Patent Publication Number: US-11385483-B2

Title: Linearization and reduction of modulated optical insertion loss for quadrature optical modulator

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a divisional of U.S. application Ser. No. 16/559,962 filed Sep. 4, 2019, which claims the benefit of U.S. Provisional Patent Application Ser. No. 62/727,979 entitled “Linearization and Reduction of Modulated Optical Insertion Loss for Quadrature Optical Modulator”, filed on Sep. 6, 2018. The entire contents of both are herein incorporated by reference. 
    
    
     INTRODUCTION 
     Unless otherwise indicated herein, the materials described herein are not prior art to the claims in the present application and are not admitted to be prior art by inclusion in this section. 
     A modulated light wave is often used in high-speed optical communication systems to carry digital information from a sender to a receiver. In many systems, information is sent using both amplitude and phase modulation schemes. By using such techniques, in contrast to amplitude-only modulation, more information can be sent over the same optical frequency band. Examples include phase shift keying modulation techniques, such as Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK), and Quadrature Amplitude Modulation (QAM) techniques, such as 8QAM, 16QAM and 64QAM realized using in-phase and quadrature modulator (IQM) 
     Insertion of an optical modulator, such as an IQM optical modulator, in an optical path creates insertion loss of the optical signal, thus impacting subsequent transmissions and receptions of the modulated signal. Furthermore, conventional amplification techniques may result in distortion to the various transmission symbols as represented by constellation points indicative of the modulated data. As such, there is a need for optical modulators with lower optical insertion loss and/or other features that improve the ability to receive the optical signal with high fidelity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present teaching, in accordance with preferred and exemplary embodiments, together with further advantages thereof, is more particularly described in the following detailed description, taken in conjunction with the accompanying drawings. The skilled person in the art will understand that the drawings, described below, are for illustration purposes only. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating principles of the teaching. The drawings are not intended to limit the scope of the Applicant&#39;s teaching in any way. 
         FIG. 1  illustrates a known in-phase and quadrature (IQ) Mach-Zehnder superstructure modulator system. 
         FIG. 2A  illustrates a graph of a field transfer function (dashed line), a power transfer function (solid line), and an example operating point for a Mach-Zehnder modulator. 
         FIG. 2B  illustrates a graph of a field transfer function (dashed line), a power transfer function (solid line), and another example operating point for a Mach Zehnder modulator. 
         FIG. 2C  illustrates a phase diagram representation of an output of a Mach-Zehnder modulator. 
         FIG. 3A  illustrates a phase diagram representing outputs from a known in-phase and quadrature (IQ) superstructure modulator system. 
         FIG. 3B  illustrates a constellation diagram for a Mach-Zehnder superstructure modulator configured for 4QAM/QPSK operation. 
         FIG. 3C  illustrates a table that includes a truth table and field and intensity values at the output for a Mach-Zehnder superstructure modulator configured for 4QAM or QPSK modulation. 
         FIG. 4  illustrates an embodiment of an IQ Mach-Zehnder superstructure modulator system of the present teaching. 
         FIG. 5A  illustrates a table including a truth table, DC and AC bias phase, and field and intensity values at an output for an embodiment of a Mach-Zehnder superstructure modulator configured for 4QAM operation of the present teaching. 
         FIG. 5B  illustrates a phase diagram representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 4QAM operation of the present teaching and the output of a known 4QAM-configured Mach-Zehnder superstructure modulator. 
         FIG. 5C  illustrates a constellation diagram representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 4QAM operation according to the present teaching and the output of a known 4QAM-configured Mach-Zehnder superstructure modulator. 
         FIG. 6A  illustrates a constellation diagram representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 16QAM operation with 1V π  drive operating point of the present teaching and a known 16QAM-configured Mach-Zehnder superstructure modulator. 
         FIG. 6B  illustrates a constellation diagram representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 16QAM operation with 2V π  drive of the present teaching and a known 16QAM-configured Mach-Zehnder superstructure modulator. 
         FIG. 6C  illustrates a constellation diagram representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 16QAM operation with 2V π  drive and linearization of the present teaching and a known 16QAM-configured Mach-Zehnder superstructure modulator. 
         FIG. 7A  illustrates a phase diagram for a 16QAM constellation. 
         FIG. 7B  illustrates a table of symbols and associated phase and amplitude of the transmitted optical carrier representing the symbols of the phase diagram of  FIG. 7A . 
         FIG. 8  illustrates an embodiment of a dual-polarization IQ Mach-Zehnder superstructure modulator system of the present teaching. 
     
    
    
     DESCRIPTION OF VARIOUS EMBODIMENTS 
     Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the teaching. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment. 
     It should be understood that the individual steps of the methods of the present teachings may be performed in any order and/or simultaneously as long as the teaching remains operable. Furthermore, it should be understood that the apparatus and methods of the present teachings can include any number or all of the described embodiments as long as the teaching remains operable. 
     The present teaching will now be described in more detail with reference to exemplary embodiments thereof as shown in the accompanying drawings. While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives, modifications and equivalents, as will be appreciated by those of skill in the art. Those of ordinary skill in the art having access to the teaching herein will recognize additional implementations, modifications, and embodiments, as well as other fields of use, which are within the scope of the present disclosure as described herein. 
     The present teaching describes a method to simultaneously linearize the in-phase and quadrature optical modulator and to reduce the modulated optical insertion loss (MOIL) by utilizing in-phase addition of the in-phase and quadrature components of an nQAM signal using two high-speed phase modulators embedded in a superstructure Mach-Zehnder modulator. Modulators of the present teaching may be realized in, for example, Lithium Niobate, Indium Phosphide, Gallium Arsenide, and Silicon Photonics technology. 
