LINEARIZED OPTICAL DIGITAL-TO-ANALOG MODULATOR

Abstract

A system for converting digital data into a modulated optical signal, comprises an electrically controllable device having M actuating electrodes. The device provides an optical signal that is modulated in response to binary voltages applied to the actuating electrodes. The system also comprises a digital-to-digital converter that provides a mapping of input data words to binary actuation vectors of M bits and supplies the binary actuation vectors as M bits of binary actuation voltages to the M actuating electrodes, where M is larger than the number of bits in each input data word. The digital-to-digital converter is enabled to map each digital input data word to a binary actuation vector by selecting a binary actuation vector from a subset of binary actuation vectors available to represent each of the input data words.

Claims

1. A method for converting digital electrical data into modulated optical streams, said method comprising inputting into an optical modulator N bits of digital data in parallel, N being larger than 1; using a digital to digital converter to map a set of N input values corresponding to said N bits of digital data to a set of M output values where M is larger than N and where the input and output values are not identical; using the M output values to drive at least M electrodes, enabled to modulate at least an optical input optical stream to provide at least a modulated output optical stream.

2. The method of claim 1, wherein the M electrodes are distributed over a plurality of waveguide branches and are enabled to modulate unmodulated optical input streams coupled to the waveguide branches.

3. The method of claim 1, wherein each value of the set of M output values drives a single electrode of the M electrodes.

4. The method of claim 3, wherein each value of the set of M output values drives a single electrode on a single branch of a plurality of waveguide branches.

5. The method of claim 3, wherein each value of the set of M output values drives a single electrode on each of a plurality of waveguide branches.

6. A method for converting N bits of digital data input to at least a modulated optical stream and transmitting the at least modulated optical stream, the method comprising: inputting the N bits of digital data input in parallel into an optical modulator where N>1; converting the N bits of digital data input to M bits of digital output using a digital to digital converter, where M>N; inputting at least an unmodulated optical stream into the optical modulator; driving M electrodes that are enabled to modulate the at least unmodulated optical input stream to generate at least a modulated optical output stream using the M bits of digital output of the digital to digital converter; and transmitting the at least a modulated optical output stream over at least an optical fiber.

7. The methods of claim 6, wherein the M electrodes are distributed over a plurality of waveguide branches and are enabled to modulate unmodulated optical input streams coupled to the waveguide branches.

8. The method of claim 6, wherein each bit of digital output drives a single electrode of the M electrodes.

9. The method of claim 8, wherein each bit of digital output drives a single electrode on a single branch of a plurality of waveguide branches.

10. The system of claim 8, wherein bit of digital output drives a single electrode on each of a plurality of waveguide branches.

11. A method of modulating and transmitting at least an optical signal over at least an optical fiber in response to N bits of digital data in parallel, the method comprising: inputting the N bits of digital data into an optical modulator having a plurality of waveguides, each carrying an unmodulated optical signal; converting the N bits of digital data to M bits of digital output, where M>N and N>1; coupling, using an electrode actuating device that is associated with the modulator, the M bits of digital output to the unmodulated optical signals, said coupling enabling modulation of the optical signals, thereby generating modulated optical signals; transmitting the modulated optical signals over at least an optical fiber.

12. The method of claim 11, wherein each bit of digital output drives a single electrode on a single waveguide.

13. The system of claim 11, wherein bit of digital output drives a single electrode on each of the plurality of waveguides.

14. A method of modulating an optical signal according to a predetermined QAM constellation in response to N bits of parallel digital data input, and transmitting the optical signal over an optical fiber, the method comprising: inputting the N bits of digital data input into an optical modulator within a module also containing at least a light source, wherein the optical modulator comprises a plurality of waveguides for receiving one or more unmodulated optical signals and outputting one or more modulated optical signals; converting the N bits of digital data input to M bits of digital output, where M>N and N>1, wherein a value of said M is selected to produce a Symbol Error Rate that is consistent with a performance graph matching the predetermined QAM constellation; coupling, using an electrode actuating device that is associated with the modulator, the M bits of digital output to the one or more unmodulated optical signals, using M actuating electrodes, said coupling causing modulation of the one or more unmodulated optical signals; and transmitting the one or more optical signals over one or more optical fibers.

15. The method of claim 14, wherein each bit of the M bits of digital output drives a single electrode on a single waveguide of the plurality of waveguides.

16. The method of claim 14, wherein each bit of the M bits of digital output drives a single electrode on each of the plurality of waveguide.

17. The method claim 14, wherein the light source comprises an optical laser.

18. The method claim 14, wherein the light source comprises a light emitting diode (LED).

19. The method of claim 18, wherein the waveguides are waveguide branches.

20. The method of claim 19, wherein each bit of the M bits of digital output drives a single electrode on a single waveguide branch of the plurality of waveguide branches.

21. The system of claim 19, wherein each bit of the M bits of digital output drives a single electrode on each of the plurality of waveguide branches.

22. The method claim 19, wherein the light source comprises an optical laser.

23. The method claim 19, wherein the light source comprises a light emitting diode (LED).

24. A method of modulating and transmitting an optical signal over an optical fiber in response to N bits of digital data, the method comprising: inputting the N bits of digital data into a module containing an optical modulator, the optical modulator having at least one waveguide carrying an unmodulated optical signal; converting the N bits of digital data to M actuating voltage outputs, where M>N and N>1; coupling, using an electrode actuating device that is associated with the optical modulator, the M actuating voltage outputs to the unmodulated optical signal, said coupling enabling modulation of the unmodulated optical signal; transmitting the modulated optical signal over the optical fiber.

