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Abstract
Wavelength-division multiplexing (WDM) schemes have greatly increased optical transmission capacity, especially when using massively parallel optical frequency combs (OFCs) as carriers. In this paper, we show that linear optical sampling (LOS) is a kind of multiheterodyne process and it can be performed with arbitrary-shaped periodic waveforms. Meanwhile, it can be used for characterizing WDM signals with only a single receiving channel. We successfully demonstrate an observation of 40 WDM channels with 1 THz total bandwidth and total 800 Gbit/s data rate by only using one sampling channel. We show that the adoption of the concept of multiheterodyne detection can improve the performance of LOS technique, and can also greatly simplify multi-channel WDM monitoring systems.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
To meet the increasing demand of new applications in modern telecommunications, optical signal processing, and microwave photonics, optical signals usually span large bandwidth. Especially for next generation optical networks, driven by the continuing demand for higher transmission capacity, optical communication signals now span 100 GHz bandwidth with advanced modulation formats [1] and these large-bandwidth high-symbol-rate coherent optical systems provide data rates up to 1 Tb/s. In optical performance monitoring systems [2], the characterization of the optical signals with high time resolution and high signal noise ratio (SNR) is often necessary to assess the quality of the signal stream or the impulse response of optical components. However, the sampling rate of the state-of-the-art commercial oscilloscope is 160 GS/s using techniques such as digital bandwidth interleaving (DBI) [3], which is inadequate to perform time-resolved measurements of the large-bandwidth signals.
Taking advantage of the optical gate effect and employing short pulses as a local oscillator, the linear optical sampling (LOS) technique has been proposed to characterize ultrafast optical waveforms [4–6]. With the capability to measure the intensity and phase profiles of signals, the LOS technique has previously been a complementary to the real-time electrical sampling approach. In previous demonstrations, such a technique has been used to characterize optical time division multiplexed (OTDM) signals, high-order modulation formats such as polarization-division multiplexed quadrature phase shift keying (PDM-QPSK), and to measure impulse responses of optical components [7–9]. However, the performances of these systems are yet to be improved considering the unestablished mutual-coherence between data signals and sampling pulses. Besides, the previous LOS systems are based on the theory of optical gate effect, which limits the sampling laser to be a pulsed one and poses high requirement on pulse quality [6, 10].
On the other hand, with the advantage of high spectral efficiency, wavelength-division multiplexing (WDM) has been the subject of extensive attention for optical networking [11]. For channel allocation, conventional WDM channel demultiplexing methods are typically based on dielectric multilayer filters or arrayed waveguide gratings, but dense WDM places stringent requirements on the precision of design, fabrication and control. Then channel-allocation-adaptive LOS-based schemes have been proposed for simultaneous WDM signal monitoring since the wavelength of the sampling laser can cover multiple WDM channels [12–14]. However, these demonstrations require N separate channel sampling systems for monitoring N WDM channels, thereby entailing very high complexity and cost when the value of N is counted in tens or even hundreds. As well, the sensitivity of the previously reported LOS systems decreases as the total bandwidth increases, further limiting the ability to simultaneously monitor multiple WDM signal channels.
Actually, the pseudo random bit sequence (PRBS) signals used to emulate data streams in the optical performance characterization systems are periodic waveforms. According to the Fourier transform theory, periodic waveforms have a comb-like spectrum. Therefore, using LOS technique to characterize formats used for high-speed optical communication can be regarded as the multiheterodyne process, which also appears in the literatures as dual-comb spectroscopy [15, 16]. This also applies equally to other applications based on LOS technique. In the multiheterodyne process, the signal under test (SUT) and the local sampling signal with slightly detuned repetition rates interfere with each other. Then the carrier frequency is down-converted and the bandwidth is compressed to radio frequency (RF) domain [17–19]. Under this interpretation, we are able to achieve the full potential of LOS with exceptional phase accuracy and shot-noise limited sensitivity. We find that LOS can also be implemented with any known flattened-spectrum sources with periodic waveform, not restricted to a pulsed laser. In the WDM signal characterization experiment, each channel is recovered in the RF domain with multiheterodyne detection. By converting each carrier to different frequencies and controlling the bandwidth compression factors to avoid the overlap of signals from different channels, we are able to simultaneously observe all channels with a single receiving channel.
