We investigate return-to-zero (RZ) to non-return-to-zero (NRZ) format conversion by means of the linear time-invariant system theory. It is shown that the problem of converting random RZ stream to NRZ stream can be reduced to constructing an appropriate transfer function for the linear filter. This approach is then used to propose novel optimally-designed single fiber Bragg grating (FBG) filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion. The spectral response of the FBG is designed according to the optical spectra of the algebraic difference between isolated NRZ and RZ pulses, and the filter order is optimized for the maximum Q-factor of the output NRZ signals. Experimental results as well as simulations show that such an optimally-designed FBG can successfully perform RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion.
© 2014 Optical Society of America
Future all-optical networks may be required to support a variety of modulation and data formats. Two standard data formats that are fairly mature and widespread in current optical transmission systems are the return-to-zero (RZ) and non-return-to-zero (NRZ) formats. Various all-optical conversion schemes from RZ to NRZ have been demonstrated to provide an important interface technology at the nodes of wavelength division multiplexing (WDM) and optical time division multiplexing (OTDM) networks [1, 2]. These conversion schemes can be classified into two categories, namely the time-domain waveform processing and frequency domain spectrum tailoring. The time domain approach is based on a variety of optical nonlinear effects and devices, including four-wave mixing, phase modulation, cross phase modulation, cross gain modulation, cross gain compression, gain clamp effect [3, 4], highly nonlinear optical fiber , photonic crystal fiber , active Michelson interferometer , nonlinear optical fiber loop mirror [8, 9]. The frequency domain approach utilizes the linear filtering process to suppress sidebands of RZ spectra and narrow frequency spectrum to broaden the pulse in time domain. The reported methods include spectral line-by-line pulse shaping technology , optical fiber delay interferometer (DI) (or Mach–Zehnder interference, or uniform fiber Bragg grating (FBG)) cascaded narrow-band filter based conversion technology [11–17], silicon microring resonator (or silicon-based DI) and arrayed waveguide grating (AWG) based conversion technology [18, 19].
Generally, the spectrum tailoring based converter is all-passive and very attractive compared with active-operation device, thanks to its advantages of simple structure, high cost performance and stable performance. However, there are many drawbacks of the reported spectrum tailoring schemes. First, these schemes cannot guarantee the best conversion results since these schemes use off-the-shelf filters rather than an optimally-designed one. Second, at least two filters are required in such schemes to fulfill the format conversion. For example, both microring resonator and DI are comb filters whose periods are determined by the free spectral range (FSR). As a result, to perform format conversion, these devices need to be combined with another band-pass filter. Additionally, in the case of DI cascaded filter scheme, the pattern effects are present for any duty cycle and they are more conspicuous for larger duty cycles such as 50% and 67%. The last but not the least, many reported schemes are limited to RZ on-off keying (RZ-OOK) to NRZ on-off keying (NRZ-OOK) or/and RZ differential phase shift keying (RZ-DPSK) to NRZ differential phase shift keying (NRZ-DPSK) format conversion, and, to the best of our knowledge, there are no reports on using the same device to fulfill RZ-OOK to NRZ-OOK, RZ-DPSK to NRZ-DPSK and RZ differential quadrature phase shift keying (RZ-DQPSK) to NRZ differential quadrature phase shift keying (NRZ-DQPSK) format conversion.
In this paper, we rigorously analyze the FBG-based RZ to NRZ format conversion by means of the linear time-invariant theory. This approach is then used to propose a novel RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK conversion scheme based on a single optimally-designed FBG. The spectral response of this FBG is designed according to the algebraic difference of the optical spectra of isolated NRZ and RZ pulses. Further, the filter order is optimized to maximize the Q-factor of the converted NRZ signals. Numerical investigations show that the optimally-designed FBG is capable of converting the input RZ-OOK/DPSK/DQPSK signals with different duty cycles to NRZ-OOK/DPSK/DQPSK signals with high Q-factor. Moreover, in our proposed scheme, the pattern effects are efficiently mitigated compared with previously reported schemes. Finally, experimental demonstration of RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK conversion with the proposed scheme is presented.
2. Frequency-domain analysis
Taking RZ-OOK to NRZ-OOK format conversion as an example, the schematic diagram of the FBG-based RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion is shown in Fig. 1. The RZ-OOK signal are coupled into the FBG via the first port of the optical circulator and reflected back by the FBG via the second port. In the process of reflection, the spectra of RZ-OOK signal are linearly tailored by the reflection spectra of the FBG to produce the output signal characterized by the spectra of NRZ-OOK signal. The converted NRZ-OOK signal is outputted from the third port of the optical circulator.
