Abstract:
A Mach-Zehnder (MZ) modulator made of semiconductor material and a method to drive the MZ-modulator are disclosed. The MZ-modulator includes a pair of arms to vary the phase of the optical beam propagating therein. One of the arms further provides the phase presetter that varies the phase of the optical beam by π. The arms are driven by modulation signals complementary to each other but with the DC bias equal to each other.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present application relates to a method to drive a Mach-Zehnder modulator (hereafter denoted as MZ-modulator), in particular, the application relates to a method to drive a semiconductor MZ-modulator. 
     2. Related Background Arts 
     Many prior arts have disclosed an MZ-modulator that provides an input optical waveguide to guide an input optical beam, a branch to divide the input optical beam into two beams, a pair of phase modulators each coupled with the branch, an optical coupler to couple two beams each divided by the optical branch and propagated in the phase modulators into a composite optical beam, and an output optical waveguide to guide the composite optical beam. These members of the input optical waveguide, the optical branch, the phase modulators, the optical coupler, and the output optical waveguide, are monolithically integrated on a substrate. Each of the phase modulators has an equivalent refractive index different from others. The phase difference between optical beams each propagating in the phase modulators are given by (2n+1)×π, where n is zero or positive integers, under a condition of no modulation signal. That is, two optical beams each output from the phase modulators countervail to each other under such a condition, which results in no optical output from the MZ-modulator. 
     As the volume to be transmitted by the optical communication system explosively increases, an additional technique fundamentally different from the conventional magnitude modulation has been requested. The optical QPSK (Quadrature Phase Shift Keying) technique is one of the solutions for such requests. A transmitter operable in the QPSK mode includes a laser diode (LD) as an optical source and an optical phase modulator to modulate the optical beam emitted from the LD by the QPSK mode. The QPSK modulator is constituted by a pair of MZ-modulators. However, when the MZ-modulator is made of semiconductor material, various subjects to be solved have been known. 
     SUMMARY OF THE INVENTION 
     One aspect of the present application relates to a MZ-modulator made of semiconductor material. The MZ-modulator includes an optical branch, a pair of arm waveguides, a phase presetter, and an optical coupler. The optical branch divides an input optical beam into two optical beams each provided to respective arm waveguides. The phase presetter is put in one of arm waveguides, and varies a phase of the optical beam propagating therein by π. The optical coupler couples the optical beam propagating in the arm waveguide without the phase presetter with the other optical beam propagating in the other arm waveguide with the phase presetter. The arm waveguides are driven by modulation signals accompanied with biases. A feature of the MZ-modulator of the invention is that the modulation signals are complementary to each other with a swing range substantially same to each other and the biases are also substantially same to each other 
     Because the phase presetter shifts the phase of the optical beam propagating therein by π, the arm waveguide without phase presetter modulates the phase of the optical beam in a range from 0 to π responding to the modulation signal from V(0) to V(π); while, the arm waveguide with the phase presetter modulates the phase of the optical beam in a range from 2π to π responding to the other modulation signals with the opposite phase from V(2π) to V(π). Thus, two modulation signals have the swing range and the bias same to each other. According to the MZ-modulator of the present application, even the MZ-modulator is made of semiconductor material that inevitably shows the non-linearity of the phase variation against the bias provided thereto, the driving conditions may be simplified. 