     The system and method of the present teaching relates to the linearization and/or reduction of modulated optical insertion loss (MOIL) for Mach-Zehnder-based in-phase quadrature optical modulators. More specifically, the systems and methods of the present teaching rely at least in part on the recognition that a coherent (phase-sensitive) optical signal combining approach can be used to reduce or eliminate the inherent modulated optical insertion loss present in known Mach-Zehnder-based in-phase quadrature optical modulators that rely on a non-coherent (phase-insensitive) optical signal combining approach. The system and method can advantageously linearize an output modulated optical signal produced by a Mach-Zehnder-based on in-phase quadrature optical modulator. Furthermore, the system and method of the present teaching can advantageously control and/or improve the distance between points of an output modulated optical signal constellation produced by a Mach-Zehnder-based in-phase quadrature optical modulator. This is sometimes referred to as a Hamming distance. 
       FIG. 1  illustrates a known IQ Mach-Zehnder superstructure modulator system  100 . A light source  110  generates an optical signal. In some configurations, the generated optical signal may be, for example, a coherent optical light wave, also referred to as an optical carrier. In various configurations, the light source  110  may be a fixed wavelength or a tunable wavelength light source. The light source  110  is connected to an input  121  of a parent IQ Mach-Zehnder superstructure modulator  120 . The optical signal at the input of the parent Mach-Zehnder modulator (MZM)  120  is split into two arms  112 , 114  of the parent MZM  120  by an optical splitter  102 . The first arm  112  includes a child MZM  130  and the second arm  114  includes a child MZM  140 . Child MZM  130  includes two arms  123 ,  124 , and child MZM  140  includes two arms  125 ,  126 . 
     Each child MZM  130 ,  140  includes a pair of modulation electrodes  131 ,  132 ,  141 ,  142 , one for each arm  123 ,  124 ,  125 ,  126 . Each child MZM  130 ,  140  also includes a pair of bias electrodes  151 ,  152 ,  161 ,  162  one for each arm  123 ,  124 ,  125 ,  126 . The modulation and bias electrodes  131 ,  132 ,  141 ,  142 ,  151 ,  152 ,  161 ,  162  are configured in a differential drive configuration, which is sometimes referred to as a push-pull configuration, which provides a positive signal to one arm  123 ,  125  and a negative signal to the other arm  124 ,  126  of each child MZM  130 ,  140 . The equal and opposite drive configuration advantageously reduces the peak voltage of a drive signal applied to the electrodes  131 ,  132 ,  141 ,  142 ,  151 ,  152 ,  161 ,  162  in order to produce a phase difference between modulated optical signals in arms  123 ,  124  or in arms  125 ,  126 . 
     The modulation electrodes  131 ,  132 ,  141 ,  142  are connected to a modulation driver  106  that supplies RF modulation signals to a respective electrode  131 ,  132 ,  141 ,  142 . For example, V RF_1_P (t), the positive RF modulation for the in-phase signal is applied to the modulation electrode  131  of child MZM  130  and V RF_1_N (t), the negative RF modulation for the in-phase signal is applied to the modulation electrode  132  of child MZM  130 . The electrodes  131 ,  132  impart a modulation phase on the optical signal passing through the first arm  112  based on the applied modulation signal. The bias electrodes  151 ,  152 ,  161 ,  162  are connected to a bias driver  108  that supplies DC bias signals to respective bias electrodes  151 ,  152 ,  161 ,  162 . For example, V DC_1_P , the positive bias signal for the child MZM  130  is applied to bias electrode  151  and V DC_1_N , the negative bias signal for the child MZM  130  is applied to bias electrode  152 . In some configurations, the DC bias signals are configured to bias child MZM  130  at a minimum transmission point and to bias the child MZM  140  at a minimum transmission point. 
     Optical signals from the two arms  112 ,  114  of the parent MZM  130  are combined to generate a combined optical signal an output  122  by a combiner  103 . The two arms  112 , 114  of the parent MZM  130  have bias electrodes  171 ,  172  that are connected to a bias driver  109  that supplies positive and negative DC bias signals to the bias electrodes  171 ,  172  to produce a bias phase for optical signals in each arm  112 ,  114  of the parent MZM superstructure  120 . In some configurations, the DC bias signals are configured to bias the parent MZM superstructure  120  at a quadrature point by generating a π/2 phase difference between the optical signals generated in the first arm  112  and in the second arm  114 . 
     The bias drivers  108 ,  109  and the modulation driver  106  are controlled by controller  104 . In various configurations, bias drivers  108 ,  109 , modulation driver  106  and/or controller  104  are constructed from one or more electrical circuits. In various configurations, the circuits can comprise FPGAs, ASICs, DSPs, ADCs, DACs and/or other discrete components and/or circuits, alone or in combination. 
     In some configurations, the modulation driver  106  and bias driver  108  are configured to produce ±1 DPSK modulation using RF modulation signals and DC bias signals so that one child MZM  130  imparts a modulation phase on an optical signal in response to a first modulation signal that results in an in-phase ±1 DPSK modulation on the optical signal passing through the first arm  112 . The other child MZM  140  imparts a modulation phase on an optical signal in response to a second modulation signal that results in a quadrature ±1 DPSK modulation on the optical signal passing through the second arm  114 . The parent MZM  120  multiplies the generated ±1 DPSK modulation in the second arm  114  by j by adding π/2 phase shift, thereby converting it to a quadrature modulation. The parent MZM  120  then adds the two DPSK modulations generated by the first and second arms  112 ,  114  to generate a QPSK or 4QAM modulation in one polarization. 
     The IQ MZM superstructure modulator system  100  may be used to implement multiple amplitude and phase-based modulation schemes. The particular modulation scheme depends on the particular multi-level signal with certain peak-to-peak voltage applied to the modulating child Mach-Zehnder modulators. For a superstructure Mach-Zehnder modulator, typically child Mach-Zehnder modulators are biased at the point of minimum transmission while parent Mach-Zehnder modulator is biased at the point of quadrature transmission. 