25. The method of claim 24, wherein in the modulated optical signal is a quadrature amplitude modulated (QAM) signal.

26. The method of claim 24, wherein the modulated optical signal is a pulse amplitude modulated (PAM) optical signal.

27. A method of modulating an optical signal according to a predetermined QAM constellation in response to N bits of parallel digital data input, and transmitting the optical signal over an optical fiber, the method comprising: inputting the N bits of digital data into an optical modulator within a module also containing at least a light source, wherein the modulator contains a plurality of waveguide branches for receiving at least an unmodulated optical signal and outputting at least a modulated optical signal; converting the N bits of digital data input to M bits of digital output, where M>N and N>1; coupling, using an electrode actuating device that is associated with the electronic input and the modulator, the M bits of digital output to the unmodulated optical signals using M actuating electrodes, said coupling causing modulation of the at least an unmodulated optical signal; and transmitting the modulated optical signals over optical fibers; wherein a value of said M and a disposition of the M actuating electrodes on the plurality of waveguide branches is selected to produce a Root Mean Square Error that is consistent with a performance graph matching the predetermined QAM constellation.

28. A method of modulating and transmitting an optical signal over an optical fiber in response to N bits of digital data, the method comprising: inputting the N bits of digital data into a module containing an optical modulator, the optical modulator having at least one waveguide carrying an unmodulated optical signal; converting the N bits of digital data to M digital bits, where M>N and N>1; using an electrode actuating device that is associated with the optical modulator and is responsive to the M digital bits, modulating the unmodulated optical signal; transmitting the modulated optical signal over the optical fiber.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0039] The invention is herein described, by way of example only, with reference to the accompanying drawings, wherein:

[0040] FIG. 1 is a schematic representation of a modulator device, constructed and operative according to the teachings of the present invention, for converting digital data into analog modulation of an optical or electrical signal;

[0041] FIG. 2A is a graph showing the intensity output generated by an unmodified Mach-Zehnder modulator employing four electrodes with lengths interrelated by factors of two and driven directly by corresponding bits of a digital input word, the output being shown relative to a line corresponding to an ideal linear response;

[0042] FIG. 2B is a graph showing an intensity output generated according to an implementation of the present invention employing a full-range Mach-Zehnder modulator with four electrodes of lengths interrelated by factors of two driven according to the teachings of the present invention;

[0043] FIG. 2C is a graph similar to FIG. 2B showing the intensity output achieved by further modifying electrode lengths according to a further aspect of the present invention;

[0044] FIG. 3A is a graph showing the intensity output achieved by the modulator of the present invention implemented with five actuating electrodes for a four bit input word, where the five electrodes have lengths interrelated by factors of two;

[0045] FIG. 3B is a graph similar to FIG. 3A showing the intensity output achieved by further modifying electrode lengths according to a further aspect of the present invention;

[0046] FIG. 4 is a table illustrating a digital-to-digital converter input and output where the input corresponds to the input data word and the output corresponds to the electrode actuation pattern for generating the outputs of FIGS. 2B and 2C;

[0047] FIG. 5 is a table illustrating unoptimized and optimized normalized electrode lengths for cases on input words of 4 and 8 bits and numbers of electrodes of 4, 5, 8, 9 and 10;

[0048] FIG. 6A is a graph showing the intensity output generated by an unmodified Mach-Zehnder modulator employing eight electrodes with lengths interrelated by factors of two and driven directly by corresponding bits of a digital input word, the output being shown relative to a line corresponding to an ideal linear response;

[0049] FIG. 6B is a graph showing an intensity output generated according to an implementation of the present invention employing a Mach-Zehnder modulator with eight electrodes of lengths interrelated by factors of two driven according to the teachings of the present invention;

[0050] FIG. 6C is a graph similar to FIG. 6B showing the intensity output achieved by further modifying electrode lengths according to a further aspect of the present invention;

[0051] FIG. 7A is a graph showing the intensity output achieved by the modulator of the present invention implemented with nine actuating electrodes for an eight bit input word, where the nine electrodes have lengths interrelated by factors of two;

[0052] FIG. 7B is a graph similar to FIG. 7A showing the intensity output achieved by further modifying electrode lengths according to a further aspect of the present invention;

[0053] FIG. 8 is a schematic representation of an alternative implementation of the present invention based upon an electro-absorption modulator (EAM);

[0054] FIG. 9 is a schematic representation of yet another alternative implementation of the present invention based upon a semiconductor laser;

[0055] FIG. 10 is a schematic representation of a modulator device, similar to the device of FIG. 1, implemented as a 16-QAM modulator;

[0056] FIG. 11A is a constellation diagram for the device of FIG. 10 illustrating a choice of constellation points, and corresponding electrode actuation patterns, for implementing a 16-QAM modulator;

[0057] FIG. 11B is a graph showing the symbol error rate performance for the devices of FIGS. 12A implemented with different numbers of electrodes;

[0058] FIGS. 12A and 12B are simplified constellation diagrams showing only closest matching points for implementation of a 64-QAM using two sets of 7 electrodes and a 256-QAM using two sets of 10 electrodes, respectively;

[0059] FIGS. 13A and 13B are graphs showing the symbol error rate performance for the devices of FIGS. 12A and 12B, respectively; and

[0060] FIG. 14 is a schematic representation of a prior art Mach-Zehnder modulator configured as a DAC.

DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

[0061] The present invention is a modulator device for converting digital data into analog modulation of an optical signal.

[0062] The principles and operation of modulator devices according to the present invention may be better understood with reference to the drawings and the accompanying description.

[0063] Referring now to the drawings, FIG. 1 shows schematically a modulator device, generally designated 10, constructed and operative according to the teachings of the present invention, for converting digital data into analog modulation of an optical signal. Generally speaking, modulator device 10 has an electronic input 12 for receiving an input data word D of N bits and an electrically controllable modulator 14 for modulating the intensity of an optical signal represented by arrow 16. Modulator 14 includes M actuating electrodes 18 where M≧N. Modulator device 10 also includes an electrode actuating device 20 responsive to the input data word D to supply an actuating voltage to the actuating electrodes 18. It is a particular feature of a first aspect of the present invention that electrode actuating device 20 actuates at least one of actuating electrodes 18 as a function of values of more than one bit of the input data word D. In other words, at least one of the electrodes is actuated in a manner differing from a simple one-to-one mapping of data bits to electrode voltage, thereby providing freedom to choose the electrode actuation pattern which best approximates a desired ideal output for the given input. According to a second complementary, or alternative, aspect of the present invention, the effective areas of actuating electrodes are optimized so that at least some of the electrode effective areas differ from a simple factor-of-two series.

[0064] The basic operation of a first preferred implementation of modulator device 10 will be understood with reference to FIGS. 2A and 2B. FIG. 2A shows the output intensity values which would be obtained by supplying a voltage sufficient to generate full dynamic range modulation to a set of four electrodes according to a direct mapping of each bit of a 4-bit input data word to a corresponding electrode. The full range of input values 0000 through 1111 and the corresponding output intensities have been normalized to the range 0-1. The marked deviation from linearity in the form of a cosine variation is clearly visible. In contrast, FIG. 2B shows the output intensity using the same four electrodes after the input data has been mapped according to the teachings of the present invention to a pattern of electrode actuation approximating more closely to a linear response. In other words, for each input value, the output value from FIG. 2A most closely approximating the corresponding theoretical linear response is determined, and the corresponding pattern of electrode actuation is applied. By way of example, in FIG. 2A, it will be noted that output point 22 corresponding to an input of 0011 is higher than desired for the ideal linear response. The outputs generated by electrode actuation patterns corresponding to value 0100 (point 24) is closer to the required value, and 0101 (point 26) is even closer. An output pattern of 0101 is thus chosen to correspond to an input of 0011. The overall result is an output which much more closely approximates to a linear response as shown.

[0065] Most preferably, electrode actuating device 20 includes a digital-to-digital converter. It will be appreciated that such a converter may be implemented from very straightforward and high-speed logic components which make it feasible to employ the present invention in high frequency systems. Electronic input 12 may be simply the input pins of digital-to-digital converter 20. FIG. 4 illustrates a preferred implementation of the digital-to-digital mapping employed to generate the output of FIG. 2B. A digital-to-digital converter suitable for implementing the various embodiments of the present invention may readily be implemented using commercially available high-speed Application Specific Integrated Circuits (“ASIC”), as will be clear to one ordinarily skilled in the art.

[0066] The first implementation described thus far features N=M=4 with lengths of the electrodes retaining the conventional ratios of factors of two and employing simple on-off level voltage switching of a common actuating voltage to all currently actuated actuating electrodes. While such an implementation offers markedly improved linearity of response compared to the unmodified response of FIG. 2A, it should be noted that the output intensity is not uniquely defined for each input value. Where uniqueness of the output values is required, or where a higher degree of linearity is needed, further modification may be required. Various forms of further modification may be employed including, but not limited to: use of multiple actuating voltage levels; use of modified electrode lengths; and addition of additional electrodes (i.e., M>N). These different options will be discussed below.

[0067] One option for further modification of the output is to modify the actuating voltage applied to each electrode, such as by switching between different distinct voltage levels.

[0068] An alternative preferred option for modifying the output to achieve a better approximation to a linear output is modification of the electrode lengths relative to the factor of two series assumed above. A non-limiting example of an approach for determining preferred electrode proportions will be presented below in the context of a Mach-Zehnder modulator. A corresponding practical example of electrode length values for N=M=4 is shown in the second column of FIG. 5. FIG. 2C illustrates the intensity output employing electrodes with lengths in the proportions listed. A comparison of the root-mean-square error from linearity for FIGS. 2B and 2C shows that the adjustment of electrode lengths results in an additional slight improvement to linearity.

[0069] A further option for modifying the performance of modulator device 10 is the addition of one or more additional electrodes, i.e., M>N. This provides an additional degree of freedom for correcting non-linearity of the response. In the case of unmodified electrode dimensions related by factors of two, each additional electrode is typically half the dimension of the previously smallest electrode. Where the electrode dimensions are further modified, the additional electrode dimension is preferably included within an optimization process in order to determine a preferred dimension for the additional electrode(s) along with the other electrodes. FIGS. 3A and 3B show outputs from the device of the present invention for an example of N=4 and M=5, with and without modification of the electrode dimensions, respectively. The electrode lengths are shown for the unmodified series in the first column of FIG. 5 and for the optimized length electrodes in the third column of FIG. 5.

