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A novel method of converting binary-level electrical pulses into multi-level optical pulses using only a conventional traveling-wave optical modulator is presented. The method provides low inter-pulse interference due to the counter-propagating pulses, low amplitude noise, and a timing jitter determined chiefly by the quality of the optical pulse source. The method only requires one electrical drive per modulator and provides low-jitter variable-amplitude optical pulses that are suitable for shaping into a wide variety of modulation formats using a programmable optical filter.
© 2014 Optical Society of America
1. Introduction
High-level modulation formats, such as 16-QAM, offer higher spectral efficiencies [1], but usually require electrical Digital to Analog Converters (DACs) at the transmitter, which consume significant power, partially because of the impedance-matched terminations on their parallel time-multiplexed high-speed electrical inputs. DACs are also required to implement electronic pre-distortion [2] and forms of optical OFDM that use Fourier-transform generated combs of subcarriers [3].
In this paper, a new method of converting variable-width electrical pulses into high-quality ultra-short multi-level optical pulses is presented. This can implement a multi-bit DAC using a conventional LiNbO3 optical modulator, but with its optical and electrical signals counter-propagating. Counter-propagating optical and electrical signals have been used previously [4,5], but with a continuous wave optical source rather than pulses, and for filtering to create optical duobinary modulation rather than to implement a DAC. The multi-level pulses are ideal for conversion to almost any modulation format, using optical filtering, as we have previously demonstrated to produce a universal transmitter [6], shown in Fig. 1, if a pair of counter-propagating modulators is used to create a complex optical modulator for quadrature amplitude modulation. An advantage is that variable width electrical pulses are easier to communicate between the digital signal processor and complex modulator than parallel binary inputs to a DAC.
Fig. 1 Application example showing pulse source, counter-propagating optical modulators, and a Reconfigurable Optical Switch (ROS) to create signals of any modulation format by appropriately filtering the modulated inputs to the ROS. For example, for OFDM, each filter generates a subcarrier by converting each modulated pulse into an integer number of cycles occupying an OFDM symbol.
In Section 2 we present the principle of this technique. Section 3 demonstrates the technique with an off-the-shelf modulator. Section 4 discusses alternative methods and performance improvements. Section 5 is the conclusions. This paper is an extension of a recent post-deadline paper at OECC/ACOFT 2014 [7], with a new low-jitter experimental setup that uses a single bit pattern generator, and new results including: jitter measurements, estimates of amplitude noise and corresponding bit error ratios, and an extended discussion including estimates of bit rates after multiplexing.
2. Principle of operation
A conventional optical modulator arranges the electrical drive to propagate along its electrical waveguide at the same velocity (i.e., direction) as the optical wave propagates along its waveguide [8]. This ensures that a small portion of the electrical signal interacts with a small portion of the optical wave, imparting a phase shift onto that part of the optical wave. This maximizes the modulation bandwidth of this travelling wave (TW) design, while retaining a long interaction length to lower the drive voltage required for enough phase shift to switch the modulator between off and on.
If the direction of the optical wave is reversed, then the electrical and optical pulses interact as they pass by one-another, as shown in Fig. 2 (top), which represents one arm of a Mach-Zehnder Interferometer (MZI) modulator. The interaction is represented in Fig. 2 (bottom) as a space-time diagram, with the variable-duration electrical pulse traveling left to right. A short optical pulse, traveling right to left, will accumulate a phase shift, Δθ, due to the electro-optic effect, which is proportional to the integral of the electrical pulse bounded by the time the optical pulses is under the electrode. The MZI structure converts this phase change into an intensity variation. The integrated phase shift, using a (chirped) modulator with sensitivity Vπ, will be:
where: vin is the electrical pulse, TSP is the single-pass propagation delay (electrical or optical) in the interaction region, and the optical and electrical pulses first cross at t = TSP (Point A in Fig. 2) and last cross at Point C.Fig. 2 Side view of one arm of the optical an optical modulator (top). Overlap of the counter-propagating electrical and optical pulses (bottom).
For a rectangular electrical pulse of amplitude vmax and width tp, the phase shift is πvmaxtp/(2VπTSP). To obtain the greatest modulation depth, vmax would be chosen to be Vπ to impart Δθ = π when tp = 2TSP; however, a greater drive voltage will mean that tp < 2TSP gives π phase shift, which mitigates the effects of timing jitter or slow edges of the electrical pulse.
