We have demonstrated for the first time to our knowledge, the conversion of 10 Gb/s non-return-to-zero (NRZ) on-off keying (NRZ-OOK) to RZ-OOK using cross-phase modulation (XPM) in a compact, Silicon (Si) nanowire and a detuned filter. The pulse format conversion resulted in a polarity-preserved, correctly-coded RZ-OOK signal, with no evidence of an error-floor for BER < 10−11. The advantages of a passive Si nanowire can lead to a compact, power-efficient, highly simplified configuration, amenable to chip-level integration.
©2009 Optical Society of America
1.1 The NRZ and RZ pulse formats
For amplitude-modulated, direct-detection optical communication systems, there are two possible pulse formats: The return-to-zero (RZ) format in which a power is transmitted for a fraction of the bit slot, and the non-return-to-zero (NRZ) format, for which a constant power is transmitted during the entire bit slot. A widely-used metric for evaluating modulation formats is receiver sensitivity, typically stated as the average received power (or optical signal-to-noise ratio (OSNR)) required to achieve a specific BER, usually set to 10−9 in the absence of forward error-correction. It has been experimentally found that for a given average optical power at the receiver, the sensitivity of a receiver improves for pulses of duration shorter than the bit slot, resulting in a sensitivity advantage in the range of 2-4 dB for RZ relative to NRZ [1–4], and this enhancement is obtained for the same receiver hardware. This advantage may be understood from the fact that as the pulse energy is more confined about the center of the bit-slot for the RZ format, its performance is determined by a rejection trade-off between signal energy and detection noise . On the other hand, since the NRZ format is constant over a bit slot, its performance is limited by a balance between inter-symbol interference (ISI) and detection noise . For the same receiver hardware, it was also found that the RZ sensitivity advantage rapidly reaches a limit as the RZ pulse duty cycle is reduced significantly below 50% [6,7].
In optically pre-amplified receivers deployed in conventional ultra long-haul (ULH) fiber-optic systems, the multiple-dB receiver sensitivity advantage of the RZ format can lead to a significant improvement in transmission distance for a given BER. For instance, a 3 dB advantage doubles the reach in an ASE-limited transmission system , which may be traded against a data-rate upgrade . An upgrade from 10 Gb/s NRZ-OOK to 40 Gb/s NRZ-OOK results in an additional 6 dB OSNR requirement for the same performance, due to a 6 dB bit-power reduction at 40 Gb/s relative to 10 Gb/s for the same average powers. However, the use of RZ-OOK instead of NRZ-OOK at 40 Gb/s can mitigate this constraint by at least 2 dB.
Other, χ (3)-induced propagation impairments, in addition to ASE, also favor the RZ format in ULH transmission systems. Since the dispersion length of a fiber span varies as the square of the pulse-width, the RZ-OOK pulse disperses rapidly as it propagates, significantly alleviating the self-phase modulation (SPM) effect in the process due to a lowered peak power, after which the pulse is re-compressed in dispersion compensating fiber (DCF) [1,10]. Combined with the receiver advantage of RZ-OOK, the net result is a significantly longer transmission distance relative to NRZ-OOK, which requires distance-dependent dispersion under-compensation prior to reception . It was also experimentally found that RZ-OOK is more robust to power variations due to its higher tolerance to SPM . The RZ benefit is not unique to OOK, and has also been confirmed for DPSK in a DWDM experiment .
Another propagation impairment to be considered, especially as transmission rates exceed 10 Gb/s, is polarization-mode dispersion (PMD), which can cause fading of the baseband signal in high bit-rate transmission . Most experimental investigations seem to be in agreement however, that the RZ format is more robust to PMD than the NRZ format even after transmission, once again due to a better energy confinement [13–17]. In a 10 Gb/s experiment for instance , it was found that RZ-OOK was more tolerant to PMD, compared to NRZ-OOK, which suffered substantially more ISI due to PMD-induced pulse broadening. However, Winzer et al.  have pointed out that the relative performance of the two formats can also be dependent on the design of the receiver.
