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Abstract
Nonlinear optical signal processing is expected to be one of promising approaches in optical networking units (ONUs) and it requires mutual conversion between data signals and optical pulse signals for the bandwidth matching between them. We investigate four-wave mixing (FWM) based bandwidth management for ONUs and experimentally demonstrate variable bandwidth adjustment and defragmentation. Experimental results show variability in bandwidth adjustment and spectral defragmentation. Bit-error-rate (BER) measurements show an error-free operation (BER<10−9) with a power penalty of 3.75 dB after FWM-based bandwidth management in simulation.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The continual demand for high performance information and communication technology presses various current building techniques and devices in optical network units (ONUs) to improve efficiency of broadband resource utilization as well as its bit rate performance [1]. Bandwidth management is the process for the network traffic optimization where bandwidth shapers play an important role to optimally allocate the available bandwidth for ONUs on the ingress and egress [2–4]. In 100G ONUs for the 100 Gb/s next-generation passive optical networks, a WDM technology is expected to play a significant role for dynamic wavelength and bandwidth allocation (DWBA) [2]. Broadband characteristics in optical signal processing enables us to attain various broadband functions disabled by electrical signal processing. In particular, optical signal processing using nonlinear optical effects (NOSP) is expected to be one of promising approaches in optical networking systems and have been actively investigated [5–8] because it can realize specific nonlinear functions such as wavelength conversion. NOSP has an inherent potential beyond electrical ones in high-speed processing performance and reduction of the number of devices with O/E conversion and such an attractive potential is expected to fit to high speed processing in WDM technology for the 100G ONUs. In fact, although NOSP still has concerns in cost and power consumption, its strengths more than makes up for its weakness for some applications in the 100 Gb/s next-generation passive optical networks because high speed applications would reveal various limitations in electrical processors like high speed A/D converters. In addition, key components for NOSP is expected to be integrated through Si photonics which could make them more cost effective and power efficient. Since, however, such nonlinear optical effects can be induced by optical short pulses of more than several hundred GHz bandwidth, the data signals of several tens GHz bandwidth for processing must be once transformed to optical pulse signals in ONUs including nonlinear optical signal processing. On the other hand, since its broadband characteristics causes severe bandwidth occupancy which impairs the degree of freedom on bandwidth management, appropriate bandwidth management for ONUs would provide both of the ingress broadband and the egress narrowband characteristics.
Here, as one of key components in ONUs, an analog-to-digital conversion (ADC) could be taken as a specific example because ADC determines the ingress and egress bandwidths and the signal quality in a post-processing in digital technology. In ADCs, the introduction of the optical technology, a so-called photonic ADC development, has already started to solve issue and limitation in electrical technology [9–11]. Recently, from the viewpoint of resolution maximization in photonic ADCs, we have demonstrated a new approach based on spectral compression to accommodate such broadband signals within C-band and avoid additional costs regarding power consumption and complexity [12]. Since this approach enable us to attain an on-demand adjustment of a subcarrier bandwidth, it can be applied not only to resolution maximization in photonic ADCs but also widely to bandwidth shaper in ONUs.
In this paper, we investigate FWM-based bandwidth management for ONUs including nonlinear signal processing and experimentally demonstrate variable bandwidth adjustment and defragmentation as representative functions at the exit of ONUs. Experimental results show that 2 different bandwidth adjustments and 9 different center wavelength selection for defragmentation. In addition, we discuss signal quality after bandwidth management by bit-error-rate (BER) measurements and an error-free operation (BER<${10^{ - 9}}$) with a power penalty of 3.75 dB after FWM-based spectral compression is confirmed in simulation.
2. Technical background and method
Nonlinear optical signal processing in ONUs requires to transform the data signals to optical pulse signals and vice versa because of the bandwidth mismatching between them. When the signals after processing exit from ONUs, the bandwidths of signals should be re-adjusted to appropriate one for data transmission with some additional treatments such as spectral defragmentation. As mentioned, FWM-based spectral compression [12] for photonic ADCs enables us to flexibly adjust both bandwidth and center wavelength of optical pulse signals. This is indeed applicable for the bandwidth management in ONUs such as bandwidth adjustment and spectral defragmentation, as shown in Fig. 1.