The resolution of the DAC will depend on the quantization of the duration of the electrical pulse, compared with its maximum duration (e.g. 2TSP). The baud rate of the DAC is limited to 1/(2TSP). Obviously short modulators (with a higher electro-optic coefficient to maintain a low drive voltage), will be beneficial to increase the baud rate, e.g. InP modulators [9]. Additionally, because the output is short pulses, pulses from multiple modulators can be time multiplexed to increase the baud rate. For Quadrature Amplitude Modulation (QAM), a complex, or IQ, modulator structure can be used.
3. Experimental demonstration of principle
Figure 3 shows the equipment set up. The technique was demonstrated using an off-the-shelf single-drive chirpless 10 Gbit/s LiNbO3 Mach-Zehnder modulator (Sumitomo T.MXH1.5-10-ADC-P-SC), with an electrode length of approx. 3.5 cm, giving TSP ≈250 ps. A JDSU Erbium-doped Glass Oscillator (ERGO) mode-locked laser (MLL), generated 2-ps pulses phase-locked to a 10.0016-GHz clock from an RF synthesizer. To suit TSP, one out of eight pulses was retained from the pulse train using an intensity modulator as a pulse carver (or selector). This was driven with short pulses – a 1:15 mark to space waveform from a programmable bit pattern generator (BPG), which is designed to produce a bit rate of twice the clock frequency of the RF generator (20.0032 Gbit/s). Thus the carved pulses are at a rate of 1.25 Gpulses/s. These are amplified by an Erbium-Doped Fiber Amplifier (EDFA) and their polarization aligned for maximum signal power of the second modulator, which is used in reverse; that is, its optical output is used as an optical input. The electrical pulses to drive the second modulator were generated by the same BPG by time-multiplexing its output. That is, for 128 bits, the BPG produces pulse-carving bits, and for 128 bits, it produces signals to drive the counter-propagating modulator. This saves the cost of an additional BPG and reduces jitter between the modulators, but requires the lengths of fibers and microwave cables to be selected so that the counter-propagating modulator receives appropriately aligned data signals to modulate the carved pulses from the first modulator. The electrical signals to both modulators were amplified by SHF807 linear amplifiers with bandwidths of 30 GHz. The electrical signal to the first modulator was shaped using a short adjustable microwave stub line with a short circuit, connected to the main line using a microwave power divider. This produced a short negative voltage pulse that could be placed just before the positive voltage pulse from the BPG to suppress the MLL pulse prior to the desired pulse. The optical output pulses of the second modulator were detected using a 16-GHz Discovery DSC-40S photodiode and digitized using an Agilent 28-GHz 80-GS/s real-time sampling oscilloscope.
Figure 4 shows two waveforms: (upper) a portion of the output waveform of the BPG that has programmed with variable-length pulses (with inserted zeros); (lower) the output of the photodiode showing the four corresponding short amplitude-modulated pulses. The electrical pulses have incremental widths, tp, in steps of 50 ps. The height of the corresponding optical pulse is approximately the integral of the electrical pulse (Eq. (1), but the nonlinearity of the modulator’s phase-to-intensity response has to be taken into account. The optical pulses each have a pre-pulse due to the limited bandwidth of the pulse-carver allowing the part of previous mode-locked laser pulse through it. This issue could be addressed with a higher-bandwidth pulse carver, a lower repetition-rate mode locked laser, or a shorter counter-propagating modulator that could operate at a higher baud rate. We found that the peak power levels of the optical pulses could be finely tuned by inserting a 0-bit in between the 1’s of a drive pulse. This works because of the limited bandwidth of the drive signal, which prevents the voltage dropping fully to zero during a single 0-bit – this can be seen with the first electrical pulse. Our previous paper [7] showed that the exact timing of the electrical pulses is unimportant.
Fig. 4 Sampling oscilloscope traces of: (top) the electrical drive to the Reverse TW modulator, (bottom) the detected optical pulses. The timebase is 400 ps per division.
Figure 5 is a color-graded eye diagram of the optical pulses, with the oscilloscope triggered off the system clock divided by 64 to superimpose the pulses. This shows that the optical pulses are all aligned in time, as they are all generated by the same mode-locked laser and travel through the same optical path. The optical pulse levels are well-defined and stable, and would support at least 5-levels of PAM; we used 5 levels in this demonstration because the BPG had sufficient memory for only 4 different pulses. The lowest output level corresponds to almost zero photocurrent; that is, the extinction ratio is good; however, there is some leakage of unwanted MLL pulses through the pulse carver due to its limited bandwidth and ringing in the output pulses from the BPG. The PAM pulses were adjusted to have equal power differences, by programming the bit sequence fed to the counter-propagating modulator: the highest pulse used a sequence of nine ‘1-bits’, each of 50 ps; the next used six 1-bits; the next used 1-1-1-0-1-1; the next 1-1-0-1-1. The purpose of the 0-bits between the 1-bits is to provide some fine tuning as the electrical response of the modulator and driver will not drop the drive level fully to a zero level. The higher level pulses have more amplitude noise, as expected from the Amplified Spontaneous Emission (ASE) from the EDFA mixing with the signal power at the photodiode, especially as there is no optical filter in the system after the EDFA.
