Patent Publication Number: US-8989600-B2

Title: Modulating apparatus

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2012-243160, filed on Nov. 2, 2012, the entire contents of which are incorporated herein by reference. 
     FIELD 
     The embodiments discussed herein are related to a modulating apparatus. 
     BACKGROUND 
     Quadrature amplitude modulation (QAM) has conventionally been known as a modulating scheme to transmit data by adjusting the amplitudes and phases of two carrier waves that are independent from each other. For example, a modulator is known as a QAM modulator, that is configured to: cause plural Mach-Zehnder modulators to execute multi-value (for example, four-value) phase modulation; and couple the acquired optical signals (see, e.g., Japanese Laid-Open Patent Publication No. 2009-244682). 
     However, according to the conventional technique, the Mach-Zehnder modulator executing the multi-value phase modulation has many components to be controlled such as a π/2 shifter and a bias supply unit. Therefore, a problem arises that the control of the Mach-Zehnder modulator is complicated. 
     SUMMARY 
     According to an aspect of an embodiment, a modulating apparatus includes a branch that branches a light beam input thereinto; a first modulating unit that modulates the phase of a first light beam of light beams branched by the branch; a second modulating unit that modulates a second light beam different from the first light beam of the light beams branched by the branch; a third modulating unit that is connected in series to the first modulating unit and transmits the first light beam without branching the first light beam, the third modulating unit modulating the phase of a light beam transmitted thereby by controlling a refractive index of the light beam transmitted thereby; a fourth modulating unit that is connected in series to the second modulating unit and transmits the second light beam without branching the second light beam, the fourth modulating unit modulating the phase of a light beam transmitted thereby by controlling a refractive index of the light beam transmitted thereby; and a coupler that couples the first light beam of which phase is modulated by the first and the third modulating units and the second light beam of which phase is modulated by the second and the fourth modulating units, at different intensities. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1A  is a diagram of an example of a modulating apparatus according to a first embodiment; 
         FIG. 1B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 1A ; 
         FIG. 2  is a diagram of an example of the relation between the intensity of the optical signal after being transmitted by a Mach-Zehnder modulator and a driving signal; 
         FIG. 3  is a diagram of an example of the relation between the intensity of the optical signal after being transmitted by a phase modulator and the driving signal; 
         FIG. 4A  is a diagram of an example of a specific configuration of the Mach-Zehnder modulator including a Y-branch; 
         FIG. 4B  is a diagram of an example of flows of light beams and electric signals in the Mach-Zehnder modulator depicted in  FIG. 4A ; 
         FIG. 5A  is a diagram of an example of a specific configuration of the Mach-Zehnder modulator including a directional coupler; 
         FIG. 5B  is a diagram of an example of flows of light beams and electric signals in the Mach-Zehnder modulator depicted in  FIG. 5A ; 
         FIG. 6A  is a diagram of an example of a specific configuration of the Mach-Zehnder modulator including a multi-mode interference (MMI); 
         FIG. 6B  is a diagram of an example of flows of light beams and electric signals in the Mach-Zehnder modulator depicted in  FIG. 6A ; 
         FIG. 7A  is a diagram of an example of a specific configuration of the phase modulator; 
         FIG. 7B  is a diagram of an example of flows of light beams and electric signals in the phase modulator depicted in  FIG. 7A ; 
         FIG. 8A  is a diagram of an example of a specific configuration of a phase shifter; 
         FIG. 8B  is a diagram of an example of flows of light beams and electric signals in the phase shifter depicted in  FIG. 8A ; 
         FIG. 9A  is a diagram of an example of a specific configuration of the attenuator including the Y-branch; 
         FIG. 9B  is a diagram of an example of flows of light beams and electric signals in the attenuator depicted in  FIG. 9A ; 
         FIG. 10A  is a diagram of an example of a specific configuration of the attenuator including the directional coupler; 
         FIG. 10B  is a diagram of an example of flows of light beams and electric signals in the attenuator depicted in  FIG. 10A ; 
         FIG. 11A  is a diagram of an example of a specific configuration of the attenuator including the MMI coupler; 
         FIG. 11B  is a diagram of an example of flows of light beams and electric signals in the attenuator depicted in  FIG. 11A ; 
         FIG. 12A  is a diagram of an example of the configuration to control a driving unit of the phase modulator; 
         FIG. 12B  is a diagram of an example of flows of light beams and electric signals in the configuration to control the driving unit depicted in  FIG. 12A ; 
         FIG. 13  is a flowchart of a control process for the driving unit of the phase modulator executed by the control unit; 
         FIG. 14A  is a diagram of another example of the configuration to control the driving unit of the phase modulator; 
         FIG. 14B  is a diagram of an example of flows of light beams and electric signals in the configuration to control the driving unit depicted in  FIG. 14A ; 
         FIG. 15A  is a diagram of an example of a specific configuration of a modulating apparatus according to a second embodiment; 
         FIG. 15B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 15A ; 
         FIG. 16A  is a diagram of a configuration of a variation of the modulating apparatus according to the second embodiment; 
         FIG. 16B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 16A ; 
         FIG. 17A  is a diagram of an example of a specific configuration of a modulating apparatus according to a third embodiment; 
         FIG. 17B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 17A ; 
         FIG. 18A  is a diagram of a configuration of variation 1 of the modulating apparatus according to a third embodiment; 
         FIG. 18B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 18A ; 
         FIG. 19A  is a diagram of a configuration of the variation 2 of the modulating apparatus according to the third embodiment; 
         FIG. 19B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 19A ; 
         FIG. 20A  is a diagram of an example of a specific configuration of a modulating apparatus according to a fourth embodiment; and 
         FIG. 20B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 20A . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Preferred embodiments will be described in detail with reference to the accompanying drawings. 
       FIG. 1A  is a diagram of an example of a modulating apparatus according to a first embodiment.  FIG. 1B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 1A . A modulating apparatus  100  depicted in  FIGS. 1A and 1B  executes quadrature amplitude modulation (QAM) for a light beam input thereinto. The modulating apparatus  100  is input with, for example, a continuous wave (CW) laser light beam from an external light source. 
     The modulating apparatus  100  includes a branch  110 , Mach-Zehnder modulators (MZMs)  121  and  122 , driving units  121   c ,  122   c ,  131   b , and  132   b , bias supply units  121   d ,  122   d ,  141   b , and  142   b , phase modulators (PMs)  131  and  132 , a phase shifter  141 , an attenuator  142 , and a coupler  150 . 
     The branch  110  branches a light beam input into the modulating apparatus  100 , and outputs the branched light beams to the Mach-Zehnder modulators  121  and  122 . 
     The Mach-Zehnder modulator  121  includes an RF electrode  121   a  and a DC electrode  121   b . The driving unit  121   c  generates a driving signal that corresponds to data  1  input thereinto, and applies the driving signal to the RF electrode  121   a . The bias supply unit  121   d  applies a bias voltage to the DC electrode  121   b.    
     The Mach-Zehnder modulator  121  executes two-value (0 and π) phase modulation for the light beam output from the branch  110 , corresponding to the driving signal applied to the RF electrode  121   a . The transmission property of the light beam in the Mach-Zehnder modulator  121  can be adjusted by controlling the bias voltage applied from the bias supply unit  121   d  to the DC electrode  121   b . The Mach-Zehnder modulator  121  outputs the light beams acquired by the phase modulation to the phase modulator  131 . 
     The Mach-Zehnder modulator  122  includes an RF electrode  122   a  and a DC electrode  122   b . The driving unit  122   c  generates a driving signal that corresponds to data  2  input thereinto, and applies the driving signal to the RF electrode  122   a . The bias supply unit  122   d  applies a bias voltage to the DC electrode  122   b.    
     The Mach-Zehnder modulator  122  executes two-value (0 and π) phase modulation for the light beam output from the branch  110 , corresponding to the driving signal applied to the RF electrode  122   a . The transmission property of the light beam in the Mach-Zehnder modulator  122  can be adjusted by controlling the bias voltage applied from the bias supply unit  122   d  to the DC electrode  122   b . The Mach-Zehnder modulator  122  outputs the light beam acquired by the phase modulation to the phase modulator  132 . 