Fig. 1. Conceptual diagram of bandwidth management in optical networking unit and bandwidth adjustment and spectral defragmentation after nonlinear optical signal processing:
Since FWM-based spectral compression enables us to attain an on-demand adjustment of a subcarrier bandwidth, it can be applied to bandwidth adjustment in ONUs. FWM-based spectral compression can be realized by degenerate four-wave mixing of the two linearly chirped pulses. This technique has been proposed and investigated for the generation of a narrow-bandwidth pulse by frequency mixing of chirped pulses [13–15]. Degenerate FWM is one of the third-order nonlinear optical effects which is used for ultrafast nonlinear signal processing. Degenerate FWM provides two idler waves from input waves of frequency ${f_1}$ and ${f_2}$, whose frequencies are $2{f_2} - {f_1}{\; and\; }2{f_1} - {f_2}$, respectively. Here, when degenerate FWM is induced by the two linearly chirped pulses which has instantaneous frequencies ${f_1}(t )= {f_1} + {C_1}t$ and ${f_2}\; (t )= {f_2} + {C_2}t$, the instantaneous frequencies of the idler pulses generated from degenerate FWM are given by,
Spectral defragmentation inevitably becomes an issue in optical networking system and wavelength conversion using nonlinear optical signal processing is expected to be one of promising approaches [16,17]. Since FWM can be regarded as one of wavelength conversion techniques, it could be also useful for spectral defragmentation. When a certain amount of relative time delay $\delta t$ between pump and signal pulses is added to FWM-based spectral compression, ${f_{idle{r_1}}}$ changes to
From Eq. (5), it can be seen that adjustment of the amount of relative time delay $\delta t$ enables us to select the center wavelength of an idler pulse ${\lambda _{idler}}$, which is given by, where, ${c_0}$ is speed of light. This suggests that FWM-based spectral compression can flexibly select the center wavelength as well as bandwidth adjustment for spectral defragmentation without changing the center wavelength of the pump pulse.Figure 2(a) and Fig. 2(b) are the calculated results of FWM-based process through split-step Fourier method based on the generalized nonlinear Schrodinger equation (NSE). Their center wavelengths in Fig. 2(a) and Fig. 2(b) fall in the same wavelength of 1544.02nm. These results also coincide with the calculation result with substituting $ {f_1} = {c_0}/1552$ and $ {f_2} = {c_0}/1548$ to the Eq. (3). Since, in addition, bandwidths after FWM become 0.116nm and 0.240nm, bandwidth adjustment is also successfully achieved. These results confirmed that the presented analytical model based on the Eq. (3) can obtain the same results for FWM-based process as those from the calculation based on NSE.
Fig. 2. Simulation results of the spectra inducing FWM (a) ${\textrm{C}_1} = 35.4[{ps/nm} ]$ and ${\textrm{C}_2} = 17.7[{ps/nm} ]$ (b) ${\textrm{C}_1} = 17.7[{ps/nm} ]$ and ${\textrm{C}_2} = 10.0[{ps/nm} ]$
3. Experimental verification
We experimentally verified the functions of this approach and demonstrated variable bandwidth adjustment and spectral defragmentation as representative functions at the exit of ONUs. Through the whole experiments, we use a HNLF longer than the usual one with postulating a future use of a Si nanowire with quite high nonlinearity, which is expected to be one of the promising integration approaches for NOSP.
3.1 Bandwidth adjustment
Figure 3 shows an experimental setup for verification of bandwidth adjustment in a communication band by using FWM-based spectrum compression. We used optical pulses irradiated from a fiber laser (Calmar FPL-M2CFF-OSU-01) as a light source for bandwidth adjustment demonstration. The pulse width, the center wavelength, and the repetition rate were 100fs, 1550nm, and 30MHz, respectively. By filtering of wavelength selective switch (WSS), output the pulses which have the center wavelength 1548nm from port1 as a pump pulse and 1552nm from port2 as a signal pulse. The bandwidth of the pulses from port1 and port2 were 1.5nm and 3nm, respectively. In order to provide linearly chirp to the pulses, they were propagated in single-mode fiber (SMF). To change the amount of frequency chirp, we changed the length of SMF. First, we used 2000m-SMF(${\textrm{C}_1} = 35.4[{ps/nm} ]$) and 970m-SMF(${\textrm{C}_2} = 17.7[{ps/nm} ]$), and then we used 970m-SMF(${\textrm{C}_1} = 17.7[{ps/nm} ]$) and 500m-SMF(${\textrm{C}_2} = 10.0[{ps/nm} ]$). They were multiplexed by 3dB coupler. They were propagated 400m-HNLF(D = 0.044[ps/nm/km], S = 0.029[ps/nm^2/km], γ=20[/W/km]) for the generation FWM.
Fig. 3. Experimental setup for bandwidth adjustment: MLFL, mode-locked fiber laser; EDFA, erbium-doped fiber amplifier; SMF, single-mode fiber; PC, polarization controller; OSA, optical spectrum analyzer; OSC, oscilloscope.