       FIG. 2A  illustrates a graph  200  of a field transfer function (dashed line), a power transfer function (solid line), and an example operating point for a Mach-Zehnder modulator. This graph illustrates an operating point with a quadrature point bias  202 , V bias =V π /2, and an applied modulation drive signal with a voltage swing  204  of V π  peak-to-peak. As shown by the solid line power transfer function, this operating point bias  202  and voltage swing  204  provides an amplitude modulation from a zero state (no power out) to a one state (full output power). The power transfer function also illustrates how the quadrature point bias  202  is at the half power point of the modulator, which results in 3 dB inherent loss. Referring back to  FIG. 1 , similarly in some configurations, the parent Mach-Zehnder modulator  120  is biased at the point of quadrature transmission to introduce π/2 phase shift in the Mach-Zehnder superstructure. 
       FIG. 2B  illustrates a graph  220  of a field transfer function (dashed line), a power transfer function (solid line), and another example operating point for a Mach Zehnder modulator. The graph  220  illustrates a minimum transmission bias  222 , where the Mach-Zehnder is biased for nominally zero optical signal at the output. An input modulation signal voltage swing  224  of 2V π  peak-to-peak that produces a ±π phase transition in the optical signal is shown from the field transfer function curve. This operating point with a 2V π  voltage swing  224  at a minimum transmission operating point bias  222  also produces peak output power at each extreme of the applied voltage, as illustrated by the power transfer curve. Referring back to  FIG. 1 , this operating point may be used to produce, for example BPSK and/or DPSK signals from child Mach-Zehnder modulators  130  and  140 . 
       FIG. 2C  illustrates a phase diagram  240  representation of an output of a Mach-Zehnder modulator. A phase diagram  240  helps to visualize the reachable signal space in the output of a Mach-Zehnder modulator. The phase diagram  240  includes a real axis  242  and an orthogonal imaginary axis  244 . The circle  245  illustrates unity amplitude transmission and phase excursions of the modulated output signal, which is represented by the angle, ϕ, subtended from the positive real axis  242 . A Mach-Zehnder modulator optical signal output generated by application of a phase modulating signal may be represented by a phase angle  246 , ϕ, and an amplitude  248 , A. Four example output signal points  250 ,  252 ,  254 ,  256  are shown as a specific example. Each of the points  250 ,  252 ,  254 ,  256  have unity amplitude but different phases. Specifically, the phases are: ϕ=45° for output  250 , ϕ=135° for output  252 , ϕ=215° for output  252 , and ϕ=315° for output  252 . 
     This set of four outputs  250 ,  252 ,  254 ,  256  can be demodulated in a coherent detector and thus information can be encoded on the optical signal by applying a modulating signal to realize one of these particular output points to code a particular symbol of the information being transmitted. With four distinct output points  250 ,  252 ,  254 ,  256  each point represents two bits of information encoded by a modulating signal. A modulation scheme relying on outputs with four different phases and equal amplitudes is referred to as QPSK. Other modulation schemes are possible, including schemes that use outputs with different amplitudes and different phases. Different amplitudes are represented by different diameter circles in a phase diagram. Various embodiments of the system and method of the present teaching can apply to one or more of these so-called coherent, or phase-sensitive, modulation schemes. 
       FIG. 3A  illustrates a phase diagram  320  representing the outputs from a known superstructure modulator system  100 . To simplify the description of the present teaching, assume that all splitters split the power in equal halves and that all combiners take the same amount of power from each contributing path. In some configurations, numerous other splitting and recombination ratios can be used. Also, excess losses owing to, for example, material transmission losses of light through various elements are not included in the analysis. 
     Referring to  FIGS. 1, 2A -C and  3 A, both the in-phase child MZM  130  and the quadrature-phase child MZM  140  are biased at the point of minimum transmission (e.g. as illustrated in  FIG. 2B ) in intensity and generate the DPSK modulation by being driven by a modulating AC waveform with a peak voltage swing of ±1 V π  or peak-to-peak voltage swing of 2 V π . Further, the parent MZM  120  is biased at the quadrature point (e.g. as illustrated in  FIG. 2A ). This bias is provided differentially by the DC bias driver  109  that supplies V DC_P_P  to bias electrode  171  and V DC_P_N  to bias electrode  172 . This bias shifts the phase in the second arm  114  by +90 degrees with respect to the first arm  112 . The resulting output signal is the constellation of points  334 ,  336 ,  338 ,  340  shown in  FIG. 3A . The quadrature bias point of the parent MZM  120  inherently creates a 3 dB insertion loss since the in-phase and quadrature modulated signals are simultaneously present at the output of the superstructure modulator. This is clear from the power transfer function of  FIG. 2A . 
