FIELD OF THE INVENTION

[0001 ] The present invention relates to optical modulation, and more particularly to multilevel modulation of optical pulses. Applications of the invention include electro-optical conversion of signals for transmission, e.g. via optical fibre, and electro-optical digital-to-analog conversion.

BACKGROUND OF THE INVENTION

[0002] It is frequently desirable to make use of the very high bandwidth of the optical spectrum for communication and/or processing of information signals. However, electronic processing generally, and digital processing in particular, remains the most practical and flexible approach to performing many complex tasks, such as sophisticated signal processing, coding, multiplexing,

demultiplexing, switching and so forth.

[0003] High-capacity information systems employing a combination of electronic and optical processing and transmission generally employ components for digital-to-analog conversion and optical-to-electrical conversion.

Conventionally, digital-to-analog converters (DACs) are electronic components having a plurality of parallel electrical inputs for receiving digital signals, and one or more analog electrical outputs providing the converted signal waveforms. Electronic DACs are used in combination with various forms of optical modulator in order to perform electrical-to-optical conversion.

[0004] A disadvantage of these conventional systems, in addition to the requirement for distinct DAC and optical modulator components, is the significant power consumption of the DACs, particularly at very high bit-rates. This power consumption results not only from the process of digital-to-analog conversion itself, but also from the requirement for impedance-matched terminations on the parallel-time-multiplexed high-speed electrical/digital inputs.

[0005] The present invention therefore addresses the need for improved devices and methods for conversion of signals between the electrical and optical domains with reduced component counts and/or power requirements.

SUMMARY OF THE INVENTION

[0006] In one aspect, the invention provides an optical modulation method comprising

applying a series of electrical pulses to an electrode of a travelling wave optical modulator, each electrical pulse being characterised by a

corresponding pulse integral, such that the electrical pulses propagate along the electrode with a first velocity; and

applying, synchronously with the electrical pulses, a series of optical pulses to an optical waveguide of the travelling-wave optical modulator which is adjacent to the electrode, such that the optical pulses propagate along the optical waveguide with a second velocity which is different from the first velocity,

whereby a modulation is imparted to each one of the series of optical pulses which is a function of the characterising pulse integral, the difference between the first and second velocities and/or a time offset of a corresponding one of the electrical pulses.

[0007] Accordingly, embodiments of the invention employ travelling wave modulators in a manner that is contrary to their conventional operation, in which the electrical and optical signals are arranged to co-propagate at substantially identical velocities so as to maximise the interactions, and hence the modulation effect, occurring during transit of the fields through the modulator. In particular, embodiments of the invention take advantage of the realisation that new and useful functionality can be obtained through the use of unconventional

arrangements in which electrical and optical signals propagate with substantially different velocities in travelling wave modulators. As will be appreciated, the term 'substantially', in the present context, refers to a difference that is sufficient to achieve, in practice, the beneficial effects of the invention as disclosed herein. In general, and as is taught in greater detail with reference to particular

embodiments of the invention, the necessary velocity difference may depend on other parameters of a modulator embodying the invention, such as the electrode length. The teachings of the present specification thus provide sufficient detail, including relevant equations, to enable the skilled person to meet the practical requirements for operation in accordance with any particular design

specifications.

[0008] Advantageously, embodiments of the invention are able to replace conventional combinations of digital-to-analog converters having multiple digital input ports, coupled to associated optical modulators or other electrical-to-optical conversion devices. By controlling parameters of the electrical pulses applied to the electrode of the travelling-wave optical modulator, the modulation imparted to each individual optical pulse can be varied. The parallel electrical inputs characteristic of conventional digital-to-analog converters are avoided, resulting in potential reductions in power consumption.

[0009] In some embodiments of the invention (characterised as 'counter- propagating' configurations) the second velocity is opposed in direction to the first velocity. In such embodiments the second velocity may be substantially equal in magnitude to the first velocity. Advantageously, this enables the invention to be embodied using conventional modulator designs, including available modulators as known in the prior art, by simply reversing the direction of propagation of the optical signals in the modulator.

[0010] Accordingly, in some embodiments, the invention provides an optical modulation method comprising:

applying a series of electrical pulses to an electrode of a

travelling-wave optical modulator, each electrical pulse being characterised by a corresponding pulse integral, such that the electrical pulses propagate along the electrode in a first direction; and

applying, synchronously with the electrical pulses, a series of optical pulses to an optical waveguide of the travelling-wave optical modulator which is adjacent to the electrode, such that the optical pulses propagate along the optical waveguide in a second direction which is opposed to the first direction,

whereby a modulation is imparted to each one of the series of optical pulses which is a function of the characterising pulse integral and/or a time offset of a corresponding one of the electrical pulses.