Due to its cost-effectiveness and simplicity of implementation, the NRZ-data transmitter is more suitable for dispersion-tolerant short-haul and metropolitan area networks where nonlinear impairments are relatively more limited: By contrast, the RZ-data transmitter requires a pulsed source that adds complexity and expense that may not be justified for short-haul networks. In fact, the RZ pulse format is either generated by sinusoidally driven modulators, or entirely in the RF domain using high-speed / bandwidth components. In the former, either an electro-optic or an electro-absorption modulator [19–22] is driven by a clock signal, requiring accurate synchronization with the data modulator ; while the latter requires gating the baseband NRZ data by the clock signal prior to impressing the data on the optical carrier [24–26]. Irrespective of implementation, as it has been shown that the RZ format is more tolerant to SPM and PMD, and due to its receiver sensitivity benefit relative to the NRZ format, some ULH systems have already been upgraded with the RZ format. Therefore, NRZ-pulsed WDM channels may be converted to the RZ format at the gateways (or cross-connects), when switched from the short-haul links to the ULH ones.
1.2 Techniques of conversion of NRZ-data to RZ-data by XPM
The established benefits of the RZ format has motivated the exploration of various format conversion techniques, which include XPM, and four-wave mixing (FWM), both of which utilize a pump-probe configuration in which a periodic pulse train serves as the pump, with the NRZ-data being the probe. Other techniques involving phase modulation followed by interferometry have also been reported. Of all these techniques, XPM tends to be the simplest as well as power-efficient, the result of which, unlike FWM, is format conversion close in wavelength to the NRZ-data.
Conversion has been carried out in active devices such as commercial bulk semiconductor optical amplifiers (SOAs) in various configurations. In SOAs, cross-gain modulation is coupled to XPM by the device Henry alpha-factor. Due to a relatively slow (~200 ps) carrier life-time, bulk SOAs usually require some form of interferometry for bit-rate scalability which can complicate the overall conversion configuration. In one experiment, Yang et al.  achieved a conversion enhancement of ~2 dB at 42.6 Gb/s, utilizing an SOA followed by a Mach-Zehnder interferometer. In another experiment, Lee et al.  used a SOA integrated with a Sagnac fiber interferometer for an enhancement of 2 dB at 10 Gb/s. SOAs present the potential of achieving signal gain along with format conversion. SOAs also tend to be polarization insensitive to within 1 dB, although the use of interferometers in such techniques can exacerbate polarization effects. Format conversion has also been carried out in SOAs using cross polarization modulation (XPolM), a form of XPM in which the TE and TM components of the probe acquire different phase shifts due to co-propagation with the intense pump. In this approach, the SOA must be followed by a polarization controller and a polarizer to affect the desired format conversion. Recently, Yang et al.  have demonstrated format conversion using XPolM in SOAs in a ‘turbo-switch’ configuration, but despite the use of a 3-ps-pulsed pump, a penalty of more than 2 dB was observed for the resultant RZ-OOK relative to baseline NRZ-OOK.
Conversion has also been carried out in fiber, utilizing the ultra-fast (~1 fs) χ (3) effect. Lee et al.  demonstrated conversion in which the pump and the probe co-propagate in a 3.5-km-long dispersion shifted fiber (DSF) integrated in a Sagnac configuration, although no BER data was presented. More recently, Kwok and Lin  have examined format conversion by XPM in both single-polarization and polarization-diversified configurations, using two fibers for each: a 64-m-long photonic crystal fiber (PCF), and a 3-km-long DSF. Respective conversion power penalties of 1 dB and 2 dB relative to baseline RZ-OOK were obtained for the PCF and DSF, and were ascribed to insufficient nonlinear phase shift. Format conversion employing fiber typically results in a large foot-print due to a weak nonlinear coefficient (0.001 – 0.01 W−1m−1), and consequently, long effective lengths and high-power requirements. However, format conversion in fiber is inherently scalable to higher bit-rates unlike SOAs, facilitated by the ultra-fast χ (3) effect. Format conversion utilizing fiber is also amenable to integration with fiber-based systems, and the use of polarization diversity can render the conversion polarization insensitive to within 1 dB, while exacerbating the overall foot-print of the implementation .
