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We propose and demonstrate by simulations a novel Nyquist-WDM (N-WDM) superchannel transmitter based on an arrayed waveguide grating router (AWGR). This approach can generate Nyquist pulses at multiple wavelengths using a single AWGR. Results for a 3-channel 960-Gbit/s QPSK superchannel system show that a 10% guard band reduces the inter-channel interference (ICI) sufficiently. The design introduces less than 0.16-dB penalty when the waveguide loss is 2 dB/cm and 0.73-dB penalty when the standard deviation of phase error is 10°. Such Nyquist pulse shapers can be realised on a chip scale using photonic integrated circuits technology, and could be compactly integrated with other functional components to create single-chip N-WDM superchannel transmitters.
© 2016 Optical Society of America
1. Introduction
Nyquist pulse shaping [1] has been proposed to improve spectral efficiency to meet the ever-increasing demands for data transmission capacity. It can increase the nonlinear impairment tolerance [2] and narrow the spectral extent of single-channel signals [3], and therefore reduce both the receiver complexity [4] and the channel spacing in WDM systems [5]. Of particular interest are sinc-shaped Nyquist pulses, which have a rectangular spectrum [6] and confine the signal to its Nyquist bandwidth, so can be used for dense wavelength division multiplexing (WDM)–known as Nyquist WDM (N-WDM) [6]. This enables the highest intra-channel spectral efficiencies and has recently enabled transmission with a spectral efficiency of 10.6 bit/s/Hz [7].
Nyquist pulse shaping can be achieved by either electrical or optical approaches. Electrical shaping can provide quite a good roll-off factor, but the baud-rate is restricted by the speed of the digital to analogue converter (DAC). Alternately, optical pulse shaping methods can circumvent the limitation of electrical speed, the methods include: modulating externally modulated lasers to generate mode locked combs [8], using a liquid crystal spatial modulator [9] or an arrayed waveguide grating router (AWGR) [10–12] to shape the Gaussian pulse from a mode-locked laser. Among all the proposed devices, photonic integrated circuits (PICs) have advantages of: compact size, low cost, robustness, and can integrate many functions onto one chip. In [10], a chirped AWGR has been proposed for implementing a fractional Fourier transform (FrFT), which produces chirped OFDM signals that can be converted to quasi N-WDM channels using a dispersive fiber (DF). However, we have shown that these channels have much wider spectra than necessary [11], so require large guard bands for a given level of inter-channel-interference (ICI) when multiplexed into an N-WDM system. Similarly, a modified chirped AWGR has been demonstrated to achieve a narrower overall spectrum, but a guard band is still needed to reduce crosstalk [11]. A direct FIR filter is proposed with amplitude weighting of each of its waveguides to give a truncated-sinc impulse response and near rectangular spectrum; however, this requires large number of splitters with designed splitter ratios [11]. A simpler structure Nyquist pulse generator based on an AWGR has been proposed, which replaces the large number of splitters by a compact Fourier transform slab [12]. To further increase the bandwidth and transmission capacity, a promising approach is to wavelength-multiplex Nyquist channels, as the spectrum of each channel is nearly rectangular. A straightforward way to implement such a system is to use separate Nyquist pulse generators to form each N-WDM channel, and then multiplex the channels together. However, this scheme increases the system complexity and cost, and could cause uneven performance of different channels due to uncorrelated fabrication errors in different chips. Thus, a multi-frequency Nyquist pulse generator is highly desirable for N-WDM implementation.
In this paper, we proposed a single AWGR with multiple outputs to generate multi-channel Nyquist pulses. Each port of the AWGR has a rectangular spectrum but with a different central frequency. System simulations show that the proposed AWGR needs at least 10% guard bands to reduce the ICI in a 960-Gbit/s N-WDM superchannel system, and illustrate its tolerance to fabrication errors in terms of waveguide loss (0.16-dB penalty when the waveguide is 2 dB/cm) and waveguide length variations (0.73-dB penalty when the standard deviation of phase error is 10°). An advantage of this design is that the AWGR can be integrated with other functional components such as modulators and lasers, opening the possibility for on-chip realization of a complete N-WDM transmitter.
The paper is organized as follows. Section 2 describes the operational principles of the AWGR with multiple outputs for N-WDM superchannel generation. Section 3 illustrates the simulation results of the proposed AWGR for Nyquist optical time division multiplexing (N-OTDM) WDM superchannel systems. The conclusion is drawn in Section 4.