Since RZ-OOK/DPSK/DQPSK data can be constructed from convolution of the RZ-OOK/DPSK/DQPSK signal with a series of delta functions representing data in the time domain, and that the FBG-based filtering is a linear process, the FBG-based RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format converter can be analyzed using linear time-invariant system theory. Thus, the complex problem of converting random RZ-OOK/DPSK/DQPSK stream to NRZ-OOK/DPSK/DQPSK stream can be reduced to constructing an appropriate transfer function for the FBG filter. This process is described below.
In principle, the time-domain electric field of the RZ-OOK/DPSK/DQPSK modulated optical signal can be expressed as2, 20], is the interval between pulses, and is the carrier angular frequency and is the shape of the isolated RZ-OOK/DPSK/DQPSK pulse. Note that the shapes of the isolated RZ-OOK, RZ-DPSK and RZ-DQPSK pulses are identical because in DPSK and DQPSK only the phase is used to encode information. Denoting the impulse response of the format converter as, for RZ input, the output electric field can be calculated in terms of the input electric field and the impulse response as follows:Eq. (1), can be written asEq. (1) (note that the shapes of the isolated NRZ-OOK, NRZ-DPSK and NRZ-DQPSK pulses are identical). Equations (1)-(3) yield the following impulse response for the RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format converter:Eq. (4) leads toEq. (5) in decibels yields
The filter described by Eq. (6) is defined as the first-order filter. Higher-order filters are typically implemented as serially-cascaded first-order filters. The transfer function of the nth-order filter can be calculated by multiplying the transfer function of the first-order filter by the ordinal number n. Therefore, the transfer function of the nth-order filter isEquation (7) describes the fundamental principle for FBG spectral response design, where the ordinal number n is free to be optimized.
3. FBG-based filter design
Taking 40-Gbit/s RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion as an example, the optimal design of FBG-based filter is demonstrated. Specifically, considering an RZ-OOK/DPSK/DQPSK signal with 50% duty cycle, and noting that the shapes of isolated RZ pulse and NRZ pulse are independent on OOK, DPSK or DQPSK modulations, we can write the time-domain electric field waveforms for isolated RZ-OOK/DPSK/DQPSK pulse and isolated raised-cosine NRZ-OOK/DPSK/DQPSK pulse as follows ,Fig. 2 shows the amplitude of the spectra of and, and their algebraic difference, namely, the ideal transfer function of the first-order filter.
The ideal transfer function (i.e. the red curve in Fig. 2) is symmetrical but complex. In particular, for some higher frequency components that are out of the NRZ-OOK/DPSK/DQPSK spectra main-lobe bandwidth of (or at bit rate of 40-Gbit/s), the value of the transfer function is greater than 0-dB, which is obviously impossible to be fulfilled by a passive filter. Fortunately, many reported studies have indicated that we should concentrate on the in band filtering rather than out of band filtering because most of the NRZ-OOK/DPSK/DQPSK signal power is in the range [12–14, 18–20]. Thus, it is reasonable to set a uniform attenuation (say, 25-dB) for out-of-band components, and eventually construct a band-pass filter as routinely done in the reported schemes [11–14,18,19]. Moreover, it is also necessary to set a physically realizable minimum reflectivity (say, 25-dB, the same as above) in the pass band. Taken together, the simplified transfer function of the first-order FBG filter is given by
It is worth noting that the nth-order FBG filter is based on one FBG rather than n FBGs. Therefore, the maximum isolation is fixed to 25-dB for any filter of order. Figure 3 displays the reflectivity spectra of the nth-order FBG filters calculated using Eq. (12) for different values of n. A noteworthy feature shown in Fig. 3 is that the higher the order of the filter, the narrower is the 3-dB bandwidth. It is interesting that the spectral response of the DI scheme is very close to that of the 2.97th-order FBG filter.
As pointed out earlier, among all the nth-order FBG filters, the first-order FBG filter is not necessarily the best one, since is different from as shown in Eqs. (7) and (11). To further investigate the effect of ordinal number on format conversion, we calculate the Q-factor of the converted NRZ-OOK signal with the ordinal number n ranging from 0.5 to 4. The results are plotted in Fig. 4, where the insert (a) is the standard deviations of the marks and spaces rail of the NRZ-OOK signal. Figure 4 shows that the 2.07th-order filter presents the minimum standard deviations and the maximum Q-factor. Hence, we chose as the optimal designed reflectivity spectra of FBG, with 3-dB bandwidth of 0.46 nm and 25-dB bandwidth of 0.64 nm as is shown in the insert (b) of Fig. 4. As analyzed above, this 2.07th-order filter is the best one for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion. Note that, the 2.97th-order filter, which is very similar to the DI scheme, has a Q-factor of 11.1.
