient Γ is the ratio of the light confined in the active layer  318  to the light in the SOA  154 . The results shown in  FIGS. 7A and 7B  were obtained when the mesa width of the SOA  154  was 2 μm, the length of the SOA was 1000 μm, and the current injected from the p-side electrode  326  and the n-side electrode  332  was 200 mA. The mesa width refers to the width of the active layer  318  in a direction of the optical path length and a direction perpendicular to the direction of the injected current. The length of the SOA refers to the length of the region in which both the active layer  318 , the p-side electrode  326 , and the n-side electrode  332  are formed in the SOA  154 , in a direction parallel to the length of the optical path. In other words, in the SOA  154 , the light is amplified within a range of the length of the SOA. 
     The graph of  FIG. 7A  shows the relationship between the gain and the intensity of the light input to the SOA  154 , when the confinement coefficient Γ is changed from 1% to 5%. The horizontal axis indicates the intensity (dBm) of the light input to the SOA  154 , and the vertical axis represents the gain (dB). In the region where the intensity of the input light is less than 0 dB, the gain has little dependence on the intensity of the input light, and when the intensity of the input light is −10 dB or less, the gain does not depend on the intensity of the input light. As the intensity of the input light increases, the dependency of the gain on the intensity of the input light increases. Furthermore, when the intensity of the input light is larger, the gain is smaller. 
     The graph of  FIG. 7B  shows the relationship between the non-linearity of the gain and the confinement coefficient Γ, when the intensity of the input light is 0 dB. A value of 0 dB is the maximum power input to a boost amp and pre-amp in long-distance optical communication. The horizontal axis indicates the confinement coefficient Γ, and the vertical axis indicates the non-linearity (dB/dBm) of the gain. The non-linearity of the gain is the amount of change in the gain per unit intensity of the input light. In other words, the non-linearity of the gain is the value of the slope of the graphed line when the intensity of the light is plotted on the horizontal axis and the gain is plotted on the vertical axis. When the confinement coefficient is smaller, the absolute value of the non-linearity of the gain is smaller. 
     The non-linearity of the gain tends to decrease linearly relative to the confinement coefficient Γ. With a confinement coefficient of 1.5% or less, the non-linearity of the gain of the SOA  154  is 0.13 dB/dBm or less. With a confinement coefficient of 1.6% or less, the non-linearity of the gain of the SOA  154  is 0.15 dB/dBm or less. Accordingly, since the PDG of the optical amplifier device  100  is 0.5 dB or less, these values are acceptable for optical communication. 
       FIGS. 8A and 8B  show the relationship between the non-linearity of the gain and the mesa width in the SOA  154  of the first embodiment. The results shown in  FIGS. 8A and 8B  were obtained when the length of the SOA  154  was 1000 μm, the confinement coefficient Γ was 2.5%, and the current injected from the p-side electrode  326  and the n-side electrode  332  was 200 mA. 
     The graph of  FIG. 8A  shows the relationship between the gain and the intensity of the light input to the SOA  154  when the mesa width is changed from 2 μm to 8 μm. The horizontal axis indicates the intensity (dBm) of the light input to the SOA  154 , and the vertical axis indicates the gain (dB). The results indicated the same trend as in the graph of  FIG. 7A . The graph of  FIG. 8B  shows the relationship between the non-linearity of the gain and the mesa width, when the intensity of the input light is 0 dB. The horizontal axis indicates the mesa width, and the vertical axis represents the non-linearity (dB/dBm) of the gain. When the mesa width is greater, the non-linearity of the gain is lower. It should be noted that a mesa width greater than 2.5 μm results in multimode operation. Accordingly, for an amplifier used in long-distance optical communication, the SOA  154  preferably has a mesa width of 2.5 μm or less. 
       FIGS. 9A and 9B  show the relationship between the non-linearity of the gain and the length of the SOA  154  according to the first embodiment. In other words,  FIGS. 9A and 9B  show the non-linearity of the gain and the gain when the intensity of the light input to the SOA  154  is changed, while changing the length of the SOA  154 . The results shown in  FIGS. 9A and 9B  were obtained when the confinement coefficient Γ of the SOA  154  was 2.5%, the mesa width was 2 μm, and the current injected from the p-side electrode  326  and the n-side electrode  332  was 200 mA. 