Instead of using XPM in nonlinear media to facilitate format conversion, the probe can be cross-modulated by a clock signal in a commercial phase modulator, after which a detuned filter can be used to convert the phase modulation to amplitude modulation. This technique was first demonstrated by Lu et al. , who showed a format conversion enhancement of ~2.4 dB. The addition of an asymmetric MZI between the phase modulator and the detuned filter could also result in regenerative format conversion . The technique has the advantage of power efficiency and although not compact, is still amenable to integration. In another technique, due to Yu et al. , the NRZ-OOK signal is passed through an asymmetric MZI, in which the signal and its replica acquire different phases. The output of the MZI then yields a RZ-duobinary (or RZ-alternate-mark-inversion) signal at the constructive (or destructive) port. A conversion enhancement of 0.8 dB was obtained. Although once again power-efficient and compact, the duty cycle of the RZ signal is limited by the rise-time of the NRZ-OOK signal. Moreover, the resultant RZ signal is incorrectly encoded in the process, requiring a decoder at the receiver for correct reception.
1.3 Potential of NRZ-data conversion by XPM in a Si nanowire
We have previously reported on the characterization of a Si nanowire. The nanowire is a single-mode waveguide, with a cross-section (h × w) of 220 nm × 500 nm, and ~5 mm in length (L). The nanowire is fabricated on SOI Unibond 200 mm wafers, with a 2-μm-thick buried oxide layer. The oxide layer ensures optical isolation for the nanowire from the high-index substrate, reducing losses due to leakage modes in the process. The device is fabricated at the IBM T. J. Watson Research Center. To ensure efficient power coupling with a fiber, a polymer, inverted-taper-geometry spot-size converter is defined at each coupling plane of the device. The device was fabricated without a top cladding, resulting in a very high Si-air index contrast (Δn) of ~2.4, and therefore tight modal confinement.
Propagation loss in the nanowire was measured to be about 3.5 dB/cm in the C-band, or < 2 dB in total for the device used. The effective length (Leff) is consequently almost identical to its physical length (L). The nanowire supports a single quasi-TE (QTE) mode over 1530-1565 nm, and has a high group-index birefringence of ~0.1, which is about a factor of 100 larger than that of polarization-maintaining fiber (10−3). The dispersion coefficient (D) is very high relative to standard single-mode fiber, at ~4400 ps/nm∙km, yielding a total dispersion of only 0.0022 ps/nm, which is negligible for most practical, nearly transform-limited pulse-widths (> 1 ps). The nonlinear coefficient (γ) is also very high at ~300 W−1m−1 due to a high Δn, many orders of magnitude larger than that of some nonlinear fibers such as PCF (~0.01 W−1m−1 ). Normalized to the same pump peak power however, the product γ∙Leff for the nanowire is 1.5, which can be ~5 times larger than that for a 30-m-long PCF , if the total coupling and Fresnel loss at the input facet is kept to 1 dB as it is in the nonlinear fiber. For a 1-cm-long nanowire which still makes the overall chip smaller than that in commercial Lithium Niobate platforms, the γ∙Leff product becomes an order of magnitude higher than PCF’s, and would enable nonlinear optical processing with moderate pump powers compatible with commercial DWDM Er-doped fiber amplifiers (EDFAs). The nanowire has demonstrated highly pronounced SPM [35,36] and XPM  effects, and would be expected to be efficacious for nonlinear optical processing. However, it has also shown significant intrapulse free-carrier absorption (FCA) due to two-photo absorption (TPA) [35,38].
Although pulse format conversion has been successfully carried in a bulk-SOA, a bulk-SOA is an active device that requires current injection electronics and a heat-sink platform, whereas the Si nanowire is a passive device that requires neither. In fact, the Si nanowire has more in common with nonlinear fibers than with SOAs, since nonlinear fibers exploit a similar nonlinearity. By contrast however, nonlinear fiber is cumbersome due to a comparatively weaker nonlinearity, which results in longer interaction lengths, and thus higher pump power requirements. The Si nanowire is thus the most amenable to chip-level integration, in a relatively compact, simple configuration. There have been some theoretical proposals for NRZ-to-RZ conversion in a nano-scale silicon waveguide , as well as NRZ-to-PRZ conversion which could be useful for clock recovery applications , but experimental demonstrations of NRZ-to-RZ conversion in Si, have yet to be reported. This work shows for the first time that the conversion of NRZ-OOK to RZ-OOK in a simple Si nanowire is feasible, demonstrating no significant receiver sensitivity degradation for converted RZ-OOK compared to baseline RZ-OOK. Further, converted RZ-OOK yielded a receiver sensitivity enhancement of about 3 dB over NRZ-OOK, similar to that of baseline RZ-OOK.
