## Abstract

We experimentally demonstrate an 8 x 12.5 Gbit/s all-optical orthogonal frequency-division multiplexing (AO-OFDM) system using arrayed waveguide gratings (AWGs), which perform discrete Fourier transform (DFT) and inverse DFT (IDFT) of a signal directly in the optical domain. The experimental results show that frequency orthogonality of OFDM sub-channels is degraded in the AWG due to the slab-diffraction effect. To restore the frequency orthogonality and improve the system performance, we propose and demonstrate a waveform reshaping scheme, that improve the bit-error-rate (BER) from 10^{−4} to 10^{−6}. We also experimentally investigate the influence of frequency mismatch between the OFDM signal and AWG at the receiver. The measured BER shows a serious degradation from 10^{−6} to 10^{−4} in case of ± 1.88 GHz frequency mismatch. To keep the BER under 10^{−5}, the frequency mismatch should be smaller than ± 0.5 GHz ( ± 4% of the channel spacing).

©2012 Optical Society of America

## 1. Introduction

Network traffic is exponentially increasing during the last decade. To meet with the demand for new bandwidth-consuming applications, many different approaches have been proposed to enhance the channel capacity and spectral efficiency in optical networks. With no doubt, orthogonal frequency division multiplexing (OFDM) is nowadays one of the most promising technologies for high-speed transmission [1–8]. An OFDM system requires an inverse discrete Fourier transform (IDFT) block at the transmitter and a discrete Fourier transform (DFT) block at the receiver. IDFT and DFT are usually implemented in the electrical domain by using high-speed digital-signal-processing (DSP) devices [1], which are expensive and energy consuming. Recently, several kinds of all-optical techniques have been investigated to reduce the energy consumption and system costs, generating and processing OFDM signals directly in the optical domain using passive optical devices and low bandwidth electronics, which are mature technologies [3–8]. The all-optical IDFT/DFT blocks can be implemented by a tree of Mach Zehnder delay interferometers (MZDIs) [3] as a fast Fourier transform (FFT) processor, or an arrayed waveguide grating (AWG) [7,8]. The latter has the advantages of simple waveguide layout and design flexibility of the port number [7]. In some papers, a wavelength interleaver is used at the transmitter instead of the IDFT block to separate the even and odd subcarriers [3,7]. In this case, however, all the data of even (odd) channels are completely synchronized and do not interfere with each other, and the inter channel interference (ICI) between even (odd) channels does not degrade the signal quality. Therefore, experimental results show much better performance than an actual system, where all the sub-channels are fully independent. To the best of our knowledge, all the previous experiments have demonstrated up to four sub-channels with independent data pattern, and 100G-class OFDM transmitter and receiver with all-optical IDFT/DFT blocks have not been demonstrated yet.

In this paper, we experimentally demonstrate, for the first time, an 8 x 12.5 Gbit/s all-optical (AO) OFDM system using AWGs as optical DFT and IDFT devices. Since the orthogonality between the sub-channels is degraded due to the slab-diffraction effect in the AWG [9], we propose a waveform reshaping technique to restore the orthogonality. In Section 2, we describe the operation principle of an AO-OFDM and the waveform reshaping technique, and show the results of numerical simulations. In Section 3, we experimentally demonstrate an 8 x 12.5 Gbit/s AO-OFDM system and the effectiveness of the waveform reshaping that drastically improve the BER performance from 10^{−4} up to 10^{−6}. In Section 4, we analyze the influence of frequency mismatch between the OFDM signal and the AWG at the receiver. The experimental results show that the frequency mismatch should be kept within the range of ± 0.5 GHz ( ± 4% of the channel spacing) to keep the BER performance under 10^{−5}. Finally, we summarize our investigation in Section 5.

## 2. Operation principle

#### 2.1 DFT and IDFT with AWG

Figure 1
shows the architecture of an AO-OFDM system using the AWGs. This device has the same configuration as a conventional AWG used in wavelength division multiplexing (WDM), but the device parameters have been suitably designed to perform DFT or IDFT [7–9]. The impulse response of the AWG *h _{i,k}*(

*t*) can be represented as [8,9],

*N*denotes the number of arrayed waveguides which is same as the number of the input and output ports,

*i*and

*k*correspond to the input and output port number, respectively.