[0070] Parenthetically, although the present invention is described herein in the context of a preferred example of linearization of a modulator device which inherently has a non-linear response, the principles of the present invention may equally be applied to any case where a natural response of a modulator provides a first function and a desired response is a different second function which may be linear or non-linear. Thus, the present invention may be employed to convert a digital input into an analog output approximating to any desired response curve within the dynamic range of the modulator. Non-limiting examples include where a desired output response curve is sinusoidal or exponential, or where it is desired to increase the resolution or “contrast” of the output within a specific range of input values.

[0071] Clearly, the present invention is not limited to applications with 4-bit data input, and can be implemented with substantially any number of data bits commensurable with other limitations of the system, such as signal-to-noise requirements. By way of example, FIGS. 6A-6C, 7A and 7B illustrate a number of implementations with 8-bit input data words. Specifically, for purpose of reference, FIG. 6A shows the unmodified output of an 8-bit arrangement where each data bit is applied directly to a corresponding electrode, again showing the underlying cosine response of the modulator. FIG. 6B illustrates the output of an implementation according to the teachings of the present invention with N=M=8 and standard lengths of electrodes interrelated by factors of 2, as in the fourth column of FIG 5. FIG. 6C shows output for a similar device where the electrode lengths have been modified according to the values shown in the fifth column of FIG. 5. FIGS. 7A and 7B show the output of similar devices for N=8 but with an extra electrode, i.e., M=9. In the case of FIG. 7A, the device has unmodified electrode lengths as shown in the fourth column of FIG. 5, while in the device of FIG. 7B, the electrode lengths are modified according to the proportions shown in the sixth column of FIG. 5.

EXAMPLE I

Mach-Zehnder Modulator

[0072] By way of example, there will now be presented a theoretical treatment of one particularly preferred example of modulator device 10 implemented using a Mach-Zehnder modulator, also referred to as a Mach-Zehnder Interferometer or “MZI”. This theoretical treatment is presented to facilitate an understanding of the present invention and as a suggested technique for calculating certain parameters. However, it should be noted that the invention as described above has been found to be effective, independent of the accuracy or otherwise of this theoretical treatment. The Mach-Zehnder modulator is an active integrated waveguide device consisting of a higher index guide region that splits into two paths which are combined again after a certain distance. Each of these paths is referred to as a leg or branch. When used as a switch, the MZI may be turned “off” by raising or lowering the index of refraction in one of the legs. This is achieved by employing the electro-optic effect to produce a 180 -degree change in phase by means of optical-path length. Intermediate optical attenuation levels can be obtained by inducing changes other than 180 degrees.

[0073] In the case described above of FIG. 1, a 4 -bit Digital-to-Analog Converter, based on a Multi-Electrode (ME) Mach-Zehnder Interferometer, is presented. The input to the device consists of 4 bits. Using the Digital-to-Digital converter, which may be thought of as a look-up table, the 4 data bits are mapped to 5 electrodes as this realization is equipped with a single excess electrode. According to one option, if an electrical rather than optical output is desired, the optical signal at the output is detected and converted to an electrical (analog) signal.

[0074] It should be noted that, in the context of a MZI, it is common to split the electrodes to act in an opposite manner on the two legs of the device, for example, one side raising and the other lowering the refractive index of the material, thereby reducing the actuation voltage required. In such cases, the value M is the number of actuating electrodes on each of the two waveguide branches of the modulator.

Mathematical Description

[0075] The properties of the MZI may be described mathematically as follows. Let I denote a vector of electrode lengths. The number of elements in I is M . Also let V denote a corresponding vector (of length M) of electrode control-voltages. When applying a voltage V.sub.j only to electrode e.sub.j, whose length is l.sub.j , the phase of light propagating in the modulating leg, shifts by

[00001]$\pi .Math.\frac{V_j.Math.l_j}{v_{\pi }.Math.l_{\pi }},$

where V.sub.π.Math.l.sub.π corresponds to the voltage-length product leading to a π shift in the phase. It is used as a merit figure of the MZI modulator. We define new normalized electrode length by:

[00002]$\begin{array}{cc}{L}_j=\frac{l_j}{l_{\pi }}& \left(1\right)\end{array}$

Gathering the total contribution from all electrodes, the following transmission function of the MZI is obtained:

[00003]$\begin{array}{cc}T\left(V,L\right)={\cos }^2\left(\frac{\pi }{2}-\frac{V.Math.L^T}{v_{\pi }}\right),.Math.& \left(2\right)\end{array}$

where the superscript T denotes transposition. The contribution from each electrode e.sub.j, j=1, 2, . . . M, to the total phase shift, is permitted by applying some non-zero voltage V.sub.j=v. We chose to work with binary values for all electrode voltages, V.sub.j=0, v, a clearly desirable requirement which, moreover, makes the design simpler as discussed next. Note that by setting the lower voltage to a value greater than zero, the maximum output level of the MZI is decreased thus reducing the dynamic range. Let D.sub.i denote a digital binary input vector of length N, where i=1, . . . , 2.sup.N. For each digital vector D.sub.i, the DDC component in FIG. 1 produces a corresponding binary vector B .sub.i, of length M. B.sub.i multiplied by v, represents the actual (internal) vector of voltages controlling the M electrodes. When multiplying a real number, B.sub.i should be interpreted as binary vector whose elements are the real numbers {0,1}. With respect to (2), this means that when V.sub.j=v, then B.sub.ij=1, V.sub.j=0. B.sub.ij=0; B.sub.ij being the j-th element of the control vector B.sub.i . At this time we define B to be a matrix of size 2.sup.N×M whose rows consist of the set of binary control vectors B.sub.i , each of length M . Hence, (2) can be rewritten as