2.1 Waveguide coupling loss characterization
A waveguide alignment station was used to enable coupling to the Si nanowire chip. Both input and output coupling is facilitated by xyz-compound-translation stages, fitted with piezoelectric actuators. Coupling to a Si nanowire on the chip was made possible by anti-reflection-coated, tapered lensed fiber (LF) fabricated using SMF-28 fiber, and commercially available from Oz Optics, Inc. The spot-size profile of the LFs was circular, ~2.5 μm in diameter, with a working distance of ~15 μm.
To estimate the coupling loss/facet for the nanowire, a 1553.5 nm, 10 Gb/s pulsed source, which was to be used as the pump in the experiment, was amplified using an EDFA then coupled to the nanowire using the LF. The full-width-at-half-maximum (FWHM) pulse-width was approximately 2.7 ps. Figure 1 shows how the measured average output power (at the output LF) varies with the average input pump power (at the input LF). As the pump power was gradually increased, it was observed that the output power began to show a salient deviation from linear behavior at ~50 mW. At about 150 mW input power, the output powerexperienced a 3 dB compression. This behavior is understood to be due to intrapulse as well as interpulse TPA-induced FCA, the latter being significant due to a high repetition rate of 100 ps, which is approximately of the same order-of-magnitude as the reported FC lifetime (500 ps) . The net effect of FCA is an additional loss that lowers the peak power of the pump in the nanowire, degrading the efficiency of XPM in the process. The total LF-chip-LF coupling loss can be obtained from the linear region of the transmission curve, and is observed to be ~10 dB. Since the propagation loss was about 1.8 dB total, this yields a total coupling loss/facet of about 4 dB, which includes Fresnel loss. However, the coupling loss may not be symmetrically split between the two coupling planes of the device. Based on Fig. 1, it may be concluded that little would be gained from injecting the nanowire with pump powers higher than about 140 mW. Consequently, the actual average pump power coupled to the nanowire was then ~50 mW (17 dBm), after accounting for an input coupling loss of ~4 dB.
2.2 Receiver sensitivity experiment
To carry out the conversion of 10 Gb/s NRZ-OOK to RZ-OOK using the Si nanowire, the experimental set-up of Fig. 2 was used. The NRZ-OOK transmitter comprised a 1540 nm, external cavity laser (ECL), externally modulated by an x-cut Lithium Niobate electro-optic modulator (EOM), biased at quadrature. A pulsed-pattern generator (PPG), driven by a 10 GHz oscillator, produced a 10 Gb/s, 231-1 pseudo-random bit sequence, which was subsequently amplified and impressed onto the optical carrier using the EOM. Due to the lack of a suitable 10 Gb/s pulsed source, a commercially available, 1553.5 nm, 40 Gb/s mode-locked laser diode (MLLD) was externally modulated in a 40 Gb/s z-cut EOM that was in turn driven by a 40 Gb/s multiplexer programmed to produce ‘1000’ periodically. Consequently, the output of the EOM, which represented the pump, was a 10 Gb/s pulse train with a FWHM pulse-width of 2.7 ps. Typical pump and probe traces are shown in Fig. 3 . In practice, a clock would have to be recovered from the NRZ-OOK probe in order to drive the pump, but this approach was not followed as it would have required an active quadrupler to drive the 40 Gb/s multiplexer. In the experiment, the PPG was synchronized to a clock signal derived from the pump hardware. The pump-probe detuning was set to 10 nm to minimize the spectral overlap, and therefore cross-talk that may otherwise occur due to co-propagation in the Si nanowire.