2. Operational principles of the AWGR as a Nyquist pulse generator
2.1 Signal processing block diagram for Nyquist pulse generation
Figure 1 shows the new multi-tap delay-line filter that generates Nyquist pulses. This filter consists of a Fourier transform (FT) block, a set of incremental time delays and phase shifts, and a combiner. The input of the FT block is fed with short pulses from mode-locked laser (MLL) that have been split by a 1 × K splitter. In order to generate a truncated sinc-like pulse, these inputs to the FT need to have uniform powers and precise phases; this means that the FT block should be fed with identical and synchronized signals copied from the same source. The N outputs of the FT feed incremental time delays, which act as a parallel-to-serial converter. If the phase shifters are not used (Δφ = 0), the sinc impulse response of the FIR filter is truncated due to the limited number of time delays, and the spectral response of the filter is simply a rectangle convolved with a sinc [12]. If the phase shifts linearly increase (Δφ ≠ 0), the spectral response will have a shifted central frequency.
Fig. 1 Principle of Nyquist pulse generation using a multi-tap delay-line photonic filter (FIR filter). (Note that the illustrated fields ignore the carrier frequency of the laser).
2.2 AWGR with multiple outputs
The FIR filter in Fig. 1 can be implemented by an AWGR-like structure, as shown in Fig. 2. Slabs 2 and 3 and the grating waveguide form a generic AWGR which, in this case, is designed to be a Fourier transform (Slab 2) followed by a parallel-to serial converter (grating waveguides and Slab 3). The waveguides have incremental path lengths, with an increment ∆L between them [12]. The phase shifts across Slab 2 are proportional to k × n. This implements the phase weighting of the discrete inverse Fourier transform [13].
To implement the Nyquist pulse generator of Fig. 1, an additional slab (S1) is needed at the input to split each mode-locked laser pulse into K copies, which feed the inputs to Slab S2. The Fourier transform (Slab 2) converts these inputs into a (truncated) sinc-shaped diffraction pattern at its right-hand side. The arrayed waveguides sample this pattern, then deliver the samples (with different delays) to Slab S3. Each output of Slab S3 is a sampled and truncated sinc pulse waveform, with a duration dependent on the number of arrayed waveguides, N, and the incremental delay of the arms, ∆t.
If Slab S3 has multiple outputs, then each output, q, will be a sum of the inputs, n, each with a different phase weight. The phase weights are dependent on the product n × q. Thus, for a given output, q, the phase weights increase (or decrease) linearly with n, or equivalently, because of the waveguides’ delays, time. As a linearly phase shift with time causes a frequency shift (serrodyne modulation), each output of Slab 3 is a truncated-sinc waveform with a different central frequency.
2.3 Design of Slab 2
In an AWGR design, usually, the FT slab has a single input. However, we require multiple inputs, with specific phase relationships, i.e. uniform phase. Unfortunately, a Rowland circle does not provide the required phase shifts, as the following analysis will show.
A Rowland Circle (RC) configuration [13] is shown in Fig. 3(a). The input waveguides terminate on a circular boundary of radius R/2 (the Rowland Circle), while the arrayed waveguides terminate on a circular boundary of the slab, radius R (Grating Circle). The Rowland circle is co-tangential with the large circle at the center of the arrayed waveguides, which is called the ‘pole’. In this slab region, the input waveguide separation is d and the arrayed waveguide separation is D. Index k is the input port, and n labels the arrayed waveguide arm. θk, θn are the diffraction angles in the input and arrayed slabs, respectively, and ns is the effective index of the slabs. The input light at position PA is radiated across the slab and then excites the arrayed waveguides, PA’. From the geometric perspective, the distance between any input (from the input waveguides) and output (arrayed waveguide), sA can be approximated to the following expression [14–16]:
where wn is the spacing between the chosen grating waveguide, n and the pole. lk is the distance from the pole to the chosen input waveguide, k. This path length introduces a phase delay which varies for different input waveguides. lk and θk are fixed for any chosen input waveguide, and wn increments from one arrayed waveguide to the next. The spatial power distribution along the slab is not sinc-like pulse due to the additional phase shifts related to lk as shown in Fig. 3(c). For OFDM signal generation, the phase terms of each subcarrier, which are exp(−2πjnslk/λ), do not degrade the system as the receiver equalizer would correct them [17]. However, the phase must be equalized when generating Nyquist-WDM signals. This could be achieved by adding phase shifters on the inputs of the AWGR.Fig. 3 (a) The enlarged input slab region (S2) containing a Rowland circle (b) confocal circle. (c) Spatial power distribution after the slab S2 (K = 20, N = 100, λ = 1.55 µm, D = λ/2, d = λ, R = λ∙100) for Rowland circle and confocal circle.