     The field at the output of the MZM superstructure system  100  may be described mathematically as: 
             E   =         E   0       2       ⁡     [       ⁢     (     exp   ⁡     (     j   ⁡     (         φ   I     ⁡     (   t   )       -     π   2       )       )       )       ±         exp   ⁡     (     j   ⁢           ⁢   ΔΦ     )       ·     ⁢     (     exp   ⁡     (     j   ⁡     (         φ   Q     ⁡     (   t   )       -     π   2       )       )       )         ]                   E   =         E   0       2       ⁡     [       ⁢     (     exp   ⁡     (     j   ⁡     (         φ   I     ⁡     (   t   )       -     π   2       )       )       )       ±       j   ·     ⁢     (     exp   ⁢     (     j   ⁡     (         φ   Q     ⁡     (   t   )       -     π   2       )       )       )         ]                       where   ⁢           ⁢       φ   I     ⁡     (   t   )         =     π   ⁢         V   I     ⁡     (   t   )         2   ⁢     V   π             ,         V   I     ⁡     (   t   )       =         ±     V   π       ⁢           ⁢   and   ⁢           ⁢       φ   Q     ⁡     (   t   )         =     π   ⁢         V   Q     ⁡     (   t   )         2   ⁢     V   π               ,     
     ⁢         V   Q     ⁡     (   t   )       =         ±     V   π       ⁢           ⁢       V   I     ⁡     (   t   )         =         V   I     ⁡     (   t   )       =         V       RF   ⁢   _   ⁢   I     ⁢     _   ⁢   P         ⁡     (   t   )       -       V       RF   ⁢   _   ⁢   I     ⁢     _   ⁢   N         ⁡     (   t   )               ,     
     ⁢         V   Q     ⁡     (   t   )       =         V   Q     ⁡     (   t   )       =         V       RF   ⁢   _   ⁢   Q     ⁢     _   ⁢   P         ⁡     (   t   )       -       V     RF     Q   N         ⁡     (   t   )             ,     and   ⁢           ⁢   ⁢     (   )             
takes a real part of a complex signal within the parenthesis. The voltage V π , also referred to as V pi , is the drive voltage that is required to produce a phase shift of π rad on the optical signal. The ±1 in the field corresponds to 0 or π rad phase shifts in the optical E-field modulated at the output of the in-phase or first arm  112  of the parent MZM  120  due to the data modulation ϕ 1 (t). The output points for V 1 (t)=±V π  are shown as signal points  326 ,  330  in the phase diagram  320  and produce a DPSK signal at the output of the child MZM  130 . Similarly, the ±1 in the field corresponds to 0 or π rad phase shifts in the optical E-field modulated at the output of the quadrature or second arm  114  of the parent MZM  120  due to a data modulation ϕ Q (t). The output points for V Q (t)=±V π  are represented by signal points  328 , 332  in the phase diagram  320  and produce a DPSK signal at the output of the child MZM  140 . These two DPSK optical signals in each arm  112 ,  114  of the parent MZM  120  are combined at the output. A quadrature bias signal from bias driver  109  is applied to the arms  112 , 114  via bias electrodes  171 ,  172 . Mathematically, this is the j that multiplies the field for the quadrature modulated signal. The quadrature bias results in an additional phase difference of Δϕ=π/2, which orthogonalizes the two DPSK signals, producing the points of a QPSK constellation, points  334 ,  336 ,  338 ,  340 .
 
       FIG. 3B  illustrates a constellation diagram  350  for the Mach-Zehnder superstructure modulator  100  as configured for 4QAM/QPSK operation. The four quadrature addition symbols are shown as points  334 ,  336 ,  338 ,  340 . The points  334 ,  336 ,  338 ,  340  each exhibit a separation from the plot origin of ±0.7±0.7j. Depending on the fidelity of the channel through which the symbols are transceived, a received symbol may vary from the ideal position of points  334 ,  336 ,  338 ,  340 . The received signal fidelity is related to the ability of the receive processor to identify a symbol correctly. That is, to identify which of the four constellation points  334 ,  336 ,  338 ,  340  was sent. Accordingly, additional separation between symbols provides additional design margins. 
     As described above, the four constellation points allow encoding of two bits per symbol, or point  334 ,  336 ,  338 ,  340 .  FIG. 3C  illustrates a table  300  that includes a truth table and field and intensity values at the output for a Mach-Zehnder superstructure modulator  100  as configured for 4QAM/QPSK operation. Table  300  illustrates the symbol, the phase modulation signal value for the I modulator (child MZM  130 ) ϕ I (t), the phase modulation signal value for the Q modulator (child MZM  140 ) ϕ Q (t), the electric field, E, at the output of the parent MZM  120 , and the intensity, I, at the output of the parent MZM  120 . 
     The value of I=1.0 in the table  300  demonstrates the 3 dB inherent loss from the quadrature bias of the parent MZM  120 . This is a manifestation of the fact that the in-phase and quadrature modulated signals are simultaneously present independent of time at the output of the parent MZM  120 . The quadrature addition combiner effectively “dumps” half of the intensity away from the output for each symbol transmitted into Mach-Zehnder superstructure substrate. Thus, these known configurations of MZM superstructure modulator systems  100  have an inherent 3 dB modulated optical insertion loss (MOIL). 
       FIG. 4  illustrates an embodiment of an IQ Mach-Zehnder superstructure modulator system  400  of the present teaching. The superstructure modulator system  400  includes many of the same or similar components of the superstructure modulator system  100  described in connection with  FIG. 1 . One feature of the present teaching is that the superstructure modulator system  400  reduces and/or eliminates the inherent MOIL in the known superstructure modulator system  100  by using an AC bias scheme. The IQ Mach-Zehnder superstructure modulator  400  has a light source  410  that generates an optical signal, E in (t)  421 , that may be, for example, an optical carrier. A parent MZM  420  includes two arms  412 ,  414 . The optical signal at the input of the parent MZM  420  is split into two arms  412 ,  414  of the parent MZM  420  by an optical splitter  408 . The optical splitter  408  can be a 50/50 splitter or can have numerous other splitting ratios in various embodiments. The first arm  412  includes a child MZM  430  and the second arm  414  includes another child MZM  440 . Each child MZM  430 ,  440  includes a pair of arms  423 ,  424 ,  425 ,  426  with a respective pair of modulation electrodes  431 ,  432 ,  441 ,  442  and a respective pair of bias electrodes  451 ,  452 ,  461 ,  462 . The modulation electrodes  431 ,  432 ,  441 ,  442  impart a modulation phase on the optical signal in respective arms  423 ,  424 ,  425 ,  426  in response to a modulation signal. The bias electrodes  451 ,  452 ,  461 ,  462  impart a bias phase on the optical signal in respective arms  423 ,  424 ,  425 ,  426  in response to a bias signal. 