[00004]$\begin{array}{cc}T\left(B_i,L\right)={\cos }^2\left(\frac{\pi }{2}.Math.\frac{v}{v_{\pi }}.Math.\underset{j=1}{\overset{M}{.Math.}}.Math.B_{\mathrm{ij}}.Math.L_j\right)& \left(3\right)\end{array}$

[0076] Without loss of generality V=V.sub.π will be assumed henceforth. (Preferably V.sub.j=v.sub.π to ensure full coverage of the modulating range and efficient use of the input optical power.) When the number of electrodes equals the number of data bits, i.e. when M=N , an implementation in a standard approach according to the system of FIG. 10 while trying to exploit the dynamic range of the transfer function (3) to its fullest results in high nonlinearity errors. This is demonstrated in FIG. 2A for M=N =4. For this demonstration it is assumed that an unoptimized straightforward selection is made, where B is the set of all 16 binary 4 -tuples, i.e. B.sup.T={0000, . . . ,1111} and L is taken as {0.5,0.25,0.125,0.0625}. In the next section, one suggested approach to optimizing L and B will be proposed.

Optimization of B and L

[0077] In order to improve the linearity as well as the dynamic range of the conversion process, we propose that the lengths of the elements of L and the control vectors B be optimized. As described above, it is possible to optimize one or both of B and L. In practice, optimization of L alone may provide a non-monotonic variation of output together with some improvement in linearity and dynamic range. This may be sufficient for applications in which the non-linearity is relatively small, such as the semiconductor laser embodiments to be discussed below. For more significantly non-linear devices, the options of optimized B with unoptimized L, and optimized B and L are typically more suitable.

[0078] We consider these options separately since their implementation require different hardware. An unoptimized set of electrode lengths L consists of

[0079] L.sub.j=2.sup.−j, with j=1 . . . M. An unoptimized matrix B will consist of 2.sup.N all binary N -tuples. In that case, with a slight abuse of notations we have that B.sub.i=D.sub.i; i=0,1,2, . . . 2.sup.N−1. Hence, designs with optimized B require Digital-to-Digital conversion while designs with optimized L only do not. Whenever B is optimized, and for any number of electrodes M; M≧N , it is understood that a binary input data vector D.sub.i has to be mapped to a control vector B.sub.i , yet B.sub.i≠D.sub.i. The DDC, implemented as all-electronic, shall perform this mapping operation.

[0080] As the optimization criterion we shall use the root mean square error (RMSE) between an ideal output, represented by a straight line, and the converter output. Let

[00005]$U_i=\frac{i}{2^N}$

denote the ideal analog value required for representing the digital input D.sub.i. The RMSE is defined as follows:

[00006]$\begin{array}{cc}g\left(B,L\right)=\sqrt{\frac{1}{2^N}.Math.\underset{i=1}{\overset{2^N}{.Math.}}.Math.{\left[U_i-{\cos }^2\left(\frac{\pi }{2}.Math.\underset{j=1}{\overset{M}{.Math.}}.Math.B_{\mathrm{ij}}.Math.L_j\right)\right]}^2}& \left(4\right)\end{array}$

[0081] The optimization problem can now be formulated as minimizing the values of g(B,L) for all possible values of the matrix B and the vector L. Note that this optimum solution is aimed at minimizing the average (squared) deviation between the desired output and the converter output. Clearly, this is only one non-limiting example, and various other linearity measures may equally be used. Similarly, as mentioned earlier, the desired output response function itself may take any desired form, and for each function, a suitable optimization criterion must be selected.

[0082] Approaching (4) as a global optimization problem with an order of O(2.sup.N×M) variables, is quite involved, especially since the variables are of mixed type, B is binary while L is real. (It is related to a nonlinear mixed integer zero-one optimization problem.) It is therefore typically preferred to employ a near-optimum two-step approach. First, B is determined assuming an unoptimized set of electrodes L, L.sub.j2.sup.−j, with j=1 . . . M. The obtained matrix is denoted by {circumflex over (B)}. Then, given {circumflex over (B)}, L is obtained such that (4) is minimized.

[0083] If L is an unoptimized set of electrodes, L.sub.j=2.sup.−j. Then, the output of the converter as given by (3) is a function of the control B.sub.i only. Since one aims at obtaining a straight line, whose quantized values are given by U.sub.i then it is not difficult to verify that the best approximated selection of {circumflex over (B)}.sub.i is given by

[00007]$\begin{array}{cc}{B}_i=\mathrm{Dec}.Math..Math.2.Math.{\mathrm{Bin}}_M\left(\frac{2}{\pi }.Math.\arccos \left(\sqrt{U_i}\right)\right),& \left(5\right)\end{array}$

where the function Dec2Bin.sub.M(x) maps a real value x, 0<x≦1, to its closest M -bit binary representation. Note that this, in effect quantization, process may result in several input data vectors having the same analog representation. In applications in which this duplicate representation is considered problematic, it is effectively mitigated by choosing M>N .