Uniquely, this combination enables characterizing massively paralleled WDM channels using a single receiving channel, thus simplifying dramatically the hardware. In the demonstrations, we verified the idea of the general LOS by performing it using a periodic waveform with a disturbed phase distribution, and finally we successfully characterized 40 WDM channels covering 1 THz total bandwidth with a single receiving channel.
2. Operation principle
The principle of modified LOS is plotted in Fig. 1(a). The idea of LOS is based on trading time for bandwidth, and the data signal is usually periodic. As mentioned before, the periodic data signal can also been considered as a comb source. We write the electrical field of data signal as
where fScq is the carrier frequency of data signal, fSq is the repetition rate (or ‘line spacing’) of the data signal, Sqk and φSqk are the intensity and phase profile of each ‘comb tooth’ of data signal. We use the subscript “q” to represent the channel number considering the multichannel signal observation in the following discussions. The slowly-varying complex envelope profile of the data signal is
Fig. 1 Principle of operation. (a) Optical sampling (multiheterodyne detection) for signal reconstruction. (b) Down-conversion for WDM channel allocation, where (a) is the close-up of Ch q surrounded by the dotted rectangle.
In the conventional LOS system, ultrashort optical pulses served as the local sampling pulses are used to reconstruct the data signal, which is the case in [20]. To extend the LOS technique to a general case, we write the local sampling signal which covers the optical spectrum of the data signal in a form of periodic signal not just a pulsed signal as
where fLcq is the frequency of a certain comb tooth that is closest to fScq, fL is the repetition rate of local comb, Lqm and φLqm are the intensity and phase profile of each comb tooth, respectively. The subscript “q” is chosen for the same reason as mentioned above. As the repetition rates between the local sampling signal and the data signal are slightly detuned, where Δf = fSq - fL (or in a general case, fSq ≈NfL or fL/N, N is a positive integer). In the optical performance monitoring system, the repetition rate of the data signal is determined by fSq = fbq/lq [8, 21, 22], where fbq is the bit rate and lq is the word length of each channel, respectively. Considering the interference between the sampling signal and the qth channel alone, the output current of the detector iswhere […] indicates the omitted profile which will be rejected by the low bandwidth PD. Equation (4) is the main result of the analysis for the interference process. The complex envelope of the output current isWhen the sampling signal satisfies the condition that its intensity and phase profile of each comb tooth are constants (Lr = C1, φLr = C2, where C1 and C2 are constants), the sampling signal is a pulsed signal, which is the case of conventional LOS system. Then by comparing Eq. (2) and Eq. (5), we find that the temporal field of data signal is reconstructed with a compressed bandwidth, and the compression ratio is Rq = fSq/Δf. Assuming the original bandwidth of the data signal is Bq, the bandwidth of constructed signal in the RF domain is now Bq/Rq. A PD with a bandwidth larger than Bq/Rq is capable of detecting the beat note, while in the conventional LOS system, PDs with a larger bandwidth than fL is required. Here, the equivalent sampling rate is determined by Rq × FS, where FS is the real sampling rate of the digitizer.Besides, there are two conclusions that can be derived from Eq. (4). First, sampling signals are not just restricted to ultrashort optical pulse, since once the intensity and phase profiles of the sampling signal are known, the data signal can be calculated from Eq. (4). Therefore using ultrashort pulse for sampling is just a special case for LOS. Second, the mutual coherence between the data signal and the sampling signal guarantees the perfect measurement of the data signal. The fluctuations between the carrier frequencies of data signal and sampling signal do not play any role in the measurement of the intensity envelope of the data signal, but directly affect the phase profile extraction.
Assume the SUT described above is the qth channel of the WDM signal, the carrier is down-converted to ΔFq = fScq – fLcq and the bandwidth is compressed to Bq/Rq. Once the condition ΔFq - ΔFq-1 > (Bq/Rq + Bq-1/Rq-1)/2 is satisfied, the compressed channels will not overlap in the RF domain, as shown in Fig. 1(b). The multiple channels then can be decomposed easily by using narrow-bandwidth finite impulse response (FIR) filters.