     The phase pre setter provides an optical waveguide with an electrode, namely, an arrangement same with that of the arm waveguide. Providing a bias V(π), where V(π) means a voltage corresponding to the phase shift of an optical beam propagating therein by π, to the electrode, the equivalent refractive index of the optical waveguide is varied, which means that the optical length thereof varies and the phase of the optical beam passing therethrough is also varied. In an altered example, the phase presetter includes only an optical waveguide whose physical length is varied by a length corresponding to the phase shift of the optical beam propagating therein by π. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other purposes, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which: 
         FIG. 1  is a plan view of an optical modulator according to a comparable embodiment; 
         FIG. 2  is the polar displays of the optical beams measured at the optical input terminal and points A to H marked in  FIG. 1 ; 
         FIG. 3  shows a relation of the phase shift and the optical loss against the bias of an optical waveguide made of semiconductor material; 
         FIG. 4A  shows the phase shift against the bias observed in an optical waveguide made of dielectric material, and  FIG. 4B  is a polar display of signal statuses obtained in the optical waveguide having the relation shown in  FIG. 4A ; 
         FIG. 5A  shows the phase shift against the bias observer in an optical waveguide made of semiconductor material, and  FIG. 5B  is a polar display of signal statuses obtained in the optical waveguide shown in  FIG. 5B  and driven by a mode same with those in  FIG. 4B : 
         FIGS. 6A and 6B  compare the constellation of the composite beam output from a MZ-modulator made of dielectric material ( FIG. 6A ) and that made of semiconductor material ( FIG. 6B ); 
         FIG. 7  is a plan view schematically showing a fundamental arrangement of the MZ-modulator made of semiconductor material; 
         FIG. 8A  shows the phase variation against the bias of the MZ-modulator  10 , and  FIG. 8B  is a polar display of output statuses of the MZ-modulator of the present embodiment; 
         FIG. 9  is a plan view of a QPSK modulator made of semiconductor material according to the second embodiment of the invention. 
         FIG. 10  shows the constellation of the composite optical beam output from the QPSK modulator shown in  FIG. 9 ; 
         FIG. 11  is a plan view of another QPSK modulator according to a modification of the aforementioned QPSK modulator shown in  FIG. 9 ; 
         FIG. 12  shows an example of the output constellation of the QPSK modulator shown in  FIG. 11 ; 
         FIG. 13  is a plan view of still another embodiment of a QPSK modulator made of semiconductor material, which is modified from that shown in  FIG. 11 ; and 
         FIG. 14  is a magnified plan view of the waveguides implemented within the QPSK modulators shown in  FIGS. 11 and 13 . 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Next, some preferred embodiments according to the present invention will be described as referring to drawings. In the description of the drawings, numerals or symbols same or similar to each other will refer to elements same or similar to each other without overlapping explanations. 
       FIG. 1  is a plan view of a QPSK modulator according to a comparable embodiment. The QPSK modulator  100  shown in  FIG. 1  includes an input terminal  101  to input an optical beam Lin to be modulated, and an output terminal  102  to output an optical beam Lout modulated by the modulation signals, V 11  to V 22 . The input terminal  101  couples with an optical branch  103  that divides the optical beam Lin into two optical beams Lin 1  and Lin 2 . 
     One of the outputs of the optical branch  103  couples with the first MZ-modulator  110  that modulates the optical beam Lin 1  by the BPSK (Binary Phase Shift Keying) mode where the optical beam output from the first MZ-modulator  110  has two phase statuses of 0 (rad) and Π (rad) each corresponding to the bits “0” and “1”. Here, the phase statuses of 0 (rad) and Π (rad) are relative conditions which merely means that assuming the phase status corresponding to bit “0” is 0 (rad), the phase status for bit “1” is shifted by Π (rad). 
     Specifically, the optical beam Lin 1  output from the optical branch  103  is further divided into two optical beams, L 11  and L 12 , by the optical branch  111 , where the former optical beam L 11  propagates within the optical waveguide  112 ; while, the latter optical beam L 12  propagates in the optical waveguide  113 . When the bit status “0” is required, a bias V 11  to advance the phase of the optical beam L 11  forward while another bias V 12  to advance the phase of the other optical beam L 12  backward are provided to respective electrodes,  115  and  116 ; which realizes the phase of 0(rad) in the composite optical beam. On the other hand, when the bit status “1” is required, the signal V 11  to advance the phase of the optical beam L 11  backward while the other signal V 12  to advance the phase of the optical beam L 12  forward are provided to respective electrodes,  115  and  116 . Thus, the composite optical beam output from the MZ-modulator  110  shows the phase status of π(rad). 