Figure 4(a) and (b) show the output spectra when we use a 400m-HNLF for generation of degenerate FWM together with two different pair of single mode fibers for variable bandwidth adjustment by the amount of linearly chirps. One is a pair of 2000m and 970m SMFs and the other is that of 970m and 500m SMFs. In this experiment, a pair of SMFs are used for experimental verification under constraints of the available equipment but commercially available dispersion compensators can be used for the real-time flexible adjustment. Figure 4(c) shows idler signal spectra as a result of filtering the other signals out. These two different bandwidth idler signals as shown in Fig. 4(a) and (b) are generated nearby 1544nm of which bandwidth were approximately 0.19nm (23.8GHz) and 0.26nm (32.5GHz), respectively as shown in Fig. 4(c). From these results, we confirmed that bandwidth of the idler signal can be adjusted by the amount of linearly chirps.
Fig. 4. Experimental results of the spectra inducing FWM using (a) a pair of 2000 m and 970 m SMFs (b) a pair of 970 m and 500 m SMFs, and (c) the obtained idler pulse after different bandwidth adjustment.
These results are corresponding to the simulation results shown in Fig. 2(a) and Fig. 2(b), respectively. Their center wavelengths in Fig. 4(a) and Fig. 4(b) are certainly same as the corresponding one of 1544.02nm in Fig. 2(a) and Fig. 2(b), respectively. Assuming this approach is applied to WDM signal or OFDM subcarrier, we changed the center wavelength of the signal from 1552nm by 1nm and did the same experiment by using 2000m, 970m-SMF.
Figure 5 shows FWM-based bandwidth adjustment results for signals of different wavelength channels. From Fig. 5, it can be seen that the center wavelength of idler pulses can be aligned in accordance with the original center wavelength of signal pulses. Since the amount of relative phase mismatch between pump and signal pulses increases, the intensity of the idler decreases as the center wavelength of the signal increases.
Fig. 5. Experimental results of FWM-based spectral adjustment for signals of different wavelength channels.
3.2 Spectral defragmentation
Figure 6 shows experimental setup for verification of spectral defragmentation by controlling relative time delay between pump and signal pulses. The experimental procedure is almost same as 3.1. A relative time delay between pump and signal pulses was provided by using tunable delay line. The center wavelength of pump and the signal pulses are 1548nm and 1554nm, respectively.
Fig. 6. Experimental setup of spectral defragmentation: MLFL, mode-locked fiber laser; EDFA, erbium-doped fiber amplifier; SMF, single-mode fiber; PC, polarization controller; OSA, optical spectrum analyzer; OSC, oscilloscope.
Figure 7 shows FWM-based spectral defragmentation results by controlling relative time delay between pump and signal pulses by 10ps step. From Fig. 7, it can be seen that the center wavelength of the idler pulse can be changed by controlling the amount of a relative time delay between pump and signal pulses. The amount of relative time delay was provided after adjusting the temporal peak positions of pump and signal pulses. From Fig. 7, it can be seen that the intensity of the idler pulse decreases as a relative time delay with respect to a pump pulse increases. This intensity decrease can be considered to be caused by increase of relative phase mismatch and decrease of the overlapped temporal area between pump and signal pulses. The increase of relative phase mismatch can be considered to be caused by mixing of a pump pulse and longer wavelength of a signal pulse due to the amount of relative time delay and anomalous dispersion by SMF. On the other hand, the idler pulse intensity increases when time delays of -10ps, -20ps, -30ps were provided. This intensity increase can be considered to be caused by the decrease of the relative phase mismatch which makes the efficiency improvement of FWM be larger than the intensity loss by decreasing the overlapped temporal area between pump and signal pulses. With time delay between signal and pump lights, unoverlapping parts in time domain occurs between them and an idler light cannot be generated from there. As a result, the more a time delay between signal and pump lights becomes, the less the power of an idler light becomes. On the other hand, the power of an idler light sometimes increases because the wavelength difference between signal and pump lights decreases depending on their condition of chirp.
Fig. 7. Experimental results of FWM-based spectral defragmentation by controlling relative time delay between pump and signal pulses by 10 ps step.
The process of ordering the signals in the wavelength domain is experimentally demonstrated to show an essential process of spectral defragmentation. Figure 8 shows the experimental setup for this demonstration. To identify two signals after ordering in the wavelength domain, two signals with different bandwidths, 2[nm] and 0.5[nm], are purposely prepared. We provided frequency chirp to the signal pulses by WSS. Figure 9(a) and Fig. 9(b) are experimental results of spectra of two idler signals after FWM with and without a time delay control. In comparison with the center wavelength order of two signals in Fig. 9(a), the order in Fig. 9(b) is successfully switched in the reverse order.
Fig. 8. Experimental setup of spectral defragmentation: MLFL, mode-locked fiber laser; EDFA, erbium-doped fiber amplifier; SMF, single-mode fiber; PC, polarization controller; OSA, optical spectrum analyzer; OSC, oscilloscope.
Fig. 9. Experimental results of spectra of two idler signals after FWM (a) without and (b) with a time delay control
4. Discussion
In order to evaluate reliability, we measured bit-error-rate (BER) measurements for the idler pulse generated by FWM-based bandwidth adjustment in simulation by the Rsoft’s OptSim. In the simulation, we used 10Gbps signal from 10GHz mode-lock pulse laser. The modulation format of the signal is on-off keying (OOK) by ${2^{10}}$-1 pseudo-random bit sequence (PRBS). The extinction ratio of a Mach-Zender modulator (MZM) is set to the ideal condition in the software and the signal power for the off state is set to zero and the effective core area of a silica HNLF is set to 10$[{\mu }{\textrm{m}^2}$]. The pump pulse for generation FWM is also from 10GHz mode-lock pulse laser. The bandwidth of the signal and the idler pulse were 3nm and 0.22nm(27.5GHz). Figure 10 shows BER characteristics of the back-to-back signal and the idler pulse under the same conditions. As shown in Fig. 10, an error-free operation (BER<${10^{ - 9}}$) with a power penalty of 3.75 dB after FWM-based spectral compression is achieved in the simulation.
Fig. 10. BER measurement results after FWM-based bandwidth adjustment for on-off keying (OOK) modulation format by ${2^{10}}$-1 pseudo-random bit sequence (PRBS).
In addition, to demonstrate its applicability to multi-level signals with phase shift keying, we used 10Gbps signal from 10GHz mode-lock pulse laser. We measured BER measurements by the MathWorks’s MATLAB because the Rsoft’s OptSim doesn’t support multi-level modulation. The modulation format of the signal is quadratic phase shift keying (QPSK) by ${2^{10}}$-1 pseudo-random bit sequence (PRBS). The idler pulse is received using a 0.1 ps time gate and a coherent receiver with 50 GHz electrical bandwidth. The BER performance is estimated through error vector magnitude (EVM) [18]. Figure 11 shows BER characteristics of the back-to-back signal and the idler pulse under the same conditions. As shown in Fig. 11, an error-free operation (BER<${10^{ - 9}}$) with a power penalty of 0 dB after FWM-based spectral compression is achieved in the simulation.
Fig. 11. BER measurement results after FWM-based bandwidth adjustment for quadratic phase shift keying (QPSK) modulation format by ${2^{10}}$-1 pseudo-random bit sequence (PRBS).
Figure 12(a) shows BER measurement results after FWM-based bandwidth adjustment for on-off keying (OOK) modulation format by ${2^{10}} - 1$ pseudo-random bit sequence (PRBS) in different signal/pump power. Since an idler light power decreases with decreasing a pump light power, an appropriate amplification is necessary for error free operation depending on the experimental condition. If the idler power decreases, influence of amplified spontaneous emission (ASE) noise becomes larger. We provide the relationship between power penalty and signal/pump power for an error-free operation (BER=${10^{ - 9}}$) in Fig. 12(b).
Fig. 12. (a) BER measurement results after FWM-based bandwidth adjustment for on-off keying (OOK) modulation format by ${2^{10}}$-1 pseudo-random bit sequence (PRBS) in different signal/pump power, (b) Power Penalty vs Signal/Pump power for BER=${10^{ - 9}}$
5. Conclusion
We proposed to apply FWM spectral compression to bandwidth management technique in ONUs and experimentally demonstrated variable bandwidth adjustment and spectral defragmentation as representative functions. Experimental results show variability in bandwidth adjustment and spectral defragmentation by control of the amount of frequency chirp and time delay of optical pulses. Bit-error-rate (BER) measurements show an error-free operation (BER<${10^{ - 9}}$) with a power penalty of 3.75 dB after FWM-based bandwidth management in simulation. Since such frequency chirp and time delay controls are very common in optical signal processing and various commercially available devices can be introduced to it, this approach is expected to be feasible and effectively utilized along with the spread of nonlinear signal processing in optical communication. Although 100G ONUs seems to be a forward-looking research, its future development comes to require finding out a cost-sensitive and preferred to use ready components in the current PON and Si photonics is expected to be one of promising approaches to satisfy those requirements.
Funding
Mitsubishi Electric Corporation.
Disclosures
The authors declare no conflicts of interest.
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