In order to verify this FBG is physically realizable, we employ layer peeling method [21,22] to synthesize the reflectivity spectra of the optimally-designed FBG. Figure 5(a) shows the synthesized grating with the grating length of 4 cm. As is shown in Fig. 5(a), the maximum refractive index modulation of and the maximum local chirp of −0.27 nm are well within the practically realizable range. Furthermore, in Fig. 5(b), we plot the simulated reflection spectra of the designed FBG with transfer matrix method. It is clear that the simulated reflection spectra (the dotted blue line) are in excellent agreement with the target reflection spectra (the solid red line).
4. RZ-OOK to NRZ-OOK format conversion simulation and discussion
In this section we investigate the performances of the FBG based RZ-OOK to NRZ-OOK format converter and compare it with the previously reported results.
Given the carrier wavelength of 1550.12 nm, we simulate the operation of designed FBG based optical filter for single channel RZ-OOK to NRZ-OOK format conversion in the case of a pseudo-random binary sequence (PRBS) of length 231-1 bits with different duty cycles. Figure 6 shows the simulation results at a bit rate of 40-Gbit/s with duty cycles of 20%, 33%, 50% and 67%. It should be noted that we only consider the duty cycles rather than the polarity of electric field waveforms. Therefore, the unipolar electric field waveforms are necessary for all 4 duty cycles in simulation. Figures 6(a)-6(c) show the waveforms, power spectra and eye diagrams of the input RZ-OOK signals, respectively, while Figs. 6(d)-6(f) depict the corresponding profiles of the output NRZ-OOK signals. In Fig. 6(a), the RZ-OOK waveforms with different duty cycles are normalized according to Eq. (10) to have unit energy over the symbol period. It is shown in Fig. 6(d) that the RZ-OOK pulses have been broadened to NRZ-OOK pulses via the filtering introduced by the optimal designed FBG. As is shown in Fig. 6(f), for four different duty cycles, all the eye diagrams are very clean and open.
To better appreciate the superior performance of the FBG based format converter, in Figs. 6(g)-6(i), we plot the simulation results of the reported DI cascaded filter scheme, where a DI with 80-GHz free spectral range (FSR) is cascaded by a filter with 3-dB bandwidth of 0.6 nm for 40-Gbit/s RZ-OOK to NRZ-OOK format conversion. As is shown in Fig. 6(g), in the case of 50% and 67% duty cycles pattern effects appear in the waveforms. That is, a single “1” bit has lower peak power than the several consecutive “1” bits (This is also shown in Fig. 2 of  by Y. Yu et al.). Figure 6(i) demonstrates that this effect seriously decreases the Q-factor of the output NRZ-OOK signal. However, our FBG based format converter can efficiently reduce the pattern effects and greatly increase the Q-factor. In particular, comparing Fig. 6(f) with Fig. 6(i), the Q-factors for our FBG-based scheme are significantly higher than the DI scheme. Physically, the pattern effects observed for the high duty cycles in the DI scheme can be attributed to the high-frequency components being excessively suppressed. As is shown in Fig. 6(b), the smaller the duty cycle, the flatter are the spectra of RZ-OOK signals. As a result, the proportions of the high-frequency components in the main lobe () increase as the duty cycle decrease.
The reduction of the pattern effects in our FBG based scheme originates from the well-designed spectra with moderate high-frequency suppression. This can be verified by comparing the spectral response of the proposed FBG scheme and the reported DI scheme.
The overall spectral response of the DI scheme with a filter with 3-dB bandwidth of 0.6 nm can be expressed asFig. 7, we plot the spectra response of the proposed 2.07th-order FBG filter and the DI based filter as well as their algebraic difference. As shown in Fig. 7, from the point of view of the spectrum, the proposed FBG filter is flatter than the DI based filter and essentially possesses moderate high-frequency suppression. The dotted line in Fig. 7 shows that the depths of high-frequency suppression have been significantly reduced. The maximal reduction is close to 10-dB compared with the DI based filter. As can be seen from Fig. 6(d), the pattern effects are perfectly suppressed in the cases of 33% and 50% duty cycles where the peak powers of a single “1” bit and the several consecutive “1” bits are similar. On the other hand, minor pattern effects exist for 20% and 67% duty cycles, i.e. the peak powers of single “1” bit are slightly greater than the several consecutive “1” bits. On the basis of these results, it can be concluded that the proposed 2.07th-order FBG filter has superior characteristics compared with the DI scheme.
