# Patent

## Title
Optical modulator having a plurality of modulator segments

## Abstract

An optical modulator apparatus may include a plurality of segment drivers, each segment driver having a unique offset voltage and driving but a portion or a segment of an electro-optical modulator. A modulating electrical signal may be applied to the segment drivers via a plurality of electrical delays. Parameters of the segment drivers may be selected so as to approximate a pre-defined transfer function, which may include a linear or a non-linear transfer function.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. patent application Ser. No. 14/879,149, filed Oct. 9, 2015, now allowed, which claims the benefit of U.S. Provisional Application No. 62/062,127, filed Oct. 9, 2014, each of which is hereby incorporated by reference herein in its entirety.


TECHNICAL FIELD
This disclosure relates to devices for modulating light and particularly to optical modulators including electrical amplifier circuitry.
BACKGROUND
An optical modulator is a device for modulating an optical signal, such as an optical carrier wave, by an electrical signal. Some property of the optical carrier wave, such as phase, amplitude, polarization, etc., may be modulated by the electrical signal by using an electro-optical effect of some kind, such as Pockels effect, electro-absorption effect, photoelasticity, etc. The electrical signal may need to be amplified to provide a degree of modulation of the optical carrier wave adequate for a particular application. Linear amplifiers are commonly used to provide amplification of an electrical signal for optical modulation, because linear amplifiers preserve the waveform of the electrical signal being amplified.
Referring to FIG. 1, a conventional modulator apparatus 100 includes a linear amplifier 102 connected to an optical modulator 104. In operation, a high-frequency electrical signal 106 creates a running electromagnetic wave 108, which propagates in a RF waveguide formed by electrodes 110 running parallel to an electro-optical waveguide 112. The electromagnetic wave 108 runs toward an RF termination 114. The electromagnetic wave 108 propagates in the electro-optical waveguide 112 at the same speed as light 114. As a result, the light 114 becomes effectively modulated.
The linear amplifier 102 provides a constant gain, which is independent on the input signal: Vout=GVin, where Vin is the input voltage, Vout is the output voltage, and G is a constant. Referring to FIG. 2, the output voltage of the linear amplifier 102 is plotted against the input voltage. In this example, the input voltage range is −0.5V to 0.5V, and the corresponding output voltage range is −1V to 1V, so that the gain G=2.
Referring back to FIG. 1, the linear amplifier 102 is typically constructed to provide a significant amount of RF power for generation of the running electromagnetic wave 108. To drive the electrodes 110 in a linear fashion at high speed, a typical linear driver amplifier may consume twenty times more power than electrical power delivered to the optical modulator 104. This factor of power consumption is referred to as “overhead.” Often, conventional linear modulators have a significant overhead.
Furthermore, to provide linear output, the electrical signal swing may need to be wider than typical output modulation range, to ensure that the output will be sufficiently close to linear in an operational range of interest. The requirement of linearity may sacrifice other performance metrics, such as amplifier power consumption or operating speed.
SUMMARY
According to one aspect of the disclosure, an optical modulator apparatus may include a plurality of drivers, each driver driving but a physical portion or segment of an electro-optical modulator. A modulating electrical signal may be applied to the segment drivers via a plurality of electrical delays, or via a single delay with a plurality of taps. The segment drivers may also be individually controlled by an external comparator module. Parameters of the segment drivers may be selected or programmed so as to approximate a pre-defined overall transfer function, for example a linear transfer function, or a non-linear transfer function if required.
In accordance with an aspect of the disclosure, there is provided an optical modulator comprising: an optical path comprising an optical input port for receiving an optical carrier wave, an optical output port for outputting a modulated optical signal, and a succession of serially optically coupled optical modulator segments extending between the input and output optical ports for modulating the optical carrier wave so as to obtain the modulated optical signal; a plurality of segment drivers, wherein each segment driver has associated: a low voltage Vlow, a high voltage Vhigh, a unique offset voltage Vos, and a threshold voltage Vth, wherein each segment driver is electrically coupled to one of the succession of the modulator segments for applying a driving voltage Vd thereto in response to a control voltage Vc, such that

    
    
        Vd=Vlow when Vc<Vos−Vth;
        Vd=Vhigh when Vc>Vos+Vth; and
        Vd varies between Vlow and Vhigh when Vc varies between Vos−Vth and Vos+Vth; an electrical input port for receiving an electrical signal to be modulated onto the optical carrier wave to obtain the modulated optical signal; and a plurality of electrical connections between the electrical input port and each segment driver.
    
    


In one exemplary embodiment, each segment driver may be implemented as a limiting amplifier having the corresponding low voltage Vlow, the high voltage Vhigh, the unique offset voltage Vos, and the threshold voltage Vth. Each electrical connection may have a corresponding delay ΔTelectrical between the electrical input port and each limiting amplifier. The delays ΔTelectrical may be selected so that in operation, the application of the driving voltage Vd to individual optical modulator segments in the succession of optical modulator segments is substantially synchronized with propagation of the optical carrier wave therein.
In another embodiment, the succession of serially optically coupled optical modulator segments includes an optical waveguide and a succession of electrodes disposed along the optical waveguide and operationally coupled to the optical waveguide. The plurality of electrical connections may include a succession of serially electrically coupled electrical delay line segments, such as a delay line with a plurality of taps. Each progressive one of the succession of electrical delay line segments or taps may be electrically coupled to a particular segment driver of the plurality of segment drivers, which is is electrically coupled to a corresponding progressive one of the succession of optical modulator segments. The offset voltage Vos of each successive segment driver is preferably greater than the offset voltage Vos of the immediately preceding segment driver, if any.
In accordance with the disclosure, there is further provided a method of modulating an optical carrier wave by an electrical signal, the method comprising: propagating the optical carrier wave in a succession of serially optically coupled optical modulator segments; and coupling the electrical signal a plurality of segment drivers, wherein each segment driver has associated: a low voltage Vlow; a high voltage Vhigh; a unique offset voltage Vos; and a threshold voltage Vth, wherein each segment driver is electrically coupled to one of the succession of the modulator segments for applying a driving voltage Vd thereto in response to a control voltage Vc, such that

    
    
        Vd=Vlow when Vc<Vos−Vth;
        Vd=Vhigh when Vc>Vos+Vth; and
        Vd varies between V10 and Vhigh when Vc varies between Vos−Vth and Vos+Vth. The electrical signal may be coupled to an electrical input port, from which the electrical signal propagates to each segment driver via a plurality of electrical connections between an electrical input port and each segment driver. Each electrical connection may be configured to have a corresponding delay ΔTelectrical between the electrical input port and each segment driver. The delays ΔTelectrical may be selected so that the application of the driving voltage Vd to individual optical modulator segments in the succession of optical modulator segments is substantially synchronized with propagation of the optical carrier wave therein. The offset voltage Vos of each successive segment driver may be pre-selected to be greater than the offset voltage Vos of the immediately preceding segment driver. Furthermore, in one embodiment, the low voltage Vlow, the high voltage Vhigh, the offset voltage Vos, and the threshold voltage Vth of each segment driver are pre-selected such that Vlow of each successive segment driver is substantially equal to Vhigh of the immediately preceding segment driver, if any.
    
    


In accordance with the disclosure, there is further provided a modulator apparatus comprising: an optical path comprising an optical input port for receiving an optical carrier wave, an optical output port for outputting a modulated optical signal, and N serially optically coupled optical modulator segments extending between the input and output optical ports for modulating the optical carrier wave so as to obtain the modulated optical signal, wherein N is an integer; an electrical input port for receiving an electrical signal to be modulated onto the optical carrier wave to obtain the modulated optical signal; an analog to digital converter operationally coupled to the electrical input port, for digitizing the electrical signal to provide input digital signals; and a digital filter operationally coupled to the analog to digital converter, for receiving and digital filtering the input digital signals to provide N output digital signals, each of which for driving one of the N optical modulator segments.



BRIEF DESCRIPTION OF THE DRAWINGS
Exemplary embodiments will now be described in conjunction with the drawings, in which:
FIG. 1 is a schematic diagram of a prior-art optical modulator having a single linear amplifier;
FIG. 2 is a transfer function of the linear amplifier shown in FIG. 1;
FIG. 3 is a schematic diagram of a modulator apparatus of the present disclosure;
FIG. 4 is a transfer characteristic of a limiting amplifier of the modulator apparatus of FIG. 3;
FIG. 5 is a schematic diagram of an embodiment of a modulator apparatus of the present disclosure;
FIG. 6A is a graph of exemplary transfer functions of limiting amplifiers of the modulator apparatuses of FIG. 3 or 5, having a threshold voltage of 0.1 V;
FIG. 6B is a graph of overall transfer function of a modulator apparatus of FIG. 3 or 5, having the limiting amplifiers with transfer functions shown in FIG. 6A;
FIG. 7A is a graph of transfer functions of fifteen limiting amplifiers according to one embodiment of the present disclosure;
FIG. 7B is a graph of overall transfer function of a modulator apparatus having the fifteen limiting amplifiers with transfer functions shown in FIG. 7A;
FIG. 8A is a graph of transfer functions of limiting amplifiers of the modulator apparatuses of FIG. 3 or 5 having a threshold voltage of 0.5V;
FIG. 8B is a graph of overall transfer function of a modulator apparatus having the limiting amplifiers with transfer functions shown in FIG. 8A;
FIG. 9 is a circuit diagram of a limiting amplifier using a differential pair of MOSFET transistors;
FIG. 10 is a circuit diagram of a limiting amplifier using a differential pair of bipolar transistors;
FIG. 11A is a graph of transfer functions of eleven segment drivers for approximating a third order overall transfer function;
FIG. 11B is a graph of the third-order overall transfer function of the modulator apparatus having the eleven segment drivers with transfer functions of FIG. 11A;
FIG. 12A is a graph of transfer functions of eleven segment drivers for approximating a second-order overall transfer function;
FIG. 12B is a graph of the second-order overall transfer function of the modulator apparatus having the eleven segment drivers with transfer functions of FIG. 12A;
FIG. 13A is a graph of transfer functions of eleven segment drivers for approximating a periodic overall transfer function;
FIG. 13B is a graph of the periodic overall transfer function of the modulator apparatus having the eleven segment drivers with transfer functions of FIG. 13A;
FIG. 14 is a flow chart of an exemplary method of modulating an optical carrier wave; and
FIG. 15 is a schematic block diagram of an embodiment of an optical modulator including an analog to digital converter (ADC) and a digital filter coupled to the ADC.



DETAILED DESCRIPTION
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 and equivalents, as will be appreciated by those of skill in the art. In FIGS. 3 and 5, similar reference numerals denote similar elements, as well as in FIGS. 6A, B; 7A, B; 8A, B; 11A, B; 12A, B; and FIGS. 13A, B.
Referring to FIG. 3, a modulator apparatus 300 of the present disclosure includes an optical path having an optical input port 304 for receiving an optical carrier wave 305, an optical output port 306 for outputting a modulated optical signal 307, and a succession 320 of serially optically coupled optical modulator segments 321, 322, 323, 324, and 325 extending between the input 304 and output 306 optical ports for modulating the optical carrier wave 305, so as to obtain the modulated optical signal 307 at the optical output port 306.
A plurality of limiting amplifiers 311, 312, 313, 314, and 315 may be provided for driving the optical modulator segments 321-325. Each limiting amplifier 311-315 is electrically coupled to a particular one of the succession of the modulator segments 321-325 for applying a driving voltage Vd thereto in response to a control voltage V,. Referring to FIG. 4, a response characteristic 400 of the limiting amplifiers 311-315 may be defined by a low voltage Vlow, a high voltage Vhigh, an offset voltage Vos, and a threshold voltage Vth. When Vc<Vos−Vth, Vd=Vlow; when Vc>Vos+Vth, Vd=Vhigh; and when Vc varies between Vos−Vth and Vos+Vth, Vd varies between Vlow and Vhigh; that is, when Vc increases between Vos−Vth and Vos+Vth, Vd increases between Vlow and Vhigh, and vice versa. The parameters Vlow, Vhigh, Vos, and Vth of different limiting amplifiers 311-315 may differ from amplifier to amplifier.
The threshold voltage parameter Vth determines how abrupt the transition is from “low” to “high”, whereas the offset voltage parameter Vos determines at which control voltage Vc a midpoint 401 of the transition occurs. A “transition slope”, defined as (Vhigh−Vlow)/(2Vm), may describe the abruptness of the transition, termed herein as “switching.” The transition slope is defined herein as the slope of a line drawn between the high and low limits of a piecewise linear representation of the transition. In the non-limiting exemplary response characteristic 400 of FIG. 4, the high level Vhigh is 1V, and the low level Vlow is −1V. The Vos is 0.2V, and Vth is approximately 0.05V. The transition slope in this example is 2V/2*0.05V=20.
Referring again to FIG. 3, the modulator apparatus 300 further includes an electrical input port 302 for receiving an electrical signal 303 to be modulated onto the optical carrier wave 305 to obtain the modulated optical signal 307. A plurality of electrical connections 310 are provided between the electrical input port 302 and each limiting amplifier 311-315. Each electrical connection is configured to provide a corresponding delay ΔTelectrical between the electrical input port 302 and each limiting amplifier 311-315. The limiting amplifiers 311-315 may introduce an additional delay ΔTamp, which may be the same, or may be different between different limiting amplifiers 311-315.
In operation, the propagating optical carrier wave 305 arrives at each successive optical modulator segment 321-325 with a delay ΔToptical. In one embodiment, the delays ΔTelectrical defined by the plurality of electrical connections 310 are selected so that the driving voltage Vd is applied substantially at the speed of propagation of the optical carrier wave 305 the optical modulator segments 321-325. The delays ΔTelectrical may take into account possible different values of ΔTamp of different limiting amplifiers 311-315. In other words, the delays ΔTelectrical may be selected so that in operation, the application of the driving voltage Vd to individual optical modulator segments 321-325 in the succession 320 of the optical modulator segments 321-325 is substantially synchronized with propagation of the optical carrier wave 305 in the optical modulator segments 321-325.
One can add delays to either or both of ΔTelectrical and ΔToptical so that the electrical signal and the optical signal propagate at the same rates, and the electrical signal 303 is faithfully amplified and modulated onto the optical carrier wave 305. In an embodiment where the ΔTamp of different limiting amplifiers 311-315 are different, the difference can be compensated by the correction applied to either or both of optical delays ΔToptical and/or electrical delays ΔTelectrical. Furthermore, at least optical modulator segments 321-325 of the succession 320 may have different optical lengths.
Referring to FIG. 5, a modulator apparatus 500 is an embodiment of the modulator apparatus 300 of FIG. 3. In the modulator apparatus 500 of FIG. 5, a succession 520 of serially optically coupled optical modulator segments 521, 522, 523, 524, and 525 includes a 3dB splitter 509A, first 540A and second 540B optical waveguides coupled to the 3dB splitter 509A, a succession of electrodes 531A, 532A, 533A, 534A, and 535A disposed along the first optical waveguide 540A and operationally coupled to the optical waveguide 540A, a succession of electrodes 531B, 532B, 533B, 534B, and 535B disposed along the second optical waveguide 540B and operationally coupled to the optical waveguide 540B, and a 3dB combiner 509B coupled to the first 540A and second 540B optical waveguides. The electrode pairs 531A-531B, 532A-532B, 533A-533B, 534A-534B, and 535A-535B may define respective modulator segments 521, 522, 523, 524, and 525. A plurality of electrical connections 510 of the modulator apparatus 500 may include a succession of serially electrically coupled electrical delay line segments 541, 542, 543, 544, and 545.
As seen in FIG. 5, each progressive one of the succession of electrical delay line segments 541-545 is electrically coupled to one of the limiting amplifiers 311-315, which is electrically coupled to a corresponding progressive one of the optical modulator segments 521-525. The delays ΔTelectrical are selected so that the application of the driving voltage Vd to individual optical modulator segments 521-525 of the succession 520 is essentially synchronized with propagation of the optical carrier wave 305 in the optical modulator segments 521-525, causing the succession of electrodes 521-525 to approximate, in a piecewise fashion, an electromagnetic wave propagating in synchronism with the optical carrier wave 305. The overall transfer function of the modulator apparatus 500 of FIG. 5, as well as the modulator apparatus 300 of FIG. 3, may be defined by selecting the parameters Vlow, Vhigh, Vos, and Vth of individual limiting amplifiers 311-315, as will now be explained.
Referring to FIG. 6A, transfer functions 601, 602, 603, 604, 605 are non-limiting examples of transfer functions of the respective limiting amplifiers 311, 312, 313, 314, 315 of FIGS. 3 and 5. As can be gleaned from FIG. 6A, the offset voltage Vos of each successive limiting amplifier 312-315 is greater than the offset voltage of the immediately preceding limiting amplifier 311-314, if any, by a same step voltage ΔVos. For the transfer functions 601, 602, 603, 604, 605 these Vos values are approximately equal to −0.4V, −0.2V, 0V, +0.2V and +0.4V, respectively, with the step voltage ΔVos=0.2V, while the threshold voltage Vth=0.1V. In operation, the limiting amplifiers 311-315 turn on in sequence such that only one limiting amplifier 311-315 is operating in its transition region at a time. The other limiting amplifiers 311-315 either remain in an “off” state if they have a higher Vos than the current control voltage Vc, or in a fully “on” state if they have a lower Vos than the current control voltage Vc. The Vos values may range over both. negative and positive values. For other embodiments, in which the input range could be different, such as 0V to +1V, or from any convenient lower limit to any convenient upper limit of input voltages, the Vos values of the successive limiting amplifiers may be selected to match the desired input voltage range.
Turning to FIG. 6B, an overall transfer function 620, i.e. optical modulation vs. control voltage Vc, of the modulator apparatus 500 of FIG. 5 is compared to a linear transfer function 630 of a conventional optical modulator, such as the optical modulator 100 of FIG. 1 having the linear amplifier driver 102. The transfer function 620 of the modulator apparatus 500 of FIG. 5 has a staircase shape centered around the linear transfer function 630. In the transfer function 620, kinks 625 are associated with the time intervals when the limiting amplifiers 311-315 turn on one by one as the control voltage Vc increases.
While the optical modulator 300 of FIG. 3 or 500 of FIG. 5 may provide an output signal in an approximation to a linear output, it may be desirable to obtain a transfer function that more closely corresponds to the linear transfer function 630. Embodiments which may provide an improved linearity of an overall transfer function of the modulator apparatus 300 of FIGS. 3 and 500 of FIG. 5 will now be described.
In one such embodiment, the total number of the limiting amplifiers 311-315, and accordingly the total number of the optical modulator segments 321-325 per operational range of the control voltage Vc, is increased. For generality, the limiting amplifiers 311-315 and the optical modulator segments 321-325 or 521-525, etc. may denote an arbitrary number N of the corresponding elements, despite that only five reference numerals e.g. 311, 312, 313, 314, 315 are used. Referring to FIG. 7A, transfer functions 701, 702, . . . , 715 correspond to fifteen limiting amplifiers having Vth=0.0333V, so that 30×Vth=1V. The respective values of Vos range from −0.471V to +0.471V, and the step voltage ΔVos= 1/15V. Turning to FIG. 7B, an overall transfer function 720 corresponds to the fifteen transfer functions 701-715 of FIG. 7A. The overall transfer function 720 is much close to a linear transfer function 730. Therefore, increasing the total number of limiting amplifiers 311-315 from five to fifteen may result in a much more linear overall transfer function. In principle, one could generate a transfer function that deviates by less than a desired amount by increasing the number of limiting amplifiers sufficiently. As a guide, five or more limiting amplifiers 311-315 may be provided. More than eight limiting amplifiers 311-315 may be provided.
In another embodiment, the threshold voltage Vth of each limiting amplifier 311-315 may be increased to make the transition from the low voltage Vlow to the high voltage Vhigh less abrupt as the control voltage V, is increased over the voltage range in which a specific limiting amplifier 311-315 is in active transition between the low voltage Vlow and the high voltage Vhigh. In particular, the transition slope of the limiting amplifier 311-315 transfer characteristic may be reduced to smoothen the kinks 615 in FIG. 6B.
Referring to FIG. 8A with further reference to FIG. 6A, transfer functions 801, 802, 803, 804, 805 have the threshold voltage Vth=0.50V, that is, five times larger than the transfer functions 601, 602, 603, 604, 605 of FIG. 6B. The respective values of Vos of the transfer functions 801-805 range from −0.4V to +0.4V with the step voltage ΔVos=0.2V. Turning to FIG. 8B, an overall transfer function 820 is much closer to a linear transfer function 830. Therefore, the limiting amplifier 311-315 implementation with the threshold voltage Vth=0.50V (FIG. 8B) provides the transfer function 820, which is much closer to the linear transfer function 830 of the conventional linear amplifier 102 (FIG. 1) than the limiting amplifier 311-315 implementation with the threshold voltage Vth=0.1V (FIG. 6B). Thus, the transition slope in this example is 1V/2*0.1V=5. In principle, one might generate a transfer function that deviates by less than a desired amount by increasing the value of Vth sufficiently. The transition slope may be selected to be less than 5, or even less than 2 in some cases.
The threshold voltage Vth, the offset voltages Vos, the slope of the limiting amplifiers 311-315, and/or the number of the limiting amplifiers 311-315 may be varied to obtain a desired overall response function. In the example above, the offset voltage Vos of each successive limiting amplifier 312-315 is greater than the offset voltage Vos of the immediately preceding limiting amplifier 311-314. More generally, at least one of the low voltage V10, the high voltage Vhigh, and the threshold voltage Vth, of at least one limiting amplifier 311-315 may be substantially different from a corresponding one of the low voltage Vlow, the high voltage Vhigh, and the threshold voltage Vth of another limiting amplifier 311-315.
In one embodiment, the low voltage Vlow, the high voltage Vhigh, and the offset voltage Vos of each limiting amplifier 311-315 are selected such that Vlow of each successive limiting amplifier 312-315 is substantially equal to Vhigh of the immediately preceding limiting amplifier 311-314. In this embodiment, the output of a jth limiting amplifier, where j runs from 1 to the number of limiting amplifiers N, reaches the upper limit Vhigh(j) when the control voltage Vc applied to the jth limiting amplifier is Vos(j)+Vth(j). The output of the (j+1)th limiting amplifier remains at Vlow(j+1) until the control voltage V, applied to the (j+1)th limiting amplifier reaches Vos(j+1)−Vth(j+1). By setting Vos(j)+Vth(j)=Vos(j+1)−Vth(j+1), one may ensure a smooth transition in the driving voltage Vd as the jth limiting amplifier saturates, and the (j+1)th amplifier begins to operate when the control voltage Vc is increased.
In one embodiment, the offset voltages Vos are selected so that the slope of a given limiting amplifier 311-315 is equal to a respective slope of a piecewise linear approximation of a segment of a curvilinear line that one wishes to approximate. The successive limiting amplifier 311-315 may have a slope that is equal to the piecewise linear approximation of the successive segment of the curvilinear line that one wishes to approximate. One can select the threshold voltage Vth(j) for the jth limiting amplifier so that the desired slope is achieved. The threshold voltages Vth of different limiting amplifiers may be the same, or may be different. One can select the offset voltages Vos(j) such that the midpoint of the line segment approximating the slope is located at the control voltage Vc corresponding to the midpoint of the respective segment of the curvilinear line that one wishes to approximate.
Implementations of Limiting Amplifiers Based on CMOS or BJT Differential Pairs
Referring to FIGS. 9 and 10, a schematic of a limiting amplifier 900 (FIG. 9) illustrates one implementation of the limiting amplifiers 311-315 (FIGS. 3 and 5) using a differential pair topology with MOSFET transistors 901 and 902. The limiting amplifier 900 is a symmetrical differential amplifier, with the MOSFET transistors 901, 902 electrically coupled to a common current source. In FIG. 10, a limiting amplifier 1000 illustrates a similar implementation of the limiting amplifiers 311-315 using a differential pair topology with bipolar transistors 1001, 1002. The limiting amplifiers 900 and 1000 have differential inputs with input voltage Vin=Vin+−Vin− and differential outputs with output voltage Vout=Vout+−Vout−. Either one or both inputs and outputs may be used. Differential signaling uses both inputs and is usually preferred for better power efficiency. Single-ended signaling can also generate limiting transfer function at a half of the output magnitude.
Capacitor Cb and resistor Rb allow the input signal DC level to be removed. A new offset level may be provided via the ports Vos1 and Vos2. The offset Vos is the difference between the two, Vos=Vos1−Vos2. Alternatively, in devices manufactured using SOI-based CMOS processes, one may change the substrate bias to change the threshold of the MOS transistors connected to Vin+ and Vin−, and the difference in the substrate bias of the two transistors is the Vos. Furthermore, in other embodiments one can have dedicated active level shifting circuitry preceding the differential pair circuit to add offset voltage to the incoming signal.
Still referring to FIGS. 9 and 10, Vhigh and Vto, may be adjusted by changing the values of a current source IS, a resistor Rd, and a supply voltage Vdd. The relationships among Vhigh, Vlow, IS and Vdd are given by:

Vhigh=Vdd 

Vlow=Vdd−ISRd 

Vth and slope may be adjusted by selecting the value of resistor Rs, which controls so-called “source degeneration.” When resistors Rd and Rs are omitted, that is, have zero resistance, one can achieve the sharpest slope. As Rd and Rs become larger the slope observed in the output voltage becomes more gradual. The polarity of the slope may also be changed. The slope of the transfer function may be positive, as the transfer function 400 of FIG. 4, or negative. The polarity may be controlled by the polarity of the input or output signal, i.e. switching between Vin+and Vin− or alternatively Vout+and Vout−. For a single-ended operation, one can use inverters as described above.
The limiting amplifiers 900 and/or 1000 of FIGS. 9 and 10 may have different parameters Vhigh, Vlow, Vos, IS, and Vdd. Furthermore, the limiting amplifiers 900 and/or 1000 may be configured to have programmable Vos, Vth, Vlow, and Vhigh. Non-linear transfer function systems, such a quadratic, cubic and higher order transfer function, sinusoidal transfer functions, and exponential transfer functions, may be realized. The optical modulator segment 321-325 and 521-525 lengths may also also be different. Even if the limiting amplifiers 311-315 have the same Vhigh and Vlow, their contributions to the overall accumulated modulation could be weighted differently by the optical modulator segment 321-325 and 521-525 lengths. Given a sufficient number of limiting amplifiers 311-315 and the optical modulator segment 321-325 and 521-525 segments, the output modulation may be flexibly configured or programmed. This may provide a useful signal processing functionality, while still maintaining power efficiency.
Using a sequence of the limiting amplifiers 311-315, implemented with the MOSFET 901, 902 and/or bipolar 1001, 1002 transistors as shown in FIGS. 9 and 10, respectively, or in other suitable configurations, may substantially reduce electrical power consumption in comparison with a single high-overhead linear drive amplifier, such as the amplifier 102 of FIG. 1. The low power overhead is a result of each limiting amplifier 311-315 only driving a small segment of the succession 320 (FIG. 3) or 520 (FIG. 5). The combination of small localized load, instead of a large distributed load in the prior-art modulator 100 of FIG. 1, may allow the use of efficient circuit blocks such as the limiting amplifiers 900 and/or 1000. Furthermore, limiting amplifiers 311-315 draw very small power when remaining in Vhigh or Vlow states, and therefore may lessen overall power overhead when only one of the limiting amplifiers 311-315 undergoes a transition between Vlow, and Vhigh at any given time.
The modulator apparatuses 300 (FIGS. 3) and 500 (FIG. 5) may be implemented using a variety of material systems. For example, the modulator apparatus 500 may include a silicon photonic chip comprising the first 540A and second 540B optical waveguides. Advantageously, the silicon photonic chip may have the limiting amplifiers 311-315 monolithically integrated on the chip. Alternatively, the limiting amplifiers 311-315 may be disposed on a separate substrate wirebonded to the substrate supporting the modulator segments 521-525 (FIG. 5). In one embodiment, the electrical connections between the limiting amplifiers 311-315 and the modulator segments 521-525 may include microball or microbump contacts, vias, copper columns, etc.
The limiting amplifiers 311-315 of the modulator apparatuses 300 (FIGS. 3) and 500 (FIG. 5) may be viewed as particular implementations of “segment drivers,” whose function is to drive individual modulator segments 321-325 (FIG. 3) or 521-525 (FIG. 5). Although the limiting amplifiers 311-315 advantageously combine a voltage discriminating function and a amplifying function in a single circuit, thus saving circuit board space and electrical power, more generic segment drivers may replace all the limiting amplifiers 311-315 in each modulator embodiment disclosed above, for each particular implementation discussed above. According to the present disclosure, these generic segment drivers replacing the limiting amplifiers 311-315 may be amplifying or non-amplifying, and may be externally controlled. Each such segment driver may have a set of associated parameters, which include the low voltage Vlow, the high voltage Vhigh, the unique offset voltage Vos, and the threshold voltage Vth.
For embodiments of the modulator apparatuses 300 and 500 including externally controlled segment drivers, a dedicated comparator module may be provided to turn on individual segment drivers when the control voltage Vc exceed thresholds set or programmed for these individual segment drivers. In such embodiment, the comparator module may be operationally coupled to the electrical input port 302 and the plurality of segment drivers, for providing individual control signals to the plurality of segment drivers when the control voltage Vc exceeds the offset voltages Vos of corresponding segment drivers of the plurality of segment drivers. The corresponding control signals are sent to the segment drivers by the comparator module. The comparator module may include an ADC, a digital filter, etc.
Following examples illustrate some of many possibilities of generating arbitrary transfer function curves. One may generate transfer functions including power functions, such as x2, x3, and so forth. In the following examples, the optical modulator segments 321-325 and/or 521-525 lengths are taken to be identical, but the lengths may be different e.g. have a binary length relationship. The segment drivers driving the optical modulator segments 321-325 and/or 521-525 may have different Vos, Vth, Vlow and Vhigh parameters. One might also achieve the same effect by having different modulator segment 321-325 and/or 521-525 lengths and keeping the output voltages Vlow and Vhigh the same, which may be convenient or advantageous in actual circuit configuration at given supply voltage constraints.
EXAMPLE 1
This embodiment illustrates a super-linear third order (x3) type overall transfer function of a modulator apparatus of the present disclosure, such as, for example, the modulator apparatus 300 of FIG. 3 or the modulator apparatus 500 of FIG. 5. Referring to FIG. 11A, graphs of transfer functions 1101, 1102, 1103, . . . , 1106, . . . , 1109, 1110 and 1111 approximating a third order overall response function, are provided for a modulator apparatus with N=11 segment drivers. Turning to FIG. 11B, an overall transfer function 1120 is compared with a transfer function 1130 of an optical modulator having a single linear amplifier.
EXAMPLE 2
This embodiment illustrates a second order (parabolic) overall transfer function of a modulator apparatus of the present disclosure. Referring to FIG. 12A, graphs of transfer functions 1201, 1202, 1203, . . . , 1206, . . . , 1209, 1210 and 1211 approximating a second order function are provided for a modulator apparatus with N=11 segment drivers. Transfer functions 1207-1211 have a negative slope. This can be achieved as explained above with reference to FIGS. 9 and 10. Turning to FIG. 12B, an overall transfer function 1220 is compared with a transfer function 1230 of an optical modulator having a single linear amplifier.
EXAMPLE 3
This embodiment illustrates a sinusoidal overall transfer function of a modulator apparatus of the present disclosure. Referring to FIG. 13A, graphs of transfer functions 1301, 1302, 1303, . . . , 1306, . . . , 1309, 1310 and 1311 approximating a sinusoid are provided for a modulator apparatus with N=11 segment drivers. In this embodiment, some transfer functions have positive slopes, and some transfer functions have negative slopes. Turning to FIG. 13B, an overall transfer function 1320 is compared with a transfer function 1330 of an optical modulator having a single linear amplifier. The approximation of a sinusoidal function may be improved by using more segment drivers, and/or by fine-tuning the slopes and voltage levels of each segment driver as explained above.
EXAMPLE 4
In this embodiment, a generalized exponential function Y=A exp(αX+β) may be obtained. This function may be recorded as Y=A [exp(αX)exp(β)]. Since exp(β) is a constant, the function may be reduced to Y=B exp(αX), where B =A exp(β). For this embodiment, piecewise linear approximations to the curve B exp(αX) may be taken between selected values of X. One may approximate each piecewise linear segment as a transfer function using one or more segment drivers as already described. One then “sums” all of the piecewise linear approximations to generate the desired approximation to the exponential curve over the range desired.
Referring to FIG. 14 with further reference to FIG. 3, a method 1400 (FIG. 14) of modulating the optical carrier wave 305 by the electrical signal 303 (FIG. 3) includes a step 1402 of propagating the optical carrier wave 305 in the succession 320 of serially optically coupled optical modulator segments 321-325. The electrical signal 303 may be coupled in a step 1404 to the plurality of the segment drivers, e.g. the limiting amplifiers 311-315. In the step 1404, each segment driver is electrically coupled to a particular one of the succession 320 of the modulator segments 321-325 for applying the driving voltage Vd to the modulator segments 321-325 in response to a control voltage Vc, such that Vd=Vlow when Vc<Vos−Vth; Vd=Vhigh when Vc>Vos+Vth; and Vd varies between Vlow and Vhigh when Vc varies between Vos−Vth and Vos+Vth. The electrical signal 303 may be coupled to the electrical input port 302, from which the electrical signal 303 propagates to each segment driver via the plurality of electrical connections 310 between the electrical input port 302 and each segment driver. Each electrical connection has a corresponding delay ΔTelectrical between the electrical input port 302 and each segment driver, such as the limiting amplifiers 311-315.
As explained above with reference to FIG. 5, the carrier optical wave 305 may be propagated in the optical waveguides 540A, B having the successions of electrodes 531A-535A and 531B-535B disposed along the respective optical waveguides 540A, B and operationally coupled to the optical waveguides 540A, B. The electrical signal 303 may be propagated in the succession 510 of serially electrically coupled electrical delay line segments 541-545. Each electrical delay line segment 541-545 may provide an electrical signal to one of the segment drivers, which is electrically coupled to corresponding progressive modulator segments 521-525 via the respective electrode pairs 531A, B 535A, B.
In one embodiment, the method 1400 may include a step 1406 of pre-selecting various parameters of the segment drivers. The parameters may also be programmed to provide a dynamically varying overall response function. By way of a non-limiting example, the offset voltage Vos of each successive segment driver may be selected to be greater than the offset voltage Vos of the immediately preceding segment driver. Furthermore, the low voltage Vlow, the high voltage Vhigh, the offset voltage Vos, and the threshold voltage Vth, of each segment driver may be selected such that Vlow of each successive segment driver is substantially equal to Vhigh of the immediately preceding segment driver. The slope (Vhigh−Vlow)/2Vth of each segment driver may be selected so as to provide a degree of modulation of the optical carrier wave 305 substantially proportional to a magnitude of the electrical signal 303 received at the electrical input port 302. Alternatively, the low voltage Vlow, the high voltage Vhigh, the offset voltage Vos, and the threshold voltage Vth, of each segment driver may be selected such that a degree of modulation of the modulated optical signal 307 is a desired function of the electrical signal 303 received at the electrical input port 302. As explained above with reference to 11A, B; 12A, B; and 13A, B, the function may include e.g. a quadratic, cubic, periodic, or an exponential function.
Turning to FIG. 15, a modulator apparatus 1500 is a variant of the modulator apparatus 300 of FIG. 3. The modulator apparatus 1500 (FIG. 5) includes an optical path having the optical input port 304 for receiving the optical carrier wave 305, the optical output port 306 for outputting the modulated optical signal 307, and a succession 1520 of N serially optically coupled optical modulator segments, similar to the segments 321-325 of FIG. 3, extending between the input 304 (FIG. 15) and output 306 optical ports for modulating the optical carrier wave 305, so as to obtain the modulated optical signal 307 at the optical output port 306. The number of elements N may be, for example, at least 8 elements, or at least 16 elements.
The modulator apparatus 1500 further includes the electrical input port 302 for receiving the electrical signal 303 to be modulated onto the optical carrier wave 305 to obtain the modulated optical signal 307. An ADC 1530 is operationally coupled to the electrical input port 302. The function of the ADC 1530 is to digitize the electrical signal 303 to provide input digital signals 1531 representative of the electrical signal 303.
A digital filter 1532 may be operationally coupled to the ADC 1530. The function of the digital filter 1532 is to filter the input digital signals 1531 by a numerical computation to provide N output digital signals 1533, each of which being used for driving one of the N optical modulator segments. To provide the digital filtering function, the digital filter 1532 may include a field-programmable gate array (FPGA), a central processing unit (CPU), a microprocessor, etc. In one embodiment, the digital filter 1532 may be configured to provide an amplitude pre-emphasis, to lessen a non-linearity of modulation of the optical carrier wave 305 by the electrical signal 303. In another embodiment, the digital filter 1532 may be configured to provide a pre-determined frequency response or frequency pre-emphasis, to compensate for a frequency dependence of the modulation efficiency. More generally, the output digital signals 1533 may be a function of amplitude, frequency, and/or any other parameter of the input digital signals 1531. The digital filter 1532 may, therefore, provide a significant flexibility in obtaining a desired response function of the modulator apparatus 1500.
In one embodiment, a photodetector 1540 may be optically coupled to the optical output port 306 via an optional optical coupler 1542, for providing a feedback signal 1543 representative of the modulated optical signal 307. A controller 1550 may be operationally coupled to the photodetector 1540 and the digital filter 1530 for receiving the feedback signal 1543 from the photodetector 1540 and providing a control signal 1551 to the digital filter 1530 in dependence on the feedback signal 1543, for example to linearize the overall response function of the modulator apparatus 1500, for calibration purposes, etc.
The hardware used to implement the various illustrative logics, logical blocks, modules, and circuits described in connection with the aspects disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but, in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. Alternatively, some steps or methods may be performed by circuitry that is specific to a given function.
The present disclosure is not to be limited in scope by the specific embodiments described herein. Indeed, other various embodiments and modifications, in addition to those described herein, will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings. Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure. Further, although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose, those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes. Accordingly, the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein.

## Claims

1. A modulator apparatus comprising:
an electrical input port for receiving an electrical signal to be modulated onto an optical carrier wave;
a succession of serially optically coupled optical modulator segments disposed in an optical path of the optical carrier wave and configured to successively modulate the optical carrier wave so as to obtain a modulated optical signal;
a plurality of segment drivers, wherein each segment driver is electrically coupled to one of the succession of the modulator segments and configured to apply a driving voltage Vd thereto in response to a control voltage Vc in accordance with a limiting voltage transfer function specific to the segment driver, wherein the driving voltage Vd transitions between a low voltage Vlow, and a high voltage high when the control voltage Vc passes an offset voltage Vos, that is specific to the segment driver; and
a plurality of electrical connections between the electrical input port and each segment driver.

2. The modulator apparatus of claim 1, wherein each segment driver is configured to generate the driving voltage Vd such that
Vd=Vlow when Vc<Vos−Vth;
Vd=Vhigh when Vc>Vos+Vth; and
Vd varies between Vlow and Vhigh when Vc varies between Vos−Vth and Vos+Vth, wherein Vth is a threshold voltage defining the width of a voltage transition region about the offset voltage Vos.

3. The modulator apparatus of claim 1, wherein each segment driver comprises a limiting amplifier characterized by the corresponding low voltage Vlow, the corresponding high voltage Vhigh, the corresponding offset voltage Vos, and the corresponding threshold voltage Vth.

4. The modulator apparatus of claim 1, wherein each electrical connection has a corresponding delay ΔTelectrical between the electrical input port and each segment driver; and
wherein the delays ΔTelectrical are such that in operation, the application of the driving voltage Vd to individual optical modulator segments in the succession of optical modulator segments is substantially synchronized with propagation of the optical carrier wave therein.

5. The modulator apparatus of claim 1, further comprising a comparator module operationally coupled to the electrical input port and the plurality of segment drivers to provide individual control signals to the plurality of segment drivers when the control voltage Vc exceeds the offset voltages Vos of corresponding segment drivers of the plurality of segment drivers.

6. The modulator apparatus of claim 1, wherein the succession of serially optically coupled optical modulator segments comprises an optical waveguide and a succession of electrodes disposed along the optical waveguide and operationally coupled thereto.

7. The modulator apparatus of claim 1, wherein the plurality of electrical connections comprise a succession of serially electrically coupled electrical delay line segments,
wherein each progressive one of the succession of electrical delay line segments is electrically coupled to a segment driver of the plurality of segment drivers, and
wherein the segment driver is electrically coupled to a corresponding progressive one of the succession of optical modulator segments.

8. The modulator apparatus of claim 1, wherein the offset voltage Vos of the segment driver of each successive optical modulator segment is greater than the offset voltage Vos of the segment driver of an immediately preceding modulator segment, if any.

9. The modulator apparatus of claim 8, wherein the offset voltage Vos of the segment driver of each successive optical modulator segment is greater than the offset voltage Vos of the segment driver of an immediately preceding modulator segment, if any, by a same step voltage ΔVos.

10. The modulator apparatus of claim 2, wherein a slope of each segment driver, defined as (Vhigh−Vlow)/2Vth, is such that in operation, a degree of modulation of the modulated optical signal is substantially proportional to a magnitude of the electrical signal received at the electrical input port.

11. The modulator apparatus of claim 2, wherein at least one of the low voltage Vlow, the high voltage Vhigh, and the threshold voltage Vth, of at least one segment driver of the plurality of segment drivers is substantially different from a corresponding one of the low voltage Vlow, the high voltage Vhigh, and the threshold voltage Vth of another segment driver of the plurality of segment drivers.

12. The modulator apparatus of claim 6, further comprising a silicon photonic chip comprising the optical waveguide.

13. The modulator apparatus of claim 12, wherein the silicon photonic chip comprises the plurality of segment drivers.

14. The modulator apparatus of claim 1, wherein the low voltage Vlow, the high voltage Vhigh, and a threshold voltage Vth defining the width of a voltage transition region in the corresponding limiting voltage transfer characteristic of each segment driver of the plurality of segment drivers are such that a degree of modulation of the modulated optical signal is a function of the electrical signal received by the electrical input port;
wherein the function is selected from the list consisting of quadratic, cubic, periodic, and an exponential function.

15. A method of modulating an optical carrier wave by an electrical signal, the method comprising:
propagating the optical carrier wave in a succession of serially optically coupled optical modulator segments;
coupling the electrical signal to a plurality of segment drivers, wherein each segment driver is electrically coupled to one of the succession of the modulator segments and is configured to apply a driving voltage Vd thereto in response to a control voltage Vc in accordance with a limiting voltage transfer function specific to the segment driver, wherein said control voltage Vc is defined by the electrical signal, and wherein the driving voltage Vd transitions between a low voltage Vlow and a high voltage Vhigh when the control voltage Vc passes an offset voltage Vos that is specific to the segment driver; and
setting one or more parameters of the limiting voltage transfer function of each of the segment drivers so that an overall voltage transfer function of the plurality of segment drivers approximates a pre-defined linear or non-linear function, so as to provide a desired dependence of a degree of modulation of the optical carrier wave by the succession of serially optically coupled optical modulator segments upon the electrical signal.

16. The method of claim 15, wherein the limiting voltage transfer function of each of the segment drivers has associated:
a low voltage Vlow;
a high voltage Vhigh;
an offset voltage Vos; and
a threshold voltage Vth,
and wherein for each of the segment drivers, the limiting voltage transfer function relating the driving voltage Vd and the control voltage Vc, is such that:
Vd=Vlow when Vc<Vos−Vth;
Vd=Vhigh when Vc>Vos+Vth; and
Vd varies between Vlow and Vhigh when Vc varies between Vos−Vth and Vos+Vth.

17. The method of claim 15 further comprising:
providing the electrical signal to each segment driver with a different electrical time delay ΔTelectrical, wherein the electrical time delays ΔTelectrical are such that the application of the driving voltages Vd to individual optical modulator segments in the succession of optical modulator segments is substantially synchronized with propagation of the optical carrier wave therein.

18. The method of claim 16, further comprising pre-selecting the offset voltage Vos of each successive segment driver to be greater than the offset voltage Vos of the immediately preceding segment driver, if any.

19. The method of claim 18, further comprising pre-selecting the low voltage Vlow, the high voltage high, the offset voltage Vos, and the threshold voltage Vth of each segment driver of the plurality of segment drivers such that Vlow of each successive segment driver is substantially equal to Vhigh of the immediately preceding segment driver, if any.

20. The method of claim 18, further comprising pre-selecting a slope of each segment driver, defined as (Vhigh−Vlow)/2Vthso as to provide a degree of modulation of the optical carrier wave substantially proportional to a magnitude of the electrical signal received at the electrical input port.