[001 1 ] In alternative embodiments (characterised as 'co-propagating' configurations) the first and second velocities have a common direction and are substantially different in magnitude. Optical modulators having this velocity mismatch characteristic would be considered undesirable in conventional data modulation applications, however can be designed and constructed using known electrical and optical waveguide engineering methods. Dispersion

characteristics, which determine group velocity of pulses, can be engineered in optical waveguides by design of waveguide geometry and dimensions, and selection of refractive index profiles. Similarly, group velocity of electrical pulses propagating along the electrode can be controlled by selection/design of various parameters, including electrode dimensions and geometry, coupling to ground conductors, choice of dielectric substrates, and the inclusion of additional discrete or distributed circuit elements. Advantageously, the first velocity (i.e. of the electrical pulses) is substantially less than the second velocity (i.e. of the optical pulses), which can be achieved, for example, via capacitive loading of the electrode.

[0012] As aspect of the invention therefore provides an optical modulator comprising:

an electrode having an electrical input wherein an electrical signal applied at the electrical input propagates along the electrode with a first velocity; and an optical waveguide positioned adjacent to the electrode and having first and second optical ports wherein an optical signal applied at the first optical port propagates along the optical waveguide with a second velocity,

wherein the electrode and the optical waveguide are configured such that the second velocity is substantially different in magnitude from the first velocity.

[0013] In some embodiments, the modulation comprises a phase shift imparted to each one of the series of optical pulses. In alternative embodiments, the modulation comprises an amplitude shift imparted to each one of the series of optical pulses. Amplitude modulation may be implemented using phase modulators configured in an interferometric arrangement, e.g. using a

Mach-Zehnder modulator.

[0014] In embodiments of the invention the electrical pulses are substantially rectangular pulses characterised by a corresponding pulse width, whereby the modulation imparted to each one of the series of optical pulses is substantially proportional to the pulse width of the corresponding one of the electrical pulses.

[0015] Advantageously, pulse width modulated electrical signals can be generated via digital signal processing units, configured to generate binary output pulses, wherein the width of each pulse is proportional to a desired analog signal level.

[0016] It is a particular advantage, in embodiments of the invention employing pulse width modulation, that there is a direct mapping between the width of one electrical pulse and the modulation applied to a corresponding optical pulse, such that inter-symbol interference is substantially avoided. More particularly, the degree of optical modulation is a function of integration of each electrical pulse bounded by the single-pass propagation delay along the electrode or optical waveguide of the travelling-wave optical modulator. With electrical and optical pulses counter-propagating at opposing velocities, the process requires only a single-pass delay to integrate over a pulse duration equivalent to twice that period, and no undesired interactions occur between adjacent optical and/or electrical pulses. Yet a further advantage is that, for electrical pulses shorter than twice the transit time of the modulator electrode, the pulse integration can be substantially independent of the precise timing of the electrical pulses, thus mitigating the effects of timing jitter.

[0017] It is also notable that, since the magnitude of the modulation applied to the optical pulses is directly related to the time integral of each electrical pulse, embodiments of the invention may also be employed to perform integration of electrical signals having general pulse shapes.

[0018] In another aspect, the invention provides an optical modulation apparatus comprising:

an electrode having an electrical input wherein an electrical signal applied at the electrical input propagates along the electrode with a first velocity;

an optical waveguide positioned adjacent to the electrode and having first and second optical ports wherein an optical signal applied at the first optical port propagates along the optical waveguide with a second velocity which is different from the first velocity;

an electrical signal source, having an output coupled to the electrical input of the electrode, which is configured to generate a series of electrical pulses wherein each pulse is characterised by a corresponding pulse integral; and

an optical pulse source synchronised with the electrical signal source and having an output coupled to the first optical port of the optical waveguide, which is configured to generate a series of optical pulses.

[0019] The electrical input and the first and second optical ports may be arranged such that the electrical signal propagates along the electrode in a first direction, and the optical signal propagates along the optical waveguide in a second direction which is opposed to the first direction. Furthermore, the electrode and the optical waveguide may be configured such that the second velocity is substantially equal in magnitude to the first velocity.

[0020] Accordingly, in some embodiments the invention provides an optical modulation apparatus comprising:

an electrode having an electrical input wherein an electrical signal applied at the electrical input propagates along the electrode in a first direction;

an optical waveguide positioned adjacent to the electrode and having first and second optical ports wherein an optical signal applied at the first optical port propagates along the optical waveguide to the second optical port in a second direction which is opposed to the first direction;

an electrical signal source, having an output coupled to the electrical input of the electrode, which is configured to generate a series of electrical pulses wherein each pulse is characterised by a corresponding pulse integral; and

an optical pulse source synchronised with the electrical signal source and having an output coupled to the first optical port of the optical waveguide, which is configured to generate a series of optical pulses.

[0021 ] Alternatively, the electrode and the optical waveguide may be configured such that the second velocity is substantially different in magnitude from the first velocity.

[0022] In embodiments of the invention, the optical waveguide is a first optical waveguide wherein a modulation is imparted to each one of the series of optical pulses which is a function of the characterising pulse integral and/or a time offset of a corresponding one of the electrical pulses. The modulation imparted to each one of the series of optical pulses may be a phase modulation.

[0023] In embodiments of the invention the optical modulation apparatus further comprises a second optical waveguide arranged in an interferometric configuration with the first optical waveguide, whereby the modulation imparted to each one of the series of optical pulses is an amplitude modulation. The interferometric configuration may be a Mach-Zehnder interferometric

configuration.