As for the operational tolerances of this scheme, we consider the detuning of the central wavelength of FBG reflection band. The central wavelength may be detuned from the carrier wavelength due to fabrication process, variations of temperature or pressure. Alternatively, the carrier wavelength of the transport system may change slightly from time to time. Figure 8 shows the Q-factor as a function of the filter wavelength detuning. It is interesting to note that in Fig. 8 each Q-factor curve has a flat top around the center (approximately within ± 0.02nm depending on the duty cycle). In this range, the Q-factor is insensitive to the detuning of the central wavelength. Supposing a detuning of 0.032 nm (i.e. 5% of the bandwidth of FBG reflection spectra), the inserts (a)-(c) show corresponding waveform, power spectra and eye diagrams of the output NRZ-OOK signal, respectively. It is clear that the performance of 0.032 nm-detuning filters is still acceptable with the Q-factor being greater than 16 for four different duty cycles. In particular, in the case of 67% duty cycle, the performance is enhanced due to partial mitigation of the excessive high-frequency suppression. Compared with Fig. 6(i), the performance shown in the insert (c) of Fig. 8 is better than that of the DI scheme, except in the case of 20% duty cycle. As expected, an over-detuning can obviously degrade the performance due to the fact that it can result in the carrier being overfiltered as well as the first order spectra spike being underfiltered and therefore seriously affect format conversions. We would also point out here that such a problem may be solved by packaging the FBG with either thermal package or mechanical package so that its central wavelength can be dynamically adjusted and controlled (thermally or mechanically) to ensure the conversion function.
As regards the impact of bit rate on the proposed filter design, according to Eq. (12), the bandwidth of the designed FBG is proportional to the bit rate. For instance, for the RZ-OOK signals with higher bit rates, such as 80- or 100-Gbit/s, the bandwidth of designed FBG should be 1.28 nm or 1.6 nm, respectively. Such FBGs are even easier to be designed and fabricated compared with the one considered here (i.e. 0.64 nm in the case of 40-Gbit/s). On the other hand, in the case of 20- or 10-Gbit/s, the bandwidth of the designed FBG should be 0.32 nm or 0.16 nm, respectively. Although such FBGs can readily be designed, their fabrication is somewhat more difficult than the ones with higher bandwidth mainly because of the issues related to controlling the bandwidth for the rising and falling edges.
5. RZ-DPSK to NRZ-DPSK format conversion simulation and discussion
The optimally-designed FBG in Section 3 can also be used to convert 40-Gbit/s RZ-DPSK signals to the corresponding NRZ-DPSK signals. Figure 9 shows the simulation results at a bit rate of 40-Gbit/s for duty cycles of 20%, 33%, 50% and 67%. Figures 9(a)-9(c) show the waveforms, power spectra and eye diagrams of the input RZ-DPSK signals, respectively, while Figs. 9(d)-9(f) depict the corresponding profiles of the output NRZ-DPSK signals. In Fig. 9(a), the RZ-DPSK waveforms with different duty cycles are normalized to have unit energy over the symbol period. As shown in Fig. 9(f), all the eye diagrams for four different duty cycles are very clean and open.
In order to compare our FBG-based scheme with the DI cascaded filter scheme, in Figs. 9(g)-9(i), we plot the simulation results of the DI cascaded filter scheme (specified by Eq. (13)) for 40-Gbit/s RZ-DPSK to NRZ-DPSK format conversion. As is shown in Fig. 9(g), in the cases of 50% and 67% duty cycles, pattern effects appear in the waveforms. Correspondingly, in Fig. 9(i), the central part of the upper eyelid of the eye diagrams is thickening with the increase of duty cycles. The constellation diagrams of the DPSK signals are shown in Fig. 10, indicating the phase alternation between “0” and “π” in DPSK pulse trains. Figures 10(a)-10(d), 10(e)-10(h) and 10(i)-10(l) are the constellations of the original RZ-DPSK, the FBG-converted NRZ-DPSK and the DI-converted NRZ-DPSK signals, respectively. In Fig. 10, starting from the left, the columns one to four correspond to 20%, 33%, 50% and 67% duty cycles, respectively. It is noteworthy that no significant constellation degradation is present in Figs. 10(e)-10(h). On the other hand, in Figs. 10(i)-10(l), constellation dispersion is clearly observable and it increases significantly with the increase of the duty cycle.
