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Abstract
As one of the promising multiplexing and multicarrier modulation technologies, Nyquist subcarrier multiplexing (Nyquist SCM) has recently attracted research attention to realize ultra-fast and ultra-spectral-efficient optical networks. In this paper, we propose and experimentally demonstrate optical subcarrier processing technologies for Nyquist SCM signals such as frequency conversion, multicast and data aggregation of subcarriers, through the coherent spectrum overlapping between subcarriers in four-wave mixing (FWM) with coherent multi-tone pump. The data aggregation is realized by coherently superposing or combining low-level subcarriers to yield high-level subcarriers in the optical field. Moreover, multiple replicas of the data-aggregated subcarriers and the subcarriers carrying the original data are obtained. In the experiment, two 5 Gbps quadrature phase-shift keying (QPSK) subcarriers are coherently combined to generate a 10 Gbps 16 quadrature amplitude modulation (QAM) subcarrier with frequency conversions through the FWM with coherent multi-tone pump. Less than 1 dB optical signal-to-noise ratio (OSNR) penalty variation is observed for the synthesized 16QAM subcarriers after the data aggregation. In addition, some subcarriers are kept in the original formats, QPSK, with a power penalty of less than 0.4 dB with respect to the original input subcarriers. The proposed subcarrier processing technology enables flexibility for spectral management in future dynamic optical networks.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
To meet the growing bandwidth demands, the transmission capacity and spectral efficiency of optical communications systems have been drastically increased through multiplexing and multi-level modulation technologies with the fast development of coherent detection and digital signal processing (DSP) techniques. In addition to multiplexing technologies such as wavelength-division multiplexing (WDM) and optical orthogonal frequency division multiplexing (OFDM), Nyquist subcarrier multiplexing (Nyquist SCM) provides an alternate approach to generating spectrally-efficient super-channels [1–4]. In Nyquist SCM, each subcarrier is modulated using sinc-shaped (Nyquist) pulses, resulting in a rectangular spectrum on each subcarrier. In particular, owing to its simplicity, half-cycle Nyquist SCM [4] has attracted much attention for applications in short reach. On the other hand, subcarrier processing technology for multi-carrier optical OFDM has been recently studied to demonstrate the subcarrier add/drop or substitution through opto-electronic interferometer [5–10]. With the increasing research interest in Nyquist SCM, it is becoming desirable to exploit optical subcarrier processing technologies for Nyquist SCM to realize a flexible, dynamic and efficient utilization of spectral resources in optical networks.
In this paper, we propose and experimentally demonstrate an optical subcarrier processing scheme to realize several network functionalities such as frequency conversion, multicast and data aggregation of subcarriers with Nyquist SCM signals, which is carried out using four-wave mixing (FWM) with a coherent multi-tone pump in highly-nonlinear fiber (HNLF). The data aggregation of subcarriers is implemented by coherently superposing two low-level subcarriers to yield a high-level subcarrier through a coherent spectrum overlapping in a coherently-pumped FWM. Furthermore, multiple replicas of the low-level subcarriers in their original formats and synthesized high-level subcarriers are simultaneously obtained at different frequencies in the same unit. In the experimental demonstration, 10 Gbps Nyquist-pulse shaped 16 quadrature amplitude modulation (QAM) subcarriers are successfully synthesized by coherently combining 2 × 5 Gbps Nyquist-pulse shaped quadrature phase-shift keying (QPSK) subcarriers. Less than 1 dB optical signal-to-noise ratio (OSNR) penalty variation is observed for the generated 16QAM subcarriers, and less than 0.4 dB OSNR penalty is obtained for the subcarriers kept in QPSK with respect to the original input subcarriers. The proposed subcarrier processing technology provides an effective way to realize the data aggregation by coherently superimposing low-speed low-level subcarriers to generate high-speed high-level subcarriers in Nyquist SCM signals. Also, it may be helpful in order to manage the subcarrier granularity in Nyquist SCM signals, providing flexibility for resource management in future dynamic optical networks.