     The graph of  FIG. 9A  shows the relationship between the gain and the intensity of the light input to the SOA  154 , when the SOA length is changed from 500 μm to 1000 μm. The horizontal axis indicates the intensity (dBm) of the light input to the SOA  154 , and the vertical axis indicates the gain (dB). The results indicated the same trend as in the graph of  FIGS. 7A and 8A . The graph of  FIG. 9B  shows the relationship between the non-linearity of the gain and the SOA length, when the intensity of the input light is 0 dB. The horizontal axis indicates the SOA length, and the vertical axis represents the non-linearity (dB/dBm) of the gain. When the SOA length is greater, the non-linearity of the gain is also greater. 
     The non-linearity gain characteristic tends to decrease with respect to the SOA length. With an SOA length of 550 μm or less, the non-linearity of the gain of the SOA  154  is 0.13 dB/dBm or less. With an SOA length of 600 μm or less, the non-linearity of the gain of the SOA  154  is 0.16 dB/dBm or less. Accordingly, since the PDG of the optical amplifier device  100  is to be 0.5 dB or less, these values are acceptable for optical communication. 
     Based on the above results, with F representing the light confinement coefficient of the SOA  154  and L indicating the SOA length, it is preferable that Γ×L be less than 1500% μm. As a result, the non-linearity of the gain of the SOA  154  is 0.16 dB/dBm or less and the PDG of the optical amplifier device  100  is 0.5 dB or less, and therefore these values are acceptable for optical communication. 
       FIG. 10  is a schematic cross-sectional view of an SOA  154  according to a second embodiment of the present invention. The SOA  154  of the optical amplifier device  100  is not limited to the SOA  154  of the first embodiment shown in  FIG. 6 , and the SOA  154  according to the second embodiment shown in  FIG. 10  may be used instead. In  FIG. 10 , components having the same reference numerals as components in  FIG. 6  may have the same function and configuration as the components described in  FIG. 6 . The SOA  154  according to the second embodiment includes a reflective film  330  and uses a different shape for the lower cladding layer  312 , the active layer  318 , the upper cladding layer  316 , the buried layer  320 , and the current stopping layer  322 , but is otherwise the same as the SOA  154  according to the first embodiment. 
     The SOA  154  is formed on the semiconductor substrate  310  mounted on the silicon bench  142 . The SOA  154  includes the semiconductor substrate  310 , the lower cladding layer  312 , the active layer  318 , the buried layer  320 , the current stopping layer  322 , the upper cladding layer  316 , the contact layer  324 , the passivation layer  328 , the reflective film  330 , the p-side electrode  326 , and the n-side electrode  332 . 
     An upper portion of the lower cladding layer  312 , the active layer  318 , and a lower portion of the upper cladding layer  316  are formed with a tapered shape. Furthermore, the top surface of the lower cladding layer  312  in a region where the active layer  318  is not formed, the side surfaces of the active layer  318 , and the side surfaces of the upper cladding layer  316  formed in the region sandwiched between the current stopping layer  322  on the active layer  318  are curved in a manner to protrude downward. 
     The buried layer  320  is formed to contact the top surface of the lower cladding layer  312  in a region where the active layer  318  is not formed, the side surfaces of the active layer  318 , and the side surfaces of the upper cladding layer  316  formed in the region sandwiched between the current stopping layer  322  on the active layer  318  are curved in a manner to protrude downward. The thickness of the current stopping layer  322  is smaller at a location closer to the center of the optical path in the SOA  154 . The current stopping layer  322  is on the buried layer  320 , and therefore the interface between the buried layer  320  and the current stopping layer  322  is a curved surface facing downward. The top surface of the current stopping layer  322  is parallel to the top surface of the semiconductor substrate  310 . 