[0084] Given {circumflex over (B)}, we proceed to optimize L. Assuming there exists a set of electrodes L such that

[00008]${\cos }^2\left(\frac{\pi }{2}.Math.\underset{j=1}{\overset{M}{.Math.}}.Math.{\hat{B}}_{\mathrm{ij}}.Math.L_j\right)\approx U_i;\forall i,$

then as an alternative to (4), we may define an equivalent cost function, which is easier to handle mathematically:

[00009]$\begin{array}{cc}h\left(L\right)=\left\{\underset{i=1}{\overset{2^N}{.Math.}}.Math.{\left[\frac{2}{\pi }.Math.\arccos \left(\sqrt{U_i}\right)-\underset{j=1}{\overset{M}{.Math.}}.Math.B_{\mathrm{ij}}.Math.L_j\right]}^2\right\}.& \left(6\right)\end{array}$

To minimize this cost function, one needs to differentiate h(L) with respect to L and equate to 0:

[00010]$\frac{\partial h}{\partial L_k}=2.Math.\left\{\underset{i=1}{\overset{2^N}{.Math.}}.Math.{\hat{B}}_{\mathrm{ik}}\left[\frac{2}{\pi }.Math.\arccos \left(\sqrt{U_i}\right)-\underset{j=1}{\overset{M}{.Math.}}.Math.{\hat{B}}_{\mathrm{ij}}.Math.L_j\right]\right\}=0;$$\forall k.$

The following equation (more precisely set of equations) is obtained

[00011]$\begin{array}{cc}\underset{i=1}{\overset{2^N}{.Math.}}.Math.\underset{j=1}{\overset{M}{.Math.}}.Math.{\hat{B}}_{\mathrm{ik}}.Math.{\hat{B}}_{\mathrm{ij}}.Math.L_j=\underset{i=1}{\overset{2^N}{.Math.}}.Math.{\hat{B}}_{\mathrm{ik}}.Math.\frac{2}{\pi }.Math.\arccos \left(\sqrt{U_i}\right),& \left(8\right)\end{array}$

where k=1,2 . . . M . In matrix notation the set of equation translates to a simple expression

[00012]$\begin{array}{cc}L={\left({\hat{B}}^T.Math.\hat{B}\right)}^{-1}.Math.{\frac{2}{\pi }\left[\arccos \left(\sqrt{U}\right).Math.\hat{B}\right]}^T,& \left(9\right)\end{array}$

where √{square root over (U)} amounts to a component-wise square root. The solution above grants us an optimized vector of lengths L .

EXAMPLE II

Electro-Absorption Modulator

[0085] As mentioned earlier, the present invention is not limited to implementations based on Mach-Zehnder modulators, and can be implemented using any device which modulates light intensity as a function of applied voltage. By way of one additional non-limiting implementation, FIG. 8 shows an analogous implementation of the present invention using an electro-absorption modulator.

[0086] An electro-absorption modulator (EAM) is a semiconductor device which allows control of the intensity of a laser beam via an electric voltage. Its operational principle is typically based on the Franz-Keldysh effect, i.e., a change of the absorption spectrum caused by an applied electric field, which usually does not involve the excitation of carriers by the electric field.

[0087] By realizing N or more electrodes we can use the EAM as a high speed electro-optical Digital-to-Analog converter, in a similar fashion as we used the MZI. As in modulator device 10 described above, this device includes an electronic input 12 for receiving an input data word D of N bits and an electrically controllable modulator 14 with M electrodes for modulating the intensity of an optical signal represented by arrow 16. An electrode actuating device 20 is responsive to the input data word D to supply an actuating voltage to the actuating electrodes 18.

[0088] Here too, to mitigate the non-linear behavior of the device, electrode actuating device 20 serves as a Digital-To-Digital Converter is employed to map an N bit input to a set of M electrodes, determining which of the M electrodes is actuated for each input value. The particular mapping varies according to the response characteristic of the particular modulator, but the principles of operation are fully analogous to those described above in the context of the Mach-Zehnder modulator implementation.

EXAMPLE III

Modulated Light Generation Device

[0089] The present invention is applicable also to other devices where digital information carried by voltage or current is translated into analog optical signals in the form of optical power. This includes also light generation devices like Light Emitting Diodes (LED) or semiconductor lasers. By way of illustration, FIG. 9 shows a semiconductor laser implementation of the present invention.

[0090] Specifically, FIG. 9 shows a semiconductor laser DAC device, generally designated 40, constructed and operative according to the teachings of the present invention. The actuating electrode, typically implemented as a single contiguous electrode, is here subdivided into a threshold electrode 42 and M actuating electrodes 18. The threshold electrode 42 is typically needed to reach a minimum activation current below which no significant output is generated. Actuating electrodes 18 are actuated as a function of the data bits of a digital input 12, in this case a 4-bit data word, to generate an analog optical signal output of intensity representing the digital input.