     A constellation  161  depicts the phase and the amplitude of the light beams output from the Mach-Zehnder modulators  121  and  122 , with the horizontal axis representing an in-phase component I and the vertical axis representing a quadrature component Q. As depicted in the constellation  161 , the phase of the light beams output from the Mach-Zehnder modulators  121  and  122  is zero or π. 
     The phase modulator  131  includes an RF electrode  131   a . The driving unit  131   b  generates a driving signal that corresponds to data  3  input thereinto and applies the driving signal to the RF electrode  131   a . The phase modulator  131  executes phase modulation to vary the phase of the optical signal output from the Mach-Zehnder modulator  121  by zero or π/2, corresponding to the driving signal applied to the RF electrode  131   a . Thus, four-value (zero, π/2, π, and 3π/2) phase modulation can be executed. The phase modulator  131  outputs to the phase shifter  141  the light beam acquired by the phase modulation. 
     The phase modulator  132  includes an RF electrode  132   a . The driving unit  132   b  generates a driving signal that corresponds to data  4  input thereinto and applies the driving signal to the RF electrode  132   a . The phase modulator  132  executes phase modulation to vary the phase of the optical signal output from the Mach-Zehnder modulator  122  by zero or π/2, corresponding to the driving signal applied to the RF electrode  132   a . Thus, four-value (zero, π/2, π, and 3π/2) phase modulation can be executed. The phase modulator  132  outputs to the attenuator  142  the light beam acquired by the phase modulation. 
     A constellation  162  depicts the optical signals output from the phase modulators  131  and  132 . As depicted in the constellation  162 , the phase of the light beams output from the phase modulators  131  and  132  is zero, π/2, π, or 3π/2. 
     The phase modulators  131  and  132  are provided downstream of the Mach-Zehnder modulators  121  and  122 , respectively. However, the arrangement is not limited to this and the phase modulators  131  and  132  may be provided upstream and the Mach-Zehnder modulators  121  and  122  may be provided downstream. 
     The phase shifter  141  includes a DC electrode  141   a . The bias supply unit  141   b  applies a bias voltage to the DC electrode  141   a . The phase shifter  141  corrects the phase of the optical signal output from the phase modulator  131  by controlling the bias voltage applied from the bias supply unit  141   b  to the DC electrode  141   a . Thus, the shift of the phase of each symbol between the optical signal output from the phase shifter  141  to the coupler  150  and the optical signal output from the attenuator  142  to the coupler  150  can be corrected. The phase shifter  141  outputs the optical signal whose phase is corrected, to the coupler  150 . 
     The attenuator  142  attenuates the optical signal output from the phase modulator  132  by a predetermined amount. For example, the attenuator  142  is a Mach-Zehnder attenuator and includes a DC electrode  142   a . The bias supply unit  142   b  applies a bias voltage to the DC electrode  142   a . The attenuator  142  attenuates by, for example, 6 [dB] the intensity of the optical signal output from the phase modulator  132  by controlling the bias voltage applied from the bias supply unit  142   b  to the DC electrode  142   a.    
     A constellation  163  depicts the optical signal output from the attenuator  142 . In the constellation  163 , the distance from the origin to each symbol is halved compared to that in the constellation  162 . Thus, the optical signal output from the attenuator  142  has the intensity that is ¼ of that of the optical signal output from the phase modulator  132 . The attenuator  142  outputs the attenuated optical signal to the coupler  150 . 
     The coupler  150  couples the optical signal output from the phase shifter  141  and that output from the attenuator  142 . A constellation  164  depicts the result of addition of the vectors from the origin to the symbols depicted in constellations  162  and  163 . For example, the constellation  164  depicts a sum (a coupled vector) of combinations of four vectors from the origin to the symbols depicted in the constellation  162  and those depicted in the constellation  163 . 
     Thus, the optical signal output from the coupler  150  becomes a 16-QAM optical signal having 16 symbols. The distance from the origin to each symbol represents the intensity of the light beam and, therefore, each of the 16 symbols takes any one of three kinds of optical intensities in the constellation  164 . 
     The Mach-Zehnder modulator  121  implements a first modulating unit that modulates the phase of a first light beam of the branched light beams. The Mach-Zehnder modulator  122  implements a second modulating unit that modulates a second light beam of the branched light beams that is different from the first light beam. The phase-modulator  131  implements a third modulating unit that is connected in series to the first modulating unit, that transmits the first light beam without branching the first light beam, and that modulates the phase of the light beam transmitted thereby by controlling the refractive index of the light beam transmitted thereby. 
     The phase-modulator  132  implements a fourth modulating unit that is connected in series to the second modulating unit, that transmits the second light beam without branching the second light beam, and that modulates the phase of the light beam transmitted thereby by controlling the refractive index of the light beam transmitted thereby. The coupler  150  implements a coupler that couples at different intensities the first light beam of which phase is modulated by the first and the third modulating units and the second light beam of which phase is modulated by the second and the fourth modulating units. The attenuator  142  implements an attenuator that attenuates at least either one of the first and the second light beams such that the intensities of the first and the second light beams to be coupled by the coupler differ from each other. 
       FIG. 2  is a diagram of an example of the relation between the intensity of the optical signal after being transmitted by the Mach-Zehnder modulator and the driving signal. In  FIG. 2 , the horizontal axis represents the voltage of the driving signal input into the Mach-Zehnder modulators  121  and  122  and the vertical axis represents the intensity (optical intensity) of the optical signal after being transmitted by each of the Mach-Zehnder modulators  121  and  122 . A driving signal  202  represents the driving signal input into the Mach-Zehnder modulators  121  and  122 . A driver amplitude  203  represents the amplitude of the driving signal  202 . 
     A transmission property  201  represents the transmission property of the light beam of each of the Mach-Zehnder modulators  121  and  122  to the voltage of the driving signal  202  input into the Mach-Zehnder modulators  121  and  122 . The driving signal  202  takes a value of zero or one. As depicted by the transmission property  201 , when the driving signal  202  takes zero, the phase of the optical signal takes zero and the intensity of the light beam becomes the highest. When the driving signal  202  takes one, the phase of the optical signal takes π and the intensity of the light beam becomes the highest. 
     The transmission property  201  can be adjusted by controlling the bias voltage applied to the DC electrodes  121   b  and  122   b . For example, when the transmission property  201  is shifted to the right or left in  FIG. 2  due to the manufacture dispersion or use for a long time and the optical intensity does not become the highest for the driving signal that takes zero or one, adjustment can be executed such that the optical intensity becomes the highest for the driving signal that takes zero or one, by controlling the bias voltage. 
       FIG. 3  is a diagram of an example of the relation between the intensity of the optical signal after being transmitted by the phase modulator and the driving signal. In  FIG. 3 , the horizontal axis represents the voltage of the driving signal input into the phase modulators  131  and  132  and the vertical axis represents the intensity (optical intensity) of the optical signals after being transmitted by the phase modulators  131  and  132 . A driving signal  302  represents the driving signal input into the phase modulators  131  and  132 . A driver amplitude  303  represents the amplitude of the driving signal  302 . 
     A transmission property  301  represents the transmission property of the light beam of each of the phase modulators  131  and  132  to the voltage of the driving signal input into the phase modulators  131  and  132 . As depicted by the transmission property  301 , the intensity is always constant (the highest) regardless of the voltage of the driving signal input into the phase modulators  131  and  132 . 
     For example, even when the transmission property  301  is shifted to the right or left in  FIG. 3  due to the manufacture dispersion or use for a long time, the optical intensity is not varied. Therefore, with the phase modulators  131  and  132 , the optical intensity becomes the highest for the driving signal  202  that takes zero and one even when control of the bias voltage is not executed as executed for the Mach-Zehnder modulators  121  and  122  (see, e.g.,  FIG. 2 ). 