*τ*is relative time delay in the arrayed waveguide. If we choose one output port for

*N*x 1 operation, the AWG can perform IDFT operation, whereas it can perform DFT operation if one input port is chosen for 1 x

*N*operation, as illustrated in Fig. 2 .

Let *S _{i}*(

*t*) be the input signal for

*i*

_{th}input port of the AWG at the transmitter that performs IDFT. The input port

*i*corresponds to the sub-carrier frequency, and therefore

*S*is the discrete spectrum of the OFDM signal. The output signal at

_{i}*k*= (

*N*-1) port is expressed as [8],

*S*(

_{i}*t*) is an impulse (i.e.

*S*(

_{i}*t*) =

*D*(

_{i}*n*)∙

*δ*(

*t-nT*) for integer

*n*,

*T*is 1-bit duration, and

*D*(

_{i}*n*) = 0, 1.), the waveform in time domain is the IDFT of the discrete spectrum

*S*(

_{i}*nT*), and expressed as,

*m*= 1, 2, …,

*N*-1. As can be seen from the above discussion, the input signal should be a pulse waveform that is short enough to be regarded as an impulse, i.e., the pulse should be short enough to have several sub-carrier components in frequency domain.

When we use the AWG as DFT processor, on the other hand, the output signal at *k*_{th} port for the input signal to (*N*-1)_{th} input port is expressed as

*S*(

_{k}*t*) at

*t*=

*nT*by time gating operation, Eq. (4) represents the DFT of the received OFDM signal. In this case, the output port

*k*corresponds to the sub-carrier frequency. We call this sampled point “DFT point”, as indicated in Fig. 2(b).

#### 2.2 Waveform reshaping

The impulse response of Eq. (1) is true only for an ideal device, in which the input light is coupled into all the arrayed waveguide uniformly, and the output waveform from the AWG at the transmitter has a uniform intensity during the symbol time-slot as illustrated in Fig. 3(a) . In this case, the orthogonal sub-channels are completely canceled at the DFT point due to the destructive interference in the AWG at the receiver.

In the actual device, however, the coupling coefficients of the input signal to the arrayed waveguides have a Gaussian distribution due to the diffraction effect in the slab-waveguide, and the intensity of the output waveform is not uniform in the 1-bit duration (Fig. 3(b)) [9]. This effect seriously degrades the frequency orthogonality between sub-channels, because the orthogonal frequency sub-channels are not cancelled at the DFT point due to the unbalanced amplitude, as shown in Fig. 3(b). To overcome this limitation, we propose a waveform reshaping technique [10]. The operation principle is illustrated in Fig. 3(c). The output signal from the AWG at the transmitter is modulated by a clock signal with low modulation depth, so that it presents a dip at the center of the symbol time-slot. In the AWG at the receiver, the amplitudes of optical field in the arrayed waveguides become same at the DFT point and the output intensity at this point become null for the inputs of orthogonal sub-channels, as illustrated in Fig. 3(c). In this way, amplitude mismatch due to the slab-diffraction effect is compensated and the orthogonality is restored.

#### 2.3 Numerical simulations

We have performed numerical simulations to demonstrate the effectiveness of the proposed technique. In the system of Fig. 1, we have considered eight sub-channels and the signal of each sub-channel is 12.5 Gbit/s non-return-to-zero on-off-keying (NRZ-OOK) with the data pattern of 2^{7}-1 pseudo random binary sequence (PRBS). The channel spacing and the number of ports of the AWG are 12.5 GHz and 16, respectively. Figure 4
shows the calculated eye-diagrams of (a) transmitted signal of ch5, (b) received signal of ch5 at port #5, (c) received signal of ch6 at port #5 with and without waveform reshaping. The received signal of ch6 at port#5 is the cross-talk from ch6 to ch5. The waveform of the cross-talk from ch4 to ch5 is almost same as Fig. 4(c). The slab-diffraction effect is simulated by a Gaussian distribution of the coupling coefficients to the arrayed waveguides. The coupling coefficient to *m*_{th} arrayed waveguide is expressed as