Fig. 5 Color-graded eye diagram of 5-PAM pulses. Horizontal scale 50ps/division. Note the ghost pulses at 100-ps intervals due to the imperfect performance of the pulse carver.
3.1 Intensity noise of pulses
A low variation in the intensity of the pulses compared with their amplitudes allows for a greater number of levels to be encoded or gives a margin for signal degradation during transmission. An advantage of the proposed system is that the modulator performs an integrating function (Eq. (1) which reduces the amplitude noise of the modulation and also ignores the jitter of the electronic signal, within the limits of integration [7]. The disadvantage is that the baud rate of a single modulator is comparatively low, unless it is redesigned, as discussed Section 4.
Figure 6 is an expanded eye diagram of a 5-PAM signal at 10 ps/division including vertical histograms taken at the peaks of the pulses (+/− 500 fs), plotted at the left-hand axis of the graph. All of the pulses were measured to be 25-ps wide (FWHM), though they are expected to actually have similar widths to the MLL pulses (2 ps), as there is no filtering in the optical path. The photodiode has a 16-GHz −3-dB response, which converts to a 22-ps rise-time; the oscilloscope has a 14.4 ps rise-time (10% – 90%). Together they average (geometrically) to a rise-time of 26 ps, which would more than account for the broadening of pulse displayed on the oscilloscope, compared with the MLL pulsewidth.
Fig. 6 Color-graded oscilloscope trace of a 5-PAM eye. Horizontal scale 10ps/division. Vertical scale is 22 mV/division. The vertical histogram plots are shown on the left hand vertical axis. The statistics for these are in Table 1.
The statistics from each pulses’ peak level were gathered individually by placing a 1-ps wide box around the peak of each pulse and forming a histogram from at least 10,000 ‘hits’ within each box (approximately 5 minutes). The standard deviations of the five levels are set out in Table 1. The average voltage between levels is 32 mV and the minimum was 29 mV, so a mean difference of 30 mV was used for Bit Error Ratio (BER) calculations. The signal quality, q, values were calculated from the mean level difference, μave, and the standard deviation of level n, σn, using
and then these q-values were used to estimate the error ratios per level based onfor the middle levels, and one half of this error rate value for the zero and highest levels (as they only see one threshold, rather than two). Note that this estimate does not account for Gray coding of pairs of bits [10]. As is well known for amplified systems, the BERs in Table 1 suggest that unequal level spacing could be used to equalize the BERs so that the average BER (4.1 × 10−11) is not dominated by the errors in the uppermost level. Alternatively, pairwise coding could be used between the best and worst levels, second-best and second-worst levels, and so on, to greatly improve the overall BER [11]. Of course, additional levels could be interspersed, though enough noise margin should be included to accommodate the noise introduced throughout the transmission system. In any case, the BERs are much better than required for systems using Forward Error Correction (FEC).
Table 1. Statistics of the Pulses in Fig. 6 Including Estimated BERs
3.2 Timing jitter of pulses
A low timing jitter enables optical time-division multiplexing of the pulses to much higher rates. The jitter of these pulses is extremely low, because they are sourced from a JDSU ERGO (Erbium Glass Oscillator) mode-locked laser that has a specified jitter of <100 fs r.m.s., and the phase locked loop provided with the ERGO indicated a jitter under 70 fs in the experiment. However, additional jitter could possibly be introduced after the MLL by preferentially selecting the rising or falling edges of the pulses during modulation, or by the addition of optical noise, for example.
The jitter of the optical pulses relative to the RF signal source was measured by triggering the oscilloscope on the highest-level optical pulses, then measuring the jitter on the optical signal. This should yield the same result as triggering on the RF source and measuring the optical pulse; however, it is more practical as the wanted optical pulse only occurs every 128 RF cycles. Figure 7 shows the measured RF sine-wave (pink) and optical pulse (yellow), plus a histogram of the timing of the zero-crossing point of the RF signal. The oscilloscope estimates the relative jitter at 351 fs r.m.s., which may be inflated by the finite vertical width of the histogram box (white). As a comparison the oscilloscope has a specified triggering jitter of
which is dominated by the noise of the optical signal. In our case the noise is around 3 mV from the histogram measurements scaled to this pulse height and the slew rate is 6 mV/ps, giving a maximum jitter due to triggering of 510 fs. Thus, the actual jitter is most probably far less than can be measured by this equipment. Even so, the measured values of jitter would enable high-rate optical time division multiplexing.Fig. 7 Measurement of the relative jitter of the optical pulses (yellow) and the RF reference clock from the RF signal generator (pink). The oscilloscope was triggered from the optical pulses, because this allows the highest optical pulse to be selected. The histogram measures the zero crossing jitter of the RF signal. The oscilloscope calculates the jitter as 350.84 fs r.m.s.
