## Abstract

An Arrayed-Waveguide Grating Router (AWGR) can be used as a demultiplexer for an optical OFDM system, as it provides both the serial-to-parallel converter and the optical Fourier transform (FT) in one component. Because an inverse FT is topologically identical to a Fourier transform, the AWGR can also be used as a FT in an OFDM transmitter. In most all-optical OFDM systems the optical modulators are fed with CW tones; however, the subcarriers (SC) will only be perfectly orthogonal if the bandwidth of the data modulators is similar to the total bandwidth of all subcarriers. Using simulations, this paper investigates the reduction in modulator bandwidth that could be achieved if the modulators are placed before an AWGR designed as a FT. This arrangement also allows the complex (IQ) modulators to be replaced with simpler and more-compact phase modulators. We show that these design improvements enable 7.5-GHz bandwidth modulators to be used in a 4 × 10 Gsymbol/s (80 Gbit/s) per polarization per wavelength system.

© 2011 OSA

## 1. Introduction

All-optical Orthogonal Frequency Division Multiplexing (OFDM) uses optical techniques to construct an OFDM symbol out of a number of Quadrature Amplitude Modulated (QAM) subcarriers (Fig. 1a,e in reference 1). All-optical OFDM offers outstanding spectral efficiencies, so could maximize the capacity of optical fiber transmission systems. Furthermore, recent work has shown that the optimal symbol rate per subcarrier, in links without dispersion compensation, could be less than 10 Gbaud [2,3]. This suggests that low-bandwidth optical modulators could be used to modulate data onto each subcarrier (SC), lowering the cost of the optical system compared with a single-carrier system using a single high-bandwidth modulator.

Most proposals for all-optical OFDM transmitters [1,4] feed each data modulator with a separate wavelength, usually obtained from an optical comb generator, such as an Mode-Locked Laser (MLL), followed by a wavelength demultiplexer. The wavelength demultiplexer feeds a single wavelength into each modulator. If an Arrayed Waveguide Grating Router (AWGR) is used as the demultiplexer, as in Scheme 1 of Fig. 1 , a series of pulses with incremental phases will be fed into each modulator within each OFDM symbol period. The AWGR is similar in function to a Fourier Transform (FT) [5], so separates the spectral comb into separate spectral lines. The data is carried by applying phase modulation to each spectral line. The outputs of the modulators are then combined without filtering to form an OFDM symbol. The drives to each modulator should be synchronized so that the transitions occur simultaneously at the edge of each OFDM symbol [6].

The key to maintaining the orthogonality between the SCs is to ensure that all of the SCs are periodic within each OFDM symbol, duration *T _{symbol}*. This means that the pulses from the AWGR into a given modulator must linearly increase or decrease in phase, with respect to the phase of the centre wavelength of the MLL, at a rate of (2π

*m/T*), where

_{symbol}*m*is an integer denoting an output of the AWGR. As shown in Fig. 1 Scheme 1, the subsequent modulation must not destroy this linear increase, that is, it must add the same phase shift (

*Δθ*) to each pulse within with a single OFDM symbol. This constraint means that the modulators must change their phase rapidly between the OFDM symbols, after the last pulse of one symbol and before the first pulse of the next [5]. This requires modulators with rise times close to the pulse spacing produced by the AWGR; this spacing is the inverse of the Free-Spectral Range (FSR) of the AWGR. Because the FSR must be greater than the total optical bandwidth of the transmitter, the modulator’s risetimes are therefore determined by the total optical bandwidth of the transmitter, rather than the baud rate of an individual subcarrier. Slower transitions will cause the subcarriers to interfere with one another, which is known as inter-carrier interference, ICI in wireless OFDM [7]. Although low-levels of ICI can be tolerated, as shown in systems demonstrations using many subcarriers and modulators with bandwidths far less than the optical bandwidth of the system [8,9], theoretically there will be some performance penalty that may manifest as an increase in required Optical Signal to Noise Ratio (ONSR) at the receiver for a given Bit Error Ratio (BER). For higher-order modulation, such as 16-QAM, the penalty will be larger and ICI will limit the order of the modulation, thus limit the ultimate spectral efficiency (bits/second/hertz) of the system.

An alternative scheme for implementing an OFDM transmitter using an AWGR is shown as Scheme 2 in Fig. 1 [10]. This has a simple wavelength-independent splitter after the mode-locked laser, so that one MLL pulse is fed to every modulator per OFDM symbol. Because the MLL pulses are short, they have wide spectra, covering the bandwidth of all of the subcarriers. The modulators are synchronized with the MLL and apply a phase shift to each pulse, to encode data onto it. The AWGR is arranged to perform an Inverse Fourier Transform (IFT) [5]; that is, for each OFDM symbol, it outputs a series of pulses dependent on the phases of the modulators. This is similar to a digital IFT, used in digital implementations of optical OFDM, in that it converts frequency domain information (the phases of the subcarriers for each OFDM symbol) into a time-domain waveform, which is a superposition of all of the phase-modulated subcarriers. Lee, Thai and Rhee [11] and Huang *et al.* [12] have also suggested placing the IFT after the modulators, but both groups used couplers to implement the IFT, which can be cumbersome.