3. Experiment and results
3.1 Proof-of-concept demonstration for modified LOS
We conducted a preliminary experiment to confirm the new understanding of LOS described above by measuring a PRBS signal. A 1-kHz linewidth fiber laser (NKT Adjustik E15) delivered optical carrier signal centers at 1550 nm. The optical carrier was data-modulated with a Mach-Zehnder modulator (MZM) driven by a train of PRBS signal from an arbitrary waveform generator (AWG, Keysight M8195A). The 10 GBaud rate PRBS signal has a word length of 40. A commercial MLL (MenloSystems) was served as the sampling source with a detuned repetition rate of (250MHz + Δf), where Δf was chosen to be 10 kHz. The short pulses of the MLL were reshaped with disorganized phase terms and arbitrary-shaped intensity. After received by a PD (Thorlabs, 470C) and filtered by a digital filter (Mini-Circuits, SLP), the interferograms were digitized by a 12-bit oscilloscope at a sampling rate of 1 GSamples/s, which corresponds to an equivalent sampling rate of 25 TSamples/s. Figure 2(a) illustrates the measurement result of the PRBS. According to Eq. (5), we removed the intensity and phase term of the local sampling pulses, and the PRBS waveform was recovered as shown in Fig. 2(b). The carrier frequency of the data signal was down-converted to about 37 MHz as shown in Fig. 2(c), which is the carrier frequency of the measurement result shown in Figs. 2(a) and (b). The effective bandwidth of the compressed PRBS signal is about 20 MHz, which is much smaller than the repetition rate of the local sampling signal. The envelope plotted in Fig. 2(d) is the reconstructed PRBS signal according to Eq. (5) with a compression ratio of 25000. Meanwhile, we compared the reconstructed PRBS signal using this arbitrary-shaped signal with that measured based on conventional LOS. We found that two results consist with each other, and this experiment verifies the general LOS theory mentioned in Section 2. This means that any known stable periodic waveforms can be used to perform LOS. For the sake of simplicity, the local sampling signals in the following experiment are still standard short pulses.
Fig. 2 Characterization of a PRBS signal using an arbitrary-shaped sampling signal. (a) Raw sampling results including the carrier frequency. (b) Reconstructed signal from (a) referencing to Eq. (4). (c) RF spectrum of the inteferogram shown in (a). (d) Recovered PRBS signal.
3.2 Proof-of-concept demonstration for channel allocation
This proposed WDM monitoring system was then tested by characterizing the dual-channel signals. The experimental setup of phase-sensitive LOS system was shown in Fig. 3. The sampling pulses were generated by a commercially available MLL operating at a repetition rate of 250 MHz. The optical spectrum was tuned to cover that of the data signals and filtered by an 8-nm bandwidth optical bandpass filter to reduce the peak power of sampling pulses. To validate the ability of the proposed method to monitor multi-channel WDM signals with a single receiving channel, we generated two-channel signals by two independent lasers, which centered at 1549.8 nm and 1550.2 nm, respectively. We generated two data trains with independent PRBSs to each channel. The MZM of Ch 1 worked at the linear area was driven by a 20 GBaud data signal and another MZM of Ch 2 worked at the null point was driven by a 32 GBaud data signal.
Fig. 3 Experimental setup of dual-channel signal monitoring system. MLL: mode-locked laser; FL: fiber laser; BPF: optical bandpass filter; MZM: Mach-Zehnder modulator; AWG: arbitrary waveform generator; BPD: balanced photodetector.