4. Discussion
The actual data rate that could be supported by this technique is dependent on the multiplexing and modulation that could be used for the pulses. Given that the pulses are 2-ps wide, it would be possible to time-division multiplex to 4 ps apart, giving 250 Gpulses/s. If each is modulated with 4-PAM, then 1 Tbit/s could be carried on two polarizations. The low amplitude jitter of the pulses shows that higher-order QAM is possible, for short links at least; 16-PAM would double the capacity. A better approach is to use complex modulation, such as 256-QAM to double the capacity yet again, to 4-Tbit/s on two polarizations. This could be achieved using complex modulators, again using counter-propagating pulses. Alternatively, the pulses could be optically filtered, to broaden and shape them into different modulation formats, and also reduce their bandwidth. Then, wavelength division multiplexing, such as OFDM or Nyquist-WDM, could be applied. Spectral broadening of the MLL spectrum can support signals covering most of the C-band, to further increase the data rate, as has been demonstrated with OFDM [12], for example.
An advantage of this technique of generating multi-level pulses is that only one electrical drive line is required to the modulator per quadrature, so there only need be one termination resistor (at the end of the modulator’s electrical waveguide), rather than at least m terminations for the inputs to a m-bit DAC. This reduction also allows many modulators to be driven from a single Field-Programmable Gate Array, with its limited number of high-speed outputs. On first sight, a simpler idea might be that an electrical filter could convert variable-duration pulses into an analog waveform, which then drives a modulator. This method is often used to provide low-speed analog outputs for microcontrollers: the low-pass filter, implemented using analog electronics, averages over many pulses, so that it strongly suppresses the clock (pulse) frequency. In our case, this would cause long-term inter-symbol interference (ISI) – the modulation intended for one optical pulse would affect many subsequent pulses. This is a key advantage of our technique, in that the interaction of optical and electrical pulses acts as a filter with a bounded impulse response with a duration 2.TSP, so theoretically has no ISI when tp< 2.TSP. It would be virtually impossible to implement such a response using passive analog components, as would be required at Gbaud rates, because such filters have unbounded responses. In short, our technique allows each pulse in a PWM system to be uniquely mapped to an amplitude-modulated pulse, which maximizes the baud rate.
The speed of this DAC is limited by two main effects. The first is the integration time 2TSP; a new electrical pulse should not be input before the previous pulse has ended. Using InP waveguides would allow a reduction of the electrode lengths to <4 mm [13], but with an increase in refractive index from 2.2 to 3.2 [14]. This could support a rate of 11 Gbaud, or more for a shorter waveguide. A silicon modulator would give a similar performance to InP. Optical time division multiplexing of the outputs of several modulators would further increase the baud rate. The second speed limit is the PWM waveform, which is usually quantized by the clock period of the electronics generating this waveform. Thus, the generating clock should be log2(m) faster than the baud rate of the system, for m-bit conversion. However, it is also possible to generate variable-length digital pulses that are not quantized by the system clock, for example by adjusting the threshold on a comparator fed with a bandwidth-limited pulse, or by selecting a tap along a chain of logic buffers, each with a delay equal to a fraction of the clock period. Also, because the area under the electrical pulse is the key variable, there are many possible pulses shapes that can be used to transfer information to the modulator. These could be constructed by summing outputs of an FPGA [15], with the advantage that the exact timing of the edges of the outputs is unimportant [7]. Furthermore, if the electronics is bandwidth limited, pulse sequences with different frequency spectra will convert to different optical levels, as we used to tune the levels of Figs. 5 and 6.
5. Conclusions
We have shown that a conventional optical modulator can convert pulse-width modulated (PWM) electrical signals into high-quality amplitude/intensity-modulated optical pulses (PAM). Advantageously, there is a direct mapping between the width of one electrical pulse and the intensity of the corresponding optical pulse, that is, zero intersymbol interference. The timing jitter and amplitude noise of the optical pulses are defined by the mode-locked laser, and are extremely low, allowing subsequent multiplexing and format conversion using optical signal processing.
Acknowledgment
AJL is supported by the Australian Research Council’s Laureate Fellowship (FL130100041).
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