     The Mach-Zehnder modulators  121  and  122  will be described with reference to  FIGS. 4A to 6B . Any one of aspects of the Mach-Zehnder modulators  121  and  122  depicted in  FIGS. 4A to 6B  only has to be used. An aspect depicted in, for example,  FIG. 4A  is used in the first embodiment. 
       FIG. 4A  is a diagram of an example of a specific configuration of the Mach-Zehnder modulator including a Y-branch.  FIG. 4B  is a diagram of an example of flows of light beams and electric signals in the Mach-Zehnder modulator depicted in  FIG. 4A . In  FIGS. 4A and 4B , configurations same as the configurations depicted in  FIGS. 1A and 1B  are given the same reference numerals and will not again be described. The specific configuration of the Mach-Zehnder modulator  121  will be described. However, the specific configuration of the Mach-Zehnder modulator  122  is same as this configuration. As depicted in  FIGS. 4A and 4B , the Mach-Zehnder modulator  121  includes optical waveguides  401 ,  402 ,  403 , and  404 , a Y-branch  410 , and a Y-coupler  411 . 
     The optical waveguide  401  transmits the light beam output from the branch  110  (see, e.g.,  FIGS. 1A and 1B ) and outputs the light beam to the Y-branch  410 . The Y-branch  410  is an optical waveguide formed in a Y-shape and branches the light beam output from the optical waveguide  401  to the optical waveguides  402  and  403 . 
     The optical waveguide  402  transmits the light beam output from the Y-branch  410  and outputs the light beam to the Y-coupler  411 . The optical waveguide  403  transmits the light beam output from the Y-branch  410  and outputs the light beam to the Y-coupler  411 . The Y-coupler  411  is an optical waveguide formed in a Y-shape, couples the light beams output from the optical waveguides  402  and  403 , and outputs the coupled light beam to the optical waveguide  404 . The optical waveguide  404  outputs the light beam output from the Y-coupler  411 , to the phase modulator  131  (see, e.g.,  FIGS. 1A and 1B ). 
     The RF electrode  121   a  is formed on the optical waveguide  402  by, for example, gold evaporation. One end of the RF electrode  121   a  is connected to the driving unit  121   c  and the other end thereof is connected to the ground (GND) through a terminal resistor  420 . 
     With the above configuration, the driving unit  121   c  can: generate the driving signal that corresponds to the data  1  input thereinto; apply the driving signal to the RF electrode  121   a ; and modulate the phase of the light beam output from the Y-branch  410  and transmitted by the optical waveguide  402 . Thus, the phase difference between the light beams coupled by the Y-coupler  411  can be controlled and the two-value phase modulation can be executed. 
       FIG. 5A  is a diagram of an example of a specific configuration of the Mach-Zehnder modulator including a directional coupler.  FIG. 5B  is a diagram of an example of flows of light beams and electric signals in the Mach-Zehnder modulator depicted in  FIG. 5A . In  FIGS. 5A and 5B , configurations same as the configurations depicted in  FIGS. 1A ,  1 B,  4 A, and  4 B are given the same reference numerals and will not again be described. As depicted in  FIGS. 5A and 5B , the Mach-Zehnder modulator  121  may include directional couplers  510  and  511  instead of the Y-branch  410  and the Y-coupler  411  depicted in  FIGS. 4A and 4B . 
     The directional coupler  510  is provided to: cause light beams input thereinto from optical waveguides  501  and  502  to interfere with each other; and output the light beams acquired by the interference from the optical waveguides  402  and  403 . However, in this case, for example, the light beam is input from the optical waveguide  501  and no light beam is input from the optical waveguide  502 . Thus, the light beam input from the optical waveguide  501  can be branched and output from the optical waveguides  402  and  403 . 
     The directional coupler  511  is provided to: cause light beams input thereinto from optical waveguides  402  and  403  to interfere with each other; and output the light beams acquired by the interference from optical waveguides  503  and  504 . For example, the light beam output from the optical waveguide  503  is output to the phase modulator  131  and the light beam output from the optical waveguide  504  is discarded. 
     With the above configuration, the driving unit  121   c  can: generate the driving signal that corresponds to the data  1  input thereinto; apply the driving signal to the RF electrode  121   a ; and modulates the phase of the light beam output from the directional coupler  510  and transmitted by the optical waveguide  402 . Thus, the phase difference between the light beams output from the directional coupler  511  can be controlled and the two-value phase modulation can be executed. 
       FIG. 6A  is a diagram of an example of a specific configuration of the Mach-Zehnder modulator including a multi-mode interference (MMI).  FIG. 6B  is a diagram of an example of flows of light beams and electric signals in the Mach-Zehnder modulator depicted in  FIG. 6A . In  FIGS. 6A and 6B , configurations same as the configurations depicted in  FIGS. 1A ,  1 B, and  4 A to  5 B are given the same reference numerals and will not again be described. As depicted in  FIGS. 6A and 6B , the Mach-Zehnder modulator  121  may include MMI couplers  610  and  611  instead of the Y-branch  410  and the Y-coupler  411  depicted in  FIGS. 4A and 4B . 
     The MMI coupler  610  is provided to: cause light beams input thereinto from optical waveguides  501  and  502  to interfere with each other; and output the light beams acquired by the interference from the optical waveguides  402  and  403 . However, in this case, for example, the light beam is input from the optical waveguide  501  and no light beam is input from the optical waveguide  502 . Thus, the light beam input from the optical waveguide  501  can be branched and output from the optical waveguides  402  and  403 . 
     The MMI coupler  611  is provided to: cause light beams input thereinto from optical waveguides  402  and  403  to interfere with each other; and output the light beams acquired by the interference from optical waveguides  503  and  504 . For example, the light beam output from the optical waveguide  503  is output to the phase modulator  131  and the light beam output from the optical waveguide  504  is discarded. 
     With the above configuration, the driving unit  121   c  can: generate the driving signal that corresponds to the data  1  input thereinto; apply the driving signal to the RF electrode  121   a ; and modulates the phase of the light beam output from the MMI coupler  610  and transmitted by the optical waveguide  402 . Thus, the phase difference between the light beams output from the MMI coupler  611  can be controlled and the two-value phase modulation can be executed. 
       FIG. 7A  is a diagram of an example of a specific configuration of the phase modulator.  FIG. 7B  is a diagram of an example of flows of light beams and electric signals in the phase modulator depicted in  FIG. 7A . In  FIGS. 7A and 7B , configurations same as the configurations depicted in  FIGS. 1A and 1B  are given the same reference numerals and will not again be described. The specific configuration of the phase modulator  131  will be described. However, the specific configuration of the phase modulator  132  is same as this configuration. 
     As depicted in  FIGS. 7A and 7B , the phase modulator  131  includes the optical waveguide  404  and the RF electrode  131   a . The RF electrode  131   a  is formed on the optical waveguide  404  by, for example, gold evaporation. One end of the RF electrode  131   a  is connected to the driving unit  131   b  and the other end thereof is connected to the ground (GND) through the terminal resistor  420 . An optical signal of which phase is modulated by the phase modulator  131  is output to the phase shifter  141  or the attenuator  142 . 
     With the above configuration, the driving unit  131   b  can: generate the driving signal that corresponds to the data  3  input thereinto; apply the driving signal to the RF electrode  131   a ; and modulate the phase of the light beam transmitted by the optical waveguide  404 . Thus, the phase modulator  131  can execute four-value phase modulation for the optical signal output from the Mach-Zehnder modulator  121  corresponding to the driving signal applied to the RF electrode  131   a.    
     The optical waveguide  404  can realize one optical waveguide that achieves an electro-optical effect. The RF electrode  131   a  can realize an electrode that applies an electric field corresponding to a voltage applied thereto, to an optical waveguide. 
       FIG. 8A  is a diagram of an example of a specific configuration of the phase shifter.  FIG. 8B  is a diagram of an example of flows of light beams and electric signals in the phase shifter depicted in  FIG. 8A . In  FIGS. 8A and 8B , configurations same as the configurations depicted in  FIGS. 1A and 1B  are given the same reference numerals and will not again be described. As depicted in  FIGS. 8A and 8B , the phase shifter  141  includes the optical waveguide  404  and the DC electrode  141   a.    