     In some embodiments, the modulation and bias electrodes  431 ,  432 ,  441 ,  442 ,  451 ,  452 ,  461 ,  462  are configured in a differential drive configuration. Modulation electrodes  431 ,  432 ,  441 ,  442  are connected to a modulation driver  404  that supplies RF modulation signals that impart a modulation phase on the optical signal passing through the arms  423 ,  424 ,  425 ,  426 . Bias electrodes  451 ,  452 ,  461 ,  462  are connected to a bias driver  405  that supplies bias signals. The child MZMs  430 ,  440  impart a modulation phase on the optical signals passing through arms  412 ,  414  in response to modulation signals applied to the modulation electrodes  431 ,  432 ,  441 ,  442 . 
     Optical signals from the two arms  412 ,  414  of the parent MZM  420  are combined to an output  422  at a combiner  409 . Parent MZM  420  has DC bias electrodes  471 ,  472  on each arm  412 ,  414  that are connected to a DC bias driver  406  and AC bias electrodes  481 ,  491  connected to AC bias driver  407 . The DC and AC bias electrodes  471 ,  472 ,  481 ,  491  impart respective DC and AC bias phases on optical signals passing through respective arms  412 ,  414 . AC bias electrode  481  modulates the optical signal in arm  412  with a bias signal that may operate at a high rate, and thus acts as a high-speed modulator. The AC bias electrode  491  modulates the optical signal in arm  414  with a bias signal that may operate at a high rate, and thus acts as a high-speed modulator. This is in contrast to the DC bias electrodes  471 ,  472  on each arm  412 ,  414  that impart a nominally constant bias phase. Thus, in some embodiments, the AC bias electrodes  481 ,  491  are constructed differently from the DC bias electrodes  471 ,  472  to support modulation of high-speed signals. 
     A controller  402  controls the modulation drivers  404 ,  405  and the bias drivers  406 ,  407 . Collectively, the drivers  404 ,  405 ,  406 ,  407  and controller  402  may be referred to as a control device  403 . In various embodiments, bias drivers  406 ,  407 , modulation drivers  404 ,  405  and/or controller  402  are constructed from one or more electrical circuits. In various embodiments, the circuits may comprise FPGAs, ASICs, DSPs, ADCs, DACs, and/or other discrete circuits, alone or in combination. 
     One feature of the present teaching is that both a DC bias signal and an AC bias signal are applied to the parent MZM  420 . This allows for a DC bias that is nominally constant over time, as well as an AC bias that changes with time. For example, the AC bias may change based on the modulation signal. Thus, the AC bias signal may operate at RF frequencies. The AC bias signal rate may track, for example, the data rate, and/or the symbol rate, of the applied RF data modulation signal. In some embodiments, the AC bias signal may change based on a particular symbol being encoded in a constellation of a phase modulated signal. For example, referring back to the constellation diagram  350  of the 4QAM modulation signal described in connection with  FIG. 3B , in some embodiments the AC bias signal depends on which point  334 ,  336 ,  338 ,  340  of the constellation is being generated by the modulating signal. Said another way, and referring back to table  300  described in connection with  FIG. 3C , in some embodiments the AC bias signal depends on which symbol of the truth table is being applied by the modulating signal. As described further below, this feature of including an AC bias signal applied through AC bias electrodes to produce and apply data dependent AC bias phase on a superstructure MZM can result in a reduced MOIL, improved constellation Hamming distance, and/or improved linearity of the superstructure MZM  400  and represent a significate improvement over the state-of-the-art. 
     Modulation signals are fed to each modulation electrode  431 ,  432 ,  441 ,  442 . The signals are supplied by the driver  404  and selected by the controller  402 . The respective modulation signals correspond to I and Q data streams provided from a data feeding source, such as a programmable controller (not shown) or other source. Respective bias signals are fed to some or all of bias electrode  451 ,  452 ,  461 ,  462 ,  471 ,  472 ,  481 ,  491  as selected by the controller  402  and supplied by the drivers  405 ,  406 ,  407 . A look-up table associated with the controller  402  can be used to store any or all of the data-dependent AC bias and/or DC bias values used to generate bias signals for the various bias electrodes described herein. In some embodiments, the electrodes can be driven directly by high-speed digital-to-analog converters. 
     In some embodiments, the DC bias signals are configured by the controller  402  to bias the child MZM  430  in the first arm  412  at a minimum transmission point and to bias the child MZM  440  in the second arm  414  at a minimum transmission point. In some embodiments, the controller  402  configures the driver  404  such that the RF modulation signals for both child modulators  430 ,  440  supply a differential voltage of ±V π , which results in a 2V π  peak-to-peak voltage swing. In some embodiments, the RF modulation signals for both child modulators  430 ,  440  are configured to supply a differential voltage of ±V π /2, which results in a 1V π  peak-to-peak voltage swing for each child MZM  430 ,  440 . 
     In one embodiment according to the present teaching, the child MZM  430  modulation electrodes  431 , 432  are differential RF electrodes for in-phase data modulation. The child MZM  440  electrodes  441 , 442  are differential RF electrodes for quadrature data modulation. The bias electrodes  451 , 452  are differential in-phase DC bias electrodes for child MZM  430 . The bias electrodes  461 , 462  are differential quadrature DC bias electrodes for child MZM  440 . The DC bias electrodes  471 ,  472  are differential DC bias electrodes for the parent MZM  420 . Also, the AC bias electrodes  481 ,  491  are complementary RF electrodes for modulating data-dependent phase shifts for AC bias of parent MZM  420 . 