[0024] In embodiments of the invention, the second optical waveguide may be arranged adjacent to a further electrode, whereby a series of electrical pulses may be applied to both electrodes, so as to modulate optical pulses propagating within the first and second optical waveguides. The configuration of the electrodes and/or characteristics of the applied electrical pulses, may be adapted to provide a balanced drive to the electrodes of the Mach-Zehnder interferometric configuration.

[0025] In embodiments of the optical modulation apparatus, the

interferometric configuration may be duplicated, and arranged in parallel to form a complex (IQ) modulator structure.

[0026] Further features, benefits and applications of the invention will be apparent to the skilled person from the following description of embodiments, which is provided in order to explain the principles of the invention, and which should not be considered to be limiting of the scope of the invention as set out in any of the foregoing statements, or in the claims appended hereto.

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Embodiments of the invention will now be described with reference to the accompanying drawings, in which:

Figure 1 is a block diagram illustrating an optical transmitter embodying the invention;

Figure 2 is a schematic diagram of an optical modulator comprising a first embodiment of the invention;

Figure 3 illustrates a travelling wave phase modulator according to the first embodiment;

Figure 4 is a space/time diagram illustrating a counter-propagating modulation method embodying the invention;

Figure 5 is a block diagram illustrating an exemplary implementation of the first embodiment of the invention;

Figure 6 shows oscilloscope traces of signals corresponding with the embodiment of Figure 5;

Figure 7 is a graded oscilloscope trace of a 5-PAM eye diagram corresponding with the embodiment of Figure 5;

Figure 8 is a schematic diagram of an optical modulator comprising a second embodiment of the invention;

Figure 9 illustrates a travelling wave phase modulator according to the second embodiment;

Figure 10 is a space/time diagram illustrating a co-propagating modulation method embodying the invention;

Figure 1 1 is a block diagram illustrating an exemplary model of the second embodiment of the invention;

Figure 12 shows a first set of simulation results of signals

corresponding with the embodiment of Figure 1 1 ; and

Figure 13 shows a second set of simulation results of signals corresponding with the embodiment of Figure 1 1 .

DETAILED DESCRIPTION OF EMBODIMENTS

[0028] Figure 1 is a block diagram illustrating an optical transmitter 100 embodying the present invention. The transmitter 100 is arranged to generate a complex, multilevel, polarisation-multiplexed optical signal. In particular, the optical signal generated by the transmitter 100 may have information modulated onto two polarisation states of an optical field, each of which may, in turn, have both in-phase and quadrature signal components. It will be appreciated, however, that the arrangement 100, or simpler arrangements of components, may be employed to generate optical signals with lesser degrees of multiplexing. The generality of the arrangement 100 shown in Figure 1 should therefore not be taken as limiting the scope of the invention to this particular arrangement, but rather is provided in order to illustrate the extensive range of benefits available through embodiments of the invention.

[0029] The transmitter 100 includes an optical pulse source 102 configured to generate a train of optical pulses 104. The optical pulse source 102 may be, for example, a mode locked laser (MLL) driven by an input data signal, or by a common clock synchronised to the data signal. As such, the pulse train 104 may be generated to be synchronous with a data signal input to the transmitter 100.

[0030] A polarisation beam splitter 106 divides the optical pulse train 104 into two orthogonal polarisation states. The resulting pulse train in a first polarisation state is input to a first complex (IQ) modulator 1 12a, while the pulse train in the second orthogonal polarisation state is input to a second IQ modulator 1 12b.

[0031 ] One or more digital data signals are provided to the transmitter 100, and input to digital signal processing units 108a, 108b, 108c, and 108d. The input data signals may originate from a single source of data, divided between the four signal processing units 108 for transmission via parallel modulated data streams, or may comprise two or more independent information sources. The signal processing units 108 may comprise custom logic circuits,

application-specific integrated circuits (ASICs), programmable logic devices configured in accordance with an embodiment of the present invention, and/or special or general purpose processing units configured with program instructions embodying the invention.

[0032] Electrical outputs 1 10a, 1 10b of the signal processing units 108a, 108b are used to drive two electrode inputs of the first IQ modulator 1 12a. Similarly, electrical outputs 1 10c, 1 10d of the signal processing units 108c, 108d drive electrode inputs of the second IQ modulator 1 12b. [0033] The modulated pulses output from the IQ modulators 1 12a, 1 12b are input to a polarisation multiplexer 1 14, and are recombined into a single

polarisation multiplexed optical signal output via port 1 16.

[0034] Figure 2 is a schematic illustration of an optical modulator 200 comprising a first embodiment the invention, and in particular embodying one of the two IQ modulators 1 12a, 1 12b of the optical transmitter 100.

[0035] The optical modulator 200 receives a train of pulses at input 202, which are divided via an optical power splitter arrangement into two separate waveguide paths. In a first waveguide path 204 (i.e. the upper path of the modulator 200) the signal is input to a Mach-Zehnder interferometer arrangement 206. The Mach-Zehnder interferometer 206 has an upper arm 208 and a lower arm 210. Adjacent, and parallel to, these two optical waveguide arms are corresponding electrodes 212, 214. The waveguides 208, 210 and electrodes 212, 214 are arranged such that respective propagating electromagnetic fields are able to interact with one another via the material properties of a substrate within which the waveguides are formed. For example, as is known in the art, the modulator 200 may be fabricated using a nonlinear material such as lithium niobate, or a semiconductor material such as indium phosphide (InP), whereby electrical fields propagating along the electrodes 212, 214 interact via the material to induce phase changes in the optical fields propagating within the waveguide arms 208, 210.