The pump and probe were subsequently amplified using high-power EDFAs (HPEs), and combined using a 10% coupler, where the pump was coupled to the 90% port to ensure highest XPM efficiency in the Si nanowire. The pump average power was ~23 dBm, while that of the probe was ~19 dBm, both referred to the input LF. Polarization controllers were used in the coupler arms to launch each signal into the nanowire in the QTE-mode. An optical delay line (ODL) was used to synchronize the pump pulses to the center of each probe data bit. The composite signal was then coupled into the nanowire using the input LF, and the output signal delivered to the receiver using the output LF as previously described. A fixed- wavelength fiber-Bragg grating (FBG), relative to which the probe wavelength was detuned by ~ + 0.35 nm, was used to reject the probe carrier reflectively through the third circulator port. As the FBG was not designed for the experiment, it had to be followed by a thin-film optical band-pass filter (OBPF1) for additional probe carrier suppression. The −3-dB-bandwidth of the filter was 0.3 nm, and its low-wavelength −3dB-cut-off was at ~1535 nm. The rest of the components made-up a standard pre-amplified receiver [41,42], common to typical terrestrial/submarine transmission systems: a high-gain, low-noise-figure (LNF), dual-stage EDFA, followed by a 0.3-nm OBPF, a power EDFA and lastly, a 0.5-nm OBPF. The LNF EDFA is essentially a 980-nm-pumped, linear amplifier, with an overall gain of > 35 dB, and a noise figure of < 4 dB (which excludes the loss of the external isolator). The power EDFA is a 1480-nm-pumped, saturated amplifier. The receiver OBPFs were all tuned for maximum transmission, irrespective of the scenario examined. A pin-receiver followed the last OBPF, and consisted of a 10% coupler to allow clock-recovery (CR), while most of the power was directed toward a pin-detector, which was followed by a transimpedance, linear amplifier (TIA). As a limiting amplifier was not essential to the success of a back-to-back experiment, the receiver threshold was instead set by the error-detector (ED). To emulate ASE-limited transmission [43,44], a VOA was used to vary the power at the receiver pre-amplifier, which resulted in a concomitant change in the pre-amplifier’s output OSNR thus emulating transmission-induced OSNR degradations. A 10% coupler was installed before the pre-amplifier to monitor receiver power (PRX) as the VOA varied that power [43,44].
3. Results and discussion
The spectra of the composite signal at various operating conditions are seen in Fig. 4 , whichalso shows the baseline composite signal. For QTE (best) polarization launch of the pump, the pump and probe respectively exhibited highly pronounced SPM and XPM (red trace) due to propagation in the Si nanowire, relative to the composite signal immediately before the input LF (dark-blue trace). The result also demonstrates that although TPA-induced FCA was present, it was not a limiting factor in the experiment, as XPM is twice-as efficient a nonlinearity as SPM. For quasi-TM (QTM)-launch of the pump (black trace), the XPM-induced wings in the probe virtually vanished. Figure 4 also shows the result of bypassing the Si chip (green trace), and although there is some evidence of SPM and XPM, it is insignificant compared to that due to propagation in the Si nanowire (red trace). Thus, the LFs played no significant role in the spectral broadening observed. A pump-probe detuning of > 10 nm ensured minimal cross-talk at the receiver for the probe that may have otherwise occurred due to spectral overlap with the SPM-broadened pump, for smaller detunings.
At the output of the Si nanowire, the probe is isolated using the FBG filter (Fig. 2), and further filtered using the 0.3-nm OBPF1. The resultant output is shown in Fig. 5(a) , which demonstrates a high-quality RZ-OOK eye-pattern. The output of the circulator’s third port is shown in Fig. 5(b), and represents NRZ-OOK components extraneous to the formation of RZ-OOK, rejected by the FBG. Figure 6 shows the location of the composite filter profile, relative to the original probe, at ~ + 0.35 nm. The filter profile is significantly asymmetric, which was required for probe carrier suppression: It can be seen that the original probe carrier has been extinguished by more than 20 dB (circled in red) in the converted RZ-OOK signal. In the process, a new carrier was created at a slightly longer wavelength of ~1540.5 nm. It should also be stressed that it was the dispersion in the composite filter’s steep roll-off that was responsible for the conversion of the XPM-induced phase modulation to amplitude modulation, where the composite filter comprised the FBG and OBPF1. The resultant RZ-OOK has a high OSNR of 40 dB (referred to a 0.1-nm resolution bandwidth), and is also fairly symmetric down to −15 dBc, which shows good chirp suppression despite the fact that none of the filters were designed for the application.