2. Operating principle of optical subcarrier processing
Figure 1 depicts the operation principle of coherent spectrum overlapping in FWM with coherent multi-tone pump. In this example, a coherent pump with 3 tones is used with spacing of Δω and 2Δω between ω1 and ω2, ω2 and ω3, respectively. With three input pumps at ω1, ω2, ω3, and an input signal at ωs, six non-degenerate FWM components are generated alongside the input signal with uniform spacing of Δω at frequencies ωsij*, where i,j ∈ [1–3], i≠j, and * represents the complex conjugate. The resultant phase in the non-degenerate components ωsij* is given by the following equation [11]:
where θoutput, θinput, ΔθPi, ΔθPj, and c. are the phases of the output components and input signal, the phase noise from pump i, j (i, j∈ [1–3]), and a constant term, respectively. It is obvious that in the resultant FWM products, the pump phase is shown as the phase difference between two of pump tones. If the 3-tone pump is coherent in phase, the pump phases appear as constant terms in the phase of the resultant products. Hence, the phase noise from pumps is cancelled out in the converted signals. Owing to the pump phase noise cancellation effect, coherent multi-carrier pump has been used in FWM to implement high-performance data exchange, wavelength conversion, multicasting and self-homodyne detection [11–16]. As shown in Fig. 1, if the bandwidth of the input signal, Δωs, is wider than Δω, spectrum overlapping will occur between the signal and the converted replicas. Due to the phase coherence between the pump tones, as shown in Eq. (1), only the constant terms remain in the phase difference between the signal and the generated non-degenerate components, indicating that these components are coherent in phase. Therefore, with Δωs>Δω in a coherently-pumped FWM, a coherent spectrum overlapping could be realized.If the input signal is modulated with Nyquist SCM, the coherent spectrum overlapping could be used to coherently superpose and merge different subcarriers to form new subcarriers, effectively realizing data aggregation. Here, the operation principle of coherent combination of subcarriers in Nyquist SCM signals is discussed with 2-tone and 3-tone coherent pumps, respectively. We assume that the input Nyquist SCM signal has two subcarriers with spacing of Δω, which is equal to the minimal spacing among coherent pump tones. In addition, the power of input Nyquist SCM should be managed in the linear regime to avoid internal nonlinear interaction between two subcarriers. As shown in Fig. 2, with such frequency arrangement, the coherent spectrum overlapping, i.e., the coherent combination or superposition, between subcarriers could be obtained after the FWM process. With the 2-tone coherent pumps spaced Δω apart, shown in Fig. 2(a), two replicas at ωs21* and ωs12* are obtained alongside the input signal at ωs after FWM. If the subcarriers of the input Nyquist SCM signal are also spaced Δω, the coherent spectrum overlapping between upper and lower subcarriers could be obtained at L and U, while the subcarriers at L1 and U1 are kept in the original formats. Four subcarriers are mainly synthesized after FWM. Table 1 summarizes the electrical fields of these four subcarriers after FWM. It confirms that the subcarriers L1 and U1 are kept in their original formats and the coherent combination of the original upper and lower subcarriers are obtained at subcarriers L and U. In the coherent combination, the relative power ratio between two subcarriers is mainly determined by the FWM efficiencies (ks21* and ks12*) and the pump power, while the relative phase difference is influenced by the phase difference between two pump tones (θP1-θP2). Figure 2(b) depicts the case with coherent 3-tone pumps. After the coherently-pumped FWM, some subcarriers (U2, U1, U, L, L1 and L2) of the input signal and replicas are coherently overlapped each other, causing the coherent combining between subcarriers, while the subcarriers at the edges (U3 and L3) remain in their original formats. Table 2 shows the electrical fields of the 8 subcarriers after FWM, which is consistent with the analysis in Fig. 2(b). Similar to the case with 2-tone coherent pump, the power ratio and phase difference between interfered subcarriers could be adjusted by properly managing the power ratio and phase difference among coherent pump tones.
Fig. 2 Operation principle of coherent superposition through FWM with coherent (a) two- and (b) three-tone pump.