[0036] In a second arm 216 of the modulator 200 a phase shift section 218 induces a 90 degree phase shift in the propagating pulses relative to the pulses propagating in the first arm 204. This results in the generation of signals that are, in terms of the phase of the optical carrier, aligned in quadrature relative to the fields propagating in the first arm 204. [0037] The resulting quadrature pulses are input to a second Mach-Zehnder interferometer arrangement 220, which again has upper and lower arms 222, 224 and adjacent electrodes 226, 228.

[0038] The outputs of the first and second Mach-Zehnder interferometers 206, 220 are recombined via a power combining arrangement to produce a signal at an output 234 comprising both in-phase and quadrature components.

[0039] The electrodes of the upper and lower Mach-Zehnder interferometers 206, 220 are driven by the output of signal processing units 230, 232, each of which has at least one data input. In particular, each of the signal processing units 230, 232 is configured or programmed to encode the input data into a sequence of electrical pulses, each of which is characterised by a corresponding pulse integral. In this context, the term 'pulse integral' refers to an equivalent total area under a trace of the voltage of the pulse as a function of time. Accordingly, pulses having different pulse integrals may be generated by varying the pulse width (i.e. pulse width modulation, PWM), by varying the pulse amplitude (i.e. pulse amplitude modulation, PAM), by varying the pulse shape, or by any other suitable encoding mechanism.

[0040] In the remainder of this specification, the particular case of varying the pulse integral via pulse width modulation is described, by way of example.

However, the use of this example in order to facilitate understanding of the invention should not be taken to be limiting. A particular advantage of the invention is that a signal suitable to modulate the optical pulses passing through the Mach-Zehnder interferometers 206, 220 may be generated in the form of a single electrical waveform applied to each one of the electrodes 212, 214, 226, 228. As described further below, with reference to Figure 4, the modulation is determined by a period of interaction between the propagating electrical and optical pulses. Various mechanisms for controlling the interaction, including pulse-width modulation, pulse shaping, and/or the introduction of timing offsets, will be described, and/or will be apparent to persons skilled in the art in view of the described examples.

[0041 ] Further details of the waveguide/electrode arrangements of the first embodiment are shown in Figure 3, which illustrates a travelling-wave phase modulator 300 embodying the invention. An electrical electrode 302 having an electrical input 304 and a matched termination 306 is disposed adjacent to an optical waveguide 308 having optical ports 310, 312.

[0042] In accordance with principles of the first embodiment of the invention, electrical signals are input to the electrode and propagate in a first direction, i.e. from left to right as shown in Figure 3. Optical fields, on the other hand, are input from the opposing port 310 of the optical waveguide 308, and propagate in a second direction, i.e. from right to left as shown in Figure 3. Accordingly, the electrical input pulses and optical input pulses are counter-propagating within the travelling-wave phase modulator 300. As will be appreciated, this is contrary to the conventional operation of travelling wave modulators, in which the electrical and optical signals are arranged to co-propagate, in order to maximise the interactions, and hence the phase shift/modulation effect, occurring during transit of the optical fields through the optical waveguide.

[0043] As will now be described, with reference to Figure 4, the counter- propagating arrangement of the electrical and optical fields in this first

embodiment is key to conversion of an electrical pulse integral, e.g. pulse width, into a modulation which is imparted to each one of a series of input optical pulses, in which the modulation is a function of characterising properties, such as the pulse integral and/or a time offset, of a corresponding electrical pulse input to the electrode 302.

[0044] Figure 4 is a space/time diagram 400, showing the position along the modulator 300 on the horizontal axis 402, and time along the vertical axis 404. The total time taken for either an electrical or optical pulse to propagate along the length of the electrode is the single pass propagation delay Tsp. Electrical pulses propagate left-to-right, while optical pulses propagate right-to-left. The velocities of the electrical and optical pulses are thus different, at least insofar as they are opposed in direction (i.e. of opposite sign, if expressed as a scalar value). As shown in the diagram 400, the magnitude of the velocities is substantially identical, as would be the case in a modulator designed for conventional use with matched electrical and optical waveguides. However, as can be appreciated by inspection of the space/time diagram, the overlap period that is essential to the operation of the first embodiment of the invention will exist whether or not the electrical and optical signal velocities have the same magnitude. The timing of the electrical and optical pulses is synchronous, i.e. each electrical pulse corresponds with an optical pulse simultaneously propagating within the modulator 300.

[0045] A rectangular electrical pulse 406 is shown (solid line), having a pulse width t _p , while a 'full-length' pulse (dashed line) has a pulse width 2T _sp . Dark shaded region 408 on the space/time diagram represents propagation of the shorter pulse along the electrode, while the lighter-shaded region 410 represents the additional propagation period of the full-length pulse.