     In an exemplary condition, when the bit status “0” is required, no biases are provided to the electrodes,  115  and  116 , which maintains the phase of the optical beams, L 11  and L 12 , same as that of the optical beam Lin 1 . While, when the bit status “1” is required, the signal V 11  to advance the phase of the optical beam L 11  forward by π(rad), while, the other signal V 12  to advance the phase of the optical beam L 12  backward by π(rad) are provided to respective electrodes,  115  and  116 . 
     The other of the outputs of the optical branch  103  couples with the second MZ-modulator  120 . The second MZ-modulator  120  also modulates the second optical beam Lin 2  by the BPSK mode. That is, the optical beam Lin 2  is further divided into two beams, L 21  and L 22 , each propagating within the optical waveguides,  122  and  123 . Two signals, V 21  and V 22 , to advance the phases of two beams, L 21  and L 22 , forward and backward, are provided to the electrodes,  125  and  126 , respectively, when the bit status “0” is required. On the other hand, when the bit status “1” is required, signals, V 21  and V 12 , to advance the phase backward and forward are provided to the electrodes,  125  and  126 . The optical coupler  124  coupled with the waveguides,  122  and  123 , merges two optical beams, L 21  and L 22 , to form the composite optical beam. 
     The output of optical coupler  114  in the first MZ-modulator  110  directly couples with one of inputs of the optical coupler  130 ; while, the output of the optical coupler  124  in the second MZ-modulator  120  couples with the other of inputs of the optical coupler  130  via the phase shifter  140 . The phase shifter  140 , which includes an optical waveguide  141  and an electrode  142  provided on the optical waveguide  141 , causes the phase shift by π/2(rad) for the composite optical beam passing therethrough by providing a bias V 3  on the electrode  142 . 
     The output of the optical coupler  130  is guided to the output terminal  102 . The optical beams, L 11  and L 12 , output from the optical coupler  114 , and other two optical beams, L 21  and L 22 , output from the phase shifter  140  are combined by the optical coupler  130  and output from the output terminal  102  as the optical output Lout modulated by the QPSK mode. 
       FIG. 2  is the polar displays of the optical beams measured at the optical input terminal  103  and nodes A to H marked in  FIG. 1 . The input optical beam Lin, as shown in  FIG. 2 , has the single phase, which assumed to be the reference phase of 0 (rad), but two optical beams, L n  and L 12 , divided from the input optical beams Lin varies the phase thereof along the respective dotted line in  FIG. 2  as a result of the BPSK modulation. Specifically, the phase of the optical beam L 11  measured at the end A of the optical waveguide  112  varies from 0 to +π along the dotted line in the upper half plane; while, that of the optical beam L 12  measured at the end B of the other optical waveguide  113  varies from 0 to −π along the dotted line in the lower half plane. Similarly, the optical beams, L 21  and L 22 , measured at the ends, C and D, of the optical waveguides,  122  and  123 , vary the phase thereof between 0 and π(rad). 
     Then, the phase measured at the end E of the optical coupler  114 , which is a composite of two beams, L 11  and L 12 , shows two phase statuses of 0(rad) and π(rad); also, the phase measured at the end F of the optical couple  124  show two phase statuses of 0(rad) and π(rad), both of them have the configuration of BPSK mode. 
     The second MZ-modulator  120  accompanies with the phase shifter  140  in downstream thereof. Because the phase shifter  140  shifts the phase of the composite optical beam by π/2(rad), the phase measured at the output G of the phase shifter  140  becomes that shown in  FIG. 2 . Finally, the phase measured at the output H of the optical coupler  130  has four phase statuses of π/4, 3π/4, 5π/4, and 7π/4, which configures the QPSK mode. 
     The first and second MZ-modulators,  110  and  120 , in particular, the waveguides,  112  to  123 , provided therein are sometimes made of semiconductor material such as InP, GaAs, and so on because of large electro-optical effect inherently attributed to those materials. For instance, an optical waveguide including, what is called, the multiple quantum well (MQW) structure show large variation in the refractive index thereof by the quantum confined stark effect, which means that large phase shift may be obtained by applying relatively small bias to the waveguide. However, such large variation of the refractive index accompanies with large optical loss by the optical absorption. 