Alternatively, the FT slab (S2) can be configured as a confocal circle [18, 19]. Figure 3(b) shows the waveguide layout with its corresponding structure parameters. It consists of two sets of waveguides positioned over two identical radii, called the focal length, R. The centers of these radii are separated by a distance, R, which is equal to the focal length. Now, we look into the design of the first free propagation region (FPR) as shown in Fig. 3(b). The input light at position PB is radiated to the FT slab and then excites the arrayed waveguides, PB’. The distance between any input (input waveguides) and output (arrayed waveguide), sB, is approximated to [19]:
where θk’ is the diffraction angle in the input slabs. The additional phase shifts related to R are now constant for each input waveguide. This structure ensures that the input phases are equalized before feeding the arrayed waveguides. Thus, the power distribution of each arrayed waveguide is an ideal truncated-sinc (red dashed lines in Fig. 3(c)).2.4 Spectra and impulse response
For an AWGR with several outputs, the impulse response for each output is a sinc pulse with its sample points have incremental phase shifts, which depend on the output, q. The impulse response can be derived similarly to the array factor in array antennas with multiple elements [20]
where α = λ·R/ns, d’ is the spacing between the output waveguides, δ(t) is the Dirac delta. The impulse response is a discrete truncated sinc pulse with width of ΔT = (λRΔt)/(KDdns) ranges from 0 to (N-1)·Δt. The corresponding transfer function is [13, 16]where: Nch = λR/(nsdD) is the number of channels in a free-spectral range (FSR). For each output, q, the frequency spectrum is a summation of sinc spectra with a width of ΔF = 1/(NΔt) and a different phases related to optical length, lk, shift the frequency by Δf = 1/(NchΔt). From Eq. (4), the roll-off factor of the spectrum depends on the widths of the sinc subcarriers’ spectra; the smaller the ∆F is, the smaller the roll-off factor becomes. Here we defined γ as the width of the sinc spectra divided by the bandwidth of the spectrum.The shape of the spectrum is determined by the duration of the truncated-sinc pulse, the incremental delay and the number of the arrayed waveguides. A large N can make the spectrum more rectangular. Practically, it is difficult to design AWGR’s with more than 128 guides. Different outputs, q, correspond to different central frequencies of the N-WDM channels. The number of N-WDM channels can be generated depends on the FT slab size.
2.5 Design rules for Nyquist pulse generation
The design of the AWGR is primarily determined by the required full-width at half-maximum (FWHM) width, ∆T, of the main lobes of the sinc pulses, which form the orthogonal time division multiplexing (OrthTDM) channels. The multiplexing ratio, M, determines the number of tributaries in the OrthTDM, that is, how many sinc pulses are to be interleaved in one period of the mode locked laser (TMLL), it is
The FSR of the filter is the inverse of the incremental delay between the waveguides, ∆t = nc·∆L/c, where c is the speed of light, ∆L is the length difference between two adjacent arms, nc is the effective index of the waveguides. The minimum FSR is the bandwidth of the spectrum, B, but this would cause difficulties in isolating one free-spectral range from the neighbors using a conventional band-pass filter or wavelength multiplexer, so we shall make the FSR equal to gB, where g is a scaling factor. Thus,A practical limitation of the AWGR is that the impulse response will not be sinc-shaped, due to the different losses in the different arrayed waveguides and across the slabs themselves due to non-uniform illumination of the output waveguides by the input waveguides. The uneven waveguide loss can be solved by adding semiconductor optical amplifiers (SOAs) into each waveguide to equalize the output powers [21]. The illumination will approximate to being uniform if the beam widths of the input waveguides are very wide, though the loss of the system will be increased. The waveguide losses can be equalized by the gains of the SOAs, and the loss due to a large beam-width can also be compensated by the same SOAs. Another limitation is the number of arrayed waveguides; a large number will give a near-ideal sinc-shaped impulse response: however, the mean lengths of the arms will be longer, so will have high losses, reducing the optical signal to noise ratio even when SOAs are added. The choice of the number of arms is inevitably a compromise. Practically, it is difficult to design AWG’s with more than 128 guides because of the widths of the waveguides and their optical modes.
3. N-WDM systems simulation using the proposed Nyquist pulse generator
3.1. Superchannel N-WDM simulation of the fiber-based transmitters
A system as in Fig. 4 generating 3-wavelength N-WDM was simulated using VPItransmissionMaker. The MLL produces 500-fs Gaussian pulses at 100-ps (TMLL) intervals (10 Gpulses/s). A single AWGR with 3 outputs is used to generate three N-WDM channels simultaneously. These are bandwidth-limited to one spectral range using 240-GHz FWHM 1st-order Gaussian band-pass filters. Each sinc pulse is optically time-division multiplexed (OTDM) to increase the data rate. OTDM involves; splitting into several paths, modulating each path, delaying the paths and recombining them to form interleaved pulses. In our case there were 16 paths giving a rate of 160 Gbaud for each N-WDM channel. The modulation was QPSK, to give a total data rate of 960 Gbit/s for a superchannel with three N-WDM channels.
To simulate the AWGR, we used VPItransmissionMaker’s star-coupler module and waveguide module, with a simulated bandwidth of 5 THz. The parameters for the structural design of the AWGR are listed in Table 1. Loss nonuniformity Lu = 0.18 dB and slab diffraction Lo = 6 dB were also considered. The incremental delay between the waveguides is 1 ps, to give a FSR of the AWGR response of 1 THz. The duration of the truncated sinc pulse ((N-1)·Δt) equals the period of the MLL. The AWGR generates near-rectangular spectra. The central-peak width ΔT = 6.25 ps, with a spectral bandwidth B = 160 GHz. This channel bandwidth is much narrower than the bandwidth of the MLL’s pulses, which ensures the WDM channels under consideration have nearly-flat passbands as shown in Fig. 4.
Table 1. Parameters used in the design of AWGR
The receiver uses another band-pass filter (BPF2), but with a bandwidth of 170 GHz, and a 2nd-order Gaussian response to de-multiplex the central channel. After the coherent receiver, a least mean square (LMS) algorithm was used to recover the signal. The optical signal to noise ratio (OSNR) is defined as the average optical signal power in one channel, divided by the power of the unpolarized amplified spontaneous emission (ASE) within a reference optical bandwidth (12.5 GHz). The Q-factor is a performance metric, and was calculated from the means and standard deviations of the real and imaginary parts of the constellation points at the optimum sample times.
Figure 5(a) plots the simulated signal quality versus OSNR for the central channel when there are no frequency guard bands (160-GHz spacing). Compared with the performance of a single channel using an ideal rectangular filter, the WDM systems suffer a small reduction in signal quality, due to the crosstalk from neighboring channels. In practical N-WDM systems, a guard band is introduced between the channels to reduce ICI. This means the channel spacing is wider than the nominal channel bandwidth, B. As we can learn from Fig. 5(b), the Q factor for the central Nyquist channel saturates when the guard band ratio reaches 10%.
Fig. 5 Q factors for the central channel in N-WDM channels as a function of: (a) OSNR (b) guard band ratio (OSNR = 10 dB).
3.2 Performance penalty due to the fabrication error of the AWGR
The practical limitations of our AWGR N-WDM scheme are that the impulse response is modified due to the uneven losses of the arrayed waveguides, and the phase errors due to the manufacturing variations in the effective indices of the arrayed waveguides between the FT slab and the third slab. The phase noise of the local oscillator can be estimated and mostly compensated after signal detection with well-established algorithms such as 4th-power law or decision-aided maximum likelihood methods [22], so here we only consider the phase errors in the AWGRs. Figure 6 plots the fabrication tolerance of arm loss and phase error for N-WDM superchannel (160-GHz spacing), with similar parameters to the 3-channel N-WDM system of Section 3.1; the pulse width is 6.25 ps and the spectral bandwidth is 160 GHz. As shown in Eq. (5), a greater N can narrow the spectral bandwidth, and so reduce the ICI. In Fig. 6, even with a waveguide loss of 2 dB/cm, the performance drops by only 0.16 dB. The Q-factor (averaged Q over 100 random phase setting) is reduced by 0.73 dB when the phase errors have a normal distribution with a standard deviation 10° [23] when OSNR = 10 dB. The phase errors change the spectral shape, so cause ICI when several channels are multiplexed together, but they do not destroy the orthogonality of the Nyquist pulses, at the receiver, some aspects of the degradation due to the phase errors are compensated by the DSP.
Fig. 6 The influence of: (a) the waveguide loss (2 dB/cm) and (b) arrayed waveguide length variation (standard deviation of the phase error = 10°) with respect to the number of waveguides for the central channel in N-WDM systems (OSNR = 10 dB).
4. Conclusion
We have demonstrated the feasibility of using an AWGR with three slabs as a high-performance multi-channel Nyquist pulse shaper, which produces several truncated sinc pulse trains at different central frequencies. A multi-channel system requires a 10% guard band ratio to reduce the ICI to acceptable levels. Then we show the designs’ tolerance to practical implementation issues such as waveguide loss (0.16-dB penalty when the waveguide is 2 dB/cm for N-WDM systems) and variation of waveguide length (0.73-dB penalty when the standard deviation of phase error is 10° for N-WDM systems).
Funding
This work is supported under the Australian Research Council’s Laureate Fellowship scheme (FL130100041).
Acknowledgments
We thank VPIphotonics (www.vpiphotonics.com) for the use of their simulator, VPItransmissionMakerWDM V9.5.
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