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We propose a banded all-optical orthogonal frequency division multiplexing (AO-OFDM) transmission system based on synthesising a number of truncated sinc-shaped subcarriers for each sub-band. This approach enables sub-band by sub-band reception and therefore each receiver’s electrical bandwidth can be significantly reduced compared with a conventional AO-OFDM system. As a proof-of-concept experiment, we synthesise 6 × 10-Gbaud subcarriers in both conventional and banded AO-OFDM systems. With a limited receiver electrical bandwidth, the experimental banded AO-OFDM system shows 2-dB optical signal to noise ratio (OSNR) benefit over conventional AO-OFDM at the 7%-overhead forward error correction (FEC) threshold. After transmission over 800-km of single-mode fiber, ≈3-dB improvement in Q-factor can be achieved at the optimal launch power at a cost of increasing the spectral width by 14%.
© 2016 Optical Society of America
1. Introduction
To cope with ever-increasing bandwidth demands on fiber optic communication systems, high capacity super-channel coherent optical transmission systems are being intensively investigated. Several approaches have been proposed based on orthogonal frequency division multiplexing (OFDM) [1, 2] and Nyquist wavelength division multiplexing (N-WDM) [3]. By incorporating digital signal processing, both transmission schemes can be made resistant to sub-system impairments such as: timing, carrier and phase offsets, and optical fiber channel distortions including chromatic dispersion (CD) and polarization mode dispersion (PMD) [4].
OFDM super-channel transmission technology is a multi-carrier transmission technique that combines several low-data-rate orthogonal subcarriers into a high-speed data super-channel [1]. The OFDM super-channel can be generated by combining multiple coherent OFDM (CO-OFDM) sub-bands, where each sub-band contains a number of subcarriers and is defined in digital domain. By designing the spacing between the adjacent sub-bands be a multiple of the subcarrier spacing, the subcarriers in the sub-bands will maintain their orthogonality [5, 6]. The per-sub-band symbol rate is limited by the digital to analog converters (DAC). All-optical OFDM (AO-OFDM) is an alternative approach for realizing an OFDM super-channel [7–11], which does not need high-bandwidth and high-resolution DAC and digital signal processing (DSP) at the transmitter side. In AO-OFDM an optical inverse Fourier transform (OIFT) is used to shape each subcarrier over a wide bandwidth. The OIFT can be implemented using, for example: multiple fiber Bragg gratings [12], arrays of phase shifters, delay lines and couplers [13, 14], or arrayed waveguide grating routers (AWGR) [15, 16]. Recently, a method of using mode-locked-laser (MLL) with a liquid-crystal-on-silicon (LCoS) wavelength selective switch (WSS) has been used for AO-OFDM [17]. This method can use lower-bandwidth modulators, as a stable modulator state is only required when the short pulses pass through. Moreover, it allows flexible subcarrier allocation and cyclic prefix (CP) insertion [18].
The reception and de-multiplexing of an OFDM super-channel can be achieved using an array of phase shifters, delay lines and couplers [19] or an AWGR [20], followed by fast optical samplers for the optical Fourier transform (OFT) operation. However, these schemes require dispersion compensation before the OIFT. Alternatively, AO-OFDM signals can be received by first using an optical band pass filter to coarsely select a portion of received spectrum corresponding to a subcarrier and its spectral tails. This is then sampled at a sufficiently high rate— a high multiple of the baud rate of each subcarrier— to reduce cross-talk between the subcarriers during demultiplexing. DSP is then used to de-multiplex the desired subcarrier [21].
In this paper, we propose splitting the AO-OFDM subcarriers in a superchannel into several distinct sub-bands, and modifying the spectrum of each subcarrier so that the spectral extent of a particular subcarrier is confined to be within only one of the sub-bands. We call this banded all-optical OFDM (B-AO-OFDM). The advantage is that the sampling rate is now set by the spectral extent of a single sub-band, rather than the theoretically infinite extent of one subcarrier. This concept is different to the digital sub-banding technique [22], which only aims for computational efficient digital processing, because our approach also reduces the hardware complexity of the receiver. The B-AO-OFDM scheme is an optical version of overlapped discrete multitoned modulation in wired communications [23] but with much higher data rate. Our approach can be implemented using the short pulse source and WSS-based AO-OFDM scheme [17], by simply modifying the original sinc-shaped response of the WSSs to a truncated-sinc response for each subcarrier.