       FIG. 3  shows a typical behavior of the phase shift and the optical loss against the reverse bias applied to an optical waveguide made of semiconductor material, where a behavior G 21  corresponds to the phase shift against the reverse bias; while, a behavior G 22  shows the optical loss against the reverse bias. As  FIG. 3  clearly shows, the phase shift G 21  and the optical loss G 22  show relations non-linear to the reverse bias. This non-linear dependence causes the following subject to be solved. 
     A dielectric material such as lithium niobate (LiNbO 3 ) is first considered, where LiNbO 3  shows a linear dependence of the phase shift against the bias, exactly, the electric field applied thereto. When the optical waveguides,  112  and  113 , are made of LiNbO 3 , a relation of the phase status against the biases is shown in  FIG. 4A . That is, setting (a) amplitude of the bias provided to the waveguide to be a half of V(2π), where V(2π) means the bias condition by which the phase of the optical beam advances forward or backward by 2π(rad), (b) setting a static bias condition of the signal V 11  for the waveguide  112  is V(π/2), while, that of the signal V 12  for the other waveguide  113  is V(3π/2), then, (c) applying the signal V 11  swinging between V(0) and V(π) and the other signal V 12  swinging between V(2π) and V(π); then two phase statuses of 0(rad) and π(rad), each corresponding to bit statuses of “0” and “1”, for the composite optical beam may be obtained.  FIG. 4A  is a polar display of such bit statuses. 
     On the other hand, when the optical waveguides,  112  and  113 , are made of semiconductor materials, which shows the non-linear dependence of the phase shift against the applied bias, the phase status of the composite beam becomes complicated such as shown in  FIG. 5A . That is, the phase shift at the condition V (2 Π)/2 no longer becomes Π but φ less than Π. Even when the static bias conditions, V U  and V L , for the waveguides,  112  and  113 , are set so as to cause the phase shift of Π/2 and 3Π/2 as those shown in  FIG. 5A  and swinging the signals from the static bias conditions described above by the magnitude of ±V(Π/2), the phase statuses of 0 (rad) and Π (rad) cannot be obtained. The waveguide  112  is in a condition of under modulation, while, the waveguide  113  is in a condition of over modulation.  FIG. 5B  shows two phase statuses, one of which corresponds to a condition when the upper waveguide  112  is set in V(0) while the lower waveguide  113  is set in V(2 Π), which is the phase status of 0 (rad) of the composite beam, the other of which shows a condition when the upper and lower waveguides are set in V(2 Π)/2. Under such signal conditions, the upper waveguide  112  advances the phase of the optical beam propagating therein forward by φ but less than Π, while, the lower waveguide  113  advances the phase backward by 2 Π-φ, which is greater than Π. Then, the polar display of the condition above becomes as that shown in  FIG. 5B , where the bit status corresponding to Π (rad) becomes offset from the real axis. It would be so hard to find adequate conditions for the initial conditions and swing magnitudes for respective biases, V 11  and V 12 . 
       FIGS. 6A and 6B  compare the constellation of the composite beam output from the QPSK modulator made of dielectric material ( FIG. 6A ) and that made of semiconductor material ( FIG. 6B ). Crosses appearing in these figures correspond to theoretical positions for the composite optical beam when the optical beams, L 11  to L 22 , are caused in the phase shift of exactly Π/2. When a waveguide shows the linear dependence of the phase shift against the bias as those of the dielectric waveguide, the optical beams, L 11  to L 22 , are caused in the phase shift with a span of substantially Π/2. On the other hand, a waveguide made of semiconductor material shows the constellation whose phase difference is deformed from Π/2. 