Figure 11 shows the demodulated Alternative Mark Inversion (AMI) signals and Dual Binary(DB)signals outputted from a one-bit-delay Mach-Zehnder delay interferometer (MZDI) which serves as the DPSK demodulator [2, 23]. To compare our FBG-based scheme with the DI scheme, the NRZ-DPSK signals shown in Fig. 9 are inputted to the DPSK demodulator and the outputs are compared. Using the FBG-generated NRZ-DPSK signals (i.e. Figure 9(d)) as the input, the AMI [DB] signals outputted by the demodulator are shown in Figs. 11(a), 11(b) [Figs. 11(e) and 11(f)]. Similarly, Figs. 11(c) and (d) and 11(g) and (h) show the corresponding outputs in the case of DI-generated NRZ-DPSK input (i.e. Figure 9(g)). A remarkable feature shown in Fig. 11 is that the demodulated FBG-generated NRZ-DPSK signal gives rise to a higher Q-factor than that for the DI-generated NRZ-DPSK.
6. RZ-DQPSK to NRZ-DQPSK format conversion simulation and discussion
DQPSK is a spectrally efficient modulation format in which two bits per symbol are encoded by multiplexing I (in-phase) and Q (quadrature) signals on a single wavelength [23–26]. In this Section, we will again use the optimally-designed FBG in Section 3 to convert a 40- Gbaud/s (PRBS of length 231-1) RZ-DQPSK signal at 1550.12 nm to the NRZ-DQPSK format. The results of the simulations for duty cycles of 20%, 33%, 50% and 67% are presented in Fig. 12. Figures 12(a)-12(c) show the waveforms, power spectra and eye diagrams of the input RZ-DQPSK signals, respectively. Figures 12(d)-12(f) depict the output NRZ-DQPSK signals using our FBG scheme. As are shown in Fig. 12(a) and Fig. 9(a), the waveforms of RZ-DQPSK and RZ-DPSK are identical because both DPSK and DQPSK are constant-amplitude formats. It should be noted that although the shape of the RZ-DQPSK power spectra is identical to that of RZ-DPSK, the RZ-DQPSK power spectra are compressed in frequency by a factor of two due to two bits encoded per symbol . Figure 12(f) shows that all the eye diagrams for four different duty cycles are very clean and open.
Once again, we compare our scheme with the DI cascaded filter scheme. In Figs. 12(g)-12(i), we present the simulation results of the DI cascaded filter (specified by Eq. (13)) scheme for 40- Gbaud/s RZ-DQPSK to NRZ-DQPSK format conversion. As is shown in Fig. 12(i), the central part of the upper eyelid of the eye diagrams is thickening with the increase of duty cycles. We further depict the constellation diagrams of the DQPSK signals in Fig. 13, where Figs. 13(a)-13(d), 13(e)-13(h), and 13(i)-13(l) are the constellations of original RZ-DQPSK, FBG-generated NRZ-DQPSK signal and DI-generated NRZ-DQPSK signal, respectively. Starting from the left, columns one to four correspond to 20%, 33%, 50% and 67% duty cycles, respectively. Figure 13 indicates the phase alternation among “π/4”, “3π/4”, “5π/4” and “7π/4” in DQPSK pulse trains. Similar to the case of DPSK, constellation dispersion in Figs. 13(i)-13(l) increases significantly with the increase of duty cycle, and is more serious than that of Figs. 13(e)-13(h). It is worth noting that in the case of DQPSK, constellations disperse along both the phase and amplitude directions rather than only along the amplitude direction as presented in the case of DPSK.
As is well known, the NRZ-DQPSK signal can be demodulated using two one-symbol-period-delay MZDIs arranged in parallel with a relative phase shift of π/4 and -π/4 for upper and lower branches, respectively, and detected by two balanced receivers to present I and Q components [23, 27].
Figures 14(a) and 14(b) [Figs. 14(e) and 14(f)] depict the waveforms and eye diagrams of the demodulated I[Q] components using the FBG-generated NRZ-DQPSK signal (i.e. Fig. 12(d)) as the input of the DQPSK demodulator. Similarly, Figs. 14(c)-14(d) and 14(g)-14(h) present the corresponding outputs in the case of DI-generated NRZ-DQPSK signal. Once again, it is found that the demodulated FBG-generated signals result in higher Q-factors than those of the DI-generated ones.
8. Experimental results and discussion
To experimentally demonstrate the single FBG-based RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion, we fabricated a FBG that is optimally designed for 40-Gbit/s (40-Gbaud/s in case of DQPSK) format conversion, with the central wavelength of 1550.12 nm, bandwidth of 0.64 nm and 30-dB isolation. The FBG was fabricated in hydrogen-loaded standard optical fiber (SMF28) with a UV laser direct-writing system. The grating structure was then stabilized by annealing at 80°C for 60 hours after the fabrication. As is shown in Fig. 15, the theoretical and the measured spectra agree very well and differ slightly in the long wavelength side.