QTE to QTM (for which pump and probe become orthogonal), the XPM effect becomes increasingly negligible. Figure 7(b) (Media 2) shows converted RZ-OOK for the QTE mode in color-grade, infinite persistence mode on the sampling oscilloscope, in a time-lapse over ten minutes. The eye-pattern showed good stability over the time of observation.
Figure 8 summarizes receiver sensitivity measurement results. To obtain baseline NRZ-OOK, the Si chip and the FBG were both bypassed, and the remaining filters were all tuned for maximum transmission to the ECL wavelength. For baseline RZ-OOK, the receiver sensitivity measurement was carried out by using the 10 Gb/s pulse train instead of the ECL used for NRZ-OOK, and the filters were tuned for maximum transmission at 1553.5 nm. Figure 8 shows that baseline RZ-OOK outperformed NRZ-OOK by about 3 dB, which is equivalent to doubling the reach in ASE-limited transmission. It is also seen that converted RZ-OOK performed almost a well as baseline RZ-OOK, albeit with a slight (< 0.5 dB) penalty. The FWHM of the converted RZ-OOK was > 20 ps (observed before the detector), substantially broader than the pump’s FWHM of ~2.7 ps. However, this temporal broadening is ascribed to filtering, and not nanowire dispersion, which was ~0.0022 ps/nm as stated in sec. 1.3. The fact that there was little (< 0.5 dB) difference between the receiver sensitivities of baseline and converted RZ-OOK signals despite different pulse-widths corroborates theoretical and experimental observations [5,6], which showed that the sensitivity advantage of RZ-OOK tapers-off toward increasingly narrower pulse-widths: In  for instance, it was shown that the relative advantage of a 20% duty cycle RZ-OOK was only 0.1 dB better than that for 30%, for the same receiver configuration. Converted RZ-OOK showed no error floor for BER < 10−11, and the signal was identical in polarity to that of the probe. The signal was also correctly coded, requiring no further electronic processing at the receiver, unlike the technique of .
It was also found that the probe suffered little in its propagation through the Si nanowire. This was verified by turning off the pump, allowing the NRZ-OOK probe to propagate by itself in the nanowire. The FBG was bypassed, and the remaining filters were tuned to the wavelength of the ECL. The receiver sensitivity of the probe in this scenario was found to be almost identical to that of baseline NRZ-OOK, seen in Fig. 8. The difference is attributed to slight experimental error, such as sub-optimal transmitter SOP.
4. Summary and conclusions
The conversion of 10 Gb/s NRZ-OOK to RZ-OOK utilizing XPM in a compact, 5-mm-long, passive Si nanowire has been successfully demonstrated for the first time. No signficiant receiver sensitivity degradation was observed for converted RZ-OOK relative to baseline RZ-OOK, and a pre-amplified receiver sensitivity enhancement of ~3 dB was achieved for converted RZ-OOK relative to baseline NRZ-OOK, about the same as that for baseline RZ-OOK. A 3-dB enhancement corresponds to double the reach in ASE-limited, long-haul transmission . The conversion resulted in a correctly encoded and polarity-preserved RZ-OOK signal, exhibiting no error floor for BER < 10−11. The experiment showed that ‘format conversion on a Si chip’ is viable. It may also be possible to integrate the input 10%-coupler, and the filter on the same chip, resulting in a compact scheme.
Comparatively, although format conversion in a bulk-SOA is possible, it is a compact active device that requires a current injection circuit and heat sink control, whereas the Si nanowire is a passive device that requires neither. The Si nanowire actually has more in common with nonlinear fibers than with SOAs, since nonlinear fibers utilize a similar nonlinearity. However, nonlinear fiber suffers from a large foot-print due to a relatively weaker nonlinearity, which results in a longer effective length, and thus higher pump power requirements. Format conversion in a Si nanowire is thus the most amenable to chip-level integration, in a relatively compact configuration.
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