Patent Publication Number: US-2019187495-A1

Title: Optical modulator and a driving circuit therefor

Description:
BACKGROUND 
     Field 
     The present disclosure relates to optical communication equipment and, more specifically but not exclusively, to optical modulators and driving circuits therefor. 
     Description of the Related Art 
     This section introduces aspects that may help facilitate a better understanding of the disclosure. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is in the prior art or what is not in the prior art. 
     An optical modulator is a device that can be used to manipulate a property of light, e.g., of an optical beam. Depending on which property of the optical beam is controlled, the optical modulator can be referred to as an intensity modulator, a phase modulator, a polarization modulator, a spatial-mode modulator, etc. A wide range of optical modulators is used, e.g., in the telecom industry. 
     SUMMARY OF SOME SPECIFIC EMBODIMENTS 
     Disclosed herein are various embodiments of an electro-optical circuit in which diode-like electrical characteristics of an optical modulator employed therein are used to generate one or more DC-offset levels that place the optical modulator into a proper electrical operating configuration for modulating light transmitted therethrough. In an example embodiment, the optical modulator includes an optical waveguide comprising at least a portion of a semiconductor diode connected to a data driver using a clamping circuit, the clamping circuit being configured to cause a data-modulated electrical signal outputted by the data driver to set a DC-offset level applied to the semiconductor diode. As a result, the use of on-chip and/or on-board bias-tees can advantageously be avoided. In some embodiments, the optical modulator can be driven using two different data signals, each used to set a different respective DC-offset level at the semiconductor diode. In various embodiments, the optical modulator can be an intensity modulator and/or a phase modulator. 
     According to one embodiment, provided is an apparatus comprising: an optical modulator comprising an optical waveguide that includes at least a portion of a semiconductor diode, the semiconductor diode being electrically connected between first and second electrical terminals, the optical waveguide being optically coupled between an optical input and an optical output of the optical modulator; and a data driver connected to the first and second electrical terminals to electrically drive the optical modulator in a manner that causes the optical modulator to modulate light traveling from the optical input to the optical output thereof in response to an input data signal received by the data driver; and wherein the data driver is electrically connected to the first and second electrical terminals in a manner that causes a first varying electrical signal generated by the data driver in response to the input data signal to set a first DC-offset level at one of the first and second electrical terminals of the semiconductor diode, the first DC-offset level being such as to cause the semiconductor diode to be reverse-biased. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other aspects, features, and benefits of various disclosed embodiments will become more fully apparent, by way of example, from the following detailed description and the accompanying drawings, in which: 
         FIG. 1  shows a block diagram of an electro-optical circuit according to an embodiment; 
         FIGS. 2A-2B  show schematic diagrams of an optical modulator that can be used in the electro-optical circuit of  FIG. 1  according to an embodiment; 
         FIGS. 3A-3B  show schematic diagrams of an optical modulator that can be used in the electro-optical circuit of  FIG. 1  according to another embodiment; 
         FIG. 4  shows a circuit diagram of an electro-optical circuit that can be used to implement the electro-optical circuit of  FIG. 1  according to an embodiment; 
         FIG. 5  graphically shows example electrical signals in the electro-optical circuit of  FIG. 4  according to an embodiment; 
         FIG. 6  shows a block diagram of an electro-optical circuit according to an alternative embodiment; and 
         FIG. 7  shows a circuit diagram of an electro-optical circuit that can be used to implement the electro-optical circuit of  FIG. 6  according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Electrical properties of some semiconductor-based optical modulators are similar to those of an electrical diode. In operation, some of such optical modulators require a forward or reverse electrical bias to place the modulator into a proper electrical operating configuration. This requirement can turn the design of the corresponding driver chip, circuit, and/or printed circuit board into a rather challenging proposition, e.g., because an appropriate (positive or negative) DC offset needs to be added to the varying electrical signal representing the data that are to be carried by the modulated optical beam outputted by the optical modulator. 
     One approach to solving this problem includes the use of a bias-tee connected to the output of an AC-coupled data driver. Designing an on-chip bias-tee for relatively high (e.g., ≥25 Gb/s) data rates can be difficult, e.g., because large inductances may be needed to implement the bias-tee. The latter problem might be further complicated when the optical modulator needs to be driven by two or more different varying electrical signals. An example of the optical modulator of this type is a differentially driven modulator, wherein the SIGNAL and SIGNAL_BAR (inverted signal) lines may require different DC offsets. 
     At least some of these and other related problems in the state of the art are addressed by different embodiments disclosed herein according to which inherent diode-like electrical characteristics of certain semiconductor-based optical modulators are used to generate a DC offset level that places the modulator into a proper electrical operating configuration. As a result, the use of on-chip and/or on-board bias-tees can advantageously be avoided. The disclosed approach can beneficially be implemented for different types of optical modulators, e.g., intensity and/or phase modulators. Some non-limiting examples of such optical modulators include a microring modulator, an electro-absorption modulator, a Mach-Zehnder modulator, and an IQ modulator, each of which can be implemented using a variety of suitable semiconductor materials known to those skilled in the pertinent art. 
       FIG. 1  shows a block diagram of an electro-optical circuit  100  according to an embodiment. Circuit  100  comprises a waveform generator  110  and an optical modulator  120  connected to one another using a capacitor C and a resistor R such as to form a positive clamping circuit. A person of ordinary skill in the art will understand that, in an alternative embodiment, waveform generator  110  and optical modulator  120  can be similarly connected using a negative clamping circuit (e.g., see  FIGS. 6-7 ). 
     Optical modulator  120  comprises an input optical waveguide  118  and an output optical waveguide  122 . Input optical waveguide  118  is connected to receive light from a suitable light source (e.g., a semiconductor laser). In operation, optical modulator  120  modulates the received light in response to an electrical drive signal applied to electrical terminals  116  and  124  thereof and outputs the resulting modulated optical beam through output optical waveguide  122 . Electrical response of optical modulator  120  to an electrical signal applied to electrical terminals  116  and  124  may be similar to that of an electrical diode. The latter characteristic of optical modulator  120  is indicated in  FIG. 1  by depicting that optical modulator using the conventional diode symbol. Example semiconductor devices that can cause optical modulator  120  to behave similar to an electrical diode are shown and described in more detail below in reference to  FIGS. 2-3 . 
     In an example embodiment, generator  110  operates as a data driver that generates a varying output voltage V OUT  between electrical output terminals  112  and  114  thereof in response to an input data signal  102 . Output voltage V OUT  oscillates around the zero (e.g., ground) level and has a peak-to-peak swing of 2V 0 . An example waveform representing output voltage V OUT  is shown and described in more detail below in reference to  FIG. 5 . 
     In the embodiment of  FIG. 1 , capacitor C, resistor R, and an electrical-diode structure of optical modulator  120  act together to add a positive offset voltage V C  to output voltage V OUT , thereby causing the drive voltage V D  between electrical terminals  116  and  124  to be approximately described by Eq. (1) as follows: 
         V   D   =V   OUT   +V   C    (1)
 
     More specifically, during the negative swing of output voltage V OUT , the electrical-diode structure of optical modulator  120  is forward-biased and conducts, thereby charging capacitor C to the peak negative value of V OUT . During the positive swing of output voltage V OUT , the electrical-diode structure of optical modulator  120  is reverse-biased and thus substantially does not conduct. The voltage across the electrical-diode structure of optical modulator  120  is therefore equal to the sum of output voltage V OUT  and the voltage across capacitor C. If capacitor C is not initially charged, then some transitory time is needed to reach a steady state. The capacitance of capacitor C and the resistance of resistor R determine the range of frequencies over which the clamping circuit formed by capacitor C, resistor R, and optical modulator  120  is effective. 
     As used herein, the term “reverse bias” refers to an electrical configuration of a semiconductor-junction diode in which the N-type material is at a high electrical potential, and the P-type material is at a low electrical potential. The reverse bias typically causes the depletion layer to grow wider due to a lack of electrons and/or holes, which presents a high impedance path across the junction and substantially prevents a current flow therethrough. However, a very small reverse leakage current can still flow through the junction. 
     Similarly, the term “forward bias” refers to an electrical configuration of a semiconductor-junction diode in which the N-type material is at a low potential, and the P-type material is at a high potential. If the forward bias is greater than the intrinsic voltage drop V pu  across the corresponding PN or PIN junction, then the corresponding potential barrier can be overcome by the electrical carriers, and a relatively large forward current can flow through the junction. For example, for silicon-based diodes the value of V pn  is approximately 0.7 V. For germanium-based diodes, the value of V pn  is approximately 0.3 V, etc. 
     The selection of V C  typically depends on the implementation specifics of optical modulator  120 , such as the choice of semiconductor materials used therein, the relative arrangement of variously doped semiconductor regions, etc. As an approximation, the value of V C  can be expressed by Eq. (2) as follows: 
         V   C   =V   0   −V   pn    (2)
 
     where V pn  is the voltage drop across the corresponding PN or PIN junction in the electrical-diode structure of optical modulator  120 . Based on Eqs. (1) and (2), the upper rail V U  and the lower rail V L  of the drive voltage V D  can be estimated using Eqs. (3)-(4), respectively, as follows: 
         V   U =2 V   0   −V   pn    (3)
 
         V   L   =−V   pn    (4)
 
     In an example embodiment, generator  110  can be configured to generate the output voltage V OUT  with the amplitude V 0  selected such that the corresponding offset voltage V C  (Eq. (2)) generated in circuit  100  places optical modulator  120  into a proper electrical operating configuration for performing its intended optical function. For example, in the embodiment of  FIG. 1 , the value of V 0  can be selected such that the corresponding offset voltage V C  causes the electrical-diode structure of optical modulator  120  to be under a proper reverse bias. As a result, a bias-tee that is typically used for this purpose in conventional driving circuits is no longer needed and is not present in circuit  100 . 
     In some embodiments, the resistance of resistor R can be selected to be significantly larger than the series resistance of the electrical-diode structure of optical modulator  120 . 
     In some embodiments, the electrical-diode structure of optical modulator  120  can be intentionally designed in a way that causes the reverse leakage current to be relatively large. The latter property can be achieved, e.g., by (i) the inherent device design, (ii) crystal defect creation in the semiconductor materials, (iii) introduction of surface states in some semiconductor layers, etc. In some embodiments, the used semiconductor materials can be selected such that the electrical-diode structure of optical modulator  120  works as a photodiode in response to the light having the intended carrier wavelength. The latter design choice has a similar effect of increasing the effective reverse leakage current under illumination. A person of ordinary skill in the art will understand that the enhanced reverse leakage current implemented in these embodiments may have a beneficial effect of improving the electrical response characteristics of optical modulator  120  and/or the corresponding clamping circuit. 
     In some embodiments, circuit  100  can be designed such that the leakage current and/or the series resistance of the electrical-diode structure of optical modulator  120  are controlled and defined in a manner that shortens the transitory time leading into the above-mentioned “steady state” and/or increases the offset voltage V C . 
     In practice, the offset voltage V C  may exhibit small variations over time in the steady operating state of circuit  100  due to (i) a small current flowing through the capacitor C during the positive swing of output voltage V OUT , which may cause a relatively small discharge of the capacitor, and (ii) recharging of the capacitor C during the negative swing of output voltage V OUT , which can restore the lost charge. As such, the offset voltage V C  can be represented as a sum of a relatively large quasi-DC component and a relatively small varying (time-dependent) component. The prefix “quasi” reflects the fact that the offset voltage V C  depends on the amplitude V 0  (e.g., as indicated in Eq. (2)), which itself may fluctuate in time, thereby inducing the corresponding fluctuations of the offset voltage V C . However, such fluctuations of the amplitude V 0  are typically relatively small (e.g., not exceeding ˜5%) for conventional data drivers. Furthermore, known amplitude-stabilization techniques can be used to make such fluctuations of the amplitude V 0  acceptably small, if appropriate or necessary. In addition, such fluctuations of the amplitude V 0  may be relatively slow on the modulation time scale and appear as slow up and down drifts of the amplitude V 0 . In any scenario, such fluctuations of the amplitude V 0  do not practically affect the reverse-bias state of the electrical-diode structure of optical modulator  120  and have negligible effect on its optical function. 
     The effective voltage shift corresponding to the above-described quasi-DC component of the offset voltage V C  is referred to herein as the “DC-offset level.” 
       FIGS. 2A-2B  show schematic diagrams of optical modulator  120  according to an embodiment. More specifically,  FIG. 2A  shows a top view of optical modulator  120 .  FIG. 2B  shows a cross-sectional side view of optical modulator  120  along the planar cross-section BB indicated in  FIG. 2A . 
     The optical modulator  120  shown in  FIGS. 2A-2B  is a microring modulator implemented using CMOS-compatible processes and materials. In an example embodiment, the optical modulator  120  of  FIGS. 2A-2B  can be fabricated using a silicon-on-insulator (SOI) substrate  202  and includes a microring waveguide  210  optically coupled to a pass-through linear waveguide  220  as indicated in  FIG. 2A . One end of waveguide  220  is configured to operate as input optical waveguide  118  (also see  FIG. 1 ). The other end of waveguide  220  is configured to operate as output optical waveguide  122  (also see  FIG. 1 ). Waveguides  210  and  220  can be formed, e.g., by properly etching down the top silicon layer supported on a silicon-oxide layer  206  of SOI substrate  202  (see  FIG. 2B ). A silicon-oxide cladding layer (not explicitly shown in  FIG. 2B ) can then be deposited over the structure shown in  FIG. 2B  to encapsulate the resulting ridge-waveguide core. 
     Microring waveguide  210  is a ridge waveguide that has a portion  212  made of n-doped silicon and a portion  214  made of p-doped silicon, the two portions forming a PN junction  212 / 214  as indicated in  FIG. 2B . The location of the PN junction  212 / 214  may be offset from the center of waveguide  210 . In the shown embodiment, the PN junction  212 / 214  takes up approximately one-half of the microring circumference. In alternative embodiments, the corresponding PN junction may take up more or less than one-half of the microring circumference. 
     Ohmic contacts between the PN junction  212 / 214  and electrical terminals  116  and  124  are implemented by varying the dopant concentration within a silicon layer  204  that is adjacent to waveguide  210 . More specifically, an n+-doped portion  222  and an n++-doped portion  232  of layer  204  are used to provide an ohmic contact between portion  212  of waveguide  210  and electrical terminal  124 . A p+-doped portion  224  and a p++-doped portion  234  of layer  204  are similarly used to provide an ohmic contact between portion  214  of waveguide  210  and electrical terminal  116 . Intermediately doped portions  222  and  224  are optional and may not be present in some embodiments. 
     In some embodiments, an optional thin-film heater  240  may be formed near ring waveguide  210 , e.g., as indicated in  FIG. 2A . For example, thin-film heater  240  can be implemented using a titanium microstrip that is vertically separated from ring waveguide  210  by a layer of silicon oxide (not explicitly shown in  FIGS. 2A-2B ). Electrical terminals  238  and  242  can then be used to drive a controllable electrical current I h  through thin-film heater  240  to provide a stable thermal environment for the PN junction  212 / 214  and ring waveguide  210 . 
     In an example embodiment, some elements of the optical modulator  120  shown in  FIGS. 2A-2B  may have the following dimensions: (i) a 30-μm diameter for microring waveguide  210 ; (ii) a 0.5-μm width W for microring waveguide  210 ; (iii) a 0.2-μm width w 1  for portion  212 ; (iv) a 0.22-μm height H for microring waveguide  210 ; (v) a 0.05-μm thickness h for layer  204 ; and (vi) a 0.5-μm width w 2  for portions  222  and  224 . 
     In operation, the PN junction  212 / 214  functions as a phase shifter. More specifically, when the reverse bias V C  is applied to the PN junction  212 / 214 , a depletion region forms within waveguide  210 . During the positive swing of output voltage V OUT , the size of this depletion region increases, thereby decreasing the effective refractive index of waveguide  210 . During the negative swing of output voltage V OUT , the size of this depletion region decreases, thereby increasing the effective refractive index of waveguide  210 . This modulation of the effective refractive index modulates the resonant frequency of the microring accordingly, which changes the transmittance of waveguide  220  at the carrier wavelength, thereby modulating the intensity of the optical beam that travels from input optical waveguide  118  to output optical waveguide  122 . 
       FIGS. 3A-3B  show schematic diagrams of optical modulator  120  according to another embodiment. More specifically,  FIG. 3A  shows a top view of optical modulator  120 .  FIG. 3B  shows a cross-sectional side view of optical modulator  120  along the planar cross-section BB indicated in  FIG. 3A . 
     The optical modulator  120  shown in  FIGS. 3A-3B  is an electro-absorption modulator. The choice of materials for this particular embodiment of optical modulator  120  depends on the intended operating wavelength. For example, GaAs, InGaAs, and/or AlGaAs may be used for carrier wavelengths in the vicinity of 850 nm. Ge, GeSi, InP, InGaAsP, and/or InGaAlAs may be used for carrier wavelengths in the vicinity of 1310 nm or 1550 nm. 
     In an example embodiment, the optical modulator  120  of  FIGS. 3A-3B  can be fabricated on a semiconductor or dielectric substrate  302  and includes a ridge waveguide  320 . One end of waveguide  320  is connected to input optical waveguide  118  (also see  FIG. 1 ). The other end of waveguide  320  is connected to output optical waveguide  122  (also see  FIG. 1 ). Ridge waveguide  320  can be made, e.g., of an intrinsically doped Ge, and be sandwiched between, e.g., a layer  318  of n-doped Ge and a layer  322  of p-doped Ge. Waveguide  320  and layers  318  and  322  are arranged to form a lateral PIN diode  318 / 320 / 322 . 
     In an example embodiment, ridge waveguide  320  can have a 0.6-μm width W and a 0.35-μm height H. 
     Ohmic contacts between the PIN diode  318 / 320 / 322  and electrical terminals  116  and  124  are implemented using silicon electrodes  316  and  324 . More specifically, electrode  316  comprises n++-doped silicon and is connected between layer  318  and electrical terminal  124 . Electrode  324  comprises p++-doped silicon and is connected between layer  322  and electrical terminal  116 . 
     The principle of operation of the embodiment of optical modulator  120  shown in  FIGS. 3A-3B  is based on the Franz-Keldysh effect due to which the optical absorption near the optical band edge of the employed bulk semiconductor material depends on the applied electric field. More specifically, when the reverse bias V C  is applied to the PIN diode  318 / 320 / 322 , waveguide  320  is subjected to an electric field of certain strength. During the positive swing of output voltage V OUT , the electric-field strength increases, thereby red-shifting the band edge. During the negative swing of output voltage V OUT , the electric-field strength decreases, thereby blue-shifting the band edge. These band-edge shifts change the transmittance of waveguide  320  at the carrier wavelength, thereby modulating the intensity of the optical beam that travels from input optical waveguide  118  to output optical waveguide  122 . 
     A person of ordinary skill in the art will understand that, in an alternative embodiment, an electro-absorption modulator  120  can be implemented using a multiple-quantum-well (MQW) structure located within the intrinsically doped portion of the optical waveguide. In this case, the band-edge shifts are primarily caused by the so-called quantum-confined Stark effect (QCSE). Compared to the electro-absorption devices that are based on the Franz-Keldysh effect, the electro-absorption devices that are based on the QCSE are typically able to provide higher depths of modulation, e.g., as quantified by the ON-OFF intensity ratios of the corresponding modulated optical beams. The geometry of the corresponding MQW PIN diode is typically different from that shown in  FIGS. 3A-3B  in that the PIN (and MQW) layers of the diode are stacked vertically rather than laterally. 
     Additional embodiments of optical modulator  120  can be implemented using some of the semiconductor devices disclosed, e.g., in U.S. Pat. Nos. 9,690,122, 8,735,868, 7,764,850, 7,672,553, 6,298,177, 6,002,510, and 5,811,838, all of which are incorporated herein by reference in their entirety. 
       FIG. 4  shows a circuit diagram of an electro-optical circuit  400  that can be used to implement circuit  100  according to an embodiment. 
     Circuit  400  is designed and configured to have transmission lines that are impedance-matched to 50 ohm. For this purpose, a waveform generator  410  includes a 50-ohm output resistor R 1  connected between a data driver  412  and electrical output terminal  114 . Similarly, a transmission line  414  that connects electrical terminals  114  and  124  is terminated using a termination circuit  430  that includes a 50-ohm resistor R 2 . 
     In circuit  400 , a capacitor C 1  implements capacitor C (see  FIG. 1 ). A capacitor C 3  is used in termination circuit  430  for the AC termination. An optional resistor R 3  connected in parallel with capacitor C 3  and in series with resistor R 2  is used to mitigate possible adverse effects on the impedance matching of any parasitic resistance of the electrical diode structure of optical modulator  120 . In some embodiments, resistor R 3  may be absent. 
       FIG. 5  graphically shows example electrical signals in circuit  400  according to an embodiment. More specifically, a waveform  502  represents output voltage V OUT  at electrical terminal  114  of generator  410  ( FIG. 4 ) measured with respect to the ground potential. A waveform  504  similarly represents drive voltage V D  at electrical terminal  124  of optical modulator  120  ( FIG. 4 ) measured with respect to the ground potential. 
     Waveform  502  is an non-return-to-zero (NRZ) waveform in which binary zeros are represented by negative pulses of amplitude V 0  and binary ones are represented by positive pulses of amplitude V 0 . Due to the above-explained clamping action, circuit  400  causes waveform  504  to be a positively shifted copy of waveform  502 , with the offset voltage V C  and the upper and lower rails V U  and V L  being indicated in  FIG. 5 . The value of the offset voltage V C  is smaller than the amplitude V 0  due to the non-zero value of the intrinsic voltage drop V pn , which is also indicated in  FIG. 5  (also see Eqs. (2)-(4)). 
       FIG. 6  shows a block diagram of an electro-optical circuit  600  according to an alternative embodiment. Similar to circuit  100  ( FIG. 1 ), circuit  600  comprises optical modulator  120  electrically connected to the data driver using a clamping circuit. However, in circuit  600 , optical modulator  120  is a part of two clamping circuits instead of just one as in circuit  100 . One of these clamping circuits is a positive clamping circuit, and the other clamping circuit is a negative clamping circuit. In an example embodiment, electro-optical circuit  600  can be configured to drive optical modulator  120  in a differential configuration, e.g., as described below. 
     The two clamping circuits of circuit  600  are configured to share a load Z 3  that is connected in parallel with an electrical-diode structure of optical modulator  120 . The positive clamping circuit includes a capacitor C 1  connected to electrical terminal  124  of optical modulator  120 . The negative clamping circuit includes a capacitor C 2  connected to electrical terminal  116  of optical modulator  120 . 
     Circuit  600  further comprises a differential amplifier  610  having (i) a non-inverting output S connected by way of an output impedance Z 1  to capacitor C 1  and (ii) an inverting output  S  connected by way of an output impedance Z 2  to capacitor C 2 . Differential amplifier  610  operates as a data driver that generates varying output voltages V OUT  and −V OUT  at outputs S and  S , respectively, in response to an input data signal  602 . 
     In an example embodiment, the impedances Z 1 , Z 2 , and Z 3  have the following relative values: Z 0 , Z 0 , and 2Z 0 , respectively. The capacitances of capacitors C 1  and C 2  can be equal to one another. In this configuration, the drive voltages (e.g., as measured with respect to the ground potential) applied to electrical terminals  124  and  116  of optical modulator  120  are V D  and −V D , respectively, where V D  can be approximated using Eq. (1). The corresponding offset voltages are V C  and −V C , respectively, where V C  can be approximated using Eq. (2). 
       FIG. 7  shows a circuit diagram of an electro-optical circuit  700  that can be used to implement circuit  100  according to an embodiment. Similar to circuit  400 , circuit  700  is designed and configured to have transmission lines that are impedance-matched to 50 ohm. As such, circuit  700  comprises (i) two instances (nominal copies) of waveform generator  410 , which are labeled in  FIG. 7  using the reference numerals  410   1  and  410   2 , and (ii) two instances of termination circuit  430 , which are labeled in  FIG. 7  using the reference numerals  430   1  and  430   2 . 
     Waveform generator  410   1  is directly driven by input data signal  602 . Waveform generator  410   2  is similarly driven by a data signal  706  that is generated by an inverter  704  by inverting input data signal  602 . In an example embodiment, inverter  704  can be implemented using a logic NOT-gate. 
     Termination circuit  430   1  is configured to terminate a transmission line  714   1  that connects waveform generator  410   1  and electrical terminal  124  of optical modulator  120 . Termination circuit  430   2  is similarly configured to terminate a transmission line  714   2  that connects waveform generator  410   2  and electrical terminal  116  of optical modulator  120 . Each of termination circuits  430   1  and  430   2  is further connected to a corresponding optional resistor R 3  (also see  FIG. 4 ), which are labeled in  FIGS. 7  as R 3   1  and R 3   2 , respectively. 
     According to an example embodiment disclosed above, e.g., in the summary section and/or in reference to any one or any combination of some or all of  FIGS. 1-7 , provided is an apparatus (e.g.,  100 ,  FIG. 1 ;  600 ,  FIG. 6 ) comprising: an optical modulator (e.g.,  120 ,  FIGS. 1-4, 6, 7 ) comprising an optical waveguide (e.g.,  210 ,  FIG. 2B ;  320 ,  FIG. 3B ) that includes at least a portion of a semiconductor diode (e.g.,  212 / 214 ,  FIG. 2B ;  318 / 320 / 322 ,  FIG. 3B ), the semiconductor diode being electrically connected between first and second electrical terminals (e.g.,  116 ,  124 ,  FIGS. 1-4, 6, 7 ), the optical waveguide being optically coupled between an optical input (e.g.,  118 ,  FIGS. 1-4, 6, 7 ) and an optical output (e.g.,  122 ,  FIGS. 1-4, 6, 7 ) of the optical modulator; and a data driver (e.g.,  110 ,  FIG. 1 ;  410 ,  FIGS. 4, 7 ;  610 ,  FIG. 6 ) connected to the first and second electrical terminals to electrically drive the optical modulator in a manner that causes the optical modulator to modulate light traveling from the optical input to the optical output thereof in response to an input data signal (e.g.,  102 ,  FIGS. 1, 4 ;  602 ,  FIGS. 6-7 ) received by the data driver; and wherein the data driver is electrically connected to the first and second electrical terminals in a manner that causes a first varying electrical signal (e.g., at  114 ,  FIGS. 1, 4 ; at S,  FIG. 6 ; at  714 ,  FIG. 7 ) generated by the data driver in response to the input data signal to set a first DC-offset level (e.g., the quasi-DC component of V C , Eqs. (1)-(2),  FIG. 5 ) at one of the first and second electrical terminals of the semiconductor diode, the first DC-offset level being such as to cause the semiconductor diode to be reverse-biased. 
     In some embodiments of the above apparatus, the apparatus further comprises: a capacitor (e.g., C,  FIG. 1 ) connected between an output terminal (e.g.,  114 ,  FIGS. 1, 4 ;  714 ,  FIG. 7 ) of the data driver and the one of the first and second electrical terminals, the output terminal being configured to carry the first varying electrical signal; and a resistor (e.g., R,  FIG. 1 ) connected to at least one of the first and second electrical terminals. 
     In some embodiments of any of the above apparatus, the apparatus further comprises an electrical clamping circuit that includes the semiconductor diode, the capacitor, and the resistor. 
     In some embodiments of any of the above apparatus, the first varying electrical signal is a bipolar signal (e.g.,  502 ,  FIG. 5 ) that has an amplitude; and the first DC-offset level depends on the amplitude (e.g., approximately in accordance with Eq. (2)). 
     In some embodiments of any of the above apparatus, the optical modulator is configured to modulate an intensity of the light traveling from the optical input to the optical output thereof in response to the input data signal received by the data driver. 
     In some embodiments of any of the above apparatus, the optical modulator is configured to modulate a phase of the light traveling from the optical input to the optical output thereof in response to the input data signal received by the data driver. 
     In some embodiments of any of the above apparatus, the optical modulator comprises an optical phase shifter (e.g., BB,  FIG. 2B ) that includes at least a portion of the optical waveguide. 
     In some embodiments of any of the above apparatus, the optical modulator comprises a ring waveguide (e.g.,  210 ,  FIG. 2A ) optically coupled to a linear waveguide (e.g.,  220 ,  FIG. 2A ); the ring waveguide comprises the optical waveguide (e.g., as indicated in  FIG. 2A ); and the optical input and the optical output are connected to opposite ends of the linear waveguide. 
     In some embodiments of any of the above apparatus, the optical modulator comprises an electro-absorption modulator (e.g., BB,  FIG. 3B ) that includes at least a portion of the optical waveguide. 
     In some embodiments of any of the above apparatus, the optical waveguide comprises a first portion (e.g.,  212 ,  FIG. 2B ) and a second portion (e.g.,  214 ,  FIG. 2B ), the first portion comprising an n-type semiconductor material, the second portion comprising a p-type semiconductor material. 
     In some embodiments of any of the above apparatus, the first portion and the second portion are attached to one another to form a PN junction, the PN junction being located within an optical core the optical waveguide (e.g., as indicated in  FIG. 2B ). 
     In some embodiments of any of the above apparatus, the semiconductor diode is a PIN diode comprising a p-type semiconductor material (e.g.,  322 ,  FIG. 3B ), an n-type semiconductor material (e.g.,  318 ,  FIG. 3B ), and an intrinsically doped semiconductor material (e.g.,  320 ,  FIG. 3B ); and the optical waveguide comprises at least a portion of the intrinsically doped semiconductor material (e.g., as indicated in  FIG. 3B ). 
     In some embodiments of any of the above apparatus, the data driver is connected to the first and second electrical terminals in a manner that causes a second varying electrical signal (e.g., at  S ,  FIG. 6 ; at  714   2 ,  FIG. 7 ) generated by the data driver in response to the input data signal to set a second DC-offset level (e.g., the quasi-DC component of −V C , Eq. (2),  FIG. 6 ) at another one of the first and second electrical terminals of the semiconductor diode, the first and second DC-offset levels being such as to cause the semiconductor diode to be reverse-biased. 
     In some embodiments of any of the above apparatus, the data driver comprises an inverter (e.g.,  704 ,  FIG. 7 ) configured to generate an inverted data signal (e.g.,  706 ,  FIG. 7 ) by inverting the input data signal; and wherein the data driver is configured to generate the second varying electrical signal in response to the inverted data signal (e.g., as indicated in  FIG. 7 ). 
     In some embodiments of any of the above apparatus, the first varying electrical signal is a bipolar signal that has a first amplitude; wherein the first DC-offset level depends on the first amplitude; wherein the second varying electrical signal is a bipolar signal that has a second amplitude; and wherein the second DC-offset level depends on the second amplitude. 
     In some embodiments of any of the above apparatus, the data driver is configured to drive the optical modulator in a differential manner using the first and second varying electrical signals. 
     In some embodiments of any of the above apparatus, the first and second DC-offset levels have opposite polarities. 
     In some embodiments of any of the above apparatus, the data driver comprises an electrical amplifier (e.g.,  610 ,  FIG. 6 ) having an inverting output (e.g.,  S ,  FIG. 6 ) and a non-inverting output (e.g., S,  FIG. 6 ) and is configured to generate the first varying electrical signal and the second varying electrical signal at the non-inverting and inverting outputs, respectively, in response to the input data signal (e.g.,  602 ,  FIG. 6 ). 
     In some embodiments of any of the above apparatus, the apparatus further comprises: a first capacitor (e.g., C 1 ,  FIG. 6 ) connected between the non-inverting output of the amplifier and the first electrical terminal; and a second capacitor (e.g., C 2 ,  FIG. 6 ) connected between the inverting output of the amplifier and the second electrical terminal; and a resistor (e.g., Z 3 ,  FIG. 6 ) connected between the first and second electrical terminals in parallel with the semiconductor diode. 
     In some embodiments of any of the above apparatus, the apparatus does not have a bias tee that electrically connects the one of the first and second electrical terminals to an external DC-voltage source. 
     In some embodiments of any of the above apparatus, the apparatus further comprises a laser connected to apply light to the optical input of the optical modulator (e.g., as indicated in  FIG. 1 ). 
     In some embodiments of any of the above apparatus, the semiconductor diode is configured to generate a photocurrent in response to the light traveling from the optical input to the optical output of the optical modulator. 
     While this disclosure includes references to illustrative embodiments, this specification is not intended to be construed in a limiting sense. Various modifications of the described embodiments, as well as other embodiments within the scope of the disclosure, which are apparent to persons skilled in the art to which the disclosure pertains are deemed to lie within the principle and scope of the disclosure, e.g., as expressed in the following claims. 
     Unless explicitly stated otherwise, each numerical value and range should be interpreted as being approximate as if the word “about” or “approximately” preceded the value or range. 
     It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain the nature of this disclosure may be made by those skilled in the art without departing from the scope of the disclosure, e.g., as expressed in the following claims. 
     Reference herein to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the disclosure. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments necessarily mutually exclusive of other embodiments. The same applies to the term “implementation.” 
     Unless otherwise specified herein, the use of the ordinal adjectives “first,” “second,” “third,” etc., to refer to an object of a plurality of like objects merely indicates that different instances of such like objects are being referred to, and is not intended to imply that the like objects so referred-to have to be in a corresponding order or sequence, either temporally, spatially, in ranking, or in any other manner. 
     Throughout the detailed description, the drawings, which are not to scale, are illustrative only and are used in order to explain, rather than limit the disclosure. The use of terms such as height, length, width, top, bottom, is strictly to facilitate the description of the embodiments and is not intended to limit the embodiments to a specific orientation. For example, height does not imply only a vertical rise limitation, but is used to identify one of the three dimensions of a three dimensional structure as shown in the figures. Such “height” would be vertical where the electrodes and layers are horizontal but would be horizontal where the electrodes and layers are vertical, and so on. Similarly, while all figures show the different layers as horizontal layers such orientation is for descriptive purpose only and not to be construed as a limitation. 
     Also for purposes of this description, the terms “couple,” “coupling,” “coupled,” “connect,” “connecting,” or “connected” refer to any manner known in the art or later developed in which energy is allowed to be transferred between two or more elements, and the interposition of one or more additional elements is contemplated, although not required. Conversely, the terms “directly coupled,” “directly connected,” etc., imply the absence of such additional elements. 
     The described embodiments are to be considered in all respects as only illustrative and not restrictive. In particular, the scope of the disclosure is indicated by the appended claims rather than by the description and figures herein. All changes that come within the meaning and range of equivalency of the claims are to be embraced within their scope. 
     The description and drawings merely illustrate the principles of the disclosure. It will thus be appreciated that those of ordinary skill in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the disclosure and are included within its spirit and scope. Furthermore, all examples recited herein are principally intended expressly to be only for pedagogical purposes to aid the reader in understanding the principles of the disclosure and the concepts contributed by the inventor(s) to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Moreover, all statements herein reciting principles, aspects, and embodiments of the disclosure, as well as specific examples thereof, are intended to encompass equivalents thereof.