     In some embodiments, the AC bias causes the part of the quadrature phase shift for the parent MZM  420  to include a data-modulation-dependent phase shift Δϕ in addition to a fixed, time-independent, DC bias phase shift of Δϕ=π/2. This is a similar concept to that for which an AC signal rides on top of a DC signal. Following this analogy, the root-mean square (rms) value of this AC modulation imposed on the quadrature phase bias, Δϕ=π/2, is what reduces the insertion loss to either less than 3 dB, or eliminates it completely (0 dB). This is achieved because the varying bias results in an in-phase addition, which is also referred to as coherent addition, of the in-phase and quadrature optical signals produced by child MZM  430  and child MZM  440 , respectively. This is in contrast to known superstructure modulators that rely on conventional quadrature addition provided by a Δϕ=π/2 DC bias only, which is an incoherent addition of the I and Q signals. The AC bias on the parent modulator  420  of the IQ Mach-Zehnder superstructure modulator system  400  of the present teaching can provide up to a 3 dB reduction in MOIL as compared to an IQ Mach-Zehnder superstructure modulator systems without an AC bias applied to the parent modulator. 
     While the discussion associated with the embodiment of  FIG. 4  is described in connection with a differential drive configuration, one skilled in the art will appreciate that numerous other drive configurations and electrode configurations can be used. For example, single electrode modulation schemes and/or single electrode bias configurations can also be used for any or all of the child MZMs  430 ,  440  and the parent MZM  420 . 
       FIG. 5A  illustrates a table  500  including a symbol truth table, DC and AC bias phase, and field and intensity values at an output for an embodiment of a Mach-Zehnder superstructure modulator configured for 4QAM operation according to the present teaching. The table  500  illustrates a 2V π  applied modulation voltage method. Such a table can be associated with, for example, an embodiment of the IQ Mach-Zehnder superstructure modulator system  400  described in connection with  FIG. 4  in which the child MZMs  430 ,  440  are biased at a minimum transmission and applied peak-to-peak modulation signal voltage is 2V π . 
     A mathematical description of operation is as follows. In the proposed scheme, as shown in table  500 , each symbol of an applied modulation is associated with an applied phase value, Δ{tilde over (ϕ)}(t) that is a logical XOR operation of the applied modulation phase for the in-phase modulator  430 , Δϕ 1 (t), and the applied modulation phase for the quadrature modulator  440 , Δϕ Q (t). The output field of modulator system  400  may be described by the following equations: 
             E   =         E   0       2       ⁡     [       ⁢       (     exp   ⁡     (     j   ⁡     (         φ   I     ⁡     (   t   )       -     π   2       )       )       )     ·     exp   ⁡     (     j   ±       Δ   ⁢     Φ   ~       2       )           ±         exp   ⁡     (     j   ⁢           ⁢   ΔΦ     )       ·     exp   ⁡     (     j   ⁢           ⁢     +   _     ⁢       Δ   ⁢     Φ   ~       2       )       ·     ⁢     (     exp   ⁡     (     j   ⁡     (         φ   Q     ⁡     (   t   )       -     π   2       )       )       )         ]                   E   =         E   0       2       ⁡     [       ⁢       (     exp   ⁡     (     j   ⁡     (         φ   I     ⁡     (   t   )       -     π   2       )       )       )     ·   exp     ⁢     (     j   ±       Δ   ⁢     Φ   ~       2       )       ±       j   ·   exp     ⁢       (     j   ⁢           ⁢     +   _     ⁢       Δ   ⁢     Φ   ~       2       )     ·     ⁢     (     exp   ⁡     (     j   ⁡     (         φ   Q     ⁡     (   t   )       -     π   2       )       )       )         ]             
where Δ{tilde over (ϕ)}(t)≈Φ 1 (t)⊕Φ Q (t), and where ⊕ corresponds to a logical XOR operation. In addition, to getting an average of
 
                 Δ   ⁢       Φ   ~     ⁡     (   t   )         ≈     π   2       ,       Δ   ⁢       Φ   ~     ⁡     (   t   )         =       0   ⁢           ⁢   whenever   ⁢           ⁢       Δ   ⁢       Φ   ~     ⁡     (   t   )         2       =     ±     π   4           ,           ⁢   and                       ⁢       Δ   ⁢       Φ   ~     ⁡     (   t   )         =       1   ⁢           ⁢   whenever   ⁢           ⁢       Δ   ⁢       Φ   ~     ⁡     (   t   )         2       =       +   _     ⁢       π   4     .                 
The table  500  presents the complex field, E, and the intensity, I=|E| 2  for each symbol in the 4QAM constellation.
 
       FIG. 5B  illustrates a phase diagram  520  representing output signal points for an embodiment of a Mach-Zehnder superstructure modulator configured for 4QAM operation according to the present teaching and a known 4QAM-configured Mach-Zehnder superstructure modulator. This phase diagram  520  illustrates a 2V π  applied peak-to-peak modulation voltage method. Referring both the table  500  described in connection with  FIG. 5A  and to the phase diagram  520  described in connection with  FIG. 5B , the vectors  501 ,  502  represent one respective path each for a symbol “0”, with vector  501  being the in-phase vector and vector  502  being the quadrature vector. Following along with the row for symbol “00”, the in-phase vector  501  gets an AC-bias phase shift of 
               +     π   4       ,         
which is shown by a positive 45° phase angle  540 , and the quadrature vector  502  is phase shifted by AC bias phase of
 
               -     π   4       ,         
which is shown by a negative 45° phase angle  541 . These vectors are then added “in-phase” to produce the symbol as point  510  with E=1+j. This is in contrast to a quadrature addition that results from no AC bias applied that leads to symbol  340  with E=0.7+0.7j similar to the example presented in connection with  FIG. 3A . AC bias phases for the other symbols in the constellation that are provided in the table  500  described in connection with  FIG. 5  are also shown. The phase rotations of the outputs of the child MZMs  430 ,  440  are data-dependent at the combiner of the parent MZM  420 , as different applied symbols result in different biases applied to electrodes  481 ,  491 , and the associated different phase shifts in each arm  412 ,  414  of the parent MZM  420 .