     First Embodiment 
     Next, a first embodiment of an MZ-modulator according to the present invention will be described in detail.  FIG. 7  is a plan view schematically showing a fundamental arrangement of the MZ-modulator made of semiconductor material. The MZ-modulator  10  shows the function of BPSK mode with the phase statuses of 0(rad) and π(rad) each corresponding to the bit statuses of “0” and “1”. The MZ-modulator  10  includes an optical branch  11 , a pair of optical waveguides,  12  and  13 , which are hereafter called as the arm waveguides, each optically coupled with respective outputs of the optical branch  11 , and an optical coupler  14  coupled with the other end of respective arm waveguides,  12  and  13 . The optical branch  11  and the optical coupler  14  are a type of, what is called, the multi-mode interference (MMI) coupler. Two arm waveguides,  12  and  13 , provide electrodes,  15  and  16 , to be provided with modulation signals with static biases thereto that modulate the refractive index of the arm waveguides,  12  and  13 . The variation of the refractive index results in a change of the optical length which brings the shift of the phase of the optical beam propagating therein at the end thereof. 
     The MZ-modulator  10  of the embodiment further provides the phase presetter  17  in only one of the arm waveguides, where the present embodiment provides the phase presetter  17  in the lower arm waveguide  13 . The phase of the optical beam propagating in the arm waveguide  13  is further shifted by the signal applied to the phase presetter  17 . In an example, the phase presetter  17  includes an optical waveguide made of semiconductor material, such as GaAs, InP, and so on, and an electrode to provide an electrical signal to the arm waveguide  13 . Applying the signal to the electrode of the phase presetter  17 ; the phase of the optical beam propagating therein shifts by Π (rad). In another example, the phase presetter  17  includes an optical waveguide without any electrodes, which is called as the supplemental waveguide. The supplemental waveguide lengthens the optical length of the arm waveguide  13  longer than that of the upper arm waveguide  12  by a length corresponding to a phase of Π, which results in a phase shift of Π (rad). However, the arrangement of the phase presetter  17  is not restricted to those described above. The phase shift by Π between two optical beams propagating in respective arm waveguides,  12  and  13 , is the only condition requested of the phase presetter  17 . 
     The operation of the MZ-modulator  10  will be described. Entering an input optical beam Lin 1  into the MZ-modulator  10 , the input optical beam Lin 1  is divided into two optical beams, L 11  and L 12 , by the optical branch  11 . One of the optical beams L 11  enters the one of the arm waveguides  12 , while, the other optical beam L 12  enters the other arm waveguide  13 , propagates therein, and enters the phase presetter  17 . The phase presetter  17  causes the phase shift by π only for the optical beam L 12 . Thus, two optical beams, L 11  and L 12 , are caused in the phase difference therebetween by π (rad) at the output of the phase presetter  17 . 
     The optical beam L 12  output from the phase presetter  17  further propagates in the arm waveguide  13  as shifting the phase thereof by the signal V 12  provided to the electrode  16 . On the hand, the other optical beam L 11  propagates in the other arm waveguide  12  as shifting the phases thereof. When the composite optical beam output from the MZ-modulator  10  corresponds to the bit status “0”; two signals, V 11  and V 12 , causing the phase difference of 0(rad) between two beams, L 11  and L 12 , are provided to respective electrodes,  15  and  16 . While, when the bit status “1” is required, two signals, V 11  and V 12 , causing the phase shift by π (rad) relative to the phase status of 0(rad) above described are provided to the electrodes,  15  and  16 . 
       FIG. 8A  shows the phase shift against the signal applied to the MZ-modulator  10 , and  FIG. 8B  is a polar display of output statuses of the MZ-modulator  10 . In  FIG. 8A , a behavior G 11  denotes the phase shift of the upper arm waveguide  12 , while, another behavior G 12  denotes the phase shift of the lower arm waveguide  13 . An arrow A 11  shown in  FIG. 8A  denotes the swing range of the signal V 11  for the upper arm waveguide  12 , and the other arrow A 12  indicates the swing range of the other signal V 12  for the lower arm waveguide  13 . 