Table 1. Electrical field of the resultant Nyquist subcarriers after the optical subcarrier processing with coherent 2-carrier pump
Table 2. Electrical field of each subcarrier in the resultant Nyquist SCM signals after the optical subcarrier processing with coherent 3-carrier pump
The coherent combination or superposition between the input signal and its replicas provides a possible approach to processing the subcarriers in Nyquist SCM signals. To enable the data aggregation in the subcarriers, the relative power and phase differences between the subcarriers involved in the interaction should be well managed. As an example (cf. Figure 3), with a field-aptitude ratio of 2:1 and a relative optical phase of zero or an integer multiple of π/2, a high-order 16QAM subcarrier could be obtained after the optical field superposition of two QPSK subcarriers in a complex plane. As aforementioned, a coherently-pumped FWM could be used to realize the coherent combination or superposition of two subcarriers. By optimizing the relative phase and power differences between the involved subcarriers, the input subcarriers modulated in low-level formats could be coherently combined to form a high-level modulated subcarrier, thus realizing data aggregation in subcarrier. The power ratio between the input signal at ωs and the replicas at ωs21* or ωs12* is mainly determined by the conversion efficiency of FWM, which could be managed by tuning the power of the pump and probe signals. The power ratios between other replicas (ωs21* and ωs32*, ωs31* and ωs32*, ωs12* and ωs23*, ωs23* and ωs13*) are affected by the power ratio between the pump tones (PP1:PP3, PP1:PP2, PP1:PP3, PP2:PP1). On the other hand, the relative phase difference between the pump tones affects the relative phase difference between these subcarriers. Thereby, to ensure the synthesis of 16QAM from two QPSK subcarriers, it is important to manipulate the phase and power of each pump tone, which could be implemented by a programmable optical processor such as a WaveShaper (WS). Note that, for easy illustration of the operation principle, we assume the phase difference between the input signal and replica is π/2 in Fig. 2.
3. Experimental setup and results
The experimental setup is illustrated in Fig. 4. Light from an external cavity laser (ECL) at 1546.5 nm was modulated by a dual-drive Mach-Zehnder modulator driven by a 10 GHz clock to generate an optical comb with a line spacing of 10 GHz. To prepare a multi-tone coherent pump, a programmable optical processor (WS) and a cascade of optical filters were used to select the desired two or three comb lines with proper line spacing. The relative power and phase difference among the comb lines was managed with the WS. Light from another ECL at 1548.4 nm was modulated by a dual parallel Mach-Zehnder modulator (DP-MZM) driven by an arbitrary waveform generator (AWG, sampling rate: 40 GS/s, vertical resolution: 9 bit) to form the input 10 Gbps Nyquist SCM signal, which consisted of two subcarriers (L and U), modulated at 2.5 GBd QPSK with raised cosine pulse shaping, a roll-off factor of 0.1, and spaced 10 GHz apart. The central carrier was suppressed by appropriately biasing the DP-MZM. After individual power amplification and out-of-band noise filtering, the signal and pump were combined at a 10:90 coupler before entering a span of highly-nonlinear fiber (HNLF), which has a length of 150 m, attenuation coefficient of 0.9 dB/km, nonlinear coefficient of 18 W/km, zero-dispersion wavelength of 1548 nm, and dispersion slope of around 0.02 ps/nm2/km. After being selected by an optical filter, each subcarrier after the HNLF was detected by a coherent receiver, which included a free-running local oscillator (LO), a 90-degree optical hybrid and two balanced photo-detectors. The wavelength of LO was tuned to that of the corresponding subcarrier for detection. The detected data was digitized at 50 GS/s by a real-time oscilloscope and processed offline for bit-error rate (BER) computation.
To avoid undesired distortions, the optimal power of pump and input signal in FWM was optimized by measuring the error vector magnitude (EVM) of the edge subcarriers when tuning the power range. As shown in Fig. 5, the optimized power of pump and input signal were measured as 21.7 dBm and −1.1 dBm, respectively. The measured optical spectra after FWM with coherent 2-tone and 3-tone pumps are shown in Figs. 6(a) and 6(b), respectively. For reference, the spectra of input signal and coherent pump are also shown in the figures. With a two-tone coherent pump spaced 10 GHz apart and similar pump power (PP1 = PP2), four subcarriers are mainly generated after FWM where the inner two subcarriers are encoded in 16QAM and the outer two are kept in QPSK. As shown in Fig. 6, the FWM efficiencies of L1 and U1 are measured both as −7 dB. When deploying a coherent 3-tone pump with adjacent carrier spacing of 10 GHz and 20 GHz and a power relationship of PP2 [dB] ≈PP3[dB] ≈PP1[dB] + 6dB, as discussed above, 8 subcarriers are mainly synthesized after the coherent spectral overlapping. With respect to the power of inner subcarriers (L and H), the FWM efficiencies of L1, U1, L2, U2, L3 and U3 are measured as −6.3 dB, −6.5 dB, −6.7 dB, −6.4 dB, −12.5 dB and −12.6 dB, respectively. Through coherent combination, the subcarriers are modulated with 16QAM except for the ones located at the edges (L3 and U3) which are kept in QPSK.