     The DC electrode  141   a  is formed on the optical waveguide  404  by, for example, gold evaporation. One end of the DC electrode  141   a  is connected to the bias supply unit  141   b . The optical signal to which the bias is applied by the DC electrode  141   a  is output to the coupler  150 . 
     With the above configuration, the bias supply unit  141   b  can correct the shift of the phase between the optical signal output from the phase shifter  141  to the coupler  150  and the optical signal output from the attenuator  142  to the coupler  150 . 
     A specific configuration of the attenuator  142  will be described with reference to  FIGS. 9A to 11A . Any one of aspects of the attenuator  142  depicted in  FIGS. 9A to 11A  only has to be used. An aspect depicted in  FIG. 9A  is used in the first embodiment. For example, a Mach-Zehnder modulator can be used as the attenuator  142 . 
       FIG. 9A  is a diagram of an example of a specific configuration of the attenuator including the Y-branch.  FIG. 9B  is a diagram of an example of flows of light beams and electric signals in the attenuator depicted in  FIG. 9A . In  FIGS. 9A and 9B , configurations same as the configurations depicted in  FIGS. 1A and 1B  are given the same reference numerals and will not again be described. As depicted in  FIGS. 9A and 9B , the attenuator  142  includes the optical waveguide  404 , a Y-branch  910 , optical waveguides  901 ,  902 , and  903 , and a Y-coupler  911 . 
     The optical waveguide  404  transmits the light beam output from the phase modulator  132  (see, e.g.,  FIGS. 1A and 1B ) and outputs the light beam to the Y-branch  910 . The Y-branch  910  is an optical waveguide formed in a Y-shape and branches the light beam output from the optical waveguide  404  to the optical waveguides  901  and  902 . 
     The optical waveguide  901  transmits the light beam output from the Y-branch  910  and outputs the light beam to the Y-coupler  911 . The optical waveguide  902  transmits the light beam output from the Y-branch  910  and outputs the light beam to the Y-coupler  911 . The Y-coupler  911  is an optical waveguide formed in a Y-shape. The Y-coupler  911  couples the light beams output from the optical waveguides  901  and  902  and outputs the coupled light beam to the optical waveguide  903 . The optical waveguide  903  outputs the light beam output from the Y-coupler  911 , to the coupler  150  (see, e.g.,  FIGS. 1A and 1B ). 
     The DC electrode  142   a  is formed on the optical waveguide  901  by, for example, gold evaporation. One end of the DC electrode  142   a  is connected to the bias supply unit  142   b . With this configuration, the bias supply unit  142   b  can apply a bias to the DC electrode  142   a  and attenuate by 6 [dB] the intensity of the optical signal output from the Y-branch  910  and transmitted by the optical waveguide  901 . 
       FIG. 10A  is a diagram of an example of a specific configuration of the attenuator including the directional coupler.  FIG. 10B  is a diagram of an example of flows of light beams and electric signals in the attenuator depicted in  FIG. 10A . In  FIGS. 10A and 10B , configurations same as the configurations depicted in  FIGS. 1A ,  1 B,  9 A, and  9 B are given the same reference numerals and will not again be described. As depicted in  FIGS. 10A and 10B , the attenuator  142  may include directional couplers  1010  and  1011  instead of the Y-branch  910  and the Y-coupler  911  depicted in  FIGS. 9A and 9B . 
     The directional coupler  1010  is provided to cause the light beams input thereinto from optical waveguides  1001  and  1002  to interfere with each other and output the light beams acquired by the interference from the optical waveguides  901  and  902 . However, in this case, for example, the light beam is input from the optical waveguide  1001  and no light beams is input from the optical waveguide  1002  into the directional coupler  1010 . Thus, the directional coupler  1010  can branch the light beam input from the optical waveguide  1001  and can output the branched light beams from the optical waveguides  901  and  902 . 
     The directional coupler  1011  is provided to cause the light beams input thereinto from optical waveguides  1001  and  1002  to interfere with each other and output the light beams acquired by the interference from optical waveguides  1003  and  1004 . For example, the light beam output from the optical waveguide  1003  is output to the coupler  150  and the light beam output from the optical waveguide  1004  is discarded. 
     With the above configuration, the bias supply unit  142   b  can apply the bias to the DC electrode  142   a  and attenuate by 6 [dB] the intensity of the optical signal output from the directional coupler  1010  and transmitted by the optical waveguide  901 . 
       FIG. 11A  is a diagram of an example of a specific configuration of the attenuator including the MMI coupler.  FIG. 11B  is a diagram of an example of flows of light beams and electric signals in the attenuator depicted in  FIG. 11A . In  FIGS. 11A and 11B , configurations same as the configurations depicted in  FIGS. 1A ,  1 B, and  9 A to  10 B are given the same reference numerals and will not again be described. As depicted in  FIGS. 11A and 11B , the attenuator  142  may include MMI couplers  1110  and  1111  instead of the Y-branch  910  and the Y-coupler  911  depicted in  FIGS. 9A and 9B . 
     The MMI coupler  1110  is provided to cause the light beams input thereinto from optical waveguides  1001  and  1002  to interfere with each other and output the light beams acquired by the interference from the optical waveguides  901  and  902 . However, in this case, for example, the light beam is input from the optical waveguide  1001  and no light beams is input from the optical waveguide  1002  into the directional coupler  1010 . Thus, the directional coupler  1010  can branch the light beam input from the optical waveguide  1001  and can output the branched light beams from the optical waveguides  901  and  902 . 
     The MMI coupler  1111  is provided to cause the light beams input thereinto from optical waveguides  1001  and  1002  to interfere with each other and output the light beams acquired by the interference from optical waveguides  1003  and  1004 . For example, the light beam output from the optical waveguide  1003  is output to the coupler  150  and the light beam output from the optical waveguide  1004  is discarded. 
     With the above configuration, the bias supply unit  142   b  can apply the bias to the DC electrode  142   a  and attenuate by 6 [dB] the intensity of the optical signal output from the MMI coupler  1110  and transmitted by the optical waveguide  901 . 
     The configuration of the Mach-Zehnder attenuator  142  has been described with reference to  FIGS. 9A to 11B . However, not limited to the one of the Mach-Zehnder type, any one of various types of attenuator can be used as the attenuator  142 . 
       FIG. 12A  is a diagram of an example of the configuration to control the driving unit of the phase modulator.  FIG. 12B  is a diagram of an example of flows of light beams and electric signals in the configuration to control the driving unit depicted in  FIG. 12A . In  FIGS. 12A and 12B , configurations same as the configurations depicted in  FIGS. 1A and 1B  are given the same reference numerals and will not again be described. As depicted in  FIGS. 12A and 12B , the modulating apparatus  100  includes a coupler  1201 , a photo detector (PD)  1202 , an alternating current (AC) detecting unit  1203 , an AC power detecting unit  1204 , and a control unit  1205 . 
     The coupler  1201  partially branches the light beam output from the coupler  150  and outputs the partially branched light beam to the PD  1202 . The PD  1202  executes photo-electric conversion for the light beam output from the coupler  1201 . The PD  1202  outputs the electric signal acquired by the photo-electric conversion to the AC current detecting unit  1203 . 
     The AC current detecting unit  1203  detects the average AC current of the electric signal output from the PD  1202 . The AC current detecting unit  1203  outputs the detected average AC current to the AC power detecting unit  1204 . The AC power detecting unit  1204  detects the average AC power based on the average AC current output from the AC current detecting unit  1203 . The AC power detecting unit  1204  outputs the detected average AC power to the control unit  1205 . 
     The control unit  1205  controls the driving units  131   b  and  132   b  using the average AC power output from the AC power detecting unit  1204  and can be realized by a control circuit such as, for example, a central processing unit (CPU). The PD  1202 , the AC current detecting unit  1203 , and the AC power detecting unit  1204  can realize a detecting unit that detects a shift of the phase modulation amount caused by the third and the fourth modulating units based on the light beam coupled by the coupler. 
     The control for the driving units  131   b  and  132   b  will be described in detail with reference to constellations  1211  to  1213 . In the constellation  1211 , a phase error of each symbol from π/2 is represented as y [deg]. In the constellation  1212 , a phase error of each symbol from π/2 is represented as x [deg]. Assuming that all the 16 symbols in the constellation  1213  are present at an equal probability, AC currents and the average AC currents are as follows that are monitored by the PD  1202  and the AC current detecting unit  1203  for the symbols (A) to (D) and (a) to (d) in the constellation  1213 .
 