     As shown in  FIG. 8A , two signals, V 11  and V 12 , have the swing range, or the amplitude, same to each other, which is equal to be V(π). When the signal V 11  is set to be 0, while the other signal V 12  is set to be V(π); then, the optical beam L 12  shifts the phase by π by the signal V 12  in addition to the phase shift of π caused by the phase presetter  17 , namely, the total phase shift becomes 2π. Because the optical beam L 11  causes no phase shift, the composite optical beam output from the coupler  14  becomes the phase status of 0(rad). On the other hand, when the composite optical beam shows the phase status of π(rad), the signal V 11  for the upper arm waveguide  12  is set to be V(π); while, the other signal V 12  for the lower arm waveguide  12  is set to be 0 to cause no phase shift therein, but the phase presetter  17  causes the phase shift of π, then the composite optical beam output from the coupler  14  shows the phase status of π(rad). Thus, the BPSK modulation may be performed. 
     The MZ-modulator  10  of the present embodiment provides the phase presetter  17  to shift the phase of the optical beam passing therethrough by π, then, the optical beam L 12  propagating in the lower arm waveguide  13  varies the phase thereof between π and 2π responding to the signal V 12  swinging between V(π) and 0. On the other hand, the phase shift of the other optical beam L 11  propagating in the upper arm  12  is between 0 and π for the signal V 11  swinging between 0 and V(π). When two signals, V 11  and V 12 , are complementary to each other, that is, when the signal V 11  is in 0, then, the other signal V 12  becomes V(π), the phase status of 0(rad) may be obtained for the composite optical beam. On the other hand, when the signal V 11  becomes V(π), then, the other signal is set to be 0, the phase status of π(rad) may be realized in the composite optical beam. 
       FIG. 8B  is the polar display of the composite optical beam output from the optical coupler  14 . The polar display of  FIG. 8B  is distinguishable from that of  FIG. 5B , that is, the phase status of π(rad) shows the phase difference of exactly π from the phase status of 0(rad). Thus, the non-linearity of the phase shift of the arm waveguides,  12  and  13 , made of semiconductor material can be compensated. 
     Second Embodiment 
       FIG. 9  is a plan view of a QPSK modulator made of semiconductor material according to the second embodiment of the invention. The BPSK modulator  1 A shown in  FIG. 9  includes the optical input terminal  2  and the optical output terminal  3 . The optical input terminal  2  couples with the optical branch  4  in downstream thereof to divide the input optical beam Lin into two optical beams, Lin 1  and Lin 2 , one of which Lin 1  enters the first MZ-modulator  20 , while, the other Lin 2  enters the second MZ-modulator  30 . These MZ-modulators,  20  and  30 , have the same arrangement with that shown in  FIG. 7 . That is, the first MZ-modulator  20  includes the optical branch  21  coupled with the optical branch  4 , two arm waveguides,  22  and  23 , each coupled with respective outputs of the optical branch  21  and providing electrodes,  25  and  26 , and the optical coupler  24  optically coupled with the end of the arm waveguides,  21  and  22 . Only the lower arm waveguide  23  provides the phase presetter  27  to shift the phase of the optical beam L 12  propagating therein by π. The phase presetter  27  provides the electrode  28  to which the static bias V 13  is provided to shift the phase of the optical beam L 12  by π. The first MZ-modulator  20  can execute the BPSK modulation of the optical beam Lin 1  to show the phase statuses of 0(rad) and π(rad) corresponding to the bit statues of “0” and “1”, respectively, by the mechanism same with that of the MZ-modulator  10 . 
     The second MZ-modulator  30  is coupled with the other output of the optical branch  4 . The second MZ-modulator  30  also provides the arrangement same with that shown in  FIG. 7  and shows the mechanism of the BPSK modulation same with that attributed to the first MZ-modulator  20  and the MZ-modulator shown in  FIG. 7 . 
     The first MZ-modulator  20  couples directly with the optical coupler  5 ; while, the second MZ-modulator  30  couples indirectly with the optical coupler  5  via the phase shifter  40 . The phase shifter  40  includes an optical waveguide  41  with an electrode  42 . Providing a bias V 3  to the waveguide  41  via the electrode  42 , the optical beam passing therethrough shifts the phase thereof by π/2. Then, the optical beams, L 21  and L 22 , modulated by the second MZ-modulator  30  further shifts the phase thereof by π/2 with respect to the phases of the optical beams, L 11  and L 12 , modulated by the first MZ-modulator  20 . The composite optical beam Lout merged by the optical coupler  5  and output from the optical output terminal  3  becomes the QPSK signal attributed with four phases of π/4, 3π/4, 5π/4, and 7π/4. 
