1. Introduction

Coherent optical orthogonal frequency division multiplexing (CO-OFDM) has received much attention as a promising technique in supporting transport capacity beyond 100Gb/s [1]. As is the case with single-carrier coherent modulation formats, the excellent transmission performance of CO-OFDM is in large part due to the advancement of high-speed digital signal processing for computationally compensating various transmission penalties. For example, tunable optical devices for compensating chromatic and polarization mode dispersion that were necessary for 40-Gb/s transmission systems are now being replaced by electronic equalizers for 100-Gb/s transmission [2]. However, like its previous optical counterpart, the electronic signal processing has to be implemented on per-channel basis. In addition, it has the drawback of high power consumption, which increases with increasing processing speed.

Thus, it is desirable to perform some of the signal processing all-optically, preferably using passive devices, so that the burden on the electronic signal processing and power consumption can be minimized. The discrete Fourier transform (DFT) is a key operation for channelizing orthogonally multiplexed sub-carriers and it can be implemented all-optically using passive optical devices [3–7]. However, the previous implementations of all-optical OFDM transmission entailed the complication of tunable optical dispersion compensation and time-gating modulators [3–6]. Recently, we have implemented an all-optical (AO) OFDM system supporting reception of 35-Gb/s (7 x 5 Gb/s NRZ-OOK) data having near-unity spectral efficiency with 1-dB dispersion margin of ~1000 ps/nm [7]. The AO-OFDM was enabled by a passive-optical DFT circuit implemented using multi-mode interference (MMI) couplers on a high index-contrast silica integrated-optic platform. This implementation of AO-OFDM is well suited for upgrading short-reach transmission systems from 10-Gb/s to 40-Gb/s and higher data rates.

In this paper, we show that the AO-OFDM implementation using MMI-based all-optical DFT can be also used for high-capacity long-haul transmission. We demonstrate that 35-Gb/s OFDM signal consisting of seven subcarriers can be transmitted over ~2000-km all-EDFA amplified fiber span consisting of standard single-mode fiber (SSMF) and dispersion-compensating fiber (DCF) without using a tunable dispersion compensating device and time-gating modulators.

2. All-optical OFDM experimental setup

In Fig. 1 , we show the experimental set up for AO-OFDM transmission. We generate 5-GHz spaced optical frequency comb by sinusoidally modulating DFB laser output (λ₄=1554.02 nm) using a lithium-niobate (LN) Mach-Zehnder modulator (MZM) followed by a LN phase modulator. The generated spectral comb lines are split into two sets (even and odd) using a delay line interferometer with 10-GHz free-spectral range. Each set is modulated by 5-Gb/s NRZ OOK data (2¹⁵-1 PRBS) that are decorrelated with each other by electrical and optical delays. After optical amplification to compensate for the optical losses in the modulators, the two data streams are polarization- and time-aligned before getting combined by a PM coupler to generate the AO-OFDM signal. We show the optical spectrum of the OFDM signal in Fig. 1, where subcarriers Ch.1 through Ch.7 are used for transmission measurements.

 

Figure 1 Experimental set up for AO-OFDM transmission. (inset: schematic of AO-DFT circuit).

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The AO-OFDM signal is further combined with six CW channels and they are launched into the recirculating loop. The CW channels (λ₃, λ₅) nearest to the AO-OFDM signal (λ₄) are separated from it by 200-GHz to facilitate the measurement of optical signal-to-noise ratios (OSNRs) while the frequency spacing among the CW channels is 100 GHz. The recirculating loop consists of four 82.5-km spans of SSMF. The span losses range from 17 to 18 dB. The average dispersion is 17 ps/nm/km and the residual dispersion of each span is roughly 42.5 ps/nm at 1550 nm. A pre-compensation of –514 ps/nm is used. A wavelength-selective switch (WSS) having channel spacing of 100 GHz and a 3-dB per channel optical bandwidth of 78 GHz is used as a dynamic gain equalizing filter.

After transmission through the spans, the delivered OFDM signal is amplified by a two-stage EDFA before being sent into the all-optical DFT circuit for channel selection. The optical DFT device we use for demultiplexing OFDM channels is shown in the inset of Fig. 1. The circuit consists of 1x8 (8x1) multi-mode interference (MMI) couplers for splitting (combining) optical signals, optical delay lines, thermo-optic phase shifters, and variable optical attenuators (VOAs). The relative temporal delays between the delay lines are 25 ps, corresponding to the free-spectral range (FSR) of 40 GHz. The device is realized on the platform of silica PLC having 4% index contrast and has an overall size of 0.8 cm x 3 cm. The VOAs are used for compensating the imbalance of the MMI splitting ratio (<1dB) and the eight phase shifters are used to properly tune the optical phase of each delay line such that the transmission of the device satisfies the DFT condition. We previously used the circuit as an optical Fourier transform correlator for optical bit pattern recognition [8], wherein more details of the device can be found. Each subcarrier is selected one at a time by tuning the optical DFT circuit thermally. We note that simultaneous reception of all subcarriers is possible with a modified DFT device having a 8x8 MMI combiner at the device output [7]. An additional optical band-pass filter having 0.2-nm spectral width is inserted to reduce the amount of ASE from the EDFAs but it does not contribute to channel selection. We note that we do not use temporal optical gating or a tunable dispersion compensating device in receiving the AO-OFDM signal and that the maximum electronic bandwidth of the device used is 12 GHz.