Our approach achieves a significant reduction in the required electrical bandwidth, with a negligible performance penalty, at the cost of a small increase in total spectral width (i.e. a small loss in spectral efficiency). Individual sub-bands can be programmed differently to contain different numbers of subcarriers to support dynamic optical routing.
We first present the system design in Section 2, and then verify the proposed method with both simulation and experimental results in Section 3 & 4. The result in Section 5 shows that after 800 km of transmission, the proposed scheme provides a 3-dB benefit compared with a conventional AO-OFDM system with the same receiver electrical bandwidth.
2. Principle
Figure 1 compares the transmitter structures of B-AO-OFDM and conventional AO-OFDM systems. In both systems, a train of short-pulses from a mode-locked laser is split into Nsc paths (Nsc = 15). In each path, the pulses are modulated with QAM symbols by an IQ modulator. Each modulator converts the comb lines to a wide white spectrum when the signal baud rate equals to the comb line spacing. Then all of the signal paths are input into an Nsc × 1 LCoS WSS. As shown in Fig. 1(a), for conventional AO-OFDM signal generation, the WSS first performs OIFT by filtering different input signal paths with identical sinc-shaped responses at different center frequencies.
Fig. 1 Conceptual diagram of transmitter structure for: (a) conventional and (b) banded AO-OFDM systems. The generated super-channels are illustrated at the right.
We propose to group a number of subcarriers into separate sub-bands to provide a banded method (B-AO-OFDM) for super-channel generation. In this case, the bank of sinc-shaped filters is replaced by a bank of truncated sinc-shaped filters, simply by reprogramming the WSS. In Fig. 1(b), Nsc subcarriers have been arranged into Nband sub-bands (Nband = 3 in this case). The truncated sinc-shaped filter for B-AO-OFDM subcarriers can be obtained by multiplying the original sinc-shaped filter response by a rectangular-shaped sub-band filter. The passband width of the rectangular truncation window is given by:
where: is the symbol rate of each subcarrier, is the number of subcarriers in the b-th sub-band and the extra ‘1’ is used to accommodate the roll-off of the main lobe of the two edge subcarriers. Here we have not added a cyclic prefix. Note that in B-AO-OFDM systems, the edge subcarriers in adjacent sub-bands do not overlap one-another. Therefore, the flexibility of generating bandwidth limited signals in B-AO-OFDM comes at the cost of lowered spectral efficiency compared with conventional AO-OFDM.3. Simulations
3.1 Truncation induced penalty and equalization
For a B-AO-OFDM system, each sub-band has truncated the tails of the subcarriers that were outside the bandwidth of the sub-bands. This may cause a penalty in the reception of each sub-band [16]. To investigate this “banding” effect on detection performance and DSP compensation scheme, we simulated a 5 subcarrier AO-OFDM PDM system, with QPSK modulation at 10-Gbaud for each subcarrier, using VPItransmissionMaker version 9.2. Figure 2 shows the simulation set-up to generate one sub-band. The signals at the output of the IFFT pass through a rectangular shape optical band pass filter (OBF), to truncate the sub-band. The signal is either noise loaded to 19-dB and 39-dB OSNR (measured in 0.1 nm), or without noise loading (‘back-to-back’). A coherent receiver with an electrical bandwidth equal to half of the truncation window bandwidth is used to receive the signals.
Fig. 2 Simulation set-up for AO-OFDM of 5 subcarriers. An optical band pass filters (OBF) is used as a truncation window by setting a rectangular shape filter with different bandwidth. The “Set OSNR” block is used to load noise to 19-dB or 39-dB OSNR levels or is removed for back to back transmission. Inset: super-channel spectrum at back to back scenario (only 160-GHz of range is shown for clarity).
We first simulate an ideal optical FFT circuit at the receiver for detection without any equalization. The eye diagrams of the in-phase path of the 3rd subcarrier when using 60-GHz and 320-GHz bandpass filters are shown in Figs. 3(a) and 3(b), respectively. In the 60-GHz case, the eye opening is reduced when the spectra tail is truncated, indicating that truncating destroys the orthogonality of the original OFDM signal and causes inter-symbol-interference (ISI) and inter-subcarrier-interference (ISCI). Fortunately, these two sources of interference can be largely mitigated by using a linear adaptive equalizer with the information from only the main lobe of all subcarriers, as we will show later.