     The QPSK modulator  1 A shown in  FIG. 9  includes two MZ-modulators,  20  and  30 , each configured with the MZ-modulator  10  shown in  FIG. 7 . The two MZ-modulators,  20  and  30 , can output the composite optical beam showing two phase statuses of 0(rad) and π(rad) with the phase difference of exactly π. Accordingly, the composite optical beam output from the QPSK modulator  1 A can reduce the phase distortion, namely, a phase difference between four phase statuses of π/4, 3π/4, 5π/4, and 7π/4, to enhance the transmission quality of optical data. 
       FIG. 10  shows the constellation of the composite optical beam output from the QPSK modulator  1 A. Crosses shown in  FIG. 10  correspond to the theoretical position of the composite optical beam. The constellation shown in  FIG. 10  shows a convergence to the theoretical points. Assuming that a penalty is a ratio of a length from the origin to one of phase statuses farthest from the theoretical point to a length from the origin to the theoretical point, the penalty of the QPSK modulator  1 A becomes 1.1 dB, which is comparable of the penalty of 3.9 dB attributed to the QPSK modulator  100  without the phase pre setter. 
     First Modification 
       FIG. 11  is a plan view of another QPSK modulator  1 B according to a modification of the aforementioned QPSK modulator  1 A shown in  FIG. 9 . The QPSK modulator  1 B has features distinguishable from those of the aforementioned QPSK modulator  1 A in an arrangement of the phase presetter. That is, the first and second MZ-modulators,  20  and  30 , of the present embodiment provides the phase presetters,  29  and  39 , instead of the phase presetters,  27  and  37 , respectively. 
     The phase presetter  29  provides an optical waveguide  29   a  whose optical length is substantially equal to the phase shift of π. That is, the optical beam L 12  propagating in the lower arm waveguide  23  and the phase presetter  29  always runs within the waveguide longer than the other waveguide  22  by a length corresponding to the phase shift of π, which also causes the phase shift by π between optical beams, L 11  and L 12 , each propagating in the upper arm waveguide  22  and the lower arm waveguide  23 . Similarly, the phase presetter  39  in the other MZ-modulator  30  shows the function same with that of the phase presetter  29 . Accordingly, the optical beams, L 21  and L 22 , each propagating within respective arm waveguides,  32  and  33 , inevitably attribute the phase difference of π. 
     The QPSK modulator  1 B of the present embodiment is also distinguishable from the aforementioned QPSK modulator  1 A by the phase shifter  50 . This phase shifter  50  includes an optical waveguide  50   a  to lengthen the optical length of the waveguide, which extends from the output of the optical coupler  34  to the input of the optical coupler  5 , by a length corresponding to the phase shift of π/2. Then, the composite optical beam reaching the optical coupler  5  is shifted in the phase thereof by π/2 with respect to the composite optical beam reaching the optical coupler  5 . 
     The QPSK modulator  1 B includes the first and second MZ-modulators,  20  and  30 , each having the configuration same with that of the MZ-modulator  10  shown in  FIG. 7 . Accordingly, the first and second MZ-modulators,  20  and  30 , may show in the output thereof the phase statuses of 0(rad) and π(rad) with a difference of exactly π. Then, the output of the QPSK modulator  1 B may show the four phase statuses of π/4, 3π/4, 5π/4, and 7π/4 to enhance the quality of the optical signal. 
       FIG. 12  shows an example of the output constellation of the QPSK modulator  1 B. As shown in  FIG. 12 , the QPSK modulator  1 B allocates four phase statuses with the difference of substantially π/2 with superior accuracy. The output constellation shown in  FIG. 12  shows the penalty of 0.4 dB which is comparable of the penalty of 1.1 dB attributed to that shown in  FIG. 10 . Based on detail analyses of the arrangement shown in  FIG. 12 , the penalty is primarily seemed to be due to the optical loses caused in the optical waveguides,  22  to  33 . 