1 2 =1  (A)
 
(2−sin  x ) 2 +cos  x   2 =5−4 sin  x   (B)
 
3 2 =9  (C)
 
(2+sin  x ) 2 +cos  x   2 =5+4 sin  x   (D)
 
(2 sin  y −sin  x ) 2 +(2 cos  y −cos  x ) 2 =5−4 sin  x  sin  y −4 cos  x  cos  y   (a)
 
(2 sin  y+ 1) 2 +(2 cos  y ) 2 =5+4 sin  y   (b)
 
(2 sin  y +sin  x ) 2 +(2 cos  y +cos  x ) 2 =5+4 sin  x  sin  y +4 cos  x  cos  y   (c)
 
(2 sin  y− 1) 2 +(2 cos  y ) 2 =5−4 sin  y   (d)
 
Average AC Current=(( A )+( B )+( C )+( D )+( a )+( b )+( c )+( d ))/8=5
 
     However, the radius of the constellation  1213  is defined to be one. The symbols are symmetrical about the origin in the constellation  1213  and, therefore, symbols other than the symbols (A) to (D) and (a) to (d) will not be described. The values that can be taken by the current detected by the PD  1202  and the AC current detecting unit  1203  are the eight discrete values. 
     The AC power monitored by the AC power detecting unit  1204  means the AC power acquired by squaring the value acquired by subtracting the average AC current from the AC current. The average AC power represents the average of the eight pieces of AC power. Therefore, the AC currents and the average power form the following ratios, that are monitored by the AC power detecting unit  1204  at the symbols (A) to (D) and (a) to (d) in the constellation  1213 . 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               ( 
                               A 
                               ) 
                             
                             - 
                             5 
                           
                           ) 
                         
                         5 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       … 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             - 
                             4 
                           
                           ) 
                         
                         2 
                       
                     
                     = 
                     16 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           ( 
                           
                             
                               ( 
                               B 
                               ) 
                             
                             - 
                             5 
                           
                           ) 
                         
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       … 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               - 
                               4 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             x 
                           
                           ) 
                         
                         2 
                       
                     
                     = 
                     
                       16 
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         x 
                         2 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               ( 
                               C 
                               ) 
                             
                             - 
                             5 
                           
                           ) 
                         
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       … 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           4 
                           ) 
                         
                         2 
                       
                     
                     = 
                     16 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           ( 
                           
                             
                               ( 
                               D 
                               ) 
                             
                             - 
                             5 
                           
                           ) 
                         
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       … 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             4 
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             x 
                           
                           ) 
                         
                         2 
                       
                     
                     = 
                     
                       16 
                       ⁢ 
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         x 
                         2 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             ( 
                             a 
                             ) 
                           
                           - 
                           5 
                         
                         ) 
                       
                       2 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
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                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             4 
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                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
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                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             y 
                           
                           + 
                           
                             4 
                             ⁢ 
                             
                                 
                             
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                             ⁢ 
                             
                                 
                             
                             ⁢ 
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                             ⁢ 
                             
                                 
                             
                             ⁢ 
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                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             y 
                           
                         
                         ) 
                       
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           ( 
                           
                             
                               ( 
                               b 
                               ) 
                             
                             - 
                             5 
                           
                           ) 
                         
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
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                       ⁢ 
                       
                         
                           ( 
                           
                             4 
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                             ⁢ 
                             
                                 
                             
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                     = 
                     
                       16 
                       ⁢ 
                       
                           
                       
                       ⁢ 
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         y 
                         2 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             ( 
                             c 
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                           - 
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                     ⁢ 
                     
                         
                     
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                       2 
                     
                   
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                   ⁢ 
                   
                     
                       
                         
                           ( 
                           
                             
                               ( 
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                       ⁢ 
                       
                           
                       
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                     = 
                     
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                       ⁢ 
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                         y 
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                           Average 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           AC 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Power 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             { 
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               ( 
                                               
                                                 
                                                   ( 
                                                   A 
                                                   ) 
                                                 
                                                 - 
                                                 5 
                                               
                                               ) 
                                             
                                             2 
                                           
                                           + 
                                           
                                             
                                               ( 
                                               
                                                 
                                                   ( 
                                                   B 
                                                   ) 
                                                 
                                                 - 
                                                 5 
                                               
                                               ) 
                                             
                                             2 
                                           
                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               ( 
                                               
                                                 
                                                   ( 
                                                   C 
                                                   ) 
                                                 
                                                 - 
                                                 5 
                                               
                                               ) 
                                             
                                             2 
                                           
                                           + 
                                           
                                             
                                               ( 
                                               
                                                 
                                                   ( 
                                                   D 
                                                   ) 
                                                 
                                                 - 
                                                 5 
                                               
                                               ) 
                                             
                                             2 
                                           
                                           + 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               ( 
                                               
                                                 
                                                   ( 
                                                   a 
                                                   ) 
                                                 
                                                 - 
                                                 5 
                                               
                                               ) 
                                             
                                             2 
                                           
                                           + 
                                           
                                             
                                               ( 
                                               
                                                 
                                                   ( 
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                                                   ) 
                                                 
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                                           + 
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               ( 
                                               
                                                 
                                                   ( 
                                                   c 
                                                   ) 
                                                 
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                                                   d 
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                                                 5 
                                               
                                               ) 
                                             
                                             2 
                                           
                                         
                                       
                                     
                                   
                                 
                               
                             
                             } 
                           
                           / 
                           8 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           4 
                           + 
                           
                             4 
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               x 
                               2 
                             
                           
                           + 
                           
                             4 
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               y 
                               2 
                             
                           
                           + 
                           
                             4 
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               x 
                               2 
                             
                             × 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               y 
                               2 
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             4 
                             ⁢ 
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                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               x 
                               2 
                             
                             × 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               y 
                               2 
                             
                           
                           + 
                           
                             8 
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             x 
                             × 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             x 
                             × 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             y 
                             × 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             y 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           10 
                           - 
                           
                             2 
                             ⁢ 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             y 
                           
                           - 
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   y 
                                 
                               
                               ) 
                             
                             × 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             x 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           2 
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           x 
                           × 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                           ⁢ 
                           y 
                         