To demonstrate the proof of concept, we only discuss the experimental results for the case of 40 Gbit/s RZ-OOK with 33% duty cycle. The experimental setup is shown in Fig. 16. The SHF optical communication system is employed to generate the RZ-OOK signal with wavelength of 1550.12 nm (the same wavelength as the peak reflection wavelength of the fabricated FBG). By controlling the modulation parameters, 40-Gbit/s RZ-OOK signals (PRBS 231-1) with 33% duty cycle can be achieved. The signal power can be controlled by the subsequent erbium doped fiber amplifier (EDFA) and an attenuator (ATT). Using a circulator, the signals are coupled to the FBG and the converted signals are coupled out to be analyzed by the communication signal analyzer (CSA), the optical spectrum analyzer (OSA) and the Error analyzer, respectively.
Figure 17 shows the experimental results of RZ-OOK to NRZ-OOK conversion. The spectra of the RZ-OOK signal (blue line), the fabricated FBG (dashed green line) and the NRZ-OOK signal (red line) are shown in Fig. 17(a). It can be seen that the first-order sidebands of converted NRZ-OOK spectra are suppressed near 30-dB by the fabricated FBG compared with the RZ-OOK spectra. Figures 17(b) and 17(c) [Figs. 17(d) and 17(e)] are the eye diagrams and the waveform of the RZ-OOK [NRZ-OOK] signals, respectively. As is shown in Fig. 17(e), the RZ-OOK pulses have been broadened to corresponding NRZ-OOK pulses owing to the filtering introduced by the fabricated FBG. Due to the all-passive format converter, no additional noise is introduced in the conversion. The eye diagrams of the converted NRZ-OOK are clear and open. Also, as is shown in the NRZ-OOK waveform, the pattern effects are negligible. Furthermore, flatter ‘0’ bits are presented in the NRZ-OOK waveform thanks to the filtering of chirps in the RZ-OOK waveform by the fabricated FBG.
The BER and power penalty measurement results are shown in Fig. 18. Figure 18(a) shows that the power penalty induced by the conversion is about 0.7-dB. This is an improvement compared with 2.2-dB that is reported in . To investigate the operational tolerances of this fabricated FBG, the power penalties for different wavelength detunings are measured (at BER of 10−9 level). The measured results and corresponding eye diagrams are shown in Fig. 18(b). When the offset of the carrier wavelength varies from −0.04nm to 0.04nm away from the central wavelength of the fabricated FBG, the power penalties are limited in 1.5 dB. On the basis of these experimental results, it can be concluded that the fabricated FBG filter presents a good-performance format conversion.
To experimentally demonstrate RZ-DPSK/DQPSK to NRZ-DPSK/DQPSK format conversion with the same fabricated FBG, we replace the RZ-OOK generator in Fig. 16 with RZ-DPSK generator and RZ-DQPSK generator, respectively. Figures 19 and 20 show the measured optical spectra, waveform and eye diagrams of DPSK and DQPSK modes, respectively. It is shown in Figs. 19(e) and 20(e) that the RZ- DPSK/DQPSK pulses have been broadened to NRZ- DPSK/DQPSK pulses via the filtering introduced by the same fabricated FBG. Furthermore, the NRZ-DPSK waveform is featured with one-level intensity dip where there is a π optical phase shift between adjacent bits. On the other hand, the NRZ-DQPSK waveform is characterized with two-level intensity dips since it contains more phase-shift information. These observations agree well with the simulation results presented in Figs. 9(d) and 12(d). From the point of view of the eye diagrams, there is no “0” level in both NRZ-DPSK and NRZ-DQPSK eye diagrams because of their constant envelope (without “0” pulses, for optical power appears in each bit slot). Again this coincides well with the simulation results in Figs. 9(f) and 12(f). One can, therefore, conclude that both RZ-DPSK to NRZ-DPSK and RZ-DQPSK to NRZ-DQPSK format conversions are successfully fulfilled with the same fabricated FBG.
It should be point out that the eye diagrams of the converted NRZ-DQPSK signals are not very clear and open. This is due the fact that the eye diagrams of the original RZ- DQPSK signals are degraded compared with those of RZ-OOK signals (i.e. The upper eyelid of the eye diagrams is thicker than that of the eye diagrams of RZ-OOK signals, as is shown in Figs. 17(b) and 20(b)). It should be noted that the RZ- DQPSK eye diagram degradation arises from the limitations of the RZ-DQPSK generator used in this experiment. However, this restriction does not prevent the demonstration of RZ-DQPSK to NRZ- DQPSK format conversion.
We have proposed and experimentally demonstrated a novel optimally-designed single fiber-Bragg grating (FBG) filter scheme for RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK format conversion. Employing the linear time-invariant system theory, the complex problem of converting random RZ stream to NRZ stream is reduced to constructing an appropriate transfer function for the FBG filter. Furthermore, theoretical analysis shows that the spectral response of the FBG can be constructed based on the algebraic difference between optical spectra of isolated NRZ-OOK and RZ-OOK pulses. The filter order is optimized for the maximum Q-factor of the output NRZ-OOK signals. Based on the optimal designed 2.07th-order filter, format conversions from RZ-OOK/DPSK/DQPSK to NRZ-OOK/DPSK/DQPSK are investigated. Simulation results consistently show superior performance for our FBG scheme than DI cascaded filter scheme. Experimental results show that such an optimally-designed single FBG filter can efficiently reduce the pattern effects, and results in a significant improvement in power penalty compared with previously reported delay interferometer scheme.
The authors thank Dr. Jie Hou and Dr. Mengyuan Ye of Huazhong University of Science and Technology for helpful discussions. This research was conducted during Dr Hui Cao’s visit to Wuhan National Laboratory for Optoelectronics & School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology (July 2013 – June 2014), and was supported by the National Natural Science Foundation of China (grant 61178030), the Natural Science Foundation of Guangdong Province, China (grant S201101000122), the Fundamental Research Funds for the Central Universities, China (HUST: 2013TS047), and the Fundamental Research Funds of Foshan University.
References and links
1. A. E. Willner, S. Khaleghi, M. R. Chitgarha, and O. F. Yilmaz, “All-optical signal processing,” J. Lightwave Technol. 32(4), 660–680 (2014). [CrossRef]
2. P. J. Winzer and R.-J. Essiambre, “Advanced optical modulation formats,” Proc. IEEE 94(5), 952–985 (2006). [CrossRef]
3. S.-G. Park, L. Spiekman, M. Eiselt, and J. Weisenfeld, “Chirp consequences of all-optical RZ to NRZ conversion using cross-phase modulation in an active semiconductor photonic integrated circuit,” IEEE Photon. Technol. Lett. 12(3), 233–235 (2000). [CrossRef]
4. T. Silveira, A. Teixeira, G. T. Beleffi, D. Forin, P. Monteiro, H. Furukawa, and N. Wada, “All-optical conversion from RZ to NRZ using gain-clamped SOA,” IEEE Photon. Technol. Lett. 19(6), 357–359 (2007). [CrossRef]
5. A.-L. Yi, L.-S. Yan, B. Luo, W. Pan, J. Ye, Z.-Y. Chen, and J. H. Lee, “Simultaneous all-optical RZ-to-NRZ format conversion for two tributaries in PDM signal using a single section of highly nonlinear fiber,” Opt. Express 20(9), 9890–9896 (2012). [CrossRef] [PubMed]
6. J. Du, Y. Dai, G. K. Lei, H. Wei, and C. Shu, “RZ-to-NRZ and NRZ-to-PRZ format conversions using a photonic crystal fiber based Mach-Zehnder interferometer,” in Optical Fiber Communication (OFC), collocated National Fiber Optic Engineers Conference, 2010 Conference on (OFC/NFOEC)(IEEE, 2010), pp. 1–3. [CrossRef]
7. B. Mikkelsen, M. Vaa, H. N. Poulsen, S. L. Danielsen, C. Jørgensen, A. Kloch, P. B. Hansen, K. E. Stubkjær, K. Wunstel, and K. Daub, “40 Gbit/s all-optical wavelength converter and RZ-to-NRZ format adapter realised by monolithic integrated active Michelson interferometer,” Electron. Lett. 33(2), 133–134 (1997). [CrossRef]
8. W. Tang, M. Fok, and C. Shu, “20 Gb/s all-optical RZ to NRZ format conversion using frequency-doubling polarization-maintaining fiber loop mirror filter,” in Lasers and Electro-Optics, 2005. CLEO/Pacific Rim 2005. Pacific Rim Conference on(IEEE, 2005), pp. 1577–1578. [CrossRef]
9. L. Wang, Y. Dai, G. K. Lei, J. Du, and C. Shu, “All-optical RZ-to-NRZ and NRZ-to-PRZ format conversions based on delay-asymmetric nonlinear loop mirror,” IEEE Photon. Technol. Lett. 23(6), 368–370 (2011). [CrossRef]
10. Z. Jiang, D. E. Leaird, and A. M. Weiner, “Line-by-line pulse shaping control for optical arbitrary waveform generation,” in Conference on Lasers and Electro-Optics(Optical Society of America, 2005), pp. CTuBB2–1- CTuBB2–2. [CrossRef]
11. Y. Yu, X. Zhang, and D. Huang, “All-optical RZ to NRZ format conversion with tunable fiber based delay interferometer,” in Optoelectronics, 2006 Optics Valley of China International Symposium on(IEEE, 2006), pp. 47–50. [CrossRef]
12. Y. Yu, X. Zhang, D. Huang, L. Li, and F. Wei, “20-Gb/s all-optical format conversions from RZ signals with different duty cycles to NRZ signals,” IEEE Photon. Technol. Lett. 19(14), 1027–1029 (2007). [CrossRef]
13. F. Wang, E. Xu, Y. Yu, and Y. Zhang, “All-optical 40 Gbit/s data format conversion between RZ and NRZ using a fiber delay interferometer and a single SOA,” in SPIE/OSA/IEEE Asia Communications and Photonics(International Society for Optics and Photonics, 2011), pp. 83080E–1-83080E–6.
14. Y. Yu, X. Zhang, and D. Huang, “Simultaneous all-optical multi-channel RZ and CSRZ to NRZ format conversion,” Opt. Commun. 284(1), 129–135 (2011). [CrossRef]
15. O. Ozolins, V. Bobrovs, and G. Ivanovs, “Conversion of 40 Gbit/s RZ-OOK to NRZ-OOK with a single uniform fibre Bragg grating,” in ELMAR, 2013 55th International Symposium(IEEE, 2013), pp. 121–124.
16. P. Groumas, V. Katopodis, C. Kouloumentas, M. Bougioukos, and H. Avramopoulos, “All-optical RZ-to-NRZ conversion of advanced modulated signals,” IEEE Photon. Technol. Lett. 24(3), 179–181 (2012). [CrossRef]
17. O. Ozolins, V. Bobrovs, and G. Ivanovs, “Cascadability of uniform fibre Bragg grating for 40 Gbit/s RZ-OOK to NRZ-OOK conversion,” Opt. Photon. J. 3(02), 337–341 (2013). [CrossRef]
18. L. Xiang, D. Gao, B. Zou, S. Hu, and X. Zhang, “Simultaneous multi-channel RZ-OOK/DPSK to NRZ-OOK/DPSK format conversion based on integrated delay interferometers and arrayed-waveguide grating,” Sci. China Technol. Sc. 56(3), 558–562 (2013). [CrossRef]
19. M. Xiong, O. Ozolins, Y. Ding, B. Huang, Y. An, H. Ou, C. Peucheret, and X. Zhang, “Simultaneous RZ-OOK to NRZ-OOK and RZ-DPSK to NRZ-DPSK format conversion in a silicon microring resonator,” Opt. Express 20(25), 27263–27272 (2012). [CrossRef] [PubMed]
20. E. Ip and J. M. Kahn, “Power spectra of return-to-zero optical signals,” J. Lightwave Technol. 24(3), 1610–1618 (2006). [CrossRef]
22. H. Cao, J. Sun, X. Zhang, L. Xiao, and D. Huang, “Novel design methodology for superstructure fiber Bragg grating comb-filter,” Acta Phys. Sin-Ch. Ed. 53, 3077–3082 (2004).
23. A. H. Gnauck and P. J. Winzer, “Optical Phase-Shift-Keyed transmission,” J. Lightwave Technol. 23(1), 115–130 (2005). [CrossRef]
24. N. Sotiropoulos, T. Koonen, and H. de Waardt, “Advanced differential modulation formats for optical access networks,” J. Lightwave Technol. 31(17), 2829–2843 (2013). [CrossRef]
25. P. J. Winzer and J. Leuthold, “Return-to-zero modulator using a single NRZ drive signal and an optical delay interferometer,” IEEE Photon. Technol. Lett. 13(12), 1298–1300 (2001). [CrossRef]
26. Y. Yu, Z. Xinliang, W. Lun, W. Fei, and D. Huang, “Simple and flexible NRZ-DQPSK demodulation scheme,” in Asia Communications and Photonics Conference and Exhibition (ACP, 2009), pp. 1–2.
27. Y. Lu, F. Liu, M. Qiu, and Y. Su, “All-optical format conversions from NRZ to BPSK and QPSK based on nonlinear responses in silicon microring resonators,” Opt. Express 15(21), 14275–14282 (2007). [CrossRef] [PubMed]