     The phase presetters,  29  and  39 , and the phase shifter  30  of the present embodiment have an advantage that the increment of the optical loss by the application of the biases or the signals becomes avoidable. Thus, the degradation of the transmission quality due to the optical loss may be suppressed. The embodiment shown in  FIG. 11  provides the phase presetters,  29  and  39 , and the phase shifter  50  with the arrangement to lengthen the physical dimension of the optical waveguide. However, a combination of the arrangement, that is, the some of the phase presetters and the phase shifter provides the arrangement shown in  FIG. 11  and rest of them provide the arrangement attributed to the QPSK modulator  1 A, is implemented in the MZ-modulator. 
     Second Modification 
       FIG. 13  is a plan view of still another embodiment of a QPSK modulator  1 C made of semiconductor material, which is modified from that  1 B of aforementioned embodiment. The QPSK modulator  1 C has a feature distinguishable from the aforementioned modulator  1 B that the second MZ-modulator  30  provides, in addition to the phase presetter  60  in the lower arm waveguide  33 , another phase presetter  61  in the upper arm waveguide  32 . That is, the MZ-modulator  30  provides two phase presetters,  60  and  61 , in respective arm waveguides,  32  and  33 . The QPSK modulator  1 C of the embodiment further provides a feature that the QPSK modulator  1 C does not provide the phase shifter in the downstream of the second MZ-modulator  30 . 
     The phase presetter  60  includes an optical waveguide  60   a  to lengthen the optical length of the lower arm waveguide  33  between the optical branch  31  and the optical coupler  34  by a length corresponding to the phase shift of 3π/2. On the other hand, the phase presetter  61  provided in the upper arm waveguide  32  lengthens the optical length between the optical branch  31  and the optical coupler  34  by a length corresponding to the phase shift of π/2. Then, the composite optical beam output from the optical coupler  34  cause a phase shift by π/2 with respect to the composite optical beam output from the optical coupler  24 . Moreover, the optical beam L 22  propagating in the lower arm waveguide  33  causes the phase shift of π with respect to the optical beam L 21  propagating in the upper arm  32 . 
     Thus, the phase presetters,  29 ,  60 , and  61 , causes the phase offset of π/2, 2π/2, and 3π/2, between optical beams, L 11  to L 22 . Accordingly, the composite optical beam output from the optical coupler  5  has the QPSK mode with the phase statuses of π/4, 3π/4, 5π/4, and 7π/4. The phase presetters,  29 ,  60 , and  61 , of the present embodiment have the arrangement to include the optical waveguides,  29   a ,  60   a , and  61   a , but some of them may include an electrode to modify the refractive index of the optical waveguide. 
     The optical length of the optical waveguides,  29   a ,  39   a ,  60   a , and  61   a , appeared in aforementioned embodiments may be determined as follows. That is, as shown in  FIG. 14 , which is a magnified plan view of the waveguides,  29   a ,  39   a ,  60   a , and  61   a , the length thereof is adjustable only by varying a physical length of the inclined portion. Assuming a supplemental physical length ΔL is added to the inclined portion whose horizontal length is L, the phase shift Δφ by this elongated length ΔL becomes:
 
Δφ=2×Δ L×n   eff /λ,
 
where n eff  is equivalent refractive index of the base semiconductor material. Assuming that the base semiconductor material is InP, namely, the MZ-modulator is made of InP, the equivalent refractive index n eff  is 3.3. Further assuming that the wavelength to be considered is 1550 nm, and the inclined angle is 45°, the supplemental length ΔL for the phase shift of π/2, 2π/2, and 3π/2 are given by 180 nm, 370 nm, and 550 m, respectively.
 
     While particular embodiments of the present invention have been described herein for purposes of illustration, many modifications and changes will become apparent to those skilled in the art. Accordingly, the appended claims are intended to encompass all such modifications and changes as fall within the true spirit and scope of this invention.