## 3. Experimental demonstration

Figure 5
shows the experimental setup of an 8 x 12.5 Gbit/s AO-OFDM system. The optical comb for eight sub-channels with 12.5 GHz frequency spacing is generated from a continuous wave (CW) light source with two cascaded electro-absorption modulators (EAMs) driven by 25 GHz and 12.5 GHz clock signals, respectively. A splitting ratio-tunable delayed interferometer (DI) is used between two EAMs as a dip-filter to generate the optical comb with flat-top spectrum. The free-spectral range (FSR) and the depth of dip of the DI filter are 160 GHz and 8 dB, respectively. The generated short pulse has full-width at half maximum (FWHM) of 5.3 ps. The frequency of CW light source is set to 193.4875 THz. The generated optical comb is split into two and modulated by 12.5 Gbit/s PRBS signals in NRZ-OOK format with pattern lengths of 2^{15}-1 for odd channels and 2^{31}-1 for even channels, respectively. Each modulated data signal is split into four branches and sent to the AWG at the transmitter to perform IDFT. Each branch has a different delay line for pattern de-correlation. It should be noted that this setup is more practical than that employs an interleaver instead of the AWG to separate even and odd frequencies, which is used in many reports but shows much better performance than the fully de-correlated systems [11]. The polarization and powers of all the sub-channels are equalized by the polarization controllers (PCs) and variable optical attenuators (VOAs). The AWG used in this experiment has 16 ports with 12.5 GHz channel spacing, and an optical phase shifter is attached to each arrayed waveguide to compensate the phase mismatch between the waveguides. The transmission spectra of the AWGs at the transmitter and receiver are shown in Fig. 6
. The channel spacing is precisely designed to be 12.5 GHz and the cross-talk from the orthogonal sub-channel is less than −20 dB. A LiNbO_{3} intensity modulator (LN-IM) is located at the output of the AWG for waveform reshaping. To avoid an extra frequency chirp, dual-drive type LN-IM is used. At the receiver side, the signal is sent to the AWG that performs DFT. The de-multiplexed signal is input to the EAM for time gating operation to extract the DFT point in the symbol time-slot. The clock signal is provided by pulse pattern generator (PPG). The waveforms and spectra at key points are shown in Fig. 7
, (a) is the optical comb, (b) and (c) are the transmitted signal of ch5 before and after waveform reshaping, and (d) is the generated OFDM signal.

In Figs. 7(b) and 7(c), when the signal is reshaped by the LN-IM, it presents a dip at the center of symbol time-slot. The eye-diagrams of ch6 received at port #5 of the AWG at the receiver, which is the cross-talk from ch6 to ch5, are shown in Fig. 8(a) . It is evident that the waveform reshaping technique successfully restores the orthogonality and suppresses the intensity at the DFT point. It means the reduction of the cross-talk from ch6 to ch5. Since the first neighboring sub-channels (ch4 and ch6 in this case) have the largest cross-talk to the target sub-channel (ch5), we focused only on the cross-talk from ch6 to ch5, and the waveform of ch4 received at port #5 (cross-talk from ch4 to ch5) is almost same as Fig. 8(a). As for the cross-talks from the other sub-channels, they are small enough and have little effect on the system performance owing to the deep dip in the transmission spectra of the AWGs shown in Fig. 6. We also note that the results of Figs. 7(b), 7(c), and Fig. 8(a) show perfect matching with the numerical simulation results in Section 2. Figures 8(b) and 8(c) show the eye-diagrams of the received signal before and after time gating operation, when all the eight sub-channels are transmitted. The eye opening is effectively improved by waveform reshaping.