 
       FIG. 5C  illustrates a constellation diagram  560  representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 4QAM operation of the present teaching and a known 4QAM-configured Mach-Zehnder superstructure modulator. This phase diagram  520  illustrates a 2V π  peak swing applied modulation voltage embodiment. It is clear that the resulting points  510 ,  511 ,  512 ,  513  representing an output from a Mach-Zehnder superstructure modulator of the present teaching have higher amplitude transmission than corresponding points  334 , 336 , 338 , 340  for known superstructure modulators. The resulting MOIL improvement is calculated theoretically to be 3.01 dB. A simulation of the resulting MOIL yielded the same value. The in-phase addition symbol points  510 ,  511 ,  512 ,  513  each exhibit a separation from the plot origin of ±1.0±1.0j. Such an increase in the separation improves the signal strength for more robustly traversing a channel. Such an increase in the separation improves the ability of a coherent receiver to decode and correctly identify the transmitted symbols. Furthermore, the in-phase addition of the quadrature signals reduces the insertion loss associated with the modulator. 
     One feature of the methods and apparatus of present teaching is that it can be applied to numerous phase-based modulation schemes that are produced by MZM superstructure modulators. This includes the QPSK and 4QAM format described above. This also includes, for example, various nQAM modulation formats for which the value n can take on numerous values including, for example, n=4, 8, 16, 64, 256, etc. The modulated optical signal from a Mach-Zehnder superstructure modulator of the present teaching may carry information, for example, by means of symbols selected from a set of at least two, four, or more different symbols. 
     One aspect of the present teaching is that, in some embodiments certain advantages can be achieved when the in-phase and quadrature components of the nQAM signals are rotated using the AC bias phase in the two-dimensional complex plane (I−Q) by data dependent phase angles that are complementary to each other. 
     As described below in the description associated with  FIGS. 6A-6C , the superstructure modulator  400  described in connection with  FIG. 4  can also be used to generate even higher-order signal constellations such as 16QAM and 64QAM and/or to generate nQAM signals with high linearity and reduced MOIL. The system and method of the present teaching thereby relaxes the requirement of having a non-linear signal constellation analyzer as a last signal processing block on the receive-side digital signal processor to do decision operations on received symbols and perform symbol-to-bits mapping operations. These features can substantially reduce cost, complexity and/or size weight and power consumption of the receiver. 
       FIG. 6A  illustrates a constellation diagram  600  representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 16QAM operation with 1V π  drive operating point of the present teaching and a known 16QAM-configured Mach-Zehnder superstructure modulator.  FIG. 6A  illustrates an improvement for a 16QAM simulation where the insertion loss may be calculated by calculating 9.0/5.0=1.8 and using the equation 10*log 10(1.8)=2.55 dB (in theory) and 2.61 dB (in simulation) for a 1 Vπ case. This corresponds to an MOIL improvement of 2.61 dB compared to MOIL of 8.55 dB. The MOIL of 8.55 dB includes 3 dB due to quadrature addition, +3 dB due to 1V π  under-drive, and +2.55 dB due to peak-to-average ratio of PAM4 signal. 
       FIG. 6B  illustrates a constellation diagram representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 16QAM operation with 2V π  drive of the present teaching and a known 16QAM-configured Mach-Zehnder superstructure modulator.  FIG. 6B  illustrates an improvement for a 16QAM simulation where the insertion loss may be calculated by calculating 9.0/5.0=1.8 and 3 dB+10*log 10(1.8)=5.55 dB (in theory) and 5.79 dB (in simulation) for a 2Vπ case. This corresponds to an MOIL improvement of 5.79 dB again compared to MIOL of 5.55 dB. However, the 1QAM constellation is somewhat distorted as 16QAM constellation points do not have equal Hamming distance. 
       FIG. 6C  illustrates a constellation diagram representing the modulated output signal for an embodiment of a Mach-Zehnder superstructure modulator configured for 16QAM operation with 2V π  drive and linearization of the present teaching and a known 16QAM-configured Mach-Zehnder superstructure modulator. The more linear signal constellation may be generated where signal constellation points have an equal Hamming distance of 2. This linearity improvement can, for example, improve the receiver sensitivity and/or make the system more tolerant of loss and noise. This configuration yields a 5.53 dB reduction in the MOIL compared to theoretical MOIL of 5.55 dB. In other words, we have recovered most of the lost signal power at the transmitter that is associated with prior art amplitude- and/or phase-based optical modulators. For some applications, a small increase in MOIL is well worth the associated improvement in linearity.  FIGS. 6A-6C  indicates that the symbols for the in-phase addition cases have maximum power transmission, which may be an advantage over other 16QAM modulation schemes. 
     The data-dependent phase shifts of the AC bias for the 4QAM or QPSK embodiments may be implemented as 
               ±     π   4       ,         
which happens to be an equal and opposite configuration. This bias condition can still be referred to as a differential AC bias drive configuration although the RF drive signals are complementary because an equal and opposite bias phase is applied to the two arms  412 ,  414  of the parent MZM  420  whose sum is
 
               π   2     .         