[0046] A short optical pulse 41 2, travelling right to left, will accumulate a phase shift, , due to the electro-optic effect, which is proportional to the integral of the electrical pulse bounded by the time the optical pulse is under a portion of the electrode in which the electrical pulse is propagating. When counter- propagating with the shorter pulse, the relevant overlap is represented by the line segment 414 (A-B), while the overlap with the full-length pulse is represented by the line segment 416 (A-C).

[0047] The integrated phase shift, using a (chirped) modulator with sensitivity V _n , will be:

[0048] In Equation (1 ), Vj _n (t) is the electrical pulse waveform, and the optical and electrical pulses first cross at t = TSP (point A in Figure 4). For a rectangular electrical pulse of amplitude v _max and width t _p , the phase shift is

n.v _ma x.t _p /(2V _n Tsp). To obtain the greatest modulation depth, v _max would be chosen to impart = π when t _p = 2TSP; however, a greater drive voltage enables t _p < 2TSP for a π phase shift, which mitigates the effects of timing jitter or slow edges of the electrical pulse. If a full π phase shift is not required (e.g. to operate a Mach-Zehnder intensity modulator within a linear range) a lower drive voltage and/or shorter pulse width may be employed.

[0049] Additionally, or alternatively, the interaction time, and hence the phase shift, may be varied by adjusting a time offset of each pulse. For example, pulses with a fixed width t _w may be used to generate variable phase shifts by adjusting the timing of the pulses to alter the period of overlap with a corresponding optical pulse propagating adjacent to the electrode. In this approach, an 'early' electrical pulse will partially exit the electrode (i.e. be absorbed by the matched termination 306) prior to arrival of the corresponding optical pulse, reducing the effective interaction time and associated phase shift.

[0050] Accordingly, in some embodiments, phase modulation of optical pulses may be achieved via pulse width modulation (PWM), pulse position modulation (PPM), or a combination of PWM and PPM, of the electrical input signal.

[0051 ] Traveling-wave phase modulators 300 may be incorporated into the modulator structure 200 to achieve in-phase and/or quadrature amplitude and/or phase modulation of optical pulse trains. For example, by driving pairs of electrodes (e.g. 212, 214 or 226, 228) in-phase, pure phase modulation of the optical pulses is obtained. By driving only a single modulator of each pair, or by driving the pairs in opposite phase at lower peak voltage, pure amplitude modulation is obtained.

[0052] In general, the modulators may be driven so as to generate any desired form of modulation based on applied electrical pulse shapes and timing. In alternative embodiments requiring less generality of operation, a simpler arrangement may be employed. For example, pure phase modulation of a single polarisation state can be achieved using a single electrode/waveguide

arrangement such as that shown schematically in Figure 3.

[0053] In embodiments employing the general waveguide arrangement 300, and in which the pulse integrals (e.g. pulse widths, or pulse positions) represent digital information, optical modulators embodying the invention combine the functions of modulation and digital-to-analogue conversion (DAC). The resolution of the DAC will depend on the quantization of the duration of the electrical pulse, compared with its maximum duration (i.e. 2TSP). The baud rate of the DAC is limited to 1 /(2Tsp). Accordingly, short modulators (with a higher electro-optic coefficient to maintain a low drive voltage, such as InP modulators), will be beneficial to increase the baud rate. Additionally, because the output comprises short pulses, signals from multiple modulators can be time multiplexed to increase the baud rate.

[0054] A further advantage of embodiments of the invention is that the time- limited interaction of optical and electrical pulses acts as a filter having a bounded impulse response. In the arrangement 300, for example, this bounded response is of duration 2T _S p. Such a filter introduces no inter-symbol interference (IS I) when t _p < 2Tsp. It would be extremely challenging to implement such a response in a conventional PWM system using passive analog components, as would be required at Gbaud rates, because such filters have unbounded (i.e. infinite) impulse responses. In short, embodiments of the invention enable each pulse in a PWM system to be uniquely mapped to an amplitude-modulated pulse, which maximises the baud rate. [0055] Figure 5 is a block diagram 500 of an exemplary implementation of the first embodiment of the invention which has been verified within a laboratory environment. The experimental embodiment 500 employs an off-the-shelf single- drive chirpless 1 0 Gbit/s LiNbO3 Mach-Zehnder modulator (Sumitomo T.MXH1 .5- 1 0-ADC-P-SC), having an electrode length of approximately 3.5 cm, giving

TSP 256 ps.

[0056] In the embodiment 500, an Ergo MLL 508, generates 2-ps pulses locked to a 1 0-GHz clock 502. To suit TSP, one out of four pulses is retained from the pulse train using an intensity modulator 51 2, driven via amplifier 51 0 by an arbitrary waveform generator (AWG) 504 running at 20 GS/s to produce a suitable carving waveform (1 -in-8) to provide a train of pulses at 2.5 Gpulse/s. The electrical pulses are generated by a 20-Gbit/s bit pattern generator (BPG) 506, locked to the same 1 0-GHz clock 502 as the MLL 508. The BPG 506 enables pulse widths of multiples of 50 ps to be programmed as a train of 1 's and 0's. These pulses are used to drive the Mach-Zehnder modulator 516 via amplifier 514. The timing may be shifted using an adjustable microwave delay line (not shown) in the clock line between the BPG (506) and the MLL (508). The optical output pulses are detected using a Discovery DSC-40 photodiode 51 8 and digitised using an Agilent 28-GHz 80-GS/s real-time sampling oscilloscope 520.