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     “x” and “y” are errors and it can be considered that these errors are significantly small. Therefore, 1−cos 2y&gt;0, cos 2x&gt;0, sin 2y&gt;0, sin 2x&gt;0 are acquired. The third term of the equation is a negative number and the fourth term thereof is a positive number. Thus, when the average AC power monitored by the AC power detecting unit  1204  is controlled to be reduced to its minimal value, the “cos 2x” of the third term is controlled to be increased to its maximal value and the “sin 2x” of the fourth term is controlled to be reduced to its minimal value. “x” converges to zero. The above equation becomes the same equation when “x” and “y” are exchanged with each other and, therefore, “y” also converges to zero. Therefore, when the average AC power monitored by the AC power detecting unit  1204  is controlled to be reduced to its minimal value, “x” and “y” both converge to zero and the phase error can be controlled to be reduced to its minimal value. 
       FIG. 13  is a flowchart of a control process for the driving unit of the phase modulator executed by the control unit. As depicted in  FIG. 13 , the control unit  1205  sets the counter i to be one (step S 1301 ) and determines whether i is equal to or smaller than a desired value p (step S 1302 ). The desired value p is, for example, a value set in advance. 
     When the control unit  1205  determines that i is equal to or smaller than p (step S 1302 : YES), the control unit  1205  monitors the average AC power in the previous session (step S 1303 ) and increases by an amplitude variation width Δa an amplitude V 3  [mVpp] of the driving signal output by the driving unit  131   b  (for example, the driver amplitude  303  depicted in  FIG. 3 ) (step S 1304 ). The amplitude variation width Δa is, for example, a value set in advance. The control unit  1205  monitors the current average AC power (step S 1305 ) and determines whether the current average AC power is lower than the average AC power in the previous session (step S 1306 ). 
     When the control unit  1205  determines at step S 1306  that the current average AC power is lower than the average AC power in the previous session (step S 1306 : YES), the control unit  1205  adds one to the counter i (step S 1307 ) and progresses to the process at step S 1302 . Thus, when the property is improved by increasing the amplitude V 3  at step S 1304 , the increased amplitude V 3  can be maintained. 
     When the control unit  1205  determines at step S 1306  that the current average AC power is equal to or higher than the average AC power in the previous session (step S 1306 : NO), the control unit  1205  decreases by 2 Δa the amplitude V 3  [mVpp] of the driving signal output by the driving unit  131   b  (step S 1308 ) and progresses to the process at step S 1307 . Thus, when the property is degraded by increasing the amplitude V 3  at step S 1304 , the increased amplitude V 3  can be reduced to an amplitude that is lower than the original amplitude V 3 . 
     When the control unit  1205  determines at step S 1302  that i exceeds p (step S 1302 : NO), the control unit  1205  progresses to the process at step S 1309 . The control unit  1205  sets the counter j to be one (step S 1309 ) and determines whether j is equal to or smaller than the desired value p (step S 1310 ). 
     When the control unit  1205  determines that j is equal to or smaller than p (step S 1310 : YES), the control unit  1205  monitors the average AC power of the previous session (step S 1311 ), increases by an amplitude variation width Δb an amplitude V 4  [mVpp] of the driving unit  132   b  (step S 1312 ), monitors the average AC power of the current session (step S 1313 ), and determines whether the average AC power of the current session is lower than the average AC power of the previous session (step S 1314 ). 
     When the control unit  1205  determines that the average AC power of the current session is lower than the average AC power of the previous session (step S 1314 : YES), the control unit  1205  adds one to the counter j (step S 1315 ) and progresses to the process at step S 1310 . When the control unit  1205  determines that the average AC power of the current session is equal to or higher than the average AC power of the previous session (step S 1314 : NO), the control unit  1205  reduces by 2 Δb the amplitude V 4  [mVpp] of the driving unit  132   b  (step S 1316 ) and progresses to the process at step S 1315 . When the control unit  1205  determines at step S 1310  that j exceeds p (step S 1310 : NO), the control unit  1205  causes the series of process steps according to the flowchart to come to an end. 
     With the above process steps, the amplitude of each of the driving signals can be controlled that are input into the phase modulators  131  and  132  such that the average AC power monitored by the AC power detecting unit  1204  is reduced. Thus, the error can be reduced in the phase modulation by the phase modulators  131  and  132 . 
     Thus, in the first embodiment: the Mach-Zehnder modulator  121  and the phase modulator  131  are connected in series and, thereby, the four- or more-value phase modulation can be executed; and the Mach-Zehnder modulator  122  and the phase modulator  132  are connected in series and, thereby, the four- or more-value phase modulation can be executed. The optical signals each applied with the four- or more-value phase modulation are coupled at different intensities and, thereby, the 16- or more-value QAM is enabled. 
     The phase modulators  131  and  132  do not branch any light beam and do not cause any light beams to interfere with each other and, therefore, their transmission factors are not varied even when any phase shift occurs. Thus, the control of the phase modulators  131  and  132  can be simplified. For example, no bias control needs to be executed for the phase modulators  131  and  132 . Therefore, the control of the modulating apparatus  100  can be simplified. 
     The phase modulators  131  and  132  can execute the phase modulation based on zero or π/2 and, therefore, no π/2 shifter needs to be provided. Thus, the configuration of the modulating apparatus  100  can be simplified. 
       FIG. 14A  is a diagram of another example of the configuration to control the driving unit of the phase modulator.  FIG. 14B  is a diagram of an example of flows of light beams and electric signals in the configuration to control the driving unit depicted in  FIG. 14A . In  FIGS. 14A and 14B , configurations same as the configurations depicted in  FIGS. 12A and 12B  are given the same reference numerals and will not again be described. As depicted in  FIGS. 14A and 14B , a PD  1401  monitors an opposite-phase light beam of the coupler  150 . For example, the PD  1401  executes photo-electric conversion for the opposite-phase light beam output from the coupler  150 . The PD  1401  outputs an electric signal acquired by the photo-electric conversion to the AC current detecting unit  1203 . 
     The control executed for the driving units  131   b  and  132   b  will be described in detail. When the opposite-phase light beam is monitored, the control can be executed in the same manner as that for the in-phase light beam. In a constellation  1211 , a phase error of each symbol from π/2 is represented by y [deg]. In a constellation  1212 , a phase error of each symbol from π/2 is represented by x [deg]. Because of the symmetry about the origin, calculation of (A) to (D) and (a) to (d) will be described. The AC current acquired when the opposite-phase light beam is monitored is a current acquired by subtracting the in-phase light beam from the total light beam intensity and, therefore, the AC current and the average AC current are acquired as follows.
 
9−1 2 =8  (A)
 
9−((2−sin  x ) 2 +cos  x   2 )=4+4 sin  x   (B)
 
9−3 2 =0  (C)
 
9−((2+sin  x ) 2 +cos  x   2 )=4−4 sin  x   (D)
 
9−((2 sin  y −sin  x ) 2 +(2 cos  y −cos  x ) 2 )=4+4 sin  x  sin  y+ 4 cos  x  cos  y   (a)
 
9−((2 sin  y+ 1) 2 +(2 cos  y ) 2 )=4−4 sin  y   (b)
 
9−((2 sin  y +sin  x ) 2 +(2 cos  y +cos  x ) 2 )=4−4 sin  x  sin  y− 4 cos  x  cos  y   (c)
 
9−((2 sin  y− 1) 2 +(2 cos  y ) 2 )=4+4 sin  y   (d)
 