Fig. 5 Measured EVM of converted QPSK subcarriers at U3 when tuning the launched (a) probe and (b) pump power.
The constellations of the input Nyquist SCM signals with two subcarriers modulated at 2.5 GBd QPSK are shown in Figs. 7(a) and 7(b), respectively. As shown in Fig. 2, without considering high-order components, only the subcarriers at the edge are free from the spectrum overlapping, remaining in QPSK formats. The corresponding constellations are shown in Figs. 7(c) and 7(d). The increase of EVM is mainly attributed to the overlapping with high-order components in FWM. Through the coherent spectrum overlapping, with proper phase and power ratio management, data carried at two input subcarriers are coherently combined at the subcarriers (U1, U2, L1 and L2), synthesizing Nyquist 16QAMs. The corresponding constellations are shown in Figs. 8(a)-8(d), respectively. Besides, by adjusting the conversion efficiency and relative phase difference in pump tones, the original input subcarriers are converted to 16QAMs as well. Figures 8(e) and 8(f) show the measured constellations.
Fig. 7 Measured constellations of the original input QPSK subcarriers at (a) L and (b) U, and the frequency converted QPSK subcarriers (c) L3 and (d) U3.
Fig. 8 Measured constellations of the data-aggregated 16QAMs from two input QPSKs at subcarriers at the subcarriers (a) U1, (b) L1, (c) U2, (d) L2, (e) L and (f) U after the FWM.
To further verify the performance, the BERs of the input and converted subcarriers were measured against the OSNR (12.5 GHz resolution bandwidth) and plotted in Fig. 9. The theoretical BER curves of Nyquist QPSK and 16QAM are also plotted as references. With respect to the theoretical sensitivity at a BER of 10−4, around 1 dB implementation penalty is observed for the input Nyquist QPSK subcarriers, while 1.4 dB penalty for the converted QPSK subcarriers at the edge (U3 and L3). Thus, around 0.4 dB penalty is obtained for the converted Nyquist QPSK subcarriers with respect to the input subcarriers. As for the synthesized 16QAM subcarriers, compared with the theoretical result, an average penalty of 3 dB at BER of 10−3 is observed. The penalty variation for the synthesized Nyquist 16QAM subcarriers is within 1 dB. For these subcarriers, no visible error floor is observed up to a BER of 10−5. This substantiates the feasibility of the proposed subcarrier processing technology for Nyquist SCM signals.
Fig. 9 Measured BER curves vs. OSNR for input Nyquist QPSK subcarriers and converted Nyquist QPSK and 16QAM subcarriers; Theoretical BER curves vs. OSNR: blue solid line: Nyquist QPSK, red solid line: Nyquist 16QAM.
4. Summary
In this paper, we have proposed and experimentally demonstrated optical subcarrier processing technology for Nyquist SCM signals by coherent spectrum overlapping based on FWM with coherent multi-tone pumps to realize network functionalities such as frequency conversion, multicast and coherent combination of subcarriers. In the experimental demonstration, two input 5 Gbps low-level QPSK Nyquist subcarriers are coherently combined to form a 10 Gbps higher level 16QAM subcarrier with multiple replicas at different frequencies. Meanwhile, these two subcarriers are kept in the original formats but converted to different frequencies. The experimental results show that a less than 0.4 dB OSNR penalty is obtained for the converted QPSK subcarriers with respect to the original input subcarriers, and a less than 1 dB OSNR penalty variation is observed for the converted 16QAM subcarriers without visible error floor at up to 10−5 BER. These results demonstrate that the proposed method provides an effective technique for the subcarrier processing and management in Nyquist SCM signals, which may enable a flexible and agile spectrum management in the future optical networks.
Funding
JSPS Grant-in-Aid for Scientific Research (C) of MEXT in Japan (15K06033).
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