[0057] Figure 6 shows a display 600 of the oscilloscope 520. Three waveforms are displayed: the output 602 of the BPG, showing the programmed variable-length pulses; the output 604 of the photodiode showing short amplitude- modulated pulses; and low-pass filtered version 606 of the pulses 604, for a better indication of the pulse amplitudes. The left-side electrical pulses have incremental widths, t _p , from 50 ps to 400 ps, every 800 ps (1 .25 Gbaud). The output pulse amplitudes 606 are not strictly linearly dependent on t _p , as expected from the raised-cosine response of the modulator 51 6.

[0058] At the right-hand side of of the display 600, a set of 150-ps electrical pulses are shown at a rate of 2.22 Gbaud, so they slide by 50 ps per pulse compared with the MLL pulses. The central optical pulses have similar amplitude, demonstrating that the timing of the electrical pulses is less important than their widths, provided that the electrical pulses are within the electrode region when the optical pulses pass under them (i.e. that pure PWM is employed, without PPM effects).

[0059] Figure 7 shows a graded eye diagram 700 generated on the display of the oscilloscope 520 by programming the electrical pulses to be 3, 4, 5 and 6 x 50 ps wide, to give five amplitude levels including the zero level. The modulator 516 is driven at about 50% of its full modulation depth for a 300 ps pulse. The optical pulse levels are well defined, and would support five-level pulse-amplitude modulation (5-PAM). The timing jitter visible on the display 700 is primarily an artefact of the experimental arrangement resulting from triggering the oscilloscope 520 using a divided clock output of the BPG 506, on its rising and falling edges. The lowest output level corresponds to zero photocurrent, indicating that the extinction ratio of the modulated pulses is good.

[0060] In accordance withthe first embodiment of the invention, an optical modulator employing counter-propagating electrical and optical fields can perform combined functions of a DAC and electro-optic conversion, by converting PWM electrical signals into amplitude/intensity-modulated optical pulses (PAM).

Advantageously, in a pure PWM embodiment there is a direct mapping between the width of one electrical pulse and the intensity of the corresponding optical pulse, i.e. intersymbol interference is avoided. This would be impossible to achieve if the PWM-PAM conversion used analog electrical filters, as in a conventional implementation.

[0061 ] More generally, such embodiments of the invention are based upon a pulse integral and/or time offset of electrical pulses, wherein optical modulation is a function of integration of each electrical pulse bounded by twice the single-pass delay. With pulses counter-propagating at opposite velocities, this process requires only one single pass delay. [0062] As a further advantage, for electrical pulses shorter than twice the transit time of the modulator electrode, this pulse integration may be made independent of the exact timing of the electrical pulse, in order to mitigate the effect of timing jitter.

[0063] Figure 8 is a schematic illustration of an optical modulator 800 comprising a second embodiment the invention which, like the first embodiment 200, may be employed in the IQ modulators 1 12a, 1 12b of the optical transmitter 100.

[0064] The optical modulator 800 receives a train of pulses at input 802, which are divided via an optical power splitter arrangement into two separate waveguide paths. In a first waveguide path 804 (i.e. the upper path of the modulator 800) the signal is input to a Mach-Zehnder interferometer arrangement 806. The Mach-Zehnder interferometer 806 has an upper arm 808 and a lower arm 810. Adjacent, and parallel to, these two optical waveguide arms are corresponding electrodes 812, 814. As is known in the art, the modulator 800 may be fabricated using a nonlinear material such as lithium niobate, or a semiconductor material such as indium phosphide (InP), whereby electrical fields propagating along the electrodes 812, 814 interact via the material to induce phase changes in the optical fields propagating within the waveguide arms 808, 810.

[0065] In a second arm 816 of the modulator 800 a phase shift section 818 induces a 90 degree phase shift in the propagating pulses relative to the pulses propagating in the first arm 804. This results in the generation of signals that are, in terms of the phase of the optical carrier, aligned in quadrature relative to the fields propagating in the first arm 804. The resulting quadrature pulses are input to a second Mach-Zehnder interferometer arrangement 820, which again has upper and lower arms 822, 824 and adjacent electrodes 826, 828. [0066] The outputs of the first and second Mach-Zehnder interferometers 806, 820 are recombined via a power combining arrangement to produce a signal at an output 834 comprising both in-phase and quadrature components.

[0067] The electrodes of the upper and lower Mach-Zehnder interferometers 806, 820 are driven by the output of signal processing units 830, 832, each of which has at least one data input. In particular, each of the signal processing units 830, 832 is configured or programmed to encode the input data into a sequence of electrical pulses, each of which is characterised by a corresponding pulse integral. As described further below, with reference to Figure 10, modulation of optical pulses in the modulator 800 is determined by a period of interaction with the propagating electrical and optical pulses.