[0091] In the particularly simple implementation illustrated here, neither L nor B is optimized. In other words, each actuating electrode 18 is part of a set interrelated with effective areas in 2:1 relation, and each electrode is actuated as a function of corresponding single bit of the input data word. The actuating current is typically roughly proportional to the area of electrodes actuated. This case is in itself believed to be patentable, and is thought to be of practical importance. Optionally, a closer approximation to a linear response can be achieved by modifying L (electrode proportions) and/or B (by including a DDC, not shown), all according to the principles discussed in detail above.

[0092] It will be appreciated that a similar device may be implemented using other semiconductor light generating devices, such as LEDs. Depending upon the details of the device used, threshold electrode 42 may not be necessary. This and any other necessary device-specific modifications will be self-evident to one ordinarily skilled in the art.

EXAMPLE IV

QAM Transmitter

[0093] Although described above in the context of devices for intensity/amplitude modulation, it should be noted that various embodiments of the present invention are also effective for modifying the phase of an optical signal, and can therefore be used as highly compact and simple QAM (Quadrature Amplitude Modulation) modulators or transmitters.

[0094] Specifically, referring back to FIG. 1, it will be noted that, by configuring the digital-to-digital converter DDC 20 to apply different actuation patterns to the electrodes on the two branches of the Mach Zehnder Modulator (MZM), modulation of the output signal phase can be achieved. Such an implementation will now be described with specific reference to FIGS. 10-13B.

[0095] Turning now to FIG. 10, there is shown a modulator device, generally designated 100, implemented as a QAM modulator. Modulator device 100 is essentially similar to the device of FIG. 1, but has been relabeled to convey more clearly its function. Specifically, modulator device 100 has a first plurality M.sub.1 of actuating electrodes 18a deployed in operative relation to a first waveguide branch of the modulator and a second plurality M.sub.2 of actuating electrodes 18b deployed in operative relation to a second waveguide branch of the modulator. In this case, M.sub.1=M.sub.2=5. giving a total number of actuating electrodes M=10. The electrode actuating device is here shown as two distinct digital-to-digital converters 20a and 20b, which are configured to actuate the first and second pluralities of actuating electrodes 18a and 18b in response to a given input data word D.sub.i so as to additionally modulate the phase of the optical signal. Clearly, digital-to-digital converters 20a and 20b can alternatively be combined into a single DDC with M=10 outputs with suitable connections to the actuating electrodes on both branches of the waveguide.

[0096] It will be appreciated that modulator device 100 can serve as an optical 16-QAM transmitter based on a single multi-electrode MZM (ME-MZM). Each electrode is divided into 5 segments, separately driven by two voltage signals, 0 and V representing binary 0 and 1, respectively. The center electrode is a common ground for the active electrode segments. The role of the modulator is to generate a desired M-QAM constellation which is composed of complex optical field values. The modulator is expected to generate 2.sup.M signals:

s.sub.i=r.sub.ie.sup.jθ.sup.i, r.sub.i>0, 0≦θ.sub.i≦2π, i=1, . . . , 2.sup.M,   (10)

[0097] In our example of a 16-QAM with two sets of 5 electrodes, as an input, the QAM transmitter accepts an electrical 4-bit digital imput word, denoted D.sub.i. The input word is mapped by two Digital-to-Digital Converters (DDC) onto each of the 10 (electrode) segments, whose lengths are the vectors L.sup.1,2. Each DDC outputs a 5-bit word, denoted as B.sub.i.sup.1 and B.sub.i.sup.2. The output of transmitter can be written as:

[00013]$\begin{array}{cc}{E}_{\mathrm{out},i}=\frac{1}{\sqrt{2}}.Math.E_{\mathrm{in}}.Math.\exp .Math.\left\{j.Math..Math.2.Math.\pi .Math.\underset{j}{\overset{N_1}{.Math.}}.Math.B_{\mathrm{ij}}^1.Math.L_j^1\right\}+\frac{1}{\sqrt{2}}.Math.E_{\mathrm{in}}.Math.\exp .Math.\left\{-j.Math..Math.2.Math.\pi .Math.\underset{j}{\overset{N_2}{.Math.}}.Math.B_{\mathrm{ij}}^2.Math.L_j^2\right\}& \left(11\right)\end{array}$

where E.sub.in the optical field amplitude entering the modulator and N.sub.1, N.sub.2 are the number of segments on each arm. The elements L.sub.j.sup.1,2∈L.sup.1,2 represent normalized electrode lengths on each arm. The two-level B.sub.ij.sup.1,2 coefficients are elements of the matrices B.sub.i.sup.1,2 and represent whether voltage v was applied to the j -th segment, on the respective arm. The index j enumerates the electrodes, j={1 . . . N.sub.1,2} on each arm. The summation is normalized to span 0≦Σ.sub.j.sup.N B.sub.ij.sup.1,2L.sub.j≦1, such that each arm induces a phaseshift of 0≦Δφ≦2π.

[0098] The application of the electrical signals is preferably directly upon the modulator without any mediating circuits, referred to herein as “Direct Digital Driving”. The modulator can be regarded as a 2D Digital-to-Analog (D/A) converter, that converts a digital word into an optical vector signal.

[0099] The design of the transmitter involves the setting of electrode lengths, L.sup.1.2 and DDC mappings, B.sub.i.sup.1,2, that will generate all the required signals given in Eq. (10). An effective combination of the electrode lengths and digital mappings may be derived either by analytical methods or numerically. A simple numerical derivation will now be presented.