Fig. 3 (a)(b) Eye diagrams for center subcarrier when using 60-GHz and 320-GHz truncation window without noise loading. (c) LMS based equalizer response when receiving 1st (red dotted line), 3rd (blue solid line) and 5th (green dashed line) subcarriers using 60-GHz truncation window at 39-dB OSNR. (d) The 3rd subcarrier Q-factor versus truncation window bandwidth for 5 subcarriers AO-OFDM system in 19-dB OSNR, 39-dB OSNR and back to back situations.
In the case where the signals are directly received using a coherent receiver without the preceding optical FFT circuit, each subcarrier is demultiplexed using a fractionally spaced 2 × 2 adaptive filter based on least-mean-square (LMS) algorithm [21, 23, 24]. During the demultiplexing and equalization, the oversampling ratio (the sampling rate relative to the sum of the subcarrier baud rate within a sub-band) is set to 2 × the receiver electrical bandwidth. As such, a narrower truncation window leads to a lower oversampling ratio and therefore a smaller DSP load.
The filters in the equalizer are converged to the desired subcarrier using pilot symbols for the error cost function calculation. Note that this filter takes the combined signals of all subcarriers as its input, and outputs only one equalized subcarrier, which is selected according to the pilot symbols that are used to train the equalizer. Therefore, it equalizes the channel response and ISI within that subcarrier, and also suppresses the ISCI from other subcarriers.
Figure 3(c) shows the converged filter shapes for 1st, 3rd and 5th subcarriers for a 39-dB OSNR; the converged filters’ responses are similar to truncated sincs. As shown in Fig. 3(d), nearly optimal performance can be achieved when the truncation window is wider than 60-GHz, i.e., when the receiver is able to cover the main lobes of the all the subcarriers. However, there is a large performance penalty for a 60-GHz truncation window. Therefore, it can be concluded that using a linear adaptive equalizer, the ISI and ISBI induced by the truncation window in AO-OFDM can be mitigated and near optimal performance can be achieved if the receiver can substantially capture the main lobe of all the subcarriers.
3.2 Super-channel transmission simulation
We simulated super-channel systems comprising fifteen 10-Gbaud QPSK subcarriers. In the B-AO-OFDM system, the subcarriers are divided into three bands of five subcarriers each, as shown in the Fig. 4. The main lobes of AO-OFDM and B-AO-OFDM super-channel systems occupy 160-GHz and 180-GHz bandwidths, respectively. 19-dB OSNR is used. The performance (i.e. Q-factor) for the two schemes is simulated with various receiver electrical bandwidths.
Fig. 4 (a) Super-channel spectrum for conventional AO-OFDM in simulation. (b) Super-channel spectrum for B-AO-OFDM in simulation.
As shown in Fig. 5(a), it is clear that the Q-factor for conventional AO-OFDM system decreases as the receiver bandwidth reduces, due to loss of orthogonality. Close to perfect de-multiplexing (Q-factor20 dB for 19 dB OSNR) can only be attained with an electrical receiver bandwidth greater than 80 GHz. When the receiver fails to capture all of the power is the multiplexed subcarriers within the conventional OFDM super-channel, the system performance is degraded. In B-AO-OFDM scheme, only the subcarriers within the same sub-band are multiplexed, so the critical receiver bandwidth thus can be reduced to the width of one sub-band main lobe width (60-GHz optical bandwidth or 30-GHz electrical bandwidth).
Fig. 5 (a) The center subcarrier Q-factor versus the receiver electrical bandwidth in both B-AO-OFDM and conventional AO-OFDM system. (b) Q-factors of all subcarrier in both B-AO-OFDM and conventional AO-OFDM for a 30-GHz electrical bandwidth receiver.
Figure 5(b) shows the Q-factors of all subcarriers in B-AO-OFDM system for a 30-GHz electrical bandwidth, where all 15 subcarriers have nearly perfect performance (Q-factor20 dB for 19 dB OSNR). The Q-factor for a conventional AO-OFDM with the same 30-GHz receiver are shown for comparison. Compared with conventional AO-OFDM systems, the proposed B-AO-OFDM system achieves a Q-factor improvement of 6 dB (from 14 dB to 20 dB) and 2 dB for the center and edge subcarriers, respectively, at the cost of a 20 GHz (2 × subcarrier baud rate) wider optical main lobe spectrum (180 GHz vs. 160 GHz in the Fig. 4). The edge subcarriers have poorer performance penalty because fewer neighboring subcarriers contribute to the Q-factor penalty when receiving conventional AO-OFDM with in-sufficient receiver electrical bandwidth. In conclusion, these simulations show that the B-AO-OFDM scheme can achieve nearly optimal detection performance for AO-OFDM super-channel with multiple low-bandwidth receivers.
4. Experiments
4.1 Experimental setup
Figure 6 shows the experimental setup to verify the B-AO-OFDM system and compare its system performance with that of conventional AO-OFDM. An erbium-doped glass oscillator (ERGO) mode locked laser (MLL) provides a 2-ps pulse width pulse train at 10.001-GHz repetition rate. An LCoS-based WSS was used to select and power equalize ten MLL comb lines, to generate periodic-sinc pulses from the mode-locked laser. The pulses were then pre-amplified by a polarization maintaining (PM) EDFA before being modulated by the optical IQ modulator. An arbitrary wave generator (AWG) generated 10.001-Gbaud QPSK baseband signals to drive the modulator. After modulation, the comb line spectrum becomes a ~110-GHz-wide white spectrum, which was split into 4 paths using three PM 3-dB couplers. Utilizing two tuneable delay lines, the data on each path was de-correlated from the other paths by different integer-numbers of symbol periods. Three polarization controllers were inserted, before coupling into a 3 × 1 WSS to align the polarizations of all signal paths at the WSS output. Each port of WSS was programed with a filter that has a sinc-shape or truncated-sinc-shape transfer functions to multiplex subcarriers for conventional AO-OFDM and B-AO-OFDM super-channel systems, and the power difference between different WSS paths were equalized using the internal attenuation setup of the WSS.
Fig. 6 Experimental set up. MLL: mode-locked-laser, WSS: wavelength selective switch, AWG: arbitrary wave generator, IQ Mod: complex Mach-Zehnder modulator, PM: polarization maintained, EDFA: Erbium-doped fiber amplifier, P.C: polarization controller, PBC: polarization beam splitter, PBS: polarization beam combiner, S-SMF: standard single mode fiber, LO: local oscillator.
For the conventional AO-OFDM scheme, the transfer function in port k can be written as [21]:
where: i is the imaginary unit, j is the subcarrier index, Nsc is the total number of subcarriers, fR is the symbol rate of each subcarrier, is the order of the OIFT of the optical filter, is the central frequency of the k-th port’s filter (k = 1, 2…M), given by: .For the B-AO-OFDM system, the transfer function of the port k in WSS is given by:
where: is the center frequency of the b-th sub-band and b is the index of sub-band.As a proof-of-concept experiment, we compared a conventional AO-OFDM system consisting of 6 subcarriers with B-AO-OFDM system which has a pair of 3-subcarriers sub-bands. Thus, N = 6, M = 3, and fR = 10.001 GHz in our experiment. From Eq. (2), a 3-point OIFT was performed to generate three independent subcarriers and same transfer functions were repeated for the other subcarriers. As such, the generated super-channel had an ABCABC subcarrier structure. In order to partially de-correlate first and second triplets of subcarriers, we applied a different phase response on later three subcarriers. (i.e. creating an ABCA`B`C` super-channel, with the subcarriers X` phase shifted compared to the X subcarriers).
Polarization division multiplexing (PDM) was emulated by splitting the single-polarization signal into two arms, delaying one arm and recombining them in a polarization beam combiner (PBC). Then the PDM AO-OFDM signal was fed into an EDFA-only optical link comprising 10 spans of standard single mode fiber with 80 km per span. Amplified spontaneous emission (ASE) noise was loaded before the receiver for back-to-back measurements. The signal was detected using a coherent receiver after out-of-band noise was filtered out by a WSS. Then the data was sampled by a real-time digital oscilloscope (Agilent DSO-X 95004Q) and finally DSP was performed to recover the signal. In DSP, after front-end correction, frequency offset compensation and frequency domain CD compensation, the signal was resampled according to the available receiver bandwidth, and then a LMS-based 2 × 2 multiple-input multiple-output (MIMO) fractionally spaced time-domain equalizer (FS-TDE) was used to de-multiplex the desired subcarrier and compensate for residual CD, PMD and sampling timing offset. Finally, Viterbi-Viterbi phase recovery was performed for carrier recovery before measuring the Q-factor.
4.2 Implement transfer functions in WSS with pre-emphasis
To generate the desired response with a WSS, we performed de-convolution to pre-compensate the optical transfer function (OTF) effect of the LCoS based WSS [25]. Figure 7(a) depicts the spectra of an ideal sinc (blue), WSS generated sinc with (green) and without (red) pre-emphasis measured by a high-resolution optical spectrum analyzer. The pre-emphasis produces a much more precise response compared to directly programming the sinc response into the WSS. Also, the measured transfer functions of each subcarrier for a single sub-band in B-AO-OFDM system are shown in Figs. 7(b)-7(d). The generated truncated sinc sub-carriers clearly truncate the tails of the conventional sinc responses outside the sub-band window. The occupied bandwidth of the truncated sinc response is still slightly wider than the ideal 40-GHz width, mainly due to the limited frequency resolution of the WSS.
Fig. 7 (a) Measured sinc function response output with pre-emphasis (green solid line); Measured sinc function response output without pre-emphasis (red dotted line); ideal sinc function response with 20-GHz main lobe (Blue dashed line), (b) (c) (d) Transfer functions for subcarriers 1, 2 &3 within one sub-band in B-AO-OFDM system. All frequency responses were measured with a resolution of 200 MHz.
At the output port of the WSS, three tributaries were coupled together, giving a single polarization OFDM super-channel with de-correlated data in each subcarrier. The overall super-channel spectra are shown in Fig. 8. The main lobe of conventional AO-OFDM super-channel is approximately 70-GHz wide while B-AO-OFDM’s spectrum consists of two 40-GHz sub-bands. The generated super-channels have some fluctuation across their bands and non-ideal extinction between two sub-bands of B-AO-OFDM system can be observed, which may be due to imperfections in implementing the desired functions using WSS or because of slight offsets in the applied de-correlating delays.
Fig. 8 (a) Measured spectrum for 6 subcarriers conventional AO-OFDM. The spectrum has 56.8-GHz 3-dB bandwidth (b) Measured spectrum for proposed B-AO-OFDM with 2 sub-bands. Each sub-band has 3 subcarriers. Sub-band 1 and 2 have 30.2-GHz and 27.2-GHz 3-dB bandwidths respectively. All spectra were measured with a resolution of 200 MHz.
5. Experimental results
5.1 Receiver setup
We investigated the conventional and banded AO-OFDM super-channel systems with different receiver setups. The photodiodes of the coherent receiver have 40-GHz electrical bandwidths, which is sufficient to capture all 6 subcarriers simultaneously. Therefore different receiver electrical bandwidths were emulated by adjusting the 3-dB electrical bandwidth of the real-time scope. The maximum electrical bandwidth of the scope is 33 GHz (at 80 GSamples/s), which is able to approximately capture the entire conventional AO-OFDM super-channel. The associated electrical bandwidth for a 40-sample/s rate is 16 GHz, which we will show is sufficient to recover a single sub-band of the B-AO-OFDM system.
5.2 Noise loading back to back transmission
Figure 9(a) shows the measured Q-factors for the 1st subcarrier in the 2nd sub-band versus different OSNR values, where the corresponding simulation results are shown in Fig. 9(b). The experimental results show good agreement with the simulation results. Compared with a single subcarrier system, near perfect de-multiplexing performance can be obtained when using 33-GHz and 16-GHz receiver electrical bandwidths in the conventional AO-OFDM and B-AO-OFDM systems, respectively. When the receiver bandwidth is 16 GHz, the conventional AO-OFDM system has more than 2-dB OSNR penalty compared with the B-AO-OFDM system.
Fig. 9 (a) Experimental and (b) simulated system Q-factor evaluated at different OSNRs for single carrier system, banded AO-OFDM (B-AO-OFDM), conventional AO-OFDM (C-AO-OFDM) with 16-GHz and 33-GHz 3-dB receiver electrical bandwidths.
5.3 Standard single mode fiber transmission over 800 km
The measured Q-factors for both systems after 800-km transmission are plotted in Fig. 10. The Q-factor versus launch power is plotted in Fig. 10(a), where the optimal launch power was found to be 4 dBm. Conventional AO-OFDM with a 33-GHz receiver electrical bandwidth achieves similar performance as the B-AO-OFDM system with a 16-GHz receiver electrical bandwidth, where around 0.5-dB performance difference results from a lower multiplexing penalty in the system because of the WSS implementation (3 subcarriers were multiplexed in one sub-band in B-AO-OFDM super-channel while 6 subcarriers were multiplexed in conventional AO-OFDM super-channel). The optimum-launch-power Q-factors of all six subcarriers are plotted in Fig. 10(b), indicating the 3-dB Q-factor improvement with B-AO-OFDM over conventional AO-OFDM using a 16-GHz electrical bandwidth receiver. The corresponding received QPSK symbol constellations are shown at the right of Fig. 10, where less spread suggests smaller ISI and ISCI.
Fig. 10 (a) Launch power sweep for B-AO-OFDM and C-AO-OFDM at 16-GHz and 33-GHz receiver electrical bandwidths in 800-km fiber transmission experiment. (b) Measured Q-factor for all subcarriers in the three systems with 4-dBm launch power. The received symbols constellation for B-AO-OFDM and C-AO-OFDM at 16-GHz receiver electrical bandwidth are shown at the right.
6. Discussion
In both simulation and experiment, B-AO-OFDM scheme has shown the ability to improve system performance for low bandwidth receiver badnwidths. However, due to the ‘banding’ operation, the spectral efficiency (SE) is slightly reduced. For a PDM super-channel system, the SE is:
where: is the modulation order, is the number of total subcarriers and is the number of sub-bands in the B-AO-OFDM super-channel. In the B-AO-OFDM system, the required receiver bandwidth for one sub-band reception is proportional to () + 1, which leads to a trade-off between the spectral efficiency and the receiver bandwidth. If more subcarriers are packed into one sub-band, meaning fewer sub-bands and higher spectral efficiency, a high receiver bandwidth and fast ADC will be required to guarantee the de-multiplexing performance. In this experiment, the spectral width expands from 70 GHz to 80 GHz for B-AO-OFDM scheme, indicating a 0.58 dB spectral efficiency loss. In this demonstration, which encodes QPSK onto each subcarrier in two polarizations, the corresponding pre-FEC spectral efficiency for conventional AO-OFDM and banded AO-OFDM are 3.4286 bits/s/Hz and 3 bits/s/Hz respectively. For comparison, conventional single-carrier 100 Gbits/s channels using 28 GBd PM-QPSK on a 50 GHz WDM grid have a pre-FEC SE of 2.24 bits/s/Hz.With the proposed scheme, the spectrum of each OFDM subcarrier is mostly confined within a sub-band using truncated sinc-shape filters. These filters combine an interleaver with sharp transition and conventional (I)FFT filtering. Furthermore, it is the filters that define the allocation of data channels to subcarrier wavelengths, which means that dynamic optical routing can be simply implemented. Compared with N-WDM implemented using optical filters [3], the optical filters have more moderate roll-offs. Compared with N-WDM implemented electrically, the modulators can have lower electrical bandwidths, because they are sampled by the optical pulses, rather than having to have fast transitions.
7. Conclusion
In this paper we proposed a banded all-optical OFDM super-channel scheme to reduce the required electrical bandwidth for close to optimal reception performance. Truncated-sinc-shaped filter bank is employed to filter and synthesise different subcarriers, where the side lobes of each sub-band are suppressed to facilitate the sub-band by sub-band reception. This function can be achieved with a short pulse source and commercial LCoS based WSS, which also allows flexible allocation of number of subcarriers in each sub-band. Using simulations and 800-km long-haul transmission experiments, we have shown that B-AO-OFDM scheme can improve the system’s Q-factor by 3-dB in a system with a bandwidth limited receiver. As a result, the proposed scheme can reduce the receiver bandwidth requirement for de-multiplexing in AO-OFDM super-channel system.
8. Funding
This work is supported under the Australian Research Council’s Laureate Fellowship (FL130100041) and CUDOS – ARC Centre of Excellence for Ultrahigh bandwidth Devices for Optical Systems (CE110001018).
Acknowledgments
We thank VPIphotonics (www.vpiphotonics.com) for the use of their simulator, VPItransmissionMakerWDM V9.2.
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