[0068] Further details of the waveguide/electrode arrangements of the second embodiment are shown in Figure 9, which illustrates a travelling-wave phase modulator 900 embodying the invention. An electrical electrode 902 having an electrical input 904 and a matched termination 906 is disposed adjacent to an optical waveguide 908 having optical ports 910, 912.

[0069] In accordance with principles of the second embodiment of the invention, electrical signals are input to the electrode and propagate from left to right as shown in Figure 9. Optical fields are input from the optical port 910 of the optical waveguide 908, and co-propagate with the electrical signals, i.e. in the same direction along the waveguide. The key to providing the desired modulation in this embodiment of the invention is to configure the electrode 902 and/or the optical waveguide 908 such that the velocities (specifically, group velocities) of the propagating electrical and optical pulses are different. As will be appreciated, this is contrary to the conventional operation of travelling wave modulators, in which the electrical and optical signals are arranged propagate at the same velocity, in order to maximise the interactions, and hence the phase

shift/modulation effect, occurring during transit of the optical fields through the optical waveguide. [0070] As will now be described, with reference to Figure 10, co-propagation of the electrical and optical fields at different velocities in this second embodiment is key to conversion of an electrical pulse integral, e.g. pulse width, into a modulation which is imparted to each one of a series of input optical pulses, in which the modulation is a function of characterising properties, such as the pulse integral and/or a time offset, of a corresponding electrical pulse input to the electrode 302.

[0071 ] Figure 10 is a space/time diagram 1000, showing the position along the modulator 900 on the horizontal axis 1002, and time along the vertical axis 1004. The time taken for electrical and optical pulses to propagate along the length of the electrode 902 is different. Hereafter, the pulse group velocities are designated v _e i _ec and v _op t respectively, while the corresponding electrode transit times are T _e i _ec and T _opt . In the example shown, v _e i _ec < v _op t, i.e. T _e i _ec > T _op t. The timing of the electrical and optical pulses is synchronous, i.e. each electrical pulse corresponds with an optical pulse simultaneously propagating within the modulator 900.

[0072] A 'short' rectangular electrical pulse 1006 is shown (solid line), having a pulse width T _s , while a 'long' pulse (dashed line) has a pulse width T|. Light shaded region 1008 on the space/time diagram represents propagation of the shorter pulse along the electrode, while the darker-shaded region 1010

represents the additional propagation period of the full-length pulse. The duration T| of the long pulse in the diagram 1000 has been selected such that it is the shortest pulse that results in interaction with an optical pulse along the full length of the electrode 902. This length is hereafter designated L.

[0073] A short optical pulse 1012, travelling left to right, will accumulate a phase shift, , due to the electro-optic effect, which is proportional to the integral of the electrical pulse bounded by the time the optical pulse is under a portion of the electrode in which the electrical pulse is propagating. With v _op t > v _e i _ec the optical pulse 'catches up' with and 'overtakes' the electrical pulse, and it is during this period T ₀ i that the overlap occurs When co-propagating with the shorter pulse, the relevant overlap is represented by the line segment 1014, while the overlap with the full-length pulse is represented by the line segment 1016.

[0074] For a case in which the period of overlap occurs entirely within the length L corresponding with the electrode 902, the duration of the overlap is given by:

T _ol = T _s (2) opt elec

The integrated phase shift, using a (chirped) modulator with sensitivity II then be:

ΔΘ = -| _ο v _in (t) dt (3)

[0076] For a rectangular electrical pulse of amplitude v _max the phase shift is n.v _ma x.t _p /(2V _n T ₀ i). It will be noted that the maximum 'useful' electrical pulse width, represented by the long pulse of duration T| in Figure 10, is given by: v opt

(4)

V opt V el ,ec

[0077] An electrical pulse longer than this cannot provide any additional interaction with the optical pulse, although longer pulses may be employed to mitigate the impact of timing jitter and/or slow electrical pulse edges. Thus, to obtain the greatest modulation depth, v _max can be chosen to impart = π when t _p = T| as computed from Equation (4). If a full π phase shift is not required (e.g. to operate a Mach-Zehnder intensity modulator within a linear range) a lower drive voltage and/or shorter pulse width may be employed. [0078] Additionally, or alternatively, the interaction time, and hence the phase shift, may be varied by adjusting a time offset of each pulse. For example, pulses with a fixed width t _w may be used to generate variable phase shifts by adjusting the timing of the pulses to alter the period of overlap with a corresponding optical pulse propagating adjacent to the electrode. In this approach, an 'early' electrical pulse will begin to exit the electrode (i.e. be absorbed by the matched termination 906) prior to the corresponding optical pulse completing its transit of the associated region of the waveguide, reducing the effective interaction time and associated phase shift.

[0079] Accordingly, in some embodiments, phase modulation of optical pulses may be achieved via pulse width modulation (PWM), pulse position modulation (PPM), or a combination of PWM and PPM, of the electrical input signal.

[0080] As with the counter-propagating configuration 300, traveling-wave phase modulators 900 in the co-propagating configuration may be incorporated into the modulator structure 200 to achieve in-phase and/or quadrature amplitude and/or phase modulation of optical pulse trains.