Figure 4(a) shows the measured power spectrum of the dual-channel optical signals using an optical spectrum analyzer with 2 GHz resolution. The channel spacing is determined by the RF synthesizer to be 50 GHz. The left peak represents the 20 GBaud OOK signal and the right peak is the 32 GBaud DPSK signal. The carrier of Ch 1 and Ch 2 were down-converted to ΔF1 ≈39 MHz and ΔF2 ≈80 MHz as shown in Fig. 4(b). To synchronize the word pattern, the actual Baud rate of OOK signal is fb1 = 20.005 GBaud with a word length of l1 = 80 and that of DPSK signal is fb2 = 31.7504 GBaud with a word length of l2 = 127. While the repetition rate of the beat note signals from two channels are Δf1 = 62.5 kHz and Δf2 = 3.15 kHz, with compression ratios of R1 = 4000 and R2 = 79365, respectively. Therefore the actual signal bandwidth of Ch 1 is smaller than that of Ch 2, but exhibits larger bandwidth in Fig. 4(b). We chose the two channels with such a great disparity in order to show that the proposed method can be applied with independent channels. The demultiplexing of the WDM signal was performed offline by applying FIR filters to the sampling interferogram. The bandpass FIR filter to filter Ch 1 was centered at 39 MHz with a bandwidth of 20 MHz and another one to decompose Ch 2 was centered at 80 MHz with a bandwidth of 1.5 MHz. The demultiplexed waveforms of OOK and DPSK signals are shown in Figs. 4(c) and 4(d) respectively. Meanwhile, the adoption of a spectral filtering strategy [23] in this measurement, enables achieving near shot-noise-limited performance. Greatly improved sampling quality has been achieved compared with the previous WDM monitoring demonstrations [14].
Fig. 4 (a) Optical spectrum of the dual-channel signal. (b) Measured dual-channel signal in electrical domain. (c) Demultiplexed 20 GBaud OOK signal. (d) Demultiplexed 32 GBaud DPSK signal.
It’s worth mentioning that in order to demodulate the DPSK signal, we calculated the phase profile, φSig(t) of the complex interferogram using Hilbert transform. The signal of DPSK format φDPSK(t) can be demodulated as
where τ is the bit period of the DPSK signal. In Fig. 4(d), we found that considerable phase vibrations exists in the recovered DPSK signal, which is caused by the carrier frequency fluctuations between the free-running fiber laser and MLL. Since the coherence of the sampling system is of great significance for perfect reconstruction of data signals, we conducted extra procedures for repetition rate locking and carrier frequency locking. For repetition rate locking, the RF synthesizer and the AWG were phase-locked to the repetition rate of the MLL, where the output clock of the MLL served as the reference clock to AWG after a twenty-five fold frequency divider. The phase noise of the fiber laser and that of the sampling laser can be represented as ϕq(t) and ϕL(t), respectively. To track the carrier frequency fluctuations between the fiber laser and the sampling laser, we set an auxiliary interferometer for recovering the mutual coherence of these two lasers. When the sampling interferogram was recorded, the interferogram of the auxiliary interferometer was captured simultaneously. After removing the 2π(fScq – fLcq)t beat-note phase profile, the random phase fluctuations of the fiber laser and the sampling laser are shown in Fig. 5(a) in the form of d[ϕq(t) - ϕL(t)]/dt. Then the phase fluctuation can be cancelled by a complex multiplication of the interferogram from the auxiliary interferometer with the interferogram of the sampling interferometer. By establishing the coherence between data signals and sampling pulses, the demodulated DPSK signal is then shown in Fig. 5(b). As a performance metric, we calculated the phase jitter around the bit center of every bit pattern, and it is measured to be 0.03 rad2.Fig. 5 Experimental results. (a) Measured carrier frequency fluctuations in 250 μs. (b) Demodulated DPSK signal with phase noise cancellation.