In general, however, the data-dependent AC bias phase is not necessarily of the same magnitude for each arm  412 ,  414 . Rather, in some embodiments, especially those with larger constellations, the AC bias phase is applied as a complementary phase bias. That is, the applied AC bias phase totals 90° so that an AC bias phase of X° is applied to one arm  412 , and 90-X° is applied to the other arm  414 . This is the case for signals that fall in the 0-90° quadrant of the phase diagram. The effect of the additional phase from the AC bias is to move a vector associated with the in-phase component of the desired symbol point and a vector associated with the quadrature component of the desired symbol point toward each other such that they add constructively “in-phase”. Note that the differential AC bias drive of the 4QAM or QPSK embodiments is a special case of a complementary phase bias with equal magnitude.
 
     Thus, for some embodiments, for example QPSK or 4QAM, for all four symbols the complementary phase shift of π/4 can be selected so that the total path phase shift of all four paths are equal. That is, the amplitudes of the applied phase biases are the same magnitude. In various other embodiments, in particular those with larger constellation size, the amplitude of the applied phase biases are not all the same magnitude. As the number of symbols increases, the applied bias phases generally increase in number. In practice, these applied biases can be predetermined and provided in a look up table that is accessed by the control device  403 . 
       FIG. 7A  illustrates a phase diagram  700  for a 16QAM constellation.  FIG. 7B  illustrates a table  750  of a symbol and associated phase and amplitude of the transmitted optical carrier representing the symbol associated with the phase diagram  700  of  FIG. 7A . Retelling to both figures, symbol point  702  has a respective vector  704  with an amplitude and a phase angle  706 . The vectors&#39;  704 ,  708 ,  710 ,  716  amplitudes and phase angles  706 ,  712 ,  714  shown indicate that there are three phase angles  706 ,  712 ,  714  in each quadrant, for example, the three phase angles  706 ,  712 ,  714  of the 0-90-degree quadrant. Vector  710  and vector  716  have the same 45-degree phase angle  712 . The points at the end of vectors  704 ,  708 ,  710 ,  716  represent the four symbols  752  shown in the table  750 . It is possible to determine for each signal point, e.g. point  702 , the complementary AC bias phase to be applied to each electrode  481 ,  491  for each of the four symbols  752  indicated in table  750 . In some embodiments, this predetermined symbol-based complementary phase can be stored in a look up table that can be accessed by the control device  403 . 
     One feature of the present teaching is that it can be applied to dual-polarization multiplexed IQ Mach-Zehnder modulators. Such modulators can advantageously provide twice the data capacity per optical carrier as compared to single polarization modulators. 
       FIG. 8  illustrates an embodiment of a dual-polarization IQ Mach-Zehnder superstructure modulator system  800  of the present teaching. A dual-polarization IQ Mach-Zehnder superstructure  802  includes two IQ Mach-Zehnder superstructure modulators  804 ,  806 , one in each arm of the dual-polarization IQ Mach-Zehnder superstructure  802 . For example, these IQ Mach-Zehnder superstructure modulators  804 ,  806  can be the IQ Mach-Zehnder superstructure modulator  420  described in connection with  FIG. 4 . Each IQ Mach-Zehnder superstructure modulator  804 ,  806  is supplied modulation signals and bias signals by respective control devices  808 ,  810  that may be the same or similar to the control device  403  as described in connection with  FIG. 4 . An input optical carrier is split to supply an optical signal to each of the IQ Mach-Zehnder superstructure modulators  804 ,  806  in each arm of the dual-polarization IQ Mach-Zehnder superstructure  802 . In various embodiments, each IQ Mach-Zehnder superstructure modulator  804 ,  806  generates a modulated optical signal that has reduced MOIL and/or improved linearization and/or improved Hamming distance as described herein by applying an AC bias to one or both of the superstructure modulators  804 ,  806 . For example, this can be any of DPSK, QPSK, 8QAM, 16 QAM, 64 QAM or other phase modulated optical signals. A polarization rotator is used to rotate the output of the signal from IQ Mach-Zehnder superstructure modulator  806  to construct an output signal that includes modulated optical signals in two orthogonal polarizations at an output of the dual-polarization IQ Mach-Zehnder superstructure  802 . This is sometimes referred to as a polarization multiplexed optical signal or a dual-polarization optical signal. 
     The system and method of the present teaching can be applied to MZMs that are fabricated using any of a variety know materials. For example, MZM modulators of the present teaching can be constructed using Lithium Niobate, Indium Phosphide, Gallium Arsenide, and/or Silicon Photonics technology. Some embodiments of the MZM superstructure in-phase and quadrature phase optical modulator may additionally include two child MZMs. The embodiments described herein can simultaneously improve linearity as well as reduce the MOIL due to, for example, quadrature addition loss, peak-to-average power ratio loss of electrical driving pulse amplitude modulation signals, and/or loss due to under-driving the child MZMs to generate nQAM signals. 
     Some embodiments of the system and method of present teaching include electrically driving the two high-speed phase modulators which rotate in-phase and quadrature-phase components of the nQAM signals in the complex plane (I-Q) by data dependent phase angles which are complementary to each other. Furthermore, some embodiments can implement an algorithm, described herein, to compute two-complementary phase angles for nQAM signal generation that allow electrically driving child in-phase and quadrature MZMs with a peak-to-peak voltage swing of 2V π , or a voltage swing between 1V π  and 2 V π . Alternatively or additionally, some embodiments of the system and methods of the present teaching construct a look-up table that stores the two-complementary data-dependent phase angles on the transmit-side that is accessible to a digital signal processor that generates data-dependent phase angles at the baud rate using two high-speed digital-to-analog converters. 
     EQUIVALENTS 
     While the Applicant&#39;s teaching is described in conjunction with various embodiments, it is not intended that the Applicant&#39;s teaching be limited to such embodiments. On the contrary, the Applicant&#39;s teaching encompass various alternatives, modifications, and equivalents, as will be appreciated by those of skill in the art, which may be made therein without departing from the spirit and scope of the teaching.