     The reflective film  330  which reflects the light is formed on both ends of the lower cladding layer  312 , the buried layer  320 , the current stopping layer  322 , the upper cladding layer  316 , and the passivation layer  328 . The carriers are injected from the p-side electrode  326  and the n-side electrode  332 , and the light released from the active layer  318  is reflected by the reflective film  330 . As a result, the light resonates in a direction perpendicular to the direction of the optical path of the SOA  154 , which is a direction parallel to the surface of the semiconductor substrate  310 . Accordingly, the gain of the SOA  154  becomes constant. In other words, the SOA  154  performs gain clamping. The gain of the SOA  154  is constant and does not depend on the intensity of the light input to the SOA  154 , and therefore the non-linearity of the gain is reduced. As a result, the PDG of the optical amplifier device  100  is also reduced. 
       FIG. 11  is a schematic overhead view of the SOA  154  according to a third embodiment of the present invention. The SOA  154  includes an optical waveguide  352 , a gain clamping waveguide  354 , a diffraction grating  356 , and an antireflection film  350 . The diffraction grating  356  is formed on both sides of the gain clamping waveguide  354 . The phrase “both sides of the gain clamping waveguide  354 ” refers to the sides in a direction perpendicular to the optical path, which is a direction parallel to the surface of the silicon bench  142 . The optical waveguide  352  is coupled to both ends of the gain clamping waveguide  354  in the optical path direction. The antireflection film  350  is formed on the end of the optical waveguide  352  that is opposite the gain clamping waveguide  354  side. In other words, the antireflection film  350  is formed on both ends in the direction of the optical path of the SOA  154 . With the antireflection film  350 , the reflection of light at both ends of the SOA  154  can be restricted. The cross-section of the SOA  154  over the line VI-VI has the same structure as shown in  FIG. 6 . 
     The light emitted by the gain clamping waveguide  354  is reflected by the diffraction grating  356 . As a result, resonance occurs in a direction perpendicular to the direction of the light path of the SOA  154 , which is a direction parallel to the surface of the silicon bench  142 . Accordingly, the gain of the SOA  154  becomes constant. In other words, the SOA  154  performs gain clamping. The gain of the SOA  154  is constant and does not depend on the intensity of the light input to the SOA  154 , and therefore the non-linearity of the gain is reduced. As a result, the PDG of the optical amplifier device  100  is also reduced. 
       FIG. 12  is a schematic cross-sectional view of the gain clamping waveguide  354  in the SOA  154  according to the third embodiment. Specifically,  FIG. 12  is a schematic cross-sectional view over the line XII-XII of  FIG. 11 . In  FIG. 12 , components having the same reference numerals as components in  FIG. 6  may have the same function and configuration as the components described in  FIG. 6 . The SOA  154  is formed on the semiconductor substrate  310  mounted on the silicon bench  142 . The SOA  154  includes, in the cross section of the gain clamping waveguide  354 , the semiconductor substrate  310 , the lower cladding layer  312 , the active layer  318 , the upper cladding layer  316 , the buried layer  320 , the current stopping layer  322 , the contact layer  324 , the p-side electrode  326 , the passivation layer  328 , and the n-side electrode  332 . 
     The lower cladding layer  312  is formed on the semiconductor substrate  310 . The active layer  318  is formed on the lower cladding layer  312 . Portions of the active layer  318  on respective sides sandwiching the central region serving as the optical path are removed. Portions of the lower cladding layer  312  in the thickness direction are removed in the region from which the active layer  318  was removed. In other words, the bottom portion of the lower cladding layer  312  in the region where the active layer  318  is removed is thinner than in other regions. The buried layer  320  is formed in the region from which the active layer  318  was removed. The current stopping layer  322  is formed on the buried layer  320 . 
     The region sandwiched between the buried layer  320  and the current stopping layer  322  becomes the gain clamping waveguide  354 . A plurality of InP buried layers  360  are formed of InP in the active layer  318 , on opposite ends of the central region serving as the light path of the active layer  318  in a manner to sandwich the buried layer  320  and the current stopping layer  322 . The InP buried layers  360  are formed with a prescribed depth in a depth direction from the top surface of the active layer  318 . Furthermore, the InP buried layers  360  are formed at prescribed intervals in the direction of the optical path. The active layer  318  in which the InP buried layers  360  are formed acts as a diffraction grating  356 , and reflects light in a direction perpendicular to the optical path. It should be noted that the diffraction grating  356  need only be configured to have a complex refractive index that is periodically perturbed, and is not limited to the active layer  318  having the InP buried layers  360  formed therein. 
     The top surface of the current stopping layer  322  protrudes beyond the top surface of the active layer  318 . The upper cladding layer  316  is formed on the active layer  318  and the current stopping layer  322 . The contact layer  324  is formed on the upper cladding layer  316 . The contact layer  324  is removed from above the current stopping layer  322 , and the passivation layer  328  is formed in this region. The p-side electrode  326  is formed on the contact layer  324 . The carriers are injected from the p-side electrode  326  and the n-side electrode  332 , and the light generated by the active layer  318  is reflected and resonated by the diffraction grating  356  including the InP buried layers  360 , and therefore gain clamping occurs in the gain clamping waveguide  354 . 
       FIG. 13  is a schematic cross-sectional view of the optical waveguide  352  in the SOA  154  according to a fourth embodiment of the present invention. The top view of the SOA  154  according to the fourth embodiment is the same as the top view of the SOA  154  according to the third embodiment shown in  FIG. 11 .  FIG. 13  is a schematic cross-sectional configuration of the SOA  154  according to the fourth embodiment, over the line VI-VI of  FIG. 11 . In  FIG. 13 , components having the same reference numerals as components in  FIG. 6  may have the same function and configuration as the components described in  FIG. 6 . 
     The SOA  154  is formed on the semiconductor substrate  310  mounted on the silicon bench  142 . The SOA  154  includes, in the optical waveguide  352 , the semiconductor substrate  310 , the lower cladding layer  312 , the active layer  318 , the upper cladding layer  316 , the contact layer  324 , the p-side electrode  326 , the passivation layer  328 , and the n-side electrode  332 . The cross section of the optical waveguide  352  of the SOA  154  according to the fourth embodiment differs from the cross section shown in  FIG. 6  in that the buried layer  320  and the current stopping layer  322  are not included and that the upper cladding layer  316  and the passivation layer  328  are shaped differently. 
     Portions of the upper cladding layer  316  in the thickness direction are removed from both sides of a central portion that is along the optical path. The upper cladding layer  316  is thinner in the region where the portions have been removed in the thickness direction than in other regions. The passivation layer  328  is formed on the upper cladding layer  316 , in the region from which the portions of the upper cladding layer  316  have been removed. The contact layer  324  is formed on the upper cladding layer  316  in the region that is thicker than other regions, which is the region sandwiching the passivation layer  328 . The p-side electrode  326  is formed on the contact layer  324 . The top surface of the passivation layer  328  protrudes above the top surface of the contact layer  324 . The p-side electrode  326  is wider than the contact layer  324 . 
       FIG. 14  is a schematic cross-sectional view of the gain clamping waveguide  354  of the SOA  154  according to the fourth embodiment. Specifically,  FIG. 14  is a schematic cross-sectional view of the SOA  154  according to the fourth embodiment, over the line XII-XII of  FIG. 11 . In  FIG. 14 , components having the same reference numerals as components in  FIG. 12  may have the same function and configuration as the components described in  FIG. 12 . The SOA  154  is formed on the semiconductor substrate  310  mounted on the silicon bench  142 . The SOA  154  includes, in the gain clamping waveguide  354 , the semiconductor substrate  310 , the lower cladding layer  312 , the active layer  318 , the InP buried layers  360 , the upper cladding layer  316 , the contact layer  324 , the p-side electrode  326 , the passivation layer  328 , and the n-side electrode  332 . The cross section of the gain clamping waveguide  354  of the SOA  154  according to the fourth embodiment differs from the cross section shown in  FIG. 12  in that the buried layer  320  and the current stopping layer  322  are not included and that the upper cladding layer  316  and the passivation layer  328  are shaped differently. 
     The upper cladding layer  316  is thinner in portions on both sides of a central portion that is along the optical path than in other regions. The passivation layer  328  is formed on the upper cladding layer  316  in the portions that are thinner than the other regions of the upper cladding layer  316 . The contact layer  324  is formed on the upper cladding layer  316  in the region of the upper cladding layer  316  that is thicker than the other region. The p-side electrode  326  is formed on the contact layer  324 . The top surface of the passivation layer  328  protrudes above the top surface of the contact layer  324 . The width of the p-side electrode  326  is greater than the width of the contact layer  324 . The carriers injected from the p-side electrode  326  and the n-side electrode  332  are focused in a central portion of the active layer  318 , by the passivation layer  328 . The light generated from the active layer  318  in response to the injection of the carriers is reflected and resonated by the diffraction grating  356  including the InP buried layers  360 , and therefore gain clamping occurs in the gain clamping waveguide  354 . The gain of the SOA  154  is constant and does not depend on the intensity of the light input to the SOA  154 , and therefore the non-linearity of the gain is reduced. As a result, the PDG of the optical amplifier device  100  is also reduced. 
       FIG. 15  is a schematic overhead view of an SOA  154  according to a fifth embodiment of the present invention. The SOA  154  includes the p-side electrode  326 , the active layer  318 , and a Bragg grating  362 . In  FIG. 15 , components having the same reference numerals as components in  FIGS. 6 and 11  may have the same function and configuration as the components described in  FIGS. 6 and 11 . The SOA  154  according to the fifth embodiment has the same configuration as the cross section shown in  FIG. 6  in the region where the p-side electrode  326  is formed. The Bragg grating  362  is formed on both ends of the active layer  318  along the optical path. The Bragg grating  362  is formed at both ends of the SOA  154  along the optical path, and provides a periodic perturbation in the sub refractive index in the direction along the optical axis of the SOA  154 . As a result, the carriers are injected by the p-side electrode  326  and the n-side electrode, which is not shown in  FIG. 15 , and the light generated by the active layer  318  is reflected and resonated by the Bragg grating  362 , thereby causing gain clamping in the SOA  154 . The gain of the SOA  154  is constant and does not depend on the intensity of the light input to the SOA  154 , and therefore the non-linearity of the gain is reduced. As a result, the PDG of the optical amplifier device  100  is also reduced. 
       FIG. 16  is a schematic overhead view of an SOA  154  according to a sixth embodiment of the present invention. The SOA  154  includes a waveguide  372 , a coupler  374 , an arm  376 , a coupler  378 , an arm  380 , an amplifying section  382 , an amplifying section  384 , a waveguide  386 , a controlled light source  388 , a waveguide  390 , and a waveguide  392 . The amplifying section  382  is formed on the arm  376  to amplify light. The amplifying section  384  is formed on the arm  380  to amplify light. The amplifying section  382  and the amplifying section  384  are SOAs. The arm  376  and the arm  380  are formed parallel to each other, and the coupler  374  and coupler  378  are formed respectively at the ends of the arms. The waveguide  372  is formed on the side of the coupler  374  opposite the arm  376  to sandwich the coupler  374 . The waveguide  390  is formed on the side of the coupler  378  opposite the arm  376  to sandwich the coupler  378 . The controlled light source  388  is formed on the end of the waveguide  390  opposite the coupler  378 . The controlled light source  388  is a DFB laser, for example. The waveguide  392  is formed on the side of the coupler  374  opposite the arm  380  to sandwich the coupler  374 . The waveguide  386  is formed on the side of the coupler  378  opposite the arm  380  to sandwich the coupler  378 . 
     The amount of light input to the amplifying section  382  and the amplifying section  384  from the controlled light source  388  via the waveguide  390  and the coupler  378  is controlled by controlling the controlled light source  388 . As a result, the gain of the amplifying section  382  and the amplifying section  384  can be controlled. By controlling the controlled light source  388  according to the intensity of the light input to the SOA  154 , the non-linearity of the gain in the SOA  154  can be decreased, thereby also decreasing the PDG of the optical amplifier device  100 . 
     While the embodiments of the present invention have been described, the technical scope of the invention is not limited to the above described embodiments. It is apparent to persons skilled in the art that various alterations and improvements can be added to the above-described embodiments. It is also apparent from the scope of the claims that the embodiments added with such alterations or improvements can be included in the technical scope of the invention. 
     The operations, procedures, steps, and stages of each process performed by an apparatus, system, program, and method shown in the claims, embodiments, or diagrams can be performed in any order as long as the order is not indicated by “prior to,” “before,” or the like and as long as the output from a previous process is not used in a later process. Even if the process flow is described using phrases such as “first” or “next” in the claims, embodiments, or diagrams, it does not necessarily mean that the process must be performed in this order.