3.3 Simultaneous massively parallel multi-channel monitoring of WDM signals
In Section 3.2 we verified that the proposed method is able to characterize multiple–channel independent signals with single receiving channel. Recently, the employment of optical frequency combs (OFCs) as WDM sources is very interesting because of their relative simplicity and the precision of their spectral line spacing. With tunable center frequency and tunable line spacing, OFC sources are often the best choice for WDM systems [24–26]. To achieve the full potential of our proposed method, we demonstrated the monitoring of a massively paralleled WDM signal by using the electro-optic frequency comb as the WDM carriers. According to the Telecommunication Standardization Sector of International Telecommunication Union [27], the channel spacing of dense WDM signal is standardized with spacing of integer times of 12.5 GHz from 12.5 GHz to 100 GHz. In this experiment, a channel spacing of 25 GHz is chosen for the carriers. An electro-optic modulator with metallic mirrors (Fabry-Perot modulator from Optocomb) served as the optical frequency comb generator (OFCG) as shown in Fig. 6(a). The arrangement provided 250 comb lines ranging from 1525 nm to 1575 nm, and only 50 comb lines were left by using a 10-nm optical filter. We amplified the WDM carriers to 5 dBm with an erbium-doped fiber amplifier (EDFA) as shown in Fig. 6(b). Typically, odd and even carriers are modulated using two independent modulators to emulate WDM transmission [24–26]. However, all 50 carriers were simultaneously modulated with 80-bit length PRBS at 20.0001 GBaud by a MZM which works at the null point as the de-multiplexer for combs lines separation is not available in our laboratory. The MZM was driven by the PRBS signal and the pulse patterns were shaped according to a raised-cosine spectrum with a roll-off factor of 0.1. Then the WDM signal was launched to a 10 km single-mode fiber (SMF, dispersion coefficient 14 ps/(km × nm)), providing about 35 ps relative delay per adjacent channel. Average power of the total WDM signal is measured to be - 2.3 dBm. The optical spectrum of the transmitted superchannel is presented in Fig. 6(c). As the bandwidth of the optical filter used after the MLL is 8 nm, only 40 channels were covered in the monitoring system.
Fig. 6 (a) Schematic of the generation of massively paralleled WDM signal. (b) Optical spectrum of the generated optical carriers. (c) Optical spectrum of the transmitted superchannel. FL: fiber laser; OFCG: optical frequency comb generator; EDFA: erbium-doped fiber amplifier.
The sampling setup structure is same as the structure plotted in Fig. 3. In this demonstration, the measurement speed is calculated to Δf = 1.25 kHz, and the exact carrier spacing is 25. 001 GHz. Therefore, the down-converted channels have equally spaced “line spacing” in the RF domain, which is calculated to be 1 MHz, while the effective bandwidth of each channel is compressed to 200 kHz. The total WDM signal obtained in the RF domain resulting after the down-conversion from the optical domain is shown in Figs. 7(a) and 7(b). Figure 7(a) shows the mixed time domain signals of all WDM channels containing 160 bits. Although all the WDM channels are modulated by the same sequence at the same instant time, the time domain signals in Fig. 7(a) are chaotic signals because the dispersive media was employed to avoid complete bit synchronization among channels. Figure 7(b) shows the electrical spectrum of 40 modulated channels. Since the interference between the sampling laser and WDM carriers is a multiheterodyne process, the measured WDM carriers were separated by 2 MHz to 41 MHz with 1-MHz line spacing. The largest power attenuation of the outermost carrier is 6 dB compared with the central carrier. The demultiplexing of WDM signals was performed by applying digital FIR bandpass filters with 400 kHz bandwidth to each channel. Figure 7(c) shows the eye diagrams of the demultiplexed DPSK signals of six randomly chosen channels: channel 7, channel 8, channel 23, channel 29, channel 34 and channel 40. We note that the signal of each channel can be recovered with open eyes even at an average power of - 18.3 dBm. It is obvious that the proposed method is an attractive option for WDM signal monitoring.
Fig. 7 (a) Mixed of time domain signals of 40 channels. (b) Electrical spectrum of 40 modulated channels. (c) Eye diagrams of six randomly chosen channels.
4. Conclusions
We have proposed and demonstrated simultaneous massively parallel WDM signal monitoring with a single sampling channel based on multiheterodyne detection. We successfully demonstrated the observation of 40-channel WDM-DPSK signal with 800 Gbit/s data rate covering 1 THz bandwidth. We show that LOS technique can be implemented in a new way, by exploiting a new paradigm which is quite different from the traditional understanding of LOS theory. We believe that the proposed technique creates new possibility for LOS technique and dense WDM signal characterization.
Funding
Natural Science Foundation of China (NSFC) (61775132, 61735015, 61620106015, 61327812).
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