[0081 ] In embodiments employing the general waveguide arrangement 900, and in which the pulse integrals (e.g. pulse widths, or pulse positions) represent digital information, optical modulators embodying the invention combine the functions of modulation and digital-to-analogue conversion (DAC). The resolution of the DAC will depend on the quantization of the duration of the electrical pulse, compared with its maximum useful duration (i.e. T|). The baud rate of the DAC is limited to 1 /T|. However, as shown by Equation (4) this will generally be higher than the maximum baud rate of an embodiment employing counter-propagating modulators of similar physical size, for which the baud rate is 1 /(2Tsp), where 2T _sp = 2Lv _op t = 2Lveiec- Furthermore, it also follows from Equation (4) that higher baud rates are achievable by designing modulators with smaller differences in optical and electrical propagation velocities, and that this approach can be combined with longer electrodes in order to maintain the interaction periods using shorter pulses, so as to reduce the required drive voltage for a given phase shift.

[0082] This baud rate advantage of co-propagating embodiments is illustrated by the examples summarised in Tables 1 and 2.

Table 1 : Relatively large difference in optical and electrical pulse velocities

Table 2: Relatively small difference in optical and electrical pulse velocities [0083] Co-propagating embodiments of the invention retain the advantage that the time-limited interaction of optical and electrical pulses acts as a filter having a bounded impulse response, being of duration T|.

[0084] In order to further demonstrate the above properties of co-propagating embodiments of the invention, a number of numerical simulations have been performed, using a modulator model as depicted in the block diagram 1 100 of Figure 1 1 . The model comprises an optical pulse source 1 102, and an electrical rectangular pulse generator 1 104. The pulse source is combined with a continuous wave (CW) source 1 106 in combiner 1 108. The CW source enables the effects of the total accumulated phase shift created by the electrical pulses to be observed in the simulation output.

[0085] A Mach-Zehnder intensity modulator is modeled via splitter 1 1 10, which dvides the combined optical signal into two optical paths. The upper path comprises a series of discrete delays 1 1 12a, 1 1 12b etc, which together represent the propagation delay in one arm of the interferometer. The bottom path comprises a corresponding series of delays 1 1 16a, 1 1 16b, etc, along with phase modulators 1 1 14a, 1 1 14b, etc, which together represent the modulation applied by the traveling-wave electrode driven by the pulses generated by the electrical source 1 104. The electrode itself is modeled by a series of delays 1 1 18a, 1 1 18b etc, which are different from the corresponding optical delays 1 1 12a, 1 1 12b, 1 1 16a, 1 1 16b etc, in order to model the mismatched propagation velocity of the electrical pulses.

[0086] The optical signals in the two paths of the interferometer are

recombined by combiner 1 120 to generate the intensity modulated output 1 122.

[0087] Figure 12 shows the simulated response 1200 for a design having T ₀ pt = 400 ps and T _e i _ec = 800 ps, in which the simulation employs eight discrete delay stages to model the modulator. The horizontal axis 1202 shows time in nanoseconds, while the vertical axis 1304 shows output power in milliwatts. The electrical pulses in the simulation were varied from 1 to 8 units in width, where each unit was 50 ps. The maximum rate of operation for this configuration is 2.5 Gbaud. A first series of output pulses shows half-rate operation (i.e. at 1 .25 Gbaud). An optical pulse output, e.g. 1206, corresponds with the pulsed inputs from source 1 102, while a 'pedestal', e.g. 1208, corresponds with the output resulting from the CW source 1 106. This enables the total response of the modulator to pulses of increasing width, as well as the pulse amplitude

modulation, to be observed. The 'steps' visible in the simulation results are an artefact of the discrete-delay model, and approximate a continuous output that would be observed in a real device. A second series of output pulses 1210 demonstrates operation at the maximum rate of 2.5 Gbaud.

[0088] Figure 13 shows a corresponding simulated response 1300 for a design having T _opt = 400 ps and T _e i _ec = 500 ps. The horizontal axis 1302 shows time in nanoseconds, while the vertical axis 1304 shows output power in milliwatts. The electrical pulses in the simulation were varied from 1 to 8 units in width, where each unit was 12.5 ps. The maximum rate of operation for this configuration is 10 Gbaud. A first series of output pulses shows half-rate operation (i.e. at 5 Gbaud). An optical pulse output, e.g. 1306, corresponds with the pulsed inputs from source 1 102, while a 'pedestal', e.g. 1308, corresponding with the output resulting from the CW source 1 106. This enables the total response of the modulator to pulses of increasing width, as well as the pulse amplitude modulation, to be observed. A second series of output pulses 1310 demonstrates operation at the maximum rate of 10 Gbaud.

[0089] While particular embodiments have been described, in order to illustrate the general principles of the invention, many variations and modifications will be apparent to persons skilled in the art. For example, embodiments of the invention employing InP waveguides would allow electrode lengths of less than 4 mm, supporting a rate of at least 1 1 Gbaud. Time division multiplexing of the outputs of several modulators may be used to further increase the baud rate. [0090] The scope of the invention is therefore not limited by the particular embodiments desclosed herein, but rather is as defined by the claims appended hereto.