Previously, Wang *et al.* [10] have simulated both schemes for the optical transmitter. Their simulations showed Scheme 1 to be less critical to the receiver sampling time when simulation-bandwidth-limited modulators and samplers were used, and they also demonstrated that, in Scheme 1, even very-high-bandwidth (50 GHz) modulators cause some eye closure in a system with 16 Gsymbol/s subcarriers. The effects of lower-bandwidth modulators were not studied.

A possible advantage of Scheme 2 over Scheme 1 could be that the modulators only have to maintain a constant phase when there is a pulse at their input. This should give the modulators most of the OFDM symbol to change their phase, so they need not be fast to maintain orthogonality between the OFDM subcarriers. In this paper we report detailed numerical simulations that confirm that placing the AWGR after the modulators to perform an IFT (Scheme 2) allows much lower bandwidth modulators to be used than if the AWGR is placed before the modulators (Scheme 1). Huang *et al.* used phase modulators in their implementation of Scheme 2 [12]; we show that these phase modulators can be low-bandwidth designs with electrical bandwidths only slightly higher than when IQ modulators are employed. We then discuss our results in the light of recent experimental results.

## 2. AWGR design for scheme 2

In electronic implementations of optical OFDM transmitters [13,14], the IFT and subsequent parallel-to-serial conversion follows the QAM modulators, converting phase-modulated inputs into a time-domain waveform, which is a superposition of the waveforms of the SCs. This waveform is then modulated onto an optical carrier using a complex (IQ) optical modulator. The digital implementation of the OFDM subcarrier generator suggests that the optical implementation should also have the inverse Fourier transform after the modulators, as in Scheme 2. Figure 2
shows our optical realization of this idea, which is based on an AWGR. This design comprises three slab couplers. The first acts as a simple splitter for the optical pulses, so could be replaced by a multi-mode interference coupler or a cascade of splitters [15]. The four copies of the pulses are sent through separate optical modulators, driven by four data signals. The second slab coupler acts as an IFT, providing a set of phase shifts across it, each shift being dependent on the particular input waveguide (*m*) and the particular output waveguide (*n*) connected to it. Thus each grating waveguide receives a phase-weighted combination of the outputs of the four modulators, which implements a FT [5,10]. The grating waveguides have incremental lengths, so the third slab coupler combines the outputs of the second slab coupler with different time delays. Thus, every input pulse becomes a train of eight output pulses, and every output pulse is a phase-weighted combination of the outputs of all of the modulators. In the frequency domain, this phase weighting means that the output of each modulator has a *sinc* spectrum if the pulses are short enough. The use of eight grating waveguides for a four-subcarrier transmitter is a deliberate design choice, as the free-spectral-range (FSR) of the AWGR will be almost twice as wide as the main lobe of the OFDM spectrum. This means that the spectral images of the OFDM subcarriers will fall well away from the required lobe, so can be removed with conventional optical filters with relatively-wide pass-band to stop-band transitions, as will be shown later by simulation.

## 3. Simulation setup

VPItransmissionMaker Version 8.5 was used to perform the simulations, with a simulation bandwidth of 320 GHz. The OFDM symbols were generated by combining the outputs of four QPSK transmitters, each carrying 20 Gbit/s of data with 10 GSymbol/s. The OFDM condition without a cyclic prefix or guard band [6], requires the subcarriers to be spaced at 10 GHz; that is, the inverse of the OFDM symbol period. Initially, complex (IQ) modulators were simulated; the speed of their transitions was modeled with first-order low-pass electrical filters in the drive paths of their I and Q modulators. The complex modulators were fed with identical pulses from a 10 Gpulse/s Mode-Locked Laser (MLL), modeled as Gaussian pulses with a defined width (FWHM). The central wavelength of the MLL was aligned to the second SC’s frequency. The MLL pulses were set to occur 81.25 ps after a data transition, so that the modulators had near maximal time to stabilize their phases before being sampled by the optical pulses. The AWGRs were modeled with 8 waveguides with a differential delay between waveguides of 12.5 ps, giving a free spectral range of 80 GHz. The output of the transmitter was optically bandlimited with a 4-th order Gaussian bandpass filter centered on the SC band (set midway between subcarriers 2 and 3). This filter represents the combined effect of wavelength multiplexing and demultiplexing in a WDM system. Dispersion was not modeled, but could be compensated electronically after sampling.

In a real system, the receiver samplers could be implemented optically or electronically. In our simulation they were placed after the homodyne coherent receivers, so are electronic [5]. The bandwidth of the receiver samplers was represented by a 50-GHz electrical filter before each sampler. The sampling time was chosen to be optimum for each simulation. The outputs of the samplers are QPSK constellations. The signal quality, *Q*, was assessed from the Cartesian mean and the variance of 1024 constellation points [16]. A *Q* of 9.8 dB translates to a bit error ratio of 10^{−3}, assuming Gaussian statistics.

## 4. Simulation results

#### 4.1 System using an AWGR after the complex optical modulators (scheme 2)

Figure 3 shows the transmitted optical spectrum before and after the transmitter’s 50-GHz optical bandpass filter, with 20-GHz complex modulators and 5-ps MLL pulses. The spectrum before the filter (blue) has two large sidelobes +/− 80 GHz from the main lobe. These are due to the periodic nature of the AWGR’s response. The sidelobes have reduced amplitudes due to the Gaussian spectrum of the mode-locked laser, which has a FWHM equal to 0.441/pulsewidth. Thus, 5 ps pulses have a spectral width of 88 GHz, 10 ps have 44 GHz, 15 ps have 29 GHz and 20 ps have 22 GHz. The demultiplexed spectra of the four subcarriers (green, yellow, red and pink) show the tails of each subcarrier: the optical filter has removed the low-frequency tail of Subcarrier 1 and the high-frequency tail of Subcarrier 4.

Figure 4
plots the signal quality *Q* of the best (Subcarrier 2) and worst (Subcarrier 4) subcarriers in a noiseless system, versus the electrical bandwidth of the complex optical modulators for the four pulse widths. Because these are back to back results, some margin is required for other systems impairments including optical amplifier noise; thus, the back-to-back signal quality should be at least 15 dB for the transmitter to be useful. The shortest MLL pulses give the best performance at all bandwidths, for both the best (2nd) and worst (4th) SCs. Thus, 7.5-GHz bandwidth modulators could be used to give a *Q* more than 19 dB.

At higher modulator bandwidths, the *Q* becomes limited by ICI, because the 50 GHz optical bandpass filter cuts the tails of the subcarrier’s spectra, so the subcarriers are no longer orthogonal. This was first confirmed by simulating a single carrier to remove the possibility of ICI: the *Q* increased to over 30 dB. The *Q* was also increased to over 30-dB with all subcarriers active by widening the bandwidth of the optical filter to 80 GHz and using 5 ps pulses. For longer MLL pulses, the 4th subcarrier receives less power due to the limited spectral width of the MLL, and so is most affected by ICI from its neighbors, thus has the lowest signal quality. This was confirmed by monitoring the *Q* of the 1st subcarrier, which is higher than the 4th, because it is closer to the centre frequency of the MLL.

#### 4.2 Placing the AWGR before the optical modulators (scheme 1)

Figure 5
shows the performance of a system where the AWGR is used as a demultiplexer prior to the modulators (Scheme 1); thus each modulator receives a CW optical tone and its phase modulation gives a *sinc-*spectrum, if the transitions are short. The results show that the modulators require bandwidths of at least 15 GHz to approach an acceptable performance. This is equivalent to 30-GHz of optical modulation bandwidth, because the modulators modulate both lower- and upper-sidebands onto their optical inputs. Subcarrier 4 also has a higher penalty than in Scheme 2, even for the shorter pulsewdths, limiting its maximum *Q* to 2-dB less than in Scheme 2.

#### 4.3 Use of phase modulators to replace the complex (IQ) modulators (scheme 2)

An advantage of using optical pulses into the modulators is that the transitions between the modulator’s states are not illuminated, so are of no consequence to the performance of the system. This means that the transitions can take any form. Huang *et al.* [12] used phase modulators in their OFDM system with a 2 × 2 FT, but did not examine the bandwidth requirement of the modulator. Phase modulators are topologically simpler than complex modulators, which require four parallel phase modulators and six couplers, but are only suitable for 4-QAM (QPSK) modulation, unless a MZI modulator is also added to the chain.

Figure 6 shows the performance of a system using two phase modulators in series: one to apply a zero or π phase shift, the second to apply a zero or π/2 shift. The second modulator is driven by an exclusive-OR function of the two data bits, so the data is Gray encoded. The required bandwidth is around 1-GHz more than for the complex modulator (Fig. 4). This is because a complex modulator nulls its transmission during transitions, effectively shortening the input pulses, whereas the phase modulators output constant intensities.

## 5. Discussion

These results show the maximum signal quality that could be obtained using four subcarriers and an optical bandwidth limited by a conventional optical filter. Comparing the results of Scheme 2 with IQ modulators (Fig. 4) with Scheme 1 (Fig. 5), it is clear that the modulators require far less electrical bandwidth in Scheme 2 than Scheme 1; that is, placing the AWGR after the modulators, so that the modulators are sampled by optical pulses, means that the modulators do not have to hold a constant phase throughout an OFDM symbol. These results also show that 10-ps pulses give acceptable signal qualities for QPSK, as they have enough bandwidth (44 GHz FWHM) to support all of the subcarriers; however, the signal qualities of the outer subcarriers are reduced by around 3 dB in Scheme 1 because of the spectral roll-off. Scheme 2 also gives good performance with low-bandwidth phase modulators, as shown in Fig. 6; however, at bandwidths below 5 GHz, the IQ modulators give better signal qualities, most likely because the IQ modulators take a direct path between phase states, whereas the phase modulators may have to transcend 270-degrees for some transitions.

It is interesting to place these results in the light of recent experimental results. For example, Qian *et al.* [17] have reported a record 101.7 Tbit/s for a C-band system using digitally-generated 128-QAM OFDM subcarriers spaced at 1 MHz, modulated onto 370 lasers, with an OSNR requirement only 2-dB higher than the theoretical limit. Following our arguments, one might ask whether each modulator should have an electrical bandwidth covering the entire C-band. Our answer to this is that the digital generation ensures that all of the subcarriers modulated onto a single laser are orthogonal, and furthermore, 200-MHz guard-bands are used between each laser’s band of subcarriers. As the guardbands are 200 × the subcarrier spacing, the tails of the subcarriers of one laser’s band do not encroach on the adjacent bands. Another recent example is the transmission of 10.6 Tbit/s and 26.1 Tbit/s by modulating 16-QAM data at onto individual spectral lines derived by demultiplexing a very broad comb source [18], similar to Scheme 1. In the discussion of the 10.8 Tbit/s system, using 40-ps symbols, the authors state that the addition of a 28% Cyclic Prefix (CP) mitigates the effect of the bandwidth of the modulators, as it gives extra time between the symbols for the transitions to occur.

Coherent WDM [19,20] also uses relatively low-bandwidth modulators after the wavelength demultiplexer. The coherent WDM transmitter is similar to Scheme 1 (and so is similar to no-guard interval OFDM [21]), but uses intensity modulation and combines the outputs of the modulators after controlling their relative phases. In this way, interference is forced into quadrature with the desired signal at the sampling times of the receiver [22]. The sensitivity of the signal quality of coherent WDM to modulator bandwidth warrants further investigation.

The examples in this paper used four subcarriers, each of 20 Gbit/s. If a greater data rate is required, then further subcarriers could be added. This could be achieved by adding more input guides to the AWGR, each fed by a modulator. Shorter MLL pulses would be required, to support the spectral width of the OFDM band. To provide a suitable guard band for multiplexing, the FSR of the AWGR could be increased by adding more array waveguides and decreasing the differential delay between them. This would not increase the size of the AWGR, as this is determined by the time delay difference of the longest and shortest array waveguides, which is close to the OFDM symbol length, which is the reciprocal of the OFDM subcarrier spacing. As in conventional WDM, the outputs of many of these transmitters could be combined to multiply the total transmission capacity of the fiber. The effect of the multiplexer and demultiplexer filters would have to be considered.

## 6. Conclusion

This paper has demonstrated that placing the optical inverse FT, implemented as an AWGR, after the optical modulators, in all-optical OFDM systems, lowers the required bandwidth of the modulators. This is because the pulses from the optical comb generator can be used to sample the state of the modulators once per OFDM symbol, which means that the modulators need only be in their correct state when sampled, rather than throughout each OFDM symbol. In contrast, using the AWGR as a wavelength demultiplexer before the modulator means that the modulated signals must have an almost constant phase during the whole OFDM symbol; otherwise inter-carrier interference will occur as a result of a loss of orthogonality.

We have also shown that low-bandwidth phase modulators can be used to replace the complex (IQ) modulators, when placed before the AWGR. Again, this is because the phase modulators are only sampled for a small portion of the OFDM symbol, giving them plenty of time to transition to their next state. These improvements mean that simple lower-bandwidth phase modulators, designed for 10 Gbit/s systems, could be combined with an AWGR and splitter to implement an 80-Gbit/s per polarization all-optical OFDM system.

## Acknowledgments

We should like to thank VPIphotonics (www.vpiphotonics.com) for the use of their simulator, VPItransmissionMakerWDM V8.5. This work is supported under the Australian Research Council’s Discovery funding scheme (DP1096782). We should like to thank the referees for their interesting comments.

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