Next, the BER performance of the OFDM system has been measured. Figure 9(a)
shows the BER performance as functions of total received power at the AWG (total power of eight sub-channels). Although the system still suffers from an error-floor, the proposed technique drastically improves the BER performance from 10^{−4} up to 10^{−6}. Figure 9(b) shows the BER of each sub-channel, when the received power is 0 dBm. Since ch1 and ch8 are the edge channels, they show better BER performance than the other sub-channels. The result shows that all the sub-channels can take the benefit of the waveform reshaping scheme. We should also note that the OFDM transmitter is configured with fiber-based optical components and the relative optical phase between sub-channels is not stable in this experiment. If all the components of the AO-OFDM transmitter are integrated, the system performance would be much enhanced.

## 4. The influence of frequency mismatch

In the previous analysis, the frequency setting of the transmitter (generated OFDM signal) and the AWG at the receiver are completely matched. In a practical situation, however, a frequency mismatch between transmitter and receiver always occurs due to some errors in operational conditions or device fabrication. A frequency mismatch in AO-OFDM systems is more critical than that in WDM systems, because the frequency orthogonality strictly depends on the transmission spectrum of the AWG. In other words, the dip of the transmission spectrum of the AWG shown in Fig. 6 must precisely match with the sub-carrier frequencies. In the case of frequency mismatch, the AWG at the receiver cannot de-multiplex the target signal correctly, and the orthogonal sub-carriers are not completely rejected [12].

We have examined the influence of frequency mismatch by changing the frequency setting of the AWG at the receiver side. The experimental setup is the same as Fig. 5 and the frequency setting of the AWG is changed by temperature controller. In this experiment, the waveform reshaping scheme is applied. Figure 10 shows the spectra and eye-diagrams of the received signals of ch5, when the temperature offsets from the optimum point are (a) −1.00 K, (b) 0 K, and (c) + 1.00 K, respectively. The wavelength-temperature coefficient of the AWG is 0.015 nm/K. Therefore, the corresponding frequency mismatches of (a) and (c) are + 1.88 and −1.88 GHz, respectively. These spectra are measured before time gating operation, and the insets show the eye-diagrams of ch4, 5, and 6 received at port #5 of the AWG. The eye-diagrams in the lower part of Fig. 10 are the received OFDM signal at port #5 after time gate operation. In case of no frequency mismatch, the orthogonal frequency subcarriers are successfully suppressed, as shown in Fig. 10(b), and the DFT points in the eye-diagrams of ch4 and 6 are null. Therefore, the eye-diagram of the gated signal shows a clear eye opening. In case of ± 1.88 GHz frequency offset, on the other hand, the orthogonal frequency subcarriers are not completely suppressed and one of the adjacent sub-channels shows serious degradation, as shown in Figs. 10(a) and 10(c). It leads to serious degradations in the eye-diagrams of gated signals (Figs. 10(a) and 10(c)).

We have measured the BER performance of the system, when the AWG at the receiver has frequency mismatch with the OFDM signal. The received optical power at the AWG is fixed at 0 dBm (total power of the eight sub-channels), where the BER curve shows a floor in Fig. 9, and the BER of all the sub-channels was measured. Figure 11
shows the BER performance as a function of frequency mismatch. When the frequency mismatch is ± 1.88 GHz, the BER is seriously degraded from 10^{−6} to 10^{−4}. The frequency mismatch of 0.5 GHz (4% of the channel spacing) is tolerable to keep the BER performance under 10^{−5}.

## 5. Summary

We have experimentally demonstrated for the first time an 8 x 12.5 Gbit/s all-optical OFDM system with AWGs which perform DFT and IDFT. The sub-channel orthogonality is degraded due to the slab-diffraction effect in the AWG and it has been restored using waveform reshaping. Both numerical and experimental results confirm the effectiveness of the proposed technique and the measured BER performance has been improved from 10^{−4} up to 10^{−6}. We also investigated the performance degradation when the AWG at the receiver has a frequency mismatch with the OFDM signal. The experimental results show that the frequency mismatch degrades the received signal because the orthogonal subcarriers are not completely suppressed. The measured BER shows a serious degradation from 10^{−6} to 10^{−4} when the frequency mismatch is ± 1.88 GHz. To keep the BER performance under 10^{−5}, the frequency mismatch should be kept within the range of ± 0.5 GHz ( ± 4% of the channel spacing).

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