[0100] A ME-MZM with N.sub.1,2 electrode segments on each arm is capable of generating 2.sup.(N.sup.1.sup.+N.sup.2.sup.) signals. Thus, by choosing carefully the electrode lengths, and assuming the number of segments sufficient to generate at least 2.sup.(N.sup.1.sup.+N.sup.2.sup.)>M different signals, all the required signals described by Eq. (10) can be picked out of the generated signals pool. As an example, FIG. 11A shows the an ideal Square-16-QAM constellation, which is the required signal constellation, and a signal pool

[0101] As an example, FIG. 11A shows the an ideal Square-16-QAM constellation, which is the required signal constellation, and a signal pool which was generated with {5,5 }electrodes. The best matched signals at the pool are marked in figure. It can be seen that there is a good match between the ideal and the best matched generated constellations.

[0102] Table 1 compares between an ideal 16-QAM constellation and a generated constellation with different combinations of number of electrodes each arm. It presents the symbol minimum distance and the root mean square error. The latter provides a measure of agreement between the ideal and the generated constellations. Configurations with {2,2}, {2,3} and {3,3} electrodes provide less than 16 different signals (minimum distance of 0) and therefore cannot be used for generation of 16-QAM.

TABLE-US-00001 TABLE 1 N.sub.1, N.sub.2 Ideal 4, 2 4, 3 4, 4 4, 5 5, 5 5, 6 6, 6 Minimum 2 1.66 1.66 1.66 1.30 1.83 1.67 1.67 Distance RMSE 0 4.64 4.64 4.53 4.42 4.64 4.52 4.57

[0103] FIG. 11B presents the Symbol Error Rate (SER) performance for a range of Signal to Noise Ratios (SNR) for an Additive White Gaussian Noise (AWGN) channel. It can be seen that when using {6,6} electrodes, the performance graph closely matches that of ideal 16-QAM constellation. Using a higher number of electrodes can lower the SER ever further toward the ideal curve. SER performance can be slightly improved by further tuning the decoding hypothesis testing at the receiver side to the generated constellation.

[0104] The electrode lengths used for the generation of FIG. 11B follow a binary sequences, L.sup.1,2=2.sup.−j. Tweaking the electrode lengths has small impact on the modulator performance. In Eq. (11), we assumed driving signals of 0 and 2V.sub.π. The high driving signal can be lowered by extending the total electrode length twice its size. The opposite signs in the exponents in the two terms of Eq. (11) are already implemented by the geometry of the electrode disposition of FIG. 10, when the signs of the voltages applied are the same, since then the electric fields have opposite directions. Other electrode dispositions exist for different cuts of the electro-optic crystals, and the appropriate way of applying the voltage with the right signs should be clear to a person skilled in the art.

[0105] Referring now to FIGS. 12A-13B, it will be appreciated that the proposed modulator is capable of generating high order QAM constellations. FIG. 12A depicts the ideal 64-QAM constellation together with one generated using a {7,7} electrodes modulator, while FIG. 12B shows an ideal 256-QAM constellation together with the one generated using a {10,10} electrodes modulator. It can be seen that there is a good match between the ideal and the generated constellations. FIGS. 13A and 13B show the Symbol Error Rate performance for the generated constellations of FIGS. 12A and 12B, respectively.

[0106] A simple implementation of this embodiment described thus far generates Non-Return-to-Zero (NRZ) signals. NRZ permits constant intensity for similar consecutive bits, and is thus more susceptible to Inter-Symbol-Interference and other nonlinear propagation distortions. Return-to-Zero (RZ) format is a pulsed modulation where the signal “returns to zero” after every bit. This format provides better performance than NRZ, but usually requires additional hardware, such as a pulse carver. A transmitter based on the modulator of an embodiment of the invention can readily be extended to produce RZ pulses with minimal if any additional hardware. By adding an RZ control line to the DDC, as shown in FIG. 10, which serves as a trigger determining whether the output optical amplitude should be zero or other, the whole modulator will be capable of generating RZ signals. When the added control line is high, the DDC will map the electrode actuation pattern to the pattern corresponding to the middle point of the constellation, which is zero.

[0107] For the constellation presented in FIG. 10, B.sub.1={00010} and B.sub.2={01110} will output zero (or minimum) power because it will generate a phase difference of π between the two arms of the MZM.

[0108] While the present invention has been presented as a digital-to-analog optical modulator, it should be noted that each embodiment of the invention may be modified to provide analog electrical output by use of an optical-to-electrical (OLE) converter. This option is illustrated in FIG. 1 as optional OLE converter 30. If the OLE converter itself has a non-linear response function, the present invention may advantageously be used to optimize the system parameters to linearize the electrical output rather than the (intermediate) optical output. Analogously, any nonlinearity induced by the optical medium used for transmitting the signal (e.g. optical fiber) can be compensated for by using OLE converter 30 as a linearizing device.

[0109] The present invention is applicable to substantially all applications requiring a DAC with optical or electrical output. Examples of particular interest include, but are not limited to, wireless communications systems, fiber-optic communication systems, cellular telephone networks, cable television, military applications, medical applications and hyper/super computer communications.

[0110] It will be appreciated that the above descriptions are intended only to serve as examples, and that many other embodiments are possible within the scope of the present invention as defined in the appended claims.