3. Transmission results

We first determine the optimum optical powers of the signal to be launched into the recirculating loop. We plot in Fig. 2(a) the bit error ratio (BER) of the central subcarrier (Ch.4) as a function of the total OFDM signal powers, where the BER is measured after transmitting 1320-km (4 loops). We observe that the BER is minimized for the signal launch powers between −2.5 and −1 dBm. This is equivalent to optical power per each subcarrier of approximately −10 dBm. BER rapidly increases when the launch power exceeds this level owing to the nonlinear optical penalty. We further discuss the nonlinear penalty in the next section. We show in Fig. 2(b) an eye diagram of a sub-carrier channel (Ch.7) with −1.4 dBm launch power after transmission over 1320-km fiber, having BER of 4x10⁻⁶. We show in Fig. 2(c) an error-free eye diagram of the subcarrier for back-to-back transmission for comparison. We previously showed that all seven subcarriers perform similarly with the required OSNR of 15 dB (22 dB) for BER of 1x10⁻³ (1x10⁻⁹) for back-to-back, where the OSNR of the entire OFDM signal channels is measured with 1-nm spectral resolution and referenced to 0.1-nm resolution.

 

Fig. 2 (a) Bit error ratio of subcarrier Ch.4 after 1320-km transmission for different signal launch power. (b) An eye diagram of Ch.7 after 1320-km (BER = 4x10⁻⁶). (c) An error-free eye diagram of Ch.7 for back-to-back transmission.

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We study the long-haul transmission performance of AO-OFDM by measuring BER for different lengths of fiber. We plot in Fig. 3(a) BER of the central subcarrier (Ch.4) against the fiber distances and the corresponding uncompensated chromatic dispersions. OSNR values of the received OFDM signal referenced to 0.1-nm resolution are also plotted. Other than the pre-compensation of −514 ps/nm and DCF in the recirculating loop, we did not use any other dispersion compensating devices. In Fig. 3(b), we show the BERs of all the subcarriers after 1980-km (solid squares) and 2310-km (hollow circles) transmission. We note that the measured BERs for 1980-km transmission are smaller than the threshold (4x10⁻³) of 7%-overhead enhanced-FEC (EFEC) and the BERs for 2310-km transmission are smaller than the 25%-overhead ultra-FEC (UFEC) threshold (1.3x10⁻²). The average BER of the 35-Gb/s OFDM signal is 1.2x10⁻³ (7x10⁻³) for 1980-km (2310-km) transmission. Due to the excellent dispersion tolerance, we show here that the AO-OFDM signal can be transmitted over ~2000 km without using tunable dispersion compensation. The residual dispersion ranges from −344 ps/nm (330 km) to 676 ps/nm (2310 km) and the wide dispersion margin should allow long-haul transmission of AO-OFDM across the C-band using only fixed DCF. The performance can be compared to prior demonstrations of long-haul transmission of ~40-Gb/s OOK modulation formats [9,10], where transmissions over up to 2000 km fiber were enabled by using tunable dispersion compensation, non-standard fiber, and Raman amplification.

 

Fig. 3 (a) BER (solid) of Ch. 4 subcarrier vs. transmission distance and corresponding uncompensated dispersion. Delivered OSNR of the OFDM signal is in dashed curve. (b) BERs of all subcarriers after 1980-km transmission (solid squares) and 2310-km transmission (hollow circles).

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4. Nonlinear penalty

In this section, we investigate potential causes of the transmission penalty and how it can be mitigated. Given the wide margin of dispersion tolerance, i.e. 1000 ps/nm for 1-dB OSNR penalty, the majority of the penalty occurring in this dispersion-managed transmission is expected to be caused by nonlinear optical interactions, such as cross-phase modulation (XPM) and four-wave mixing (FWM). In particular, it is well known that transmission of OOK signals is highly susceptible to inter-channel nonlinear collision due to XPM [11]. For example, in the presence of −514 ps/nm pre-compensation, the AO-OFDM signal does not experience chromatic dispersion larger than ~2100 ps/nm during the transmission over 2310 km, which is equivalent to maximum temporal walk-off of less than three symbol periods among the subcarriers. Thus, XPM among the subcarriers and resulting temporal jitter is expected to substantially contribute to the nonlinear penalty, considering the narrow temporal window within which inter-subcarrier interference is suppressed for eye opening. Not surprisingly, we experimentally find that the XPM-induced penalty is a significant cause of the nonlinear penalty: first, we plot in Fig. 4 measured BERs of the center subcarrier channel (Ch.4) as a function of distance for the transmission without using the pre-compensation (solid squares). We also plot the data previously shown in Fig. 3 obtained for transmission using −514 ps/nm pre-compensation for comparison (hollow circles). The main difference between the two situations is that two adjacent subcarrier channels, once initially synchronized, will continue to walk away from each other for the case without the pre-compensation, while they will suffer multiple mini-collisions with each other in the case with the pre-compensation. The reduction of BER for the case without the pre-compensation implies the substantial contribution of inter-subcarrier XPM and also suggests means to reduce such penalty.

 

Fig. 4 (a) BER of subcarrier channel 4 vs. distance with (circle) and without (square) −514 ps/nm pre-compensation. (b) Accumulated dispersion for the case without (solid curve) and with (dashed curve) the-514 ps/nm pre-compensation.

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Further evidence is shown in Fig. 5 demonstrating the contribution of the XPM. Here we measure the changes in BER of the subcarrier Ch. 4 when the odd subcarrier channels, in particular Ch. 3 and Ch. 5, are modulated by NRZ binary phase-shift keying (BPSK) instead of NRZ-OOK. Switching between NRZ-OOK and NRZ-BPSK is achieved by adjusting the bias point of the lithium niobate MZM for the odd-channels and the amplitude of the driving signal. The motivation is to see if there is any change when the neighboring channels are modulated by a constant-amplitude modulation format, such as NRZ-BPSK, