Patent Publication Number: US-2022236620-A1

Title: Method for manufacturing optical modulator, testing method, non-transitory storage medium, and light transmission apparatus

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority based on Japanese Patent Application No. 2021-012460, filed on Jan. 28, 2021, and the entire contents of the Japanese patent application are incorporated herein by reference. 
     TECHNICAL FIELD 
     The present disclosure relates to a method for manufacturing an optical modulator, a testing method, a non-transitory storage medium, and a light transmission apparatus. 
     BACKGROUND ART 
     A Mach-Zehnder modulator formed of a semiconductor layer and modulating light has been developed (Patent Documents 1 and 2).
     [Patent Document 1] Japanese Unexamined Patent Application Publication No. 2014-164243   [Patent Document 2] Japanese Unexamined Patent Application Publication No. 2016-111398   

     SUMMARY OF THE INVENTION 
     A method according to the present disclosure is a method for manufacturing optical modulator, the optical modulator including a Mach-Zehnder modulator. The Mach-Zehnder modulator includes an electrode and an arm waveguide, the electrode being disposed on the arm waveguide. The method includes a step of preparing the Mach-Zehnder modulator, a step of acquiring, based on a light transmittance in the arm waveguide, a relationship between a voltage applied to the electrode and a phase change amount of light propagating through the arm waveguide, a step of acquiring, based on the relationship, a voltage in which a range of a phase change amount of light in the Mach-Zehnder modulator has a predetermined range, and a step of storing the voltage acquired in the step of acquiring the voltage in a storage unit. 
     A testing method according to the present disclosure is a method for testing an optical modulator. The optical modulator includes a Mach-Zehnder modulator, the Mach-Zehnder modulator including an electrode and arm waveguide, the electrode being disposed on the arm waveguide. The method includes a step of acquiring, based on a light transmittance in the arm waveguide, a relationship between a voltage applied to the electrode and a phase change amount of light propagating through the arm waveguide, and a step of acquiring, based on the relationship, a voltage in which a range of a phase change amount of light in the Mach-Zehnder modulator has a predetermined range. 
     A non-transitory storage medium according to the present disclosure is a non-transitory storage medium storing a program for testing an optical modulator. The optical modulator includes a Mach-Zehnder modulator. The Mach-Zehnder modulator includes an electrode and an arm waveguide, the electrode being disposed on the arm waveguide. The program causes a computer to execute a process of acquiring, based on a light transmittance in the arm waveguide, a relationship between a voltage applied to the electrode and a phase change amount of light propagating through the arm waveguide, and a process of acquiring, based on the relationship, a voltage in which a range of a phase change amount of light in the Mach-Zehnder modulator has a predetermined range. 
     A light transmission apparatus according to the present disclosure includes a plurality of Mach-Zehnder modulators, and a storage unit. The plurality of Mach-Zehnder modulators each include an electrode and an arm waveguide. The electrode is disposed on the arm waveguide. The storage unit stores, for each of the plurality of Mach-Zehnder modulators, a voltage in which a range of a phase change amount of light in the Mach-Zehnder modulator has a predetermined range. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a block diagram illustrating a light transmission apparatus according to a first embodiment. 
         FIG. 1B  is a block diagram illustrating a hardware configuration of a control unit. 
         FIG. 2A  is a plan view illustrating an optical modulator. 
         FIG. 2B  is a cross-sectional view taken along line A-A of  FIG. 2A . 
         FIG. 3  is a diagram illustrating a relationship between a differential voltage and a phase change amount in a sub Mach-Zehnder modulator. 
         FIG. 4A  is a diagram illustrating a relationship between a voltage and a phase change amount. 
         FIG. 4B  is a diagram illustrating a relationship between a voltage and a phase change amount. 
         FIG. 5A  is a diagram illustrating a relationship between a differential voltage and a phase change amount. 
         FIG. 5B  is a diagram illustrating a relationship between a differential voltage and a phase change amount. 
         FIG. 6A  is a diagram illustrating a relationship between a voltage and a change amount of light absorption loss. 
         FIG. 6B  is a diagram illustrating a relationship between a voltage and a change amount of light absorption loss. 
         FIG. 7A  is a diagram illustrating a relationship between a differential voltage and a phase change amount. 
         FIG. 7B  is a diagram illustrating a relationship between a differential voltage and a phase change amount. 
         FIG. 8  is a flowchart illustrating a method for manufacturing an optical modulator. 
         FIG. 9  is a flow chart illustrating a testing. 
         FIG. 10A  is a diagram illustrating a calculated phase change amount. 
         FIG. 10B  is a diagram illustrating a calculated change amount of absorption loss. 
         FIG. 11A  is a diagram illustrating calculated transmittances. 
         FIG. 11B  is a diagram illustrating a measured transmittance and a transmittance after optimization. 
         FIG. 12A  is a diagram illustrating a phase change amount after optimization. 
         FIG. 12B  is a diagram illustrating a change amount of absorption loss after optimization. 
         FIG. 13  is a diagram illustrating a relationship between a central voltage and a phase adjusting range. 
         FIG. 14  is a diagram illustrating a measured transmittance and a transmittance after optimization. 
         FIG. 15A  is a diagram illustrating a phase change amount after optimization. 
         FIG. 15B  is a diagram illustrating a change amount of absorption loss after optimization. 
         FIG. 16  is a diagram illustrating a relationship between a central voltage and a phase adjusting range. 
         FIG. 17  is a diagram illustrating a measured transmittance and a transmittance after optimization. 
         FIG. 18A  is a diagram illustrating a phase change amount after optimization. 
         FIG. 18B  is a diagram illustrating a change amount of absorption loss after optimization. 
         FIG. 19  is a diagram illustrating a relationship between a central voltage and a phase adjusting range. 
         FIG. 20A  is a diagram illustrating an amount of absorption loss. 
         FIG. 20B  is a diagram illustrating an extinction ratio. 
         FIG. 21A  is a diagram illustrating an amount of absorption loss. 
         FIG. 21B  is a diagram illustrating an extinction ratio. 
         FIG. 22A  is a diagram illustrating an amount of absorption loss. 
         FIG. 22B  is a diagram illustrating an extinction ratio. 
         FIG. 23A  is a diagram illustrating an amount of absorption loss. 
         FIG. 23B  is a diagram illustrating an extinction ratio. 
         FIG. 24A  is a diagram illustrating an amount of absorption loss. 
         FIG. 24B  is a diagram illustrating an extinction ratio. 
         FIG. 25A  is a diagram illustrating an amount of absorption loss. 
         FIG. 25B  is a diagram illustrating an extinction ratio. 
         FIG. 26  is a plan view illustrating an optical modulator. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Light propagates through an arm waveguide of the Mach-Zehnder modulator. A phase of light can be adjusted by applying a voltage to the Mach-Zehnder modulator. In order to adjust the phase to a desired magnitude, it is important to set a range of a phase change amount (phase adjusting range) by application of the voltage to a predetermined magnitude. 
     The magnitude of the phase change amount with respect to the voltage (phase adjusting efficiency) varies from Mach-Zehnder modulator to Mach-Zehnder modulator. When the same voltage is applied to a plurality of Mach-Zehnder modulators, the phase change amount in one Mach-Zehnder modulator is large and the phase change amount in another Mach-Zehnder modulator is small. Even in the Mach-Zehnder modulator having a small phase adjusting efficiency, the voltage may be increased in order to set the phase adjusting range to a predetermined magnitude. However, there is a positive correlation between the phase adjusting efficiency and the absorption loss of light. Increasing the voltage also increases the absorption loss of light. Therefore, it is an object of the present disclosure to provide a method for manufacturing optical modulator, a testing method, a non-transitory storage medium, and light transmission apparatus capable of suppressing an increase in light absorption loss. 
     First, contents of embodiments of the present disclosure will be listed and described. 
     An aspect of the present disclosure is (1) a method for manufacturing an optical modulator, the optical modulator including a Mach-Zehnder modulator. The Mach-Zehnder modulator includes an electrode and an arm waveguide, the electrode being disposed on the arm waveguide. The method includes a step of preparing the Mach-Zehnder modulator, a step of acquiring, based on a light transmittance in the arm waveguide, a relationship between a voltage applied to the electrode and a phase change amount of light propagating through the arm waveguide, a step of acquiring, based on the relationship, a voltage in which a range of a phase change amount of light in the Mach-Zehnder modulator has a predetermined range, and a step of storing the voltage acquired in the step of acquiring the voltage in a storage unit. By applying the acquired voltage to the Mach-Zehnder modulator, the range of the phase change amount can be set to a predetermined magnitude, and an increase in light absorption loss can be suppressed. 
     (2) The step of preparing the Mach-Zehnder modulator may be a step of preparing a plurality of the Mach-Zehnder modulators, and the step of acquiring the relationship between the voltage and the phase change amount and the step of acquiring the voltage may be performed on each of the plurality of Mach-Zehnder modulators. The voltage is optimized for each of the plurality of Mach-Zehnder modulators. By applying the optimized voltage to the Mach-Zehnder modulator, the range of the phase change amount can be set to a predetermined magnitude, and an increase in the absorption loss of light can be suppressed.
 
(3) The step of preparing the Mach-Zehnder modulator may include a step of preparing a main Mach-Zehnder modulator and a step of preparing a sub Mach-Zehnder modulator, and the step of acquiring the relationship between the voltage and the phase change amount and the step of acquiring the voltage may be performed on each of the main Mach-Zehnder modulator and the sub Mach-Zehnder modulator. The range of the phase change amount of the main Mach-Zehnder modulator and the sub Mach-Zehnder are set to a predetermined magnitude and an increase of the absorption loss of light can be suppressed.
 
(4) The step of preparing the Mach-Zehnder modulator may include a step of preparing the Mach-Zehnder modulator including a first arm waveguide, and a second arm waveguide, a first electrode, and a second electrode. The first electrode is disposed on the first arm waveguide, and the second electrode is disposed on the second arm waveguide. The step of acquiring the relationship between the voltage and the phase change amount may include a step of acquiring a relationship between a voltage applied to the first electrode and a phase change amount of light propagating through the first arm waveguide, and a step of acquiring a relationship between a voltage applied to the second electrode and a phase change amount of light propagating through the second arm waveguide. The range of the phase change amount of the light in the Mach-Zehnder modulator may be a range of a difference between the phase change amount of the light propagating through the first arm waveguide and the phase change amount of the light propagating through the second arm waveguide. The step of acquiring the voltage may be a step of acquiring a voltage applied to the first electrode and a voltage applied to the second electrode, in which the range of the phase change amount of the light in the Mach-Zehnder modulator the predetermined range. The range of the phase change amount is set to a predetermined magnitude, and the increase of the absorption loss of light can be suppressed.
 
(5) The voltage applied to the first electrode may be a sum of a first voltage and a second voltage, the voltage applied to the second electrode may be a difference between the first voltage and the second voltage, and the step of acquiring the voltage may be a step of acquiring the first voltage in which the range of the phase change amount of the light in the Mach-Zehnder modulator has the predetermined range. The Mach-Zehnder modulator is differentially driven by using the first voltage as a central voltage and the second voltage as a differential voltage. The range of the phase change amount is set to a predetermined magnitude, and the increase of the absorption loss of light can be suppressed.
 
(6) The method may further include a step of measuring a first transmittance which is a light transmittance in the arm waveguide, and a step of calculating a second transmittance which is a light transmittance in the arm waveguide. In the step of calculating the second transmittance, the second transmittance is represented by a function of the phase change amount of the light propagating through the arm waveguide, the phase change amount of the light propagating through the arm waveguide is represented by a function of the voltage applied to the electrode, and thus the second transmittance is calculated. In the step of acquiring the relationship between the voltage and the phase change amount, the second transmittance is adjusted such that the second transmittance approaches the first transmittance, and thus the relationship between the voltage and the phase change amount is acquired. By bringing the second transmittance closer to the first transmittance, a highly accurate relationship between the voltage and the phase change amount can be obtained. The range of the phase change amount is set to a predetermined magnitude, and the increase of the absorption loss of light can be suppressed.
 
(7) The step of preparing the Mach-Zehnder modulator may include a step of forming the Mach-Zehnder modulator, and the step of forming the Mach-Zehnder modulator may include a step of forming the arm waveguide including a first semiconductor layer, a core layer, and a second semiconductor layer. The first semiconductor layer, the core layer, and the second semiconductor layer are stacked in order. The first semiconductor layer may have a first conductivity type, and the second semiconductor layer may have a second conductivity type. Dopants are added to the first semiconductor layer and the second semiconductor layer. The phase adjusting efficiency of the Mach-Zehnder modulator varies due to the variation in the amount of thermal diffusion of the dopants. By applying the acquired voltage to the Mach-Zehnder modulator, the range of the phase change amount can be set to a predetermined magnitude, and an increase in light absorption loss can be suppressed.
 
(8) Another aspect of the present disclosure is a method for testing an optical modulator. The optical modulator includes a Mach-Zehnder modulator, the Mach-Zehnder modulator including an electrode and arm waveguide, the electrode being disposed on the arm waveguide. The method includes a step of acquiring, based on a light transmittance in the arm waveguide, a relationship between a voltage applied to the electrode and a phase change amount of light propagating through the arm waveguide, and a step of acquiring, based on the relationship, a voltage in which a range of a phase change amount of light in the Mach-Zehnder modulator has a predetermined range. By applying the acquired voltage to the Mach-Zehnder modulator, the range of the phase change amount can be set to a predetermined magnitude, and an increase in light absorption loss can be suppressed.
 
(9) Another aspect of the present disclosure is a non-transitory storage medium storing a program for testing an optical modulator. The optical modulator includes a Mach-Zehnder modulator. The Mach-Zehnder modulator includes an electrode and an arm waveguide, the electrode being disposed on the arm waveguide. The program causes a computer to execute a process of acquiring, based on a light transmittance in the arm waveguide, a relationship between a voltage applied to the electrode and a phase change amount of light propagating through the arm waveguide, and a process of acquiring, based on the relationship, a voltage in which a range of a phase change amount of light in the Mach-Zehnder modulator has a predetermined range. By applying the acquired voltage to the Mach-Zehnder modulator, the range of the phase change amount can be set to a predetermined magnitude, and an increase in light absorption loss can be suppressed.
 
(10) Another aspect of the present disclosure is a light transmission apparatus. The apparatus includes a plurality of Mach-Zehnder modulators, and a storage unit. The plurality of Mach-Zehnder modulators each include an electrode and an arm waveguide. The electrode is disposed on the arm waveguide. The storage unit stores, for each of the plurality of Mach-Zehnder modulators, a voltage in which a range of a phase change amount of light in the Mach-Zehnder modulator has a predetermined range. By applying the stored voltage to the Mach-Zehnder modulator, the range of the phase change amount can be set to a predetermined magnitude, and an increase in light absorption loss can be suppressed.
 
     DETAILED DESCRIPTION OF EMBODIMENTS OF THE DISCLOSURE 
     Specific examples of a method for manufacturing an optical modulator, a testing method, a non-transitory storage medium storing a testing program, and a light transmission apparatus according to embodiments of the present disclosure will be described below with reference to the drawings. Note that the present disclosure is not limited to these examples, but is defined by the scope of the claims, and is intended to include all modifications within the meaning and scope equivalent to the scope of the claims. 
     First Embodiment 
     (Light Transmission Apparatus) 
       FIG. 1A  is a block diagram illustrating a light transmission apparatus  100  according to a first embodiment. As illustrated in  FIG. 1A , light transmission apparatus  100  includes a control unit  10 , a wavelength tunable laser element  22 , an automatic bias control (ABC) circuit  24 , a driver integrated circuit (IC)  26 , and an optical modulator  40 . 
     Wavelength tunable laser element  22  is a light emitting element including, for example, a semiconductor laser element. ABC circuit  24  applies a voltage for phase adjustment to optical modulator  40  to perform an automatic bias control. Driver IC  26  inputs a modulation signal to optical modulator  40 . Optical modulator  40  modulates light incident from wavelength tunable laser element  22  and emits modulated light. Control unit  10  includes a computer such as a personal computer (PC). 
       FIG. 1B  is a block diagram illustrating a hardware configuration of control unit  10 . As illustrated in  FIG. 1B , control unit  10  includes a CPU (Central Processing Unit)  30 , a RAM (Random Access Memory)  32 , a storage device  34  (storage unit), and an interface  36 . CPU  30 , RAM  32 , storage device  34 , and interface  36  are connected to each other via a bus or the like. RAM  32  is a volatile memory that temporarily stores programs, data, and the like. Storage device  34  is, for example, a read only memory (ROM), a solid state drive (SSD) such as a flash memory, or a hard disk drive (HHD). Storage device  34  stores a program for executing processing described later, a voltage obtained in the processing, and the like. 
     When CPU  30  executes the program stored in RAM  32 , a phase control unit  12 , a laser control unit  14 , a calculation unit  15 , a modulation control unit  16 , and a storage control unit  18  illustrated in  FIG. 1A  are implemented in control unit  10 . Phase control unit  12  controls ABC circuit  24  to adjust the voltage applied to optical modulator  40  by ABC circuit  24 . Laser control unit  14  controls wavelength tunable laser element  22 . Calculation unit  15  calculates a transmittance, a phase change amount, a phase adjusting range, and the like as described later. Modulation control unit  16  controls driver IC  26 . Storage control unit  18  controls RAM  32  and storage device  34  illustrated in  FIG. 1B  to store data therein. Each unit of control unit  10  may be hardware such as a circuit. 
     (Modulator) 
       FIG. 2A  is a plan view illustrating an optical modulator  40   a . In the first embodiment, optical modulator  40   a  is used as optical modulator  40  illustrated in  FIG. 1A . Optical modulator  40   a  is an In-phase Quadrature (IQ) modulator, and includes a substrate  41 , two sub Mach-Zehnder modulators  42   a  and  42   b , and a main Mach-Zehnder modulator  44   a . Substrate  41  is an insulating substrate made of, for example, ceramic. A module including optical modulator  40   a  may be formed by providing substrate  41  with ABC circuit  24  and driver IC  26  of  FIG. 1A , and lenses and the like (not illustrated). 
     A semiconductor substrate  80  and two termination elements  78   a  and  78   b  are mounted on an upper surface of substrate  41 . Termination elements  78   a  and  78   b  include, for example, a termination resistor and a capacitor. Two sub Mach-Zehnder modulators  42   a  and  42   b , main Mach-Zehnder modulator  44   a , an input waveguide  50 , and an output waveguide  56  are formed on semiconductor substrate  80 . Semiconductor substrate  80  has four end surfaces  80   a ,  80   b ,  80   c  and  80   d . End surface  80   a  and end surface  80   b  face each other. End surface  80   c  and end surface  80   d  face each other. 
     A first end portion of input waveguide  50  is located on end surface  80   a  of the four end surfaces of semiconductor substrate  80 . A second end portion of input waveguide  50  is connected to a coupler  58 . A first end portion of output waveguide  56  is connected to a coupler  64 . A second end portion of output waveguide  56  is located on end surface  80   b  of the four end surfaces of semiconductor substrate  80 . Coupler  58  is a one input two output (1×2) multimode interference (MMI) coupler. Coupler  64  is a two input one output (2×1) MMI coupler. Two sub Mach-Zehnder modulators  42   a  and  42   b  are arranged in parallel between coupler  58  and coupler  64 . Main Mach-Zehnder modulator  44   a  is arranged between two sub Mach-Zehnder modulators  42   a  and  42   b  and coupler  64 . 
     (Sub Mach-Zehnder Modulator) 
     Sub Mach-Zehnder modulator  42   a  is, for example, a modulator for an In-phase channel (Ich). Sub Mach-Zehnder modulator  42   b  is, for example, a modulator for a Quadrature channel (Qch). Sub Mach-Zehnder modulator  42   a  includes arm waveguides  52   a ,  54   a  and  54   b , modulation electrodes  66   a  and  66   b , phase adjusting electrodes  68   a  and  68   b , and ground electrodes  66   c  and  68   c . Arm waveguide  54   a  is, for example, a p-side waveguide. Arm waveguide  54   b  is, for example, an n-side waveguide. 
     A first end portion of arm waveguide  52   a  is connected to a first output end of two output ends of coupler  58 . A second end portion of arm waveguide  52   a  is connected to an input end of a coupler  60   a . A first end portion of arm waveguide  54   a  (first arm waveguide) is connected to a first output end of two output ends of coupler  60   a . A second end portion of arm waveguide  54   a  is connected to a first input end of two input ends of a coupler  62   a . A first end portion of arm waveguide  54   b  (second arm waveguide) is connected to a second output end of the two output ends of coupler  60   a . A second end portion of arm waveguide  54   b  is connected to a second input end of the two input ends of coupler  62   a.    
     Arm waveguide  52   a  bends in the vicinity of coupler  58 . Arm waveguides  54   a  and  54   b  bend in the vicinity of coupler  60   a  and bend in the vicinity of coupler  62   a . Except for these bent portions, arm waveguides  52   a ,  54   a  and  54   b  are parallel to each other and parallel to end surface  80   c  of semiconductor substrate  80 . 
     Modulation electrode  66   a  and phase adjusting electrode  68   a  are disposed on arm waveguide  54   a . Modulation electrode  66   a  and phase adjusting electrode  68   a  (first electrode) are separated from each other and arranged in order from coupler  60   a  toward coupler  62   a . Modulation electrode  66   b  and phase adjusting electrode  68   b  are disposed on arm waveguide  54   b . Modulation electrode  66   b  and phase adjusting electrode  68   b  (second electrode) are separated from each other and arranged in order from coupler  60   a  toward coupler  62   a.    
     Modulation electrode  66   a  and modulation electrode  66   b  face each other in a direction intersecting the extending direction of arm waveguides  54   a  and  54   b . Ground electrode  66   c  is located between modulation electrode  66   a  and modulation electrode  66   b . Phase adjusting electrode  68   a  and phase adjusting electrode  68   b  face each other. Ground electrode  68   c  is located between phase adjusting electrode  68   a  and phase adjusting electrode  68   b . Modulation electrodes  66   a  and  66   b , phase adjusting electrodes  68   a  and  68   b , and ground electrodes  66   c  and  68   c  extend in the same direction as arm waveguides  54   a  and  54   b , and are parallel to end surface  80   c  of semiconductor substrate  80 . 
     Wiring lines  72   a  and  74   a  are electrically connected to modulation electrode  66   a . Wiring line  72   a  extends from a first end portion of modulation electrode  66   a  to end surface  80   a  of semiconductor substrate  80 . Wiring line  74   a  extends from a second end portion of modulation electrode  66   a  to end surface  80   c  of semiconductor substrate  80 . Wiring lines  72   b  and  74   b  are electrically connected to modulation electrode  66   b . Wiring line  72   b  extends from a first end portion of modulation electrode  66   b  to end surface  80   a . Wiring line  74   b  extends from a second end portion of modulation electrode  66   b  to end surface  80   c . Wiring lines  72   c  and  74   c  are electrically connected to ground electrode  66   c . Wiring line  72   c  extends from a first end portion of ground electrode  66   c  to end surface  80   a . Wiring line  74   c  extends from a second end portion of ground electrode  66   c  to end surface  80   c.    
     Modulation electrode  66   a  is electrically connected to driver IC  26  illustrated in  FIG. 1A  via wiring line  72   a . Modulation electrode  66   b  is electrically connected to driver IC  26  via wiring line  72   b . Ground electrode  66   c  is electrically connected to driver IC  26  via wiring line  72   c . Wiring lines  74   a ,  74   b  and  74   c  are electrically connected to termination element  78   a  by bonding wires. 
     A wiring line  75   a  is electrically connected to phase adjusting electrode  68   a . A wiring line  75   b  is electrically connected to phase adjusting electrode  68   b . A wiring line  75   c  is electrically connected to ground electrode  68   c . Wiring lines  75   a ,  75   b  and  75   c  extend to end surface  80   c . Phase adjusting electrode  68   a  is electrically connected to ABC circuit  24  via wiring line  75   a . Phase adjusting electrode  68   b  is electrically connected to ABC circuit  24  via wiring line  75   b . Ground electrode  68   c  is electrically connected to ABC circuit  24  via wiring line  75   c.    
     Sub Mach-Zehnder modulator  42   b  includes arm waveguides  52   b ,  54   c  and  54   d , modulation electrodes  66   d  and a  66   e , phase adjusting electrodes  68   d  and a  68   e , and ground electrodes  66   f  and  68   f . Arm waveguide  54   c  (first arm waveguide) is, for example, a p-side waveguide. Arm waveguide  54   d  (second arm waveguide) is, for example, an n-side waveguide. 
     A first end portion of arm waveguide  52   b  is connected to the second output end of coupler  58 . A second end portion of arm waveguide  52   b  is connected to the input end of a coupler  60   b . Arm waveguides  54   c  and  54   d  are connected to coupler  60   b  and a coupler  62   b . The lengths of arm waveguides of sub Mach-Zehnder modulator  42   b  are equal to the lengths of the corresponding arm waveguides of sub Mach-Zehnder modulator  42   a . The shapes of arm waveguides of sub Mach-Zehnder modulator  42   b  are the same as the shapes of the corresponding arm waveguides of sub Mach-Zehnder modulator  42   a.    
     A modulation electrode  66   d  and phase adjusting electrode  68   d  (first electrode) are provided on arm waveguide  54   c . A modulation electrode  66   e  and phase adjusting electrode  68   e  (second electrode) are provided on arm waveguide  54   d . Ground electrode  66   f  is provided between modulation electrode  66   d  and modulation electrode  66   e . Ground electrode  68   f  is provided between phase adjusting electrode  68   d  and phase adjusting electrode  68   e.    
     Wiring lines  72   d  and  74   d  are electrically connected to modulation electrode  66   d . Wiring lines  72   e  and  74   e  are electrically connected to modulation electrode  66   e . Wiring lines  72   f  and  74   f  are electrically connected to ground electrode  66   f  Wiring lines  72   d ,  72   e  and  72   f  extend to end surface  80   a  of semiconductor substrate  80 . Modulation electrode  66   d  is electrically connected to driver IC  26  via wiring line  72   d . Modulation electrode  66   e  is electrically connected to driver IC  26  via wiring line  72   e . Ground electrode  66   f  is electrically connected to driver IC  26  via wiring line  72   f  Wiring lines  74   d ,  74   e  and  74   f  extend to end surface  80   d  of semiconductor substrate  80  and are electrically connected to termination element  78   b.    
     A wiring line  75   d  is electrically connected to phase adjusting electrode  68   d . A wiring line  75   e  is electrically connected to phase adjusting electrode  68   e . A wiring line  75   f  is electrically connected to ground electrode  68   f  Wiring lines  75   d ,  75   e  and  75   f  extend to end surface  80   d . Phase adjusting electrode  68   d  is electrically connected to ABC circuit  24  via wiring line  75   d . Phase adjusting electrode  68   e  is electrically connected to ABC circuit  24  via wiring line  75   e . Ground electrode  68   f  is electrically connected to ABC circuit  24  via wiring line  75   f.    
     The lengths of modulation electrodes  66   a ,  66   b ,  66   d  and  66   e  and the lengths of ground electrodes  66   c  and  66   f  are equal to each other. The lengths of phase adjusting electrodes  68   a ,  68   b ,  68   d  and  68   e  are equal to each other and smaller than the lengths of modulation electrodes. The lengths of ground electrodes  68   c  and  68   f  are equal to each other and smaller than the lengths of phase adjusting electrodes. 
     (Main Mach-Zehnder Modulator) 
     Main Mach-Zehnder modulator  44   a  has arm waveguides  55   a  and  55   b , phase adjusting electrodes  70   a  and  70   b , and a ground electrode  70   c . A first end portion of arm waveguide  55   a  (first arm waveguide) is connected to an output end of coupler  62   a . A first end portion of arm waveguide  55   b  (second arm waveguide) is connected to an output end of coupler  62   b . A second end portion of each of arm waveguides  55   a  and  55   b  is connected to an input end of coupler  64 . Portions of arm waveguides  55   a  and  55   b  near sub Mach-Zehnder modulator are parallel to end surface  80   c  of semiconductor substrate  80 , and portions of arm waveguides  55   a  and  55   b  near coupler  64  are bent. 
     A phase adjusting electrode  70   a  (first electrode) is provided on arm waveguide  55   a . A phase adjusting electrode  70   b  (second electrode) is provided on arm waveguide  55   b . Ground electrode  70   c  is provided between arm waveguide  55   a  and arm waveguide  55   b . Phase adjusting electrodes  70   a  and  70   b  and ground electrode  70   c  extend in the same direction as the arm waveguides and are parallel to end surface  80   c.    
     A wiring line  76   a  is electrically connected to an end portion of phase adjusting electrode  70   a  and extends to end surface  80   c . A wiring line  76   b  is electrically connected to an end portion of phase adjusting electrode  70   b  and extends to end surface  80   d . A wiring line  76   c  is electrically connected to an end portion of ground electrode  70   c  and extends to end surface  80   c . Phase adjusting electrode  70   a  is electrically connected to ABC circuit  24  via wiring line  76   a . Phase adjusting electrode  70   b  is electrically connected to ABC circuit  24  via wiring line  76   b . Ground electrode  70   c  is electrically connected to ABC circuit  24  via wiring line  76   c.    
       FIG. 2B  is a cross-sectional view taken along line A-A of  FIG. 2A  illustrating a cross section of sub Mach-Zehnder modulator  42   a . Sub Mach-Zehnder modulator  42   b  and main Mach-Zehnder modulator  44   a  also have the same configuration as sub Mach-Zehnder modulator  42   a.    
     As illustrated in  FIG. 2B , a cladding layer  82  (first semiconductor layer) is provided on an upper surface of semiconductor substrate  80 . Cladding layer  82  protrudes to the opposite side (upper side in the drawing) of semiconductor substrate  80  at two positions. Core layer  84 , a cladding layer  86 , and a contact layer  88  are sequentially stacked on the protruding portion. Cladding layer  82 , core layer  84 , cladding layer  86 , and contact layer  88  form mesa-shaped arm waveguides  54   a  and  54   b . Cladding layer  86  and contact layer  88  correspond to the second semiconductor layer. 
     Semiconductor substrate  80  is formed of, for example, semi-insulating indium phosphide (InP). Cladding layer  82  is formed of, for example, n-type InP (n-InP) having a thickness of 800 nm. Cladding layer  86  is formed of, for example, p-InP having a 1300 nm. Contact layer  88  is formed of, for example, p-InGaAs having a thickness of 200 nm. The n-type cladding layer  82  is doped with, for example, silicon (Si). The p-type cladding layer  86  and contact layer  88  are doped with, for example, zinc (Zn). 
     Core layer  84  has, for example, a multiple quantum well (MQW) structure. Core layer  84  includes a plurality of well layers and barrier layers alternately stacked. The well layer is formed of, for example, aluminum gallium indium arsenide (AlGaInAs). The barrier layer is formed of, for example, aluminum indium arsenide (AlInAs). Core layer  84  is, for example, a thickness of 500 nm. 
     The upper surface of semiconductor substrate  80 , surfaces of cladding layer  82 , and side surfaces and upper surfaces of arm waveguides  54   a  and  54   b  are covered with an insulating film  81 . Insulating film  81  is formed of an insulator such as silicon oxide (SiO 2 ). A resin layer  85  is formed of, for example, benzocyclobutene (BCB) and covers a surface of insulating film  81 . Insulating film  81  and resin layer  85  have openings in a portion of an upper surface of cladding layer  82  between arm waveguides  54   a  and  54   b , and on arm waveguides  54   a  and  54   b.    
     Modulation electrode  66   a  is provided on arm waveguide  54   a . Modulation electrode  66   b  is provided on arm waveguide  54   b . Modulation electrodes  66   a  and  66   b  are electrically connected to contact layer  88  exposed from the openings of insulating film  81  and resin layer  85 . Ground electrode  66   c  is disposed on cladding layer  82  and electrically connected to cladding layer  82  exposed from insulating film  81  and resin layer  85 . Phase adjusting electrodes  68   a  and  68   b  illustrated in  FIG. 2A  are also provided on an upper surface of contact layer  88 . A ground electrode  68   c  is also provided on the upper surface of cladding layer  82 . 
     Modulation electrode and phase adjusting electrode each have an ohmic electrode layer and wiring line layer. The ohmic electrode layer includes, for example, a platinum (Pt) layer, a titanium (Ti) layer, a platinum (Pt) layer, and a gold (Au) layer. These layers are laminated in order on contact layer  88 . Wiring line layer is formed of, for example, Au or the like in contact with an upper surface of the ohmic electrode layer. Ground electrode has, for example, an alloy layer and an Au layer. The alloy layer is formed of, for example, an alloy of Au, germanium (Ge), and nickel (Ni). The Au layer is in contact with an upper surface of the alloy layer. Wiring line illustrated in  FIG. 2A  is provided on resin layer  85  illustrated in  FIG. 2B  and is made of a metal such as Au. 
     (Operation of Light Transmission Apparatus) 
     Next, the operation of light transmission apparatus  100  will be described. Laser control unit  14  of control unit  10  illustrated in  FIG. 1A  causes wavelength tunable laser element  22  to emit light. Light incident on input waveguide  50  of optical modulator  40   a  illustrated in  FIG. 2A  is branched at coupler  58  and propagates through arm waveguides  52   a  and  52   b . The light propagating in arm waveguide  52   a  is branched in coupler  60   a  and propagates through arm waveguides  54   a  and  54   b . The light propagating in arm waveguide  52   b  is branched in coupler  60   b  and propagates through arm waveguides  54   c  and  54   d.    
     Modulation control unit  16  of control unit  10  illustrated in  FIG. 1A  generates a modulation signal based on transmission data and inputs the modulation signal to driver IC  26 . Modulation signals are input from driver IC  26  to modulation electrodes  66   a  and  66   b  of sub Mach-Zehnder modulator  42   a . Modulation signals are input from driver IC  26  to modulation electrodes  66   d  and  66   e  of sub Mach-Zehnder modulator  42   b . The refractive indices of the arm waveguides change by inputting the modulation signals, thereby the lights are modulated. 
     The modulated light propagating in arm waveguide  54   a  and the modulated light propagating in arm waveguide  54   b  are multiplexed in coupler  62   a . The modulated light after multiplexing propagates through arm waveguide  55   a  of main Mach-Zehnder modulator  44   a . The modulated light propagating in arm waveguide  54   c  and the modulated light propagating in arm waveguide  54   d  are multiplexed in coupler  62   b . The modulated light after multiplexing propagates through arm waveguide  55   b  of main Mach-Zehnder modulator  44   a . The light propagating through arm waveguide  55   a  and the light propagating through arm waveguide  55   b  are multiplexed by coupler  64  and propagate through output waveguide  56 . The modulated light is emitted from output waveguide  56  to the outside of optical modulator  40   a.    
     Phase control unit  12  of control unit  10  performs automatic bias control using ABC circuit  24  to adjust the phase of light. When ABC circuit  24  applies a voltage to phase adjusting electrode, the refractive index of arm waveguide changes and the optical path length changes. The change of the optical path length changes the phase of light propagating through arm waveguide. Phase control unit  12  can independently control the phase of light in main Mach-Zehnder modulator  44   a  and the phase of light in each of sub Mach-Zehnder modulators  42   a  and  42   b.    
     In a state where a modulation signal is not input to sub Mach-Zehnder modulator  42   a , a phase shift between light propagating through arm waveguide  54   a  and light propagating through arm waveguide  54   b  is π (rad) or π±27π×n (n is a negative or positive integer). That is, sub Mach-Zehnder modulator  42   a  is adjusted to an extinction point. Sub Mach-Zehnder modulator  42   b  is also adjusted to the extinction point. The state adjusted to the extinction point is an operating point of sub Mach-Zehnder modulator. 
     The phase shift between the modulated light propagating in arm waveguide  55   a  of main Mach-Zehnder modulator  44   a  and the modulated light propagating in arm waveguide  55   b  of main Mach-Zehnder modulator  44   a  is 0.57π (rad) or a value equivalent to 0.57π. Values equivalent to 0.57π are 0.57π±2π×n and 1.57π±2π×n (n is a negative or positive integer). The modulated light propagating in arm waveguide  55   a  and the modulated light propagating in arm waveguide  55   b  are orthogonal to each other. 
     A phase shift ϕ between two arm waveguides that form a pair such as arm waveguide  52   a  and arm waveguide  52   b  is expressed as the sum of an initial phase shift φ0 and a phase change amount Δφ as illustrated in the following equation. 
       ϕ=ϕ0+Δϕ  [Equation 1]
 
     The initial phase shift ϕ0 is determined by an optical path length difference between the arm waveguides of optical modulator  40   a . A wavelength λ of light in the arm waveguide is, for example, 484 nm (1550 nm in vacuum). Each length of arm waveguides  54   a ,  54   b ,  54   c  and  54   d  of sub Mach-Zehnder modulators are, for example, 6 mm, which is 10,000 times or more of the wavelength λ. The optical path length of arm waveguide varies due to a manufacturing error or the like. A relationship between an optical path length difference ΔP between the two arm waveguides and the initial phase shift φ0 of light between the two arm waveguides is expressed by the following expression using an integer m. 
       ϕ0+2 mπ= 2π×Δ P/λ   [Equation 2]
 
     The optical path length difference ΔP between two arm waveguides paired with each other such as arm waveguide  52   a  and arm waveguide  52   b  may be 1/10,000 or more of the designed dimension. In this case, the optical path length difference ΔP is equal to or greater than the light wavelength λ. The initial phase shift ϕ0 is distributed in a range of 0 (rad) or more and 2 π (rad) or less. 
     The initial phase shift ϕ0 may also change during operation of light transmission apparatus  100 . This is because the optical path length of the arm waveguide changes due to physical stresses applied to the optical modulator  40   a  and temperature changes. A change amount of the initial phase shift φ0 during operation ranges from −2π to 2π, for example. 
     The phase change amount Δφ is the phase change amount of light propagating through the arm waveguide. The phase change amount Δφ is adjusted by applying a voltage from ABC circuit  24  to the phase adjusting electrode and changing the optical path length of the arm waveguide. In response to the initial phase shift φ0, phase control unit  12  changes the voltage applied from ABC circuit  24  to the phase adjusting electrode (automatic bias control). The phase change amount in the automatic bias control is determined in consideration of the initial phase shift and the phase change during operation. 
     When the voltage applied to phase adjusting electrode is swept, a range in which the phase change amount is changed is defined as a phase adjusting range. In order to adjust the operating points of sub Mach-Zehnder modulators  42   a  and  42   b  to the extinction points, the phase adjusting range of each of sub Mach-Zehnder modulators  42   a  and  42   b  is preferably, for example, a range of 6π from −3π to 3π. In order to make the phases of the two modulated lights in main Mach-Zehnder modulator  44   a  orthogonal to each other, the phase adjusting range of main Mach-Zehnder modulator  44   a  is preferably, for example, a range of 5π from −2.5π to 2.5π. 
     (Voltage) 
     The voltage applied to sub Mach-Zehnder modulator  42   a  by ABC circuit  24  will be described. A voltage Vp applied to phase adjusting electrode  68   a  on arm waveguide  54   a  is expressed as follows using a central voltage Vcc (first voltage) and a differential voltage Vdc (second voltage). 
         Vp=Vcc+Vdc   [Equation 3]
 
     A voltage Vn applied to phase adjusting electrode  68   b  on arm waveguide  54   b  is expressed by the following equation. 
         Vn=Vcc−Vdc   [Equation 4]
 
     The difference between the voltage Vp and the voltage Vn is 2Vdc. Phase control unit  12  fixes the central voltage Vcc to a fixed value and changes the differential voltage Vdc, thereby changing the voltages Vp and Vn so that the operating point of sub Mach-Zehnder modulator  42   a  is adjusted. The voltage Vp is applied to phase adjusting electrode  68   d  of sub Mach-Zehnder modulator  42   b , and the voltage Vn is applied to phase adjusting electrode  68   e.    
     The voltage applied to main Mach-Zehnder modulator  44   a  by ABC circuit  24  will be described. A voltage VI applied to phase adjusting electrode  70   a  on arm waveguide  55   a  is expressed as follows using a central voltage Vcp (first voltage) and a differential voltage Vdp (second voltage). 
         VI=Vcp+Vdp   [Equation 5]
 
     A voltage VQ applied to phase adjusting electrode  55   b  on arm waveguide  70   b  is expressed by the following equation. 
         VQ=Vcp−Vdp   [Equation 6]
 
     The difference between the voltage VI and the voltage VQ is 2 Vdp. Phase control unit  12  fixes the central voltage Vcp to a fixed value and changes the differential voltage Vdp, thereby changing the voltages VI and VQ so that the operating point of main Mach-Zehnder modulator  44   a  is adjusted. 
     The magnitude of the voltage will be described by taking the voltages Vp and Vn of the sub Mach-Zehnder modulator as an example. The minimum values of the voltages Vp and Vn are defined as Vmin, and the maximum values thereof are defined as Vmax. The wider the adjusting range of the differential voltage Vdc, the wider the phase adjusting range. In order to widen the adjusting range of the differential voltage Vdc, the central voltage Vcc and the differential voltage Vdc are defined as follows, for example. 
         Vcc =( V  min+ V  max)/2 
     Adjusting range of Vdc: range of Vmax−Vmin, from −(Vmax−Vmin)/2 to (Vmax−Vmin)/2. The minimum value Vmin and the maximum value Vmax are determined according to, for example, the power consumption and the breakdown voltage of optical modulator  40 . In the case of Vmin=0 V and Vmax=20 V, Vcc is equal to 10 V. The range of the differential voltage Vdc is from −10 V to 10 V (−Vcc≤Vdc≤Vcc). The voltages applied to sub Mach-Zehnder modulator  42   b  and main Mach-Zehnder modulator  44   a  can be set in the same manner as described above. 
       FIG. 3  is a diagram illustrating a relationship between a differential voltage and a phase change amount Δφ in sub Mach-Zehnder modulator  42   a . The horizontal axis represents the differential voltage Vdc, and the vertical axis represents the phase change amount Δφ. The dashed line represents the phase change amount in arm waveguide  54   a . The dotted line represents the phase change amount in arm waveguide  54   b . The solid line represents the phase change amount of sub Mach-Zehnder modulator  42   a . The phase change amount in sub Mach-Zehnder modulator  42   a  is a phase shift between the arm waveguides (phase change amount in arm waveguide  54   a  minus phase change amount in arm waveguide  54   b ). The central voltage Vcc is 10 V and the differential voltage Vdc ranges from −10 V to 10 V. 
     As illustrated in  FIG. 3 , as the differential voltage Vdc increases to the positive side, the phase change amount in arm waveguide  54   a  increases to the positive side. The phase change amount in arm waveguide  54   b  approaches 0. The phase change amount (phase shift) indicated by the solid line increases to the positive side. As the differential voltage Vdc increases to the negative side, the phase change amount in arm waveguide  54   b  increases to the positive side, the phase change amount in arm waveguide  54   a  approaches 0, and the phase shift increases to the negative side. When the differential voltage Vdc ranges from −10 V to 10 V, the phase shift ranges from approximately −9π to 9π. 
     In the case of  FIG. 3 , the range of the phase change amount Δφ (phase adjusting range) of sub Mach-Zehnder modulator  42   a  is approximately in the range of −9π to 9π, and exceeds the phase adjusting range 6π required for sub Mach-Zehnder modulator which is from −3π to 3π. In order to reduce the power consumption and set the phase adjusting range to a predetermined magnitude, the central voltage Vc is set to a value lower than 10 V, for example, 7 V. The differential voltage Vdc may range from −7 V to 7 V. 
     In each Mach-Zehnder modulator, variation may occur in the phase adjusting efficiency which represents the rate of change of the phase with respect to the voltage. The difference in the phase adjusting efficiency is believed to be due to variations in the amount of thermal diffusion of dopants doped in cladding layers  82  and  86 , and in contact layer  88 . The difference in the amount of thermal diffusion of the dopant causes a difference in the intensity of an electric field generated in core layer  84  when a voltage is applied. When there is a difference in the intensity of the electric field, there is also a difference in refractive index, and the phase change amount also has a different magnitude. Since the band gap energy also varies due to the variation in the thermal diffusion amount of the dopant, the phase change amount also changes. 
     Variations in the phase adjusting efficiency may occur between sub Mach-Zehnder modulator  42   a  and sub Mach-Zehnder modulator  42   b  within one optical modulator  40   a . In addition, variations in the phase adjusting efficiency may occur among the plurality of optical modulators  40   a.    
     Take two optical modulators  40   a - 1  and  40   a - 2  as an example. Each of optical modulators  40   a - 1  and  40   a - 2  has the configuration illustrated in  FIG. 2A . First, the phase adjusting efficiency between the sub Mach-Zehnder modulators will be described.  FIG. 4A  and  FIG. 4B  are diagrams illustrating relationships between voltages and phase change amounts. The horizontal axes represent voltages (Vp and Vn) applied to phase adjusting electrodes of sub Mach-Zehnder modulators. The vertical axes represent the phase change amount in the arm waveguides. 
       FIG. 4A  illustrates relationships between voltages and phase change amounts in the arm waveguides of sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 1 . The solid line represents the phase change amount of arm waveguide  54   a  which is the arm waveguide of the p-side. The dotted line represents the phase change amount of arm waveguide  54   b  which is the arm waveguide of the n-side.  FIG. 4B  illustrates relationships between voltages and phase change amounts in the arm waveguides of sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1 . The solid line represents the phase change amount of arm waveguide  54   c  on the p-side. The dotted line represents the phase change amount of arm waveguide  54   d  on the n-side. Due to the difference in the phase adjusting efficiency, the phase change amount of the arm waveguide on the p-side is slightly different from the phase change amount of the arm waveguide on the n-side in each of  FIG. 4A  and  FIG. 4B . The difference in the phase change amount between the sub Mach-Zehnder modulators is larger than the difference in the difference in the phase change amount between the arm waveguides. 
     When the same voltage is applied in  FIG. 4A  and  FIG. 4B , the phase change amount Δφ in  FIG. 4A  is small and the phase change amount Δφ in  FIG. 4B  is large. For example, at the voltage of 10 V, the phase change amounts Δφ of the two arm waveguides  54   a  and  54   b  in  FIG. 4A  are about 1.5π. At the voltage of 10 V, the phase change amounts Δφ of the two arm waveguides  54   c  and  54   d  in  FIG. 4B  are about 2.5π. The phase adjusting efficiency of sub Mach-Zehnder modulator  42   b  illustrated in  FIG. 4B  is higher than the phase adjusting efficiency of sub Mach-Zehnder modulator  42   a  illustrated in  FIG. 4A . As described above, in the same optical modulator  40   a - 1 , the phase adjusting efficiencies vary due to a variation in thermal diffusions of dopants. 
       FIG. 5A  and  FIG. 5B  are diagrams illustrating relationships between differential voltages and phase change amounts. The horizontal axes represent the differential voltages Vdc. The vertical axes represent phase change amounts Δφ. The central voltage Vcc is 7 V. 
       FIG. 5A  illustrates the phase change amount in sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 1 . The dashed line represents the phase change amount of arm waveguide  54   a  on the p-side. The dotted line represents the phase change amount of arm waveguide  54   b  on the n-side. The solid line indicates the phase change amount (phase shift between arm waveguides) in sub Mach-Zehnder modulator  42   a . Since sub Mach-Zehnder modulator  42   a  is differentially driven, the phase change amount is symmetrical with respect to Vdc=0. When the differential voltage Vdc is swept from −7 V to 7 V, the phase change amount is −3 π or more and 3 π or less. 
       FIG. 5B  illustrates the phase change amount in sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1 . The dashed line represents the phase change amount of arm waveguide  54   c  on the p-side. The dotted line represents the phase change amount of arm waveguide  54   d  on the n-side. The solid line represents the phase change amount in sub Mach-Zehnder modulator  42   b . The phase adjusting efficiency of sub Mach-Zehnder modulator  42   b  is higher than that of sub Mach-Zehnder modulator  42   a . Therefore, the phase change amount in  FIG. 5B  is larger than that in  FIG. 5A , and is equal to or larger than −4 π and equal to or smaller than 4πE. 
     Even in sub Mach-Zehnder modulator  42   a  having a small phase adjusting efficiency, in order to set the range of the phase change amount (phase adjusting range) to a predetermined magnitude of −3 π or more and 3 π or less, as illustrated in  FIG. 5A , the central voltage may be set to Vcc=7 V and the differential voltage Vdc may be set to a range from −7 V to 7 V. However, as illustrated in  FIG. 5B , the phase adjusting range of sub Mach-Zehnder modulator  42   b  having a large phase adjusting efficiency becomes 8π from −4π to 4π, which exceeds the predetermined range of 6ϕ. The absorption loss of light increases. 
     There is a positive correlation between the phase adjusting efficiency and the absorption loss of light in the arm waveguide. This is because a Kramers-Kronig relationship is applicable between the change in the refractive index of arm waveguide and the amount of light absorption. The smaller the phase adjusting efficiency, the smaller the absorption loss. The greater the phase adjusting efficiency, the greater the absorption loss. 
       FIG. 6A  and  FIG. 6B  are diagrams illustrating relationships between voltages and change amounts of absorption losses of light. The horizontal axes represent voltages (Vp and Vn) applied to phase adjusting electrodes of the sub Mach-Zehnder modulators. The vertical axes represent change amounts of absorption losses of light. 
       FIG. 6A  illustrates the change amounts of absorption losses in the arm waveguides of sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 1 . The solid line represents the change amount of absorption loss of arm waveguide  54   a  on the p-side. The dotted line represents the change amount of absorption loss of arm waveguide  54   b  on the n-side. 
       FIG. 6B  illustrates the change amounts of absorption losses in the arm waveguides of sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1 . The solid line represents the change amount of absorption loss of arm waveguide  54   c  on the p-side. The dotted line represents the change amount of absorption loss of arm waveguide  54   d  on the n-side. 
     When the same voltage is applied in  FIG. 6A  and  FIG. 6B , the change amount of absorption loss in  FIG. 6A  is small and the change amount of absorption loss in  FIG. 6B  is large. For example, when the voltage is 15 V, the change amount of absorption loss in  FIG. 6A  is less than 1 dB, while the change amount of absorption loss in  FIG. 6B  exceeds 3 dB. The absorption loss increases non-linearly with respect to the voltage, and increases greatly as the voltage increases. 
     In both sub Mach-Zehnder modulator  42   b  having the large phase adjusting efficiency and sub Mach-Zehnder modulator  42   a  having the small phase adjusting efficiency, the phase adjusting range is set to a predetermined magnitude of, for example, 6π ranging from −3π to 3π. For this purpose, for both sub Mach-Zehnder modulators  42   a  and  42   b , the central voltage Vcc may be set to 7 V and the differential voltage Vdc may be set to a range from −7 V to 7 V. However, as illustrated in  FIG. 5B , the phase adjusting range of sub Mach-Zehnder modulator  42   b  exceeds the predetermined range of 6π. The change amount of absorption loss of sub Mach-Zehnder modulator  42   b  illustrated in  FIG. 6B  is larger than that of sub Mach-Zehnder modulator  42   a . That is, if the voltage is determined in accordance with sub Mach-Zehnder modulator  42   a  having the small phase adjusting efficiency, the phase adjusting range becomes excessive and the absorption loss increases in sub Mach-Zehnder modulator  42   b  having the large phase adjusting efficiency. The insertion loss of light increases, and the extinction ratio decreases as described later. 
     In  FIG. 4A  to  FIG. 6B , two sub Mach-Zehnder modulators  42   a  and sub Mach-Zehnder modulator  42   b  in one optical modulator  40   a - 1  have been described. The plurality of optical modulators also have different phase adjusting efficiencies. 
     Optical modulator  40   a - 2  is another optical modulator different from optical modulator  40   a - 1 . It is assumed that sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 2  has almost the same phase adjusting efficiency and absorption loss as sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 1  (see  FIG. 4A ,  FIG. 5A , and  FIG. 6A ). It is assumed that sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 2  has almost the same phase adjusting efficiency and absorption loss as sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1  (see  FIG. 4B ,  FIG. 5B , and  FIG. 6B ). Main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  has higher phase adjusting efficiency and larger absorption loss compared to main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1 . 
       FIG. 7A  and  FIG. 7B  are diagrams illustrating relationships between differential voltages and phase change amounts. The horizontal axes represent the differential voltages Vdp. The vertical axes represent phase change amount Δφ. The central voltage Vcp is 7.4 V. 
       FIG. 7A  illustrates the phase change amount in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1 . The dashed line represents the phase change amount of arm waveguide  55   a  on the Ich side. The dotted line represents the phase change amount of arm waveguide  55   b  on the Qch side. The solid line represents the phase change amount in main Mach-Zehnder modulator  44   a  (phase change amount of arm waveguide  55   a  minus phase change amount of arm waveguide  55   b ). When the differential voltage Vdc ranges from −7 V to 7.4 V, the phase change amount ranges from −2.5π to 2.5π. 
       FIG. 7B  illustrates the phase change amount in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2 . The phase adjusting efficiency of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  is higher than that of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1 . In case the differential voltage Vdc ranges from −5.5 V to 5.1 V, the phase change amount ranges from −2.5π to 2.5π. The phase change amount in  FIG. 7G  is larger than that in  FIG. 7A . For example, if Vdp is equal to 4 V, the phase change amount in  FIG. 7A  is approximately π, while the phase change amount in  FIG. 7B  is approximately 2π. 
     As described above, there is a positive correlation between the phase adjusting efficiency and the absorption loss of light in the arm waveguide. Compared with main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1 , main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  has high phase adjusting efficiency and large absorption loss. If the voltage is determined in accordance with main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1  having the small phase adjusting efficiency, the phase adjusting range becomes larger than the predetermined range (5π) and the absorption loss increases in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  having the large phase adjusting efficiency. 
     In the single optical modulator  40   a - 1 , there is a difference in phase adjusting efficiency between the sub Mach-Zehnder modulators. There is also a difference in phase adjusting efficiency between optical modulator  40   a - 1  and optical modulator  40   a - 2 . In order to set the phase change amount to a predetermined value and suppress an increase in light absorption loss, it is preferable to optimize the voltage applied to phase adjusting electrode for each Mach-Zehnder modulator. 
     (Manufacturing Method) 
       FIG. 8  is a flow chart illustrating a method for manufacturing optical modulator  40   a , including the step of optimizing the voltage. As illustrated in  FIG. 8 , a Mach-Zehnder modulator is formed (steps S 1  to S 3 ). A cladding layer  82 , a core layer  84 , a cladding layer  86 , and a contact layer  88  are epitaxially grown on an upper surface of a wafer (semiconductor substrate  80 ) by a metal organic chemical vapor deposition (MOCVD) method or the like. The n-type cladding layer  82 , the p-type cladding layer  86 , and contact layer  88  are formed by adding a dopant to the source gas (step S 1 ). When the amount of thermal diffusion of the dopant varies, the phase adjusting efficiency also varies as illustrated in  FIG. 4A  and  FIG. 4B , and  FIG. 7A  and  FIG. 7B . 
     A mesa-shaped arm waveguide as illustrated in  FIG. 2B  is formed by dry etching or the like (step S 2 ). Insulating film  81  and resin layer  85  are formed. Openings are formed in insulating film  81  and resin layer  85  by dry etching or the like. Electrodes (modulation electrode, phase adjusting electrode and ground electrode) are formed by vacuum evaporation or the like (step S 3 ). Sub Mach-Zehnder modulators  42   a  and  42   b  and main Mach-Zehnder modulator  44   a  are formed on semiconductor substrate  80 . The wafer is diced to form a plurality of optical modulators  40   a.    
     Each of the plurality of optical modulators  40   a  is disposed on substrate  41 , and is electrically connected to ABC circuit  24  and driver IC  26 . Testing is performed for each optical modulator  40   a . Specifically, sub Mach-Zehnder modulator  42   a  is tested and the voltages applied to phase adjusting electrodes  68   a  and  68   b  are optimized (step S 4 ). Testing of sub Mach-Zehnder modulator  42   b  is performed, and the voltages applied to phase adjusting electrodes  68   d  and  68   e  are optimized (step S 5 ). Main Mach-Zehnder modulator  44   a  is tested to optimize the voltages applied to phase adjusting electrodes  70   a  and  70   b  (step S 6 ). Optical modulator  40   a  is formed by the above steps. 
     (Testing) 
       FIG. 9  is a flow chart illustrating the testing. Each of steps S 4 , S 5  and S 6  in  FIG. 8  is a step of performing the testing illustrated in  FIG. 9 . 
     First, testing of optical modulator  40   a - 1  among the plurality of optical modulators  40   a  will be described. In optical modulator  40   a - 1 , the testing of sub Mach-Zehnder modulator  42   a , the testing of sub Mach-Zehnder modulator  42   b , and the testing of main Mach-Zehnder modulator  44   a  are sequentially performed. 
     In the testing of sub Mach-Zehnder modulator  42   a  (step S 4  in  FIG. 8 ), phase control unit  12  of control unit  10  applies a voltage to phase adjusting electrode  68   b  of sub Mach-Zehnder modulator  42   b  to adjust the operating point of sub Mach-Zehnder modulator  42   b  to the extinction point. Laser control unit  14  of control unit  10  drives wavelength tunable laser element  22  and causes light to enter optical modulator  40   a - 1  from wavelength tunable laser element  22 . A light receiving element (not illustrated) receives light emitted from sub Mach-Zehnder modulator  42   a . Control unit  10  measures the light transmittance in the arm waveguide by comparing the intensity of the incident light with the intensity of the emitted light. 
     Control unit  10  measures the light transmittance (first transmittance) in arm waveguide  54   a  of sub Mach-Zehnder modulator  42   a  while sweeping the voltage applied from ABC circuit  24  to phase adjusting electrode  68   a  of sub Mach-Zehnder modulator  42   a . Control unit  10  measures the light transmittance (first transmittance) in arm waveguide  54   b  of sub Mach-Zehnder modulator  42   a  while sweeping the voltage applied from ABC circuit  24  to phase adjusting electrode  68   b  (step S 10  in  FIG. 9 ). Calculation unit  15  of control unit  10  calculates the light transmittance (second transmittance) in arm waveguide  54   a  and the light transmittance (second transmittance) in arm waveguide  54   b  (step S 12 ). 
     Calculation unit  15  performs optimization of the transmittance so that the transmittance calculated in step S 12  approaches the transmittance measured in step S 10  (step S 14 ). Based on the optimization of the transmittance, calculation unit  15  acquires a relationship between the voltage applied to the phase adjusting electrode and the phase change amount in the arm waveguide (step S 16 ). Storage control unit  18  acquires, based on the relationship between the voltage and the phase change amount, a voltage in which the phase adjusting range of sub Mach-Zehnder modulator  42   a  has a predetermined magnitude, and then storage control unit  18  stores the voltage in, for example, storage device  34  (step S 18 ). 
     Testing will be specifically described. Calculation unit  15  calculates the transmittance T as a function of the change amount ΔL 1  of absorption loss, the initial phase shift ϕ0, and the phase change amount Δφ. Calculation unit  15  calculates the phase change amount Δφ in one arm waveguide as a function of the voltage V applied to the phase adjusting electrode as expressed in the following equation. 
       Δϕ= k 1× V+k 2× V   2   +k 3× V   3   +k 4× V   4   +k 5× V   5   +k 6× V   6   [Equation 7]
 
     An example of the initial values of the coefficients is illustrated below. 
         k 1=3×10 −1 (π/ V ), k 2=3×10 −2 (π/ V   2 ), k 3=3×10 −3 (π/ V   3 ), k 4=1×10 −4 (π  V   4 ),
 
         k 5=1×10 −6 (π/ V   5 ), and  k 6=1×10 −8 (π/ V   6 )
 
       FIG. 10A  is a diagram illustrating a calculated phase change amount. 
     The horizontal axis represents the voltage applied to phase adjusting electrodes  68   a  and  68   b  of sub Mach-Zehnder modulator  42   a . The vertical axis represents the phase change amount Δφ. The solid line represents the phase change amount of arm waveguide (arm waveguide  54   a ) on the p-side and the phase change amount of arm waveguide (arm waveguide  54   b ) on the n-side. Since calculation unit  15  performs calculation using the same function (equation 7) and the same coefficient (initial value) for arm waveguides  54   a  and  54   b , the phase change amount Δφ is also equal between arm waveguides. 
     Calculation unit  15  calculates the change amount ΔL 1  of the absorption loss of light in the arm waveguide as a function of the voltage V applied to the phase adjusting electrode as in the following equation. 
       Δ L 1= a 1×(1−exp(− V/a 2))  [Equation 8]
 
     The initial values of the coefficients a1 and a2 are illustrated below. 
         a 1=1×10 −3  (dB), a 2=2 ( V ).
 
       FIG. 10B  is a diagram illustrating a calculated change amount of absorption loss. The horizontal axis represents the voltage applied to phase adjusting electrodes  68   a  and  68   b  of sub Mach-Zehnder modulator  42   a . The vertical axis represents the change amount ΔL 1  of absorption loss. Since the calculation is performed using the same function (Equation 8) and the same coefficient for arm waveguides  54   a  and  54   b , the change amounts ΔL 1  of the absorption loss of light in the arm waveguides are also the same as each other as indicated by the solid line. 
     Calculation unit  15  calculates the transmittance T (step S 12 ). The transmittance Tin each arm waveguide is expressed as a function of the change amount ΔL 1  of absorption loss, the initial phase shift ϕ0, and the phase change amount Δφ. 
         T =(1+10{circumflex over ( )}(Δ L 1/10)+2×10{circumflex over ( )}(Δ L 1/20)×cos(ϕ0±Δϕ))/(1+10{circumflex over ( )}(Δ L 1/10)) 2   [Equation 9]
 
     The phase change amount Δφ is expressed by Equation 7. The change amount ΔL 1  of absorption loss is expressed by Equation 8. The sign in the cosine function “cos” of Equation 9 is positive for the arm waveguide on the p-side and negative for the arm waveguide on the n-side. The initial phase shift φ0 is expressed by the following equation. In Equation 10, “acos” is an inverse cosine function. 
       ϕ0± a  cos ( T 0 0.5 )  [Equation 10]
 
     T0 is the transmittance when the applied voltage is 0 V and is measured in step S 10 . When the voltage applied to phase adjusting electrode  68   a  is swept, the sign of the initial phase shift ϕ0 is positive in case the first peak of the transmittance is the minimum peak, and is negative in case the first peak is the maximum peak. In the example of sub Mach-Zehnder modulator  42   a, ϕ 0 is equal to 0.28π. 
       FIG. 11A  is a diagram illustrating calculated transmittances.  FIG. 11B  is a diagram illustrating measured transmittances and transmittances after optimization. The horizontal axes in  FIG. 11A  and  FIG. 11B  represent the voltage applied to the phase adjusting electrode of sub Mach-Zehnder modulator  42   a . The vertical axes represent light transmittances. 
     The solid line in  FIG. 11A  represents the transmittance of the arm waveguide (arm waveguide  54   a ) on the p-side. The dotted line represents the transmittance of the arm waveguide (arm waveguide  54   b ) on the n-side. The transmittances illustrated in  FIG. 11A  are calculated by calculation unit  15  using Equation 9 and the initial value in step S 12  of  FIG. 9 . The solid line in  FIG. 11B  represents the transmittance after optimization of arm waveguide  54   a . The dotted line represents the transmittance after optimization of arm waveguide  54   b . Circles represent the measurement result of the transmittance of arm waveguide  54   a . Triangles represent the measurement result of the transmittance of arm waveguide  54   b.    
     The optimization in step S 14  in  FIG. 9  means that the transmittance calculated in step S 12  is brought close to the transmittance measured in step S 10  to reduce the error therebetween. The transmittance illustrated by the solid line in  FIG. 11B  varies from the transmittance illustrated by the solid line in  FIG. 11A  and approaches the measured transmittance illustrated by the circles in  FIG. 11B . The transmittance illustrated in dotted lines in  FIG. 11B  varies from the transmittance illustrated in dotted lines in  FIG. 11A  and approaches the measured transmittance illustrated in the triangles in  FIG. 11B . 
     By optimizing the transmittance, the initial phase shift ϕ0, the phase change amount Δφ, and the change amount ΔL 1  of the absorption loss included in the expression (Equation 9) of the transmittance are also optimized. The phase change amount Δφ and the absorption loss change amount ΔL 1  are functions indicating more accurately the relationship with the voltage (step S 16  in  FIG. 9 ). 
     More specifically, the initial values of the coefficients k1 to k6 in the Equation 7 of the phase change amount Δφ and the coefficients a1 and a2 in the Equation 8 of the change amount ΔL 1  change. The coefficients after optimization are illustrated below. 
     Coefficients for arm waveguide  54   a    
         k 1=1.32×10 −1 (π/ V ), k 2=1.90×10 −2 (π/ V   2 ), k 3=3.33×10 −3 (π/ V   3 ), k 4=1.43×10 −4 (π/ V   4 ),
 
         k 5=9.50×10 −7 (π/ V   5 ), k 6=9.50×10 −8 (π/ V   6 ), a 1=1×10 −3  (dB), a 2=2.5( V )
 
     Coefficients for arm waveguide  54   b    
         k 1=1.40×10 −1 (π/ V ), k 2=2.00×10 −2 (π/ V   2 ), k 3=3.50×10 −3 (π/ V   3 ), k 4=1.50×10 −4 (π/ V   4 ),
 
         k 5=1.00×10 −6 (π/ V   5 ), k 6=1.00×10 −7 (π/ V   6 ), a 1=1.2×10 −3  (dB), a 2=2.4 ( V )
 
     The initial phase shift ϕ0 after optimization of transmittance is 0.25π. 
       FIG. 12A  is a diagram illustrating phase change amounts after the optimization. The horizontal axis, the vertical axis, the solid line, and the broken line are the same as corresponding ones in  FIG. 4A . As illustrated in  FIG. 12A , a phase change amount similar to that illustrated in  FIG. 4A  is obtained by substituting the coefficient obtained by optimization of transmittance into Equation 7.  FIG. 12B  is a diagram illustrating change amounts of absorption losses after optimization. The horizontal axis, the vertical axis, the solid line, and the broken line are the same as corresponding ones in  FIG. 6A . As illustrated in  FIG. 12B , the change amount of absorption loss similar to that in  FIG. 6A  can be obtained by substituting the coefficient obtained by optimization of transmittance into Equation 8. 
       FIG. 13  is a diagram illustrating a relationship between the central voltage and the phase adjusting range. The horizontal axis represents the central voltage Vcc, which in this example is swept from 0 V to 10 V. For each value of the central voltage Vcc, the differential voltage Vdc ranges from −Vcc to Vcc. The vertical axis represents the range of the phase change amount (phase adjusting range). Calculation unit  15  applies the coefficients k1 to k6 after optimization to Equation 7 to calculate the phase change amount of arm waveguide  54   a  and the phase change amount of arm waveguide  54   b  for each voltage. Calculation unit  15  calculates a difference between the phase change amount of arm waveguide  54   a  and the phase change amount of arm waveguide  54   b  to obtain the phase adjusting range in sub Mach-Zehnder modulator  42   a . In sub Mach-Zehnder modulator  42   a , the phase adjusting range may be 6π(from −3π to 3π). The minimum value of the central voltage Vcc is determined so that the phase adjusting range becomes 6n. As illustrated in  FIG. 13 , in order to set the phase adjusting range to 6π, the central voltage Vcc may be 7 V. Storage device  34  illustrated in  FIG. 1B  stores the central voltage Vc of sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 1  as 7 V. 
     Next, testing of sub Mach-Zehnder modulator  42   b  is performed (step S 5  in  FIG. 8 ). Phase control unit  12  of control unit  10  applies a voltage to phase adjusting electrode of sub Mach-Zehnder modulator  42   a  to adjust the operating point of sub Mach-Zehnder modulator  42   a  to the extinction point. Control unit  10  measures the light transmittance in arm waveguides  54   c  and  54   d  of sub Mach-Zehnder modulator  42   b  while sweeping the voltage applied from ABC circuit  24  to phase adjusting electrode of sub Mach-Zehnder modulator  42   b  (step S 10  in  FIG. 9 ). Calculation unit  15  of control unit  10  calculates the light transmittance in arm waveguide  54   c  and the light transmittance in arm waveguide  54   d  (step S 12 ). 
     Calculation unit  15  performs optimization such that the transmittance calculated in step S 12  approaches the transmittance measured in step S 10  (step S 14 ). Calculation unit  15  acquires the relationship between the voltage applied to the phase adjusting electrode and the phase change amount (step S 16 ). Storage control unit  18 , based on the relationship between the voltage and the phase change amount, acquires the voltage in which the range of the phase change amount of sub Mach-Zehnder modulator  42   b  has the predetermined magnitude, and stores the voltage in storage device  34  (step S 18 ). 
       FIG. 14  is a diagram illustrating measured transmittances and transmittances after optimization. The horizontal axis represents the voltage applied to phase adjusting electrodes  68   d  and  68   e  of sub Mach-Zehnder modulator  42   b . The vertical axis represents light transmittance. The solid line represents the transmittance after optimization of the arm waveguide (arm waveguide  54   c ) on the p-side. The dotted line represents the transmittance after optimization of the arm waveguide (arm waveguide  54   d ) on the n-side. The circles represent the measurement result of the transmittance of arm waveguide  54   c . The triangles represent the measurement result of the transmittance of arm waveguide  54   d . By optimizing the transmittance, the phase change amount and the absorption loss change amount are obtained. 
       FIG. 15A  is a diagram illustrating phase change amounts after optimization. The horizontal axis, the vertical axis, the solid line, and the dotted line are the same as the corresponding ones in  FIG. 4B . As illustrated in  FIG. 15A , a phase change amount similar to that illustrated in  FIG. 4B  is obtained by optimization.  FIG. 15B  is a diagram illustrating change amounts of absorption loss after optimization. The horizontal axis, the vertical axis, the solid line, and the dotted line are the same as the corresponding ones in  FIG. 6B . As illustrated in  FIG. 15B , the change amount of absorption loss similar to that in  FIG. 6B  is obtained by optimization. 
       FIG. 16  is a diagram illustrating the relationship between a central voltage and a phase adjusting range. The horizontal axis represents the central voltage Vcc. The vertical axis represents the range of the phase change amount (phase adjusting range). Calculation unit  15  applies the phase adjusting range for each voltage by applying the coefficients k1 to k6 after optimization to Equation 7. As illustrated in  FIG. 16 , in order to set the phase adjusting range to 6π in sub Mach-Zehnder modulator  42   b , the central voltage Vcc may be 5.7 V. Storage device  34  stores the central voltage Vcc of sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1  as 5.7 V. 
     Next, main Mach-Zehnder modulator  44   a  is tested (step S 6  in  FIG. 8 ). Phase control unit  12  of control unit  10  sets sub Mach-Zehnder modulators  42   a  and  42   b  to a maximum transmission point. Control unit  10  measures the light transmittance (first transmittance) in arm waveguide  55   a  of main Mach-Zehnder modulator  44   a  while sweeping the voltage applied from ABC circuit  24  to phase adjusting electrode  70   a  of main Mach-Zehnder modulator  44   a . Control unit  10  measures the light transmittance (first transmittance) at arm waveguide  55   b  while sweeping the voltage applied to phase adjusting electrode  70   b  (step S 10  in  FIG. 9 ). Calculation unit  15  of control unit  10  calculates the light transmittance (second transmittance) in arm waveguide  55   a  and the light transmittance (second transmittance) in arm waveguide  55   b  (step S 12 ). 
     Calculation unit  15  performs optimization such that the transmittance calculated in step S 12  approaches the transmittance measured in step S 10  (step S 14 ). Calculation unit  15  acquires the relationship between the voltage applied to phase adjusting electrode  70   a  and the phase change amount in arm waveguide  55   a  (step S 16 ). Based on the relationship between the voltage and the phase change amount, storage control unit  18  acquires a voltage in which the range of the phase change amount has a predetermined magnitude, and storage control unit  18  stores the voltage in storage device  34  (step S 18 ). 
     The phase adjusting range in the  44   a  of main Mach-Zehnder modulator may be, for example, 5 π (from −2.5 π to 2.5 π. Storage device  34  stores 7 V as the central voltage Vcp in which the phase adjusting range of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1  is 5π. 
     Next, optical modulator  40   a - 2  different from optical modulator  40   a - 1  is tested. The testing process of each Mach-Zehnder modulator is the same as the corresponding testing process of optical modulator  40   a - 1 . It is assumed that 7 V is obtained as the central voltage of sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 2  in the same way as sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 1 . It is assumed that 5.7 V is obtained as the central voltage of sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 2  in the same way as sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1 . 
     Main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  is also tested.  FIG. 17  is a diagram illustrating measured transmittances and transmittances after optimization. The horizontal axis represents the voltage applied to phase adjusting electrodes  70   a  and  70   b  of main Mach-Zehnder modulator  44   a . The vertical axis represents light transmittance. The solid line represents the transmittance after optimization of the arm waveguide (arm waveguide  55   a ) on the Ich side. The dotted line represents the transmittance after optimization of the arm waveguide (arm waveguide  55   b ) on the Qch side. The circles represent the measurement result of the transmittance of arm waveguide  55   a . The triangles represent the measurement result of the transmittance of arm waveguide  55   b . Optimization of transmittance changes the coefficients in Equation 7 and the coefficients in Equation 8. 
       FIG. 18A  is a diagram illustrating phase change amounts after optimization. The horizontal axis represents the voltage applied to phase adjusting electrodes  70   a  and  70   b . The vertical axis represents the phase change amount. The solid line represents the phase change amount in arm waveguide  55   a . The dashed line represents the phase change amount in arm waveguide  55   b .  FIG. 18B  is a diagram illustrating change amounts of absorption loss after optimization. The horizontal axis represents the voltage applied to phase adjusting electrodes  70   a  and  70   b . The vertical axis represents the change amount of absorption loss. The solid line represents the change amount in arm waveguide  55   a . The dashed line represents the change amount in arm waveguide  55   b.    
       FIG. 19  is a diagram illustrating a relationship between a central voltage and a phase adjusting range. The horizontal axis represents the central voltage Vcp. The vertical axis represents the range of the phase change amount (phase adjusting range). Calculation unit  15  acquires a phase adjusting range in main Mach-Zehnder modulator  44   a  for each voltage. As illustrated in  FIG. 19 , in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2 , the central voltage Vcp may be 5.7 V in order to set the phase adjusting range to 5π. Storage device  34  stores the central voltage Vc of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  as 5.7 V. 
     Table 1 is an example of a data table stored in storage device  34 . 
     
       
         
           
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                 MODULATOR 40a-1 
                 MODULATOR 40a-2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Vcc OF Ich [V]  
                 7.0 
                 7.0 
               
               
                   
                 Vcc OF Qch [V]  
                 5.7 
                 5.7 
               
               
                   
                 Vcp [V] 
                 7.4 
                 5.7 
               
               
                   
               
            
           
         
       
     
     Vcc of Ich illustrated in Table 1 is a central voltage of sub Mach-Zehnder modulator  42   a . Vcc of Qch is the central voltage of sub Mach-Zehnder modulator  42   b . Vcp is the central voltage of main Mach-Zehnder modulator  44   a . In optical modulators  40   a - 1  and  40   a - 2 , Vcc of Ich is 7.0 V, and Vcc of Qch is 5.7 V. Vcp in optical modulator  40   a - 1  is 7.4 V. Vcp in optical modulator  40   a - 2  is 5.7 V. 
     Storage device  34  stores the central voltage Vcc of sub Mach-Zehnder modulator  42   a , the central voltage Vcc of sub Mach-Zehnder modulator  42   b , and the central voltage Vcp of main Mach-Zehnder modulator  44   a  for each of optical modulators  40   a - 1  and  40   a - 2 . The differential voltage Vcd of sub Mach-Zehnder modulator is to −Vcc or more and +Vcc or less. The differential voltage Vdp of main Mach-Zehnder modulator is set to −Vcp or more and +Vcp or less. The testing of  FIG. 9  optimizes the voltages. When optical modulators  40   a - 1  and  40   a - 2  are used, by applying the voltages, the phase adjusting range can be set to a predetermined magnitude and an increase in light absorption loss can be suppressed. 
     (Absorption Loss Amount and Extinction Ratio of Sub Mach-Zehnder Modulator) 
     The absorption loss amount and the extinction ratio of sub Mach-Zehnder modulator will be described with reference to  FIG. 20A  to  FIG. 22B .  FIG. 20A  to  FIG. 21B  are examples in which the testing illustrated in  FIG. 9  is performed and the voltage is optimized as illustrated in Table 1, and correspond to the first embodiment.  FIG. 22A  and  FIG. 22B  illustrate an example in which the same voltage is applied to a plurality of sub Mach-Zehnder modulators without optimizing each of the voltages. 
       FIG. 20A ,  FIG. 21A  and  FIG. 22A  are diagrams illustrating change amounts of absorption loss. The horizontal axes represent the differential voltages Vdc. The vertical axes represent the amounts of light absorption loss. The broken line represents the amount of absorption loss in the arm waveguide (arm waveguide  54   a  or  54   c ) on the p-side. The dotted line represents the amount of absorption loss in the n-side arm waveguide (arm waveguide  54   b  or  54   d ). The solid line represents the difference ΔL 2  between the absorption loss amounts of arm waveguides (the absorption loss amount of the p-side arm waveguide—the absorption loss amount of the n-side arm waveguide). 
       FIG. 20B ,  FIG. 21B , and  FIG. 22B  are diagrams illustrating extinction ratios. The horizontal axes represent the differential voltage Vdc. The vertical axes represent the extinction ratio. The extinction ratio (ER) is calculated by the following equation. 
       ER=20×log 10 ((10{circumflex over ( )}(Δ L 2/20)+1)/(10{circumflex over ( )}(Δ L 2/20)−1))  [Equation 11]
 
     The extinction ratio ER increases as the difference ΔL 2  between the absorption loss amounts decreases. The extinction ratio ER decreases as the difference ΔL 2  increases. When the value of the difference ΔL 2  becomes excessively large, the lights cannot be extinguished after the lights from the two arm waveguides are multiplexed with the opposite phase. As a result, the extinction ratio ER becomes small. 
       FIG. 20A  illustrates the amount of absorption loss in sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 1  when the central voltage Vcc is 7 V. The differential voltage Vdc takes a value within a range from −6.8 V to 7 V. As the differential voltage Vdc increases to the negative side, the amount of absorption loss in arm waveguide  54   b  increases, and the amount of absorption loss in arm waveguide  54   a  approaches 0. The difference ΔL 2  between the absorption loss amounts increases on the negative side. As the differential voltage Vdc increases to the positive side, the amount of absorption loss in arm waveguide  54   a  increases, and the amount of absorption loss in arm waveguide  54   b  approaches 0. The difference ΔL 2  in the amount of absorption loss on the positive side. The maximum value of the absolute values of the absorption loss amount difference ΔL 2  is 0.38 dB. 
       FIG. 20B  illustrates the extinction ratio of sub Mach-Zehnder modulator  42   a  of optical modulator  40   a - 1 . The extinction ratio ER in  FIG. 20B  is calculated from the difference ΔL 2  in  FIG. 20A . As the differential voltage Vdc increases to the positive side and the negative side, the extinction ratio ER decreases. The minimum value of the extinction ratio ER is 33.3 dB. 
       FIG. 21A  illustrates the amount of absorption loss in sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1  when the central voltage Vcc is 5.7 V. The differential voltage Vdc takes a value within a range from −5.8 V to 5.5 V. The maximum value of the absolute values of the absorption loss amount difference ΔL 2  is 0.50 dB. 
       FIG. 21B  illustrates the extinction ratio in sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1 . The extinction ratio ER in  FIG. 21B  is calculated from the difference ΔL 2  in  FIG. 21A . The minimum extinction ratio ER is 30.8 dB. 
       FIG. 22A  illustrates the amount of absorption loss in sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1  when the central voltage Vcc is 7 V. The maximum value of the absolute values of the absorption loss amount difference ΔL 2  is 0.88 dB. 
       FIG. 22B  illustrates the extinction ratio in sub Mach-Zehnder modulator  42   b  of optical modulator  40   a - 1 . The extinction ratio ER in  FIG. 22B  is calculated from the difference ΔL 2  in  FIG. 22A . The minimum value of the extinction ratio ER is 26.0 dB. 
     As illustrated in  FIG. 22A  and  FIG. 22B , when the central voltage of sub Mach-Zehnder modulator  42   b  is made equal to the central voltage of sub Mach-Zehnder modulator  42   a , the amount of absorption loss increases and the extinction ratio decreases. 
     As illustrated in  FIG. 21A  and  FIG. 21B , according to the first embodiment, by optimizing the central voltage of sub Mach-Zehnder modulator  42   b , it is possible to reduce the amount of light absorption loss and suppress a decrease in extinction ratio. Thus, the extinction ratios of 30 dB or more can be achieved for both of sub Mach-Zehnder modulators  42   a  and  42   b.    
     (Absorption Loss Amount and Extinction Ratio of Main Mach-Zehnder Modulator) 
     The absorption loss amount and extinction ratio of the main Mach-Zehnder modulator will be described with reference to  FIG. 23A  to  FIG. 25B . Each of  FIG. 23A  to  FIG. 24B  illustrates an example in which the testing illustrated in  FIG. 9  is performed and the voltage is optimized as illustrated in Table 1. Each of  FIG. 25A  and  FIG. 25B  illustrates an example in which the same voltage is applied to a plurality of main Mach-Zehnder modulators without optimizing the voltage. 
       FIG. 23A ,  FIG. 24A , and  FIG. 25A  are diagrams illustrating amounts of absorption losses. The horizontal axes represent the differential voltage Vdp. The vertical axes represent the amount of light absorption loss. The broken line represents the amount of absorption loss of the arm waveguide (arm waveguide  55   a ) on the Ich side. The dotted line represents the amount of absorption loss of the arm waveguide (arm waveguide  55   b ) on the Qch side. The solid line represents the difference ΔL 2  between the absorption loss amounts of arm waveguides (the absorption loss amount of the arm waveguide for Ich minus the absorption loss amount of the arm waveguide for Qch).  FIG. 23B ,  FIG. 24B , and  FIG. 25B  are diagrams illustrating extinction ratios. The horizontal axes represent the differential voltage Vdp. The vertical axes represent the extinction ratio. 
       FIG. 23A  illustrates the amount of absorption loss in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1  when the central voltage Vcp is 7.4 V. The differential voltage Vdp takes a value within a range of −7 V or more and 7.4 V or less. The maximum value of the absolute values of the absorption loss amount difference ΔL 2  is 0.53 dB. 
       FIG. 23B  illustrates the extinction ratio in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1 . The extinction ratio ER in  FIG. 23B  is calculated from the difference ΔL 2  in  FIG. 23A . The minimum extinction ratio ER is 30.3 dB. 
       FIG. 24A  illustrates the amount of absorption loss in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  when the central voltage Vcp is 5.7 V. The maximum value of the absolute values of the absorption loss amount difference ΔL 2  is 0.44 dB. 
       FIG. 24B  illustrates the extinction ratio in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2 . The extinction ratio ER in  FIG. 24B  is calculated from the difference ΔL 2  in  FIG. 24A . The minimum value of the extinction ratio ER is 31.9 dB. 
       FIG. 25A  illustrates the amount of absorption loss in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  when the central voltage Vcp is 7.4 V. The differential voltage Vdp takes a value within a range of −5.5 V or more and 5.1 V or less. The maximum value of the absolute values of the absorption loss amount difference ΔL 2  is 0.89 dB. 
       FIG. 25B  illustrates the extinction ratio in main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2 . The extinction ratio ER in  FIG. 25B  is calculated from the difference ΔL 2  in  FIG. 25A . The minimum value of the extinction ratio ER is 25.8 dB. 
     As illustrated in  FIG. 25A  and  FIG. 25B , when the central voltage of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  is made equal to the central voltage of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1 , the amount of absorption loss increases and the extinction ratio decreases. 
     As illustrated in  FIG. 24A  and  FIG. 24B , according to the first embodiment, by optimizing the central voltage of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2 , it is possible to reduce the amount of light absorption loss and suppress a decrease in extinction ratio. In main Mach-Zehnder modulator  44   a  of both optical modulators  40   a - 1  and  44   a - 2 , an extinction ratio of 30 dB or more can be obtained. 
     According to the first embodiment, control unit  10  acquires the relationship between the voltage applied to phase adjusting electrode and the phase change amount, and acquires the voltage in which the phase adjusting range has a predetermined magnitude. The phase of light in a Mach-Zehnder modulator is adjusted with a voltage optimized for each Mach-Zehnder modulator. It is possible to set a phase adjusting range to a predetermined magnitude and to suppress an increase in absorption loss of light. 
     The voltage is optimized for each of a plurality of Mach-Zehnder modulators in one optical modulator, such as sub Mach-Zehnder modulators  42   a  and  42   b  in optical modulator  40   a - 1 . In each Mach-Zehnder modulator, the phase adjusting range can be set to a predetermined magnitude, and an increase in light absorption loss can be suppressed. For example, the central voltage Vcc of sub Mach-Zehnder modulator  42   a  is set to 7 V, and the central voltage Vcc of sub Mach-Zehnder modulator  42   b  is set to 5.7 V. As illustrated in  FIG. 13  and  FIG. 16 , in both sub Mach-Zehnder modulators  42   a  and  42   b , the phase adjusting range can be 6n. As illustrated in  FIG. 20A  to  FIG. 21B , by suppressing the increase in absorption loss, the extinction ratio can be 30 dB or more. 
     A voltage is optimized in a plurality of optical modulators such as optical modulator  40   a - 1  and optical modulator  40   a - 2 . The central voltage Vcp of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 1  is set to 7 V, and the central voltage Vcp of main Mach-Zehnder modulator  44   a  of optical modulator  40   a - 2  is set to 5.7 V. In the two main Mach-Zehnder modulators  44   a , the phase adjusting range can be 5π. As illustrated in  FIG. 23A  to  FIG. 24B , by suppressing the increase in absorption loss, the extinction ratio can be 30 dB or more. 
     The phase adjusting range in the sub Mach-Zehnder modulator is, for example, a range of 6π from −3π to 3π, but may be 6π or more or 6π or less. The phase adjusting range in the main Mach-Zehnder modulator is, for example, 5π from −2.5π to 2.5π, but may be 5π or more or 5π or less. The phase adjusting range may have a suitable magnitude according to, for example, the initial phase shift φ0. The phase adjusting range of sub Mach-Zehnder modulator may be, for example, 5π or 7π. The phase adjusting range of main Mach-Zehnder modulator may be, for example, 4π or 6π. 
     Sub Mach-Zehnder modulator  42   a  has two paired arm waveguides  52   a  and  52   b . Phase adjusting electrode  68   a  is provided on arm waveguide  52   a . Phase adjusting electrode  68   b  is provided on arm waveguide  52   b . Control unit  10  acquires the relationship between the voltage applied to phase adjusting electrode  68   a  and the phase change amount in arm waveguide  52   a  and the relationship between the voltage applied to phase adjusting electrode  68   b  and the phase change amount in arm waveguide  52   b  ( FIG. 12A ). Based on the relationship between the voltage and the phase change amount as illustrated in  FIG. 13 , control unit  10  can acquire a voltage in which the phase adjusting range in sub Mach-Zehnder modulator  42   a  to be  67   t . Control unit  10  acquires, each for sub Mach-Zehnder modulator  42   b  and for main Mach-Zehnder modulator  44   a , the relationship between the voltage applied to the phase adjusting electrode and the phase change amount in the arm waveguide, and acquires the voltage in which the phase adjusting range has a desired magnitude based on the relationship. 
     The Mach-Zehnder modulator is differentially driven. The voltage Vp applied to the sub Mach-Zehnder modulator is Vcc+Vdc, and the voltage Vn is Vcc-Vdc. The voltage VI applied to the main Mach-Zehnder modulator is Vcp+Vdp, and the voltage VQ is Vcp-Vdp. In step S 18  of  FIG. 9 , control unit  10  acquires the central voltages Vcc and Vcp. As illustrated in  FIG. 13 ,  FIG. 16 , and  FIG. 19 , by acquiring the optimal central voltage, the phase adjusting range becomes the predetermined magnitude. As illustrated in Table 1, storage device  34  stores the optimum central voltages Vcc and Vcp for each Mach-Zehnder modulator. When driving the Mach-Zehnder modulator, control unit  10  acquires the central voltage stored in storage device  34  and calculates the sum and difference of the central voltage and the differential voltage to acquire the voltages Vp, Vn, VI, and VQ. ABC circuit  24  applies the voltage to the phase adjusting electrode. In each Mach-Zehnder modulator, the predetermined phase adjusting range can be obtained, and the increase in absorption loss can be suppressed. In the first embodiment, the central voltage in the differential drive is optimized. The Mach-Zehnder modulator may be driven by a method other than the differential driving. Regardless of a driving method, the phase adjusting range of a Mach-Zehnder modulator can be controlled with the optimum voltage, and the increase in absorption loss can be suppressed. 
     The differential voltage Vdc of the sub Mach-Zehnder modulator is set to a value between −Vcc or more and Vcc or less. The differential voltage Vdp of the main Mach-Zehnder modulator is set to a value between −Vcp or more and Vcp or less. The differential voltage may vary from that described above. 
     In step S 12  of  FIG. 9 , the transmittance is calculated as a function of the phase change amount (Equation 9). The transmittance is fitted, and the calculated transmittance is brought close to the measured transmittance. By optimizing the transmittance, the phase change amount is also optimized. The phase change amount illustrated in Equation 7 is a function of voltage. By the fitting of the transmittance, the coefficients in Equation 7 change, and the relationship between the voltage and the phase change amount becomes more accurate. Control unit  10  acquires, based on the phase change amount, the voltage in which the phase adjusting range has the predetermined magnitude. It is possible to set the phase adjusting range to the predetermined magnitude and suppress the increase in absorption loss of light. The transmittance, the phase change amount, and the absorption loss change amount may be calculated from expressions other than the above-described expressions. 
     As illustrated in  FIG. 2B , each of arm waveguides  54   a  and  54   b  has cladding layer  82 , core layer  84 , cladding layer  86  and contact layer  88 . The other arm waveguides have the same configuration. Cladding layer  82  is an n-type semiconductor layer. Cladding layer  86  and contact layer  88  are p-type semiconductor layers. Dopants are added to obtain n-type and p-type conductivity types. The variation in the thermal diffusion amount of the dopant causes variation in the phase adjusting efficiency of the Mach-Zehnder modulator. According to the first embodiment, the voltage in which the phase adjusting rage has the predetermined magnitude is acquired for each Mach-Zehnder modulator. It is possible to set the phase adjusting range to the predetermined range and suppress the increase in absorption loss. 
     In the steps of  FIG. 8  and  FIG. 9 , light transmission apparatus  100  of  FIG. 1A  is utilized as a testing apparatus for optical modulator  40 . One optical modulator  40  (e.g. optical modulator  40   a - 1 ) is incorporated into light transmission apparatus  100  for testing. Then, optical modulator  40   a - 1  is replaced with optical modulator  40   a - 2  for testing. Storage device  34  stores the voltages for both optical modulators  40   a - 1  and  40   a - 2  as illustrated in Table 1. In case light transmission apparatus  100  is used for communication, one optical modulator  40   a  included in light transmission apparatus  100  may be tested. Storage device  34  may store only the voltage for the one optical modulator  40   a.    
     Second Embodiment 
     In the second embodiment, a dual polarization (DP)-IQ modulator is used as optical modulator  40 . The configuration of light transmission apparatus  100  is the same as that of the first embodiment. 
       FIG. 26  is a plan view illustrating an optical modulator  40   b . Optical modulator  40   b  is a DP-IQ modulator and has two optical modulators  43   a  and  43   b.    
     Semiconductor substrate  80  and four termination elements  78   a ,  78   b ,  78   c , and  78   d  are mounted on the upper surface of substrate  41 . Termination elements  78   a ,  78   b ,  78   c , and  78   d  include, for example, resistors and capacitors. Termination elements  78   a  and  78   b  face end surface  80   c  of semiconductor substrate  80 . Termination elements  78   c  and  78   d  face end surface  80   d  of semiconductor substrate  80 . An input waveguide  51 , optical modulators  43   a  and  43   b  are formed on semiconductor substrate  80 . 
     A first end portion of input waveguide  51  is located on end surface  80   a  of semiconductor substrate  80 . A second end portion of input waveguide  51  is connected to a coupler  59 . Two optical modulators  43   a  and  43   b  are arranged in parallel after coupler  59 . 
     Optical modulator  43   a  is the IQ modulator, and has two sub Mach-Zehnder modulators  42   a  and  42   b  and main Mach-Zehnder modulator  44   a , similar to optical modulator  40   a  of  FIG. 2A . Optical modulator  43   b  is the IQ modulator, and has two sub Mach-Zehnder modulators  42   c  and  42   d  and main Mach-Zehnder modulator  44   b . The configurations of sub Mach-Zehnder modulators  42   c  and  42   d  are the same as those of sub Mach-Zehnder modulators  42   a  and  42   b . The configuration of main Mach-Zehnder modulator  44   b  is the same as that of main Mach-Zehnder modulator  44   a.    
     Optical modulator  43   a  generates modulated light of an X channel (X polarization). Optical modulator  43   b  generates modulated light of a Y channel (Y polarization). The polarization plane of the X-polarized wave is orthogonal to the polarization plane of the Y-polarized wave. Two modulated lights are multiplexed so that the planes of polarization are orthogonal to each other by using a polarization rotation element and a multiplexing element (not illustrated). 
     The manufacturing method of optical modulator  40   b  is similar to that of  FIG. 8 . Control unit  10  performs the testing of  FIG. 9  for each Mach-Zehnder modulator in optical modulator  40   b . When testing sub Mach-Zehnder modulators  42   a  and  42   b  and main Mach-Zehnder modulator  44   a  in optical modulator  43   a , the operating points of sub Mach-Zehnder modulators  42   c  and  42   d  of optical modulator  43   b  are adjusted to the extinction points. When testing sub Mach-Zehnder modulators  42   c  and  42   d  and main Mach-Zehnder modulator  44   b  of optical modulator  43   b , the operating points of sub Mach-Zehnder modulators  42   a  and  42   b  of optical modulator  43   a  are adjusted to the extinction points. 
     Table 2 is an example of a data table stored in storage device  34 . Storage device  34  stores the voltages of each of the plurality of optical modulators  40   b  (optical modulators  40   b - 1  and  40   b - 2  in Table 2). 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                 MODULATOR 40b-1 
                 MODULATOR 40b-2 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Vcc OF XI [V] 
                 5.8 
                 . 
               
               
                   
                 Vcc OF XQ [V]  
                 6.2 
                 . 
               
               
                   
                 Vcc OF YI [V]  
                 6.0 
                 . 
               
               
                   
                 Vcc OF YQ [V]  
                 6.1 
                   
               
               
                   
                 Vcp OF Xch [V]  
                 5.9 
                   
               
               
                   
                 Vcp OF Ych [V]  
                 6.0 
               
               
                   
               
            
           
         
       
     
     Vcc of XI is the central voltage of sub Mach-Zehnder modulator  42   a  of optical modulator  43   a  on the Xch side of optical modulator  40   b . Vcc of XQ is the central voltage of sub Mach-Zehnder modulator  42   b  of optical modulator  43   a . Vcc of YI is the central voltage of sub Mach-Zehnder modulator  42   c  of optical modulator  43   b  on the Qch side of optical modulator  40   b . Vcc of YQ is a central voltage of sub Mach-Zehnder modulator  42   d  of optical modulator  43   b . Vcp of Xch is the central voltage of main Mach-Zehnder modulator  44   a . Vcp of Ych is the central voltage of main Mach-Zehnder modulator  44   b . The voltages in optical modulator  40   b - 1  are, for example, 5.8 V, 6.2 V, 6.0 V, 6.1 V, 5.9 V, and 6.0 V. Specific values of the voltages of optical modulator  40   b - 2  are omitted. 
     According to the second embodiment, by driving the Mach-Zehnder modulator with the voltages optimized for each Mach-Zehnder modulator, the phase adjusting range can be set to the predetermined magnitude and the increase in light absorption loss can be suppressed. 
     An example of optical modulator  40  is IQ modulator in the first embodiment, and DP-IQ modulator in the second embodiment. The present disclosure may be applied to other optical modulators. 
     Although the embodiments of the present disclosure have been described in detail above, the present disclosure is not limited to the specific embodiments, and various modifications and changes can be made within the scope of the gist of the present disclosure described in the claims.