Average Current=(( A )+( B )+( C )+( D )+( a )+( b )+( c )+( d ))/8=4
 
     The AC power and the average AC power at this moment are as follows. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     The completely same calculation result as that of the in-phase light beam is acquired as the average AC power. “x” and “y” are the errors and it can be considered that x and y are significantly smaller than π/4. Therefore, 1−cos 2y&gt;0, cos 2x&gt;0, sin 2y&gt;0, sin 2x&gt;0 are acquired and the third term of the equation is a negative number and the fourth term thereof is a positive number. Thus, when the average AC power is controlled to be reduced to its minimal value, “cos 2x” in the third term is controlled to be increased to its maximal value and “sin 2x” in the fourth term is controlled to be reduced to its minimal value. “x” converges to zero. The above equation becomes the same equation when “x” and “y” are exchanged with each other and, therefore, “y” also converges to zero. Therefore, when the average AC power is controlled to be reduced to its minimal value, “x” and “y” both converge to zero and the phase error can be controlled to be reduced to its minimal value. 
     Thus, for the case where the opposite-phase light beam is monitored, similarly to the case where the in-phase light beam is monitored, the amplitude of each of the driving signals input into the phase modulators  131  and  132  can be controlled such that the average AC power monitored by the AC power detecting unit  1204  is reduced. Thus, the error of the phase modulation caused by the phase modulators  131  and  132  can be reduced. 
     The second embodiment of the modulating apparatus will be described. In the second embodiment, the portions will be described that differ from the first embodiment. 
       FIG. 15A  is a diagram of an example of a specific configuration of a modulating apparatus according to the second embodiment.  FIG. 15B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 15A . In  FIGS. 15A and 15B , configurations same as the configurations depicted in  FIGS. 1A and 1B  are given the same reference numerals and will not again be described. 
     As depicted in  FIGS. 15A and 15B , the modulating apparatus  100  according to the second embodiment does not need to include the attenuator  142 . The branch  110  branches the light beam input into the modulating apparatus  100  into light beams at different intensities. For example, the branch  110  branches the input light beam at the intensity ratios of 1:¼. The phase modulator  132  outputs the light beam acquired by the phase modulation to the coupler  150 . 
     The coupler  150  couples the optical signal output from the phase shifter  141  and the optical signal output from the phase modulator  132 . For example, the coupler  150  couples the optical signal output from the phase shifter  141  and the optical signal output from the phase modulator  132  at the intensity ratios of 1:1. Thus, the intensity ratios can be set to be 1:¼ of the optical signal modulated by the Mach-Zehnder modulator  121  and the phase modulator  131  and the optical signal modulated by the Mach-Zehnder modulator  122  and the phase modulator  132 . With the above configuration, the optical signal output from the coupler  150  is converted into a 16-QAM optical signal. 
     A variation of the modulating apparatus according to the second embodiment will be described. In the variation of the modulating apparatus according to the second embodiment, the case will be described where the intensity ratio of each of the input and the output light beams is made variable.  FIG. 16A  is a diagram of a configuration of a variation of the modulating apparatus according to the second embodiment.  FIG. 16B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 16A . In  FIGS. 16A and 16B , configurations same as the configurations depicted in  FIGS. 15A and 15B  are given the same reference numerals and will not again be described. As depicted in  FIGS. 16A and 16B , the branch  110  branches the light beam input into the modulating apparatus  100  into light beams at different intensity ratios. 
     For example, the branch  110  branches the input light beam at the intensity ratios of 1:½. The coupler  150  couples the light beam from the phase shifter  141  and the light beam from the phase modulator  132  at different intensity ratios. For example, the coupler  150  couples the optical signal output from the phase shifter  141  and the optical signal output from the phase modulator  132  at the intensity ratios of 1:½. 
     Thus, the intensity ratios can be set to be 1:¼ of the optical signal modulated by the Mach-Zehnder modulator  121  and the phase modulator  131  and the optical signal modulated by the Mach-Zehnder modulator  122  and the phase modulator  132 . With the above configuration, the optical signal output from the coupler  150  is converted into a 16-QAM optical signal. 
     Thus, according to the modulating apparatus  100  according to the second embodiment, similarly to the first embodiment, the control and the configuration of the modulating apparatus  100  can be simplified. Especially, the modulating apparatus  100  according to the second embodiment can be configured not to include the attenuator  142  and, therefore, no bias control needs to be executed for the attenuator  142 . Thus, the control and the configuration of the modulating apparatus  100  can further be simplified. 
     The third embodiment of the modulating apparatus will be described. In the third embodiment, a modulating apparatus will be described that modulates a 4 N -QAM optical signal (“N” is an integer that is two or greater). In the third embodiment, the portions will be described that differ from the first and the second embodiments. 
       FIG. 17A  is a diagram of an example of a specific configuration of a modulating apparatus according to the third embodiment.  FIG. 17B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 17A . In  FIGS. 17A and 17B , configurations same as the configurations depicted in  FIGS. 1A and 1B  are given the same reference numerals and will not again be described. 
     As depicted in  FIGS. 17A and 17B , the modulating apparatus  100  includes the branch  110 , the Mach-Zehnder modulators  121  to  12 N, the phase modulators  131  to  13 N, the attenuators  142  to  14 N, phase shifters  1702  to  170 N, and the coupler  150 . 
     The branch  110  N-branches the light beam input into the modulating apparatus  100  and outputs the N-branched light beams to the Mach-Zehnder modulators  121  to  12 N. The Mach-Zehnder modulators  121  to  12 N execute two-value phase modulation for the light beams output from the branch  110  and respectively output the light beams acquired by the phase modulation, to the phase modulators  131  to  13 N. 
     The phase modulators  131  to  13 N respectively execute four-value phase modulation for the optical signals output from the Mach-Zehnder modulators  121  to  12 N, corresponding to the driving signal. The phase modulator  131  outputs the light beam acquired by the phase modulation to the coupler  150 . The phase modulators  132  to  13 N respectively output the light beams acquired by the phase modulation to the attenuators  142  to  14 N. The attenuators  142  to  14 N attenuate by, for example, 6 N-1  [dB] the intensities of the optical signals output from the phase modulators  132  to  13 N. 
     The attenuators  142  to  14 N respectively output the attenuated optical signals to the phase shifters  1702  to  170 N. The phase shifters  1702  to  170 N respectively correct the phase shifts of the optical signals output from the attenuators  142  to  14 N and output the corrected optical signals to the coupler  150 . The coupler  150  couples the optical signal output from the phase modulator  131  and those output from the phase shifters  1702  to  170 N. 
     Thus, the intensity ratios can be set to be 1:¼: . . . :¼ N-1  of the optical signal modulated by the Mach-Zehnder modulator  121  and the phase modulator  131  and the optical signals modulated by the Mach-Zehnder modulators  122  to  12 N and the phase modulators  132  to  13 N. Therefore, the optical signal output from the coupler  150  can be converted into a 4 N -QAM optical signal. 
     Thus, according to the modulating apparatus  100  according to the third embodiment, the control and the configuration of the modulating apparatus  100  can be simplified that modulates the 4 N -QAM optical signal. 
     A variation 1 of the modulating apparatus according to the third embodiment will be described. For the variation 1 of the modulating apparatus according to the third embodiment, the case will be described where the attenuators  142  to  14 N are not included.  FIG. 18A  is a diagram of a configuration of the variation 1 of the modulating apparatus according to the third embodiment.  FIG. 18B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 18A . In  FIGS. 18A and 18B , configurations same as the configurations depicted in  FIGS. 17A and 17B  are given the same reference numerals and will not again be described. 
     As depicted in  FIG. 18A , the branch  110  N-branches the light beam input into the modulating apparatus  100 , into light beams at different intensity ratios. For example, the branch  110  branches the input light beam at the intensity ratios of 1:¼: . . . :¼ N-1 . 
     The phase modulators  132  to  13 N respectively output the light beams acquired by the phase modulation to the phase shifters  1702  to  170 N. The phase shifters  1702  to  170 N respectively correct phase shifts of the optical signals output from the phase modulators  132  to  13 N and output the corrected optical signals to the coupler  150 . 
     The coupler  150  couples the optical signal output from the phase modulator  131  and those output from the phase shifters  1702  to  170 N at equal intensity ratios Thus, the intensity ratios can be set to be 1:¼: . . . :¼ N-1  of the optical signal modulated by the Mach-Zehnder modulator  121  and the phase modulator  131  and those modulated by the Mach-Zehnder modulators  122  to  12 N and the phase modulators  132  to  13 N. With this configuration, similarly to the third embodiment, the optical signal output from the coupler  150  can be converted into a 4 N -QAM optical signal. 
     Thus, according to the modulating apparatus  100  according to the variation 1 of the third embodiment, similarly to the modulating apparatus  100  according to the third embodiment, the control and the configuration of the modulating apparatus  100  can be simplified. Especially, the modulating apparatus  100  according to the variation 1 of the third embodiment can be configured not to include the attenuators  142  to  14 N and, therefore, the bias control does not need to be executed for each of the attenuators  142  to  14 N. Thus, the control and the configuration of the modulating apparatus  100  can be further simplified. 
     A variation 2 of the modulating apparatus according to the third embodiment will be described. For the variation 2 of the modulating apparatus according to the third embodiment, the case will be described where the intensity ratio of each of the input and the output light beams is made variable.  FIG. 19A  is a diagram of a configuration of the variation 2 of the modulating apparatus according to the third embodiment.  FIG. 19B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 19A . In  FIGS. 19A and 19B , configurations same as the configurations depicted in  FIGS. 17A to 18B  are given the same reference numerals and will not again be described. 
     As depicted in  FIGS. 19A and 19B , the branch  110  branches the light beam input into the modulating apparatus  100 , into light beams at different intensity ratios. For example, the branch  110  branches the input light beam at the intensity ratios of 1:½: . . . :½ N-1 . 
     The coupler  150  couples the optical signal output from the phase modulator  131  and those output from the phase shifters  1702  to  170 N at different intensity ratios. For example, the coupler  150  couples the optical signals output from the phase shifters  1702  to  170 N and the optical signal output from the phase modulator  131  at the intensity ratios of 1:½: . . . :½ N-1 . Thus, the intensity ratios can be set to be 1:¼: . . . :¼ N-1  of the optical signal modulated by the Mach-Zehnder modulator  121  and the phase modulator  131  and those modulated by the Mach-Zehnder modulators  122  to  12 N and the phase modulators  132  to  13 N. With this configuration, similarly to the third embodiment, the optical signal output from the coupler  150  can be converted into a 4 N -QAM optical signal. 
     Thus, according to the modulating apparatus  100  according to the variation 2 of the third embodiment, similarly to the modulating apparatus  100  according to the variation 1 of the third embodiment, the control and the configuration of the modulating apparatus  100  can be simplified. 
     The fourth embodiment of the modulating apparatus will be described. In the fourth embodiment, the case will be described where the Mach-Zehnder modulators  121  and  122  and the phase modulators are not provided in series but the phase modulators are provided in series. In the fourth embodiment, portions will be described that differ from the first to the third embodiments. 
       FIG. 20A  is a diagram of an example of a specific configuration of a modulating apparatus according to the fourth embodiment.  FIG. 20B  is a diagram of an example of flows of light beams and electric signals in the modulating apparatus depicted in  FIG. 20A . In  FIGS. 20A and 20B , configurations same as the configurations depicted in  FIGS. 1A and 1B  are given the same reference numerals and will not again be described. 
     As depicted in  FIGS. 20A and 20B , a modulating apparatus  100  according to the fourth embodiment includes phase modulators  2001  and  2011  in stead of the Mach-Zehnder modulators  121  and  122  described in the first embodiment (see, e.g.,  FIGS. 1A and 1B ). For example, the modulating apparatus  100  includes the phase modulators  2001  and  2011 , and driving units  2003  and  2013  in stead of the Mach-Zehnder modulators  121  and  122 , the driving units  121   c  and  122   c , and the bias supply units  121   d  and  122   d  that are described in the first embodiment. 
     The branch  110  branches the light beam input into the modulating apparatus  100  and outputs the branched light beams to the phase modulators  2001  and  2011 . The phase modulator  2001  includes an RF electrode  2002 . The driving unit  2003  generates a driving signal that corresponds to the data  1  input thereinto and applies the driving signal to the RF electrode  2002 . 
     The phase modulator  2001  executes phase modulation to vary by zero or π the phase of the optical signal output from the branch  110 . Thus, two-value (zero and π) phase modulation can be executed. The phase modulator  2001  outputs the light beam acquired by the phase modulation to the phase modulator  131 . 
     The phase modulator  2011  includes an RF electrode  2012 . The driving unit  2013  generates a driving signal that corresponds to the data  2  input thereinto and applies the driving signal to the RF electrode  2012 . The phase modulator  2011  executes phase modulation to vary by zero or π the phase of the optical signal output from the branch  110  corresponding to the driving signal applied to the RF electrode  2012 . Thus, two-value (zero and π) phase modulation can be executed. The phase modulator  2011  outputs the light beam acquired by the phase modulation to the phase modulator  132 . 
     The phase modulator  131  executes the phase modulation to vary by zero or π the phase of the optical signal output from the phase modulator  2001  corresponding to the driving signal applied to the RF electrode  131   a . Thus, four-value (zero, π/2, π, and 3π/2) phase modulation can be executed. 
     The phase modulator  132  executes the phase modulation to vary by zero or π the phase of the optical signal output from the phase modulator  2011  corresponding to the driving signal applied to the RF electrode  132   a . Thus, four-value (zero, π/2, π, and 3π/2) phase modulation can be executed. 
     With this configuration, similarly to the first embodiment, such optical signals can be coupled at the intensity ratios of 1:¼ as that modulated by the phase modulators  2001  and  131  and that modulated by the phase modulators  2011  and  132 . Thus, the optical signal output from the coupler  150  can be converted into the 16-QAM optical signal. 
     The units to be controlled can be reduced to six units as a total that are: the driving units  131   b ,  132   b ,  2003 , and  2013 ; and the bias supply units  141   b  and  142   b . Therefore, the configuration and the control can further be simplified compared to the first embodiment. 
     The modulating apparatus  100  according to the fourth embodiment may be configured not to include the attenuator  142 . For example, as described for the second embodiment (see, e.g.,  FIGS. 15A to 16B ), the modulating apparatus  100  may be configured for the branch  110  to branch the light beam into light beams at different intensities or may also be configured for the coupler  150  to couple the light beams at different intensities. 
     The modulating apparatus  100  according to the fourth embodiment is configured to modulate the 16-QAM optical signal while may be configured to modulate a 4 N -QAM optical signal. For example, the modulating apparatus  100  according to the fourth embodiment may be configured to have three or more stages with N that is N≧2 as described for the third embodiment (see, e.g.,  FIGS. 17A to 19B ). 
     Thus, in the fourth embodiment: the phase modulators  2001  and  131  are connect to each other in series and, thereby, the four- or more-value phase modulation can be executed; and the phase modulators  2011  and  132  are connect to each other in series and, thereby, the four- or more-value phase modulation can be executed. The optical signals each applied with the four- or more-value phase modulation are coupled at different intensities and, thereby, the 16- or more-value QAM is enabled. 
     The phase modulators  131 ,  132 ,  2001 , and  2011  do not branch any light beam and do not cause any light beams to interfere with each other and, therefore, their transmission factors are not varied even when any phase shift occurs. Thus, the control of the phase modulators  131 ,  132 ,  2001 , and  2011  can be simplified. For example, no bias control needs to be executed for the phase modulators  131 ,  132 ,  2001 , and  2011 . Therefore, the control of the modulating apparatus  100  can be simplified. 
     According to an aspect of the present invention, an effect is achieved that the control can be simplified. 
     All examples and conditional language provided herein are intended for pedagogical purposes of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.