Optical modulator having a plurality of modulator segments

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 V d thereto in response to a control voltage V c in accordance with a limiting voltage transfer function specific to the segment driver, wherein the driving voltage V d transitions between a low voltage V low , and a high voltage high when the control voltage V c passes an offset voltage V os , 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 V d such that

V d =V low when V c <V os −V th ;

V d =V high when V c >V os +V th ; and

V d varies between V low and V high when V c varies between V os −V th and V os +V th , wherein V th is a threshold voltage defining the width of a voltage transition region about the offset voltage V os .

3. The modulator apparatus of claim 1 , wherein each segment driver comprises a limiting amplifier characterized by the corresponding low voltage V low , the corresponding high voltage V high , the corresponding offset voltage V os , and the corresponding threshold voltage V th .

4. The modulator apparatus of claim 1 , wherein each electrical connection has a corresponding delay ΔT electrical between the electrical input port and each segment driver; and

wherein the delays ΔT electrical are such that in operation, the application of the driving voltage V d 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 V c exceeds the offset voltages V os 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 V os of the segment driver of each successive optical modulator segment is greater than the offset voltage V os of the segment driver of an immediately preceding modulator segment, if any.

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

10. The modulator apparatus of claim 2 , wherein a slope of each segment driver, defined as (V high −V low )/2V th , 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 V low , the high voltage V high , and the threshold voltage V th , of at least one segment driver of the plurality of segment drivers is substantially different from a corresponding one of the low voltage V low , the high voltage V high , and the threshold voltage V th 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 V low , the high voltage V high , and a threshold voltage V th 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 V d thereto in response to a control voltage V c in accordance with a limiting voltage transfer function specific to the segment driver, wherein said control voltage V c is defined by the electrical signal, and wherein the driving voltage V d transitions between a low voltage V low and a high voltage V high when the control voltage V c passes an offset voltage V os 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 V low ;

a high voltage V high ;

an offset voltage V os ; and

a threshold voltage V th ,

and wherein for each of the segment drivers, the limiting voltage transfer function relating the driving voltage V d and the control voltage V c , is such that:

V d =V low when V c <V os −V th ;

V d =V high when V c >V os +V th ; and

V d varies between V low and V high when V c varies between V os −V th and V os +V th .

17. The method of claim 15 further comprising:

providing the electrical signal to each segment driver with a different electrical time delay ΔT electrical , wherein the electrical time delays ΔT electrical are such that the application of the driving voltages V d 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 V os of each successive segment driver to be greater than the offset voltage V os of the immediately preceding segment driver, if any.

19. The method of claim 18 , further comprising pre-selecting the low voltage V low , the high voltage high , the offset voltage V os , and the threshold voltage V th of each segment driver of the plurality of segment drivers such that V low of each successive segment driver is substantially equal to V high 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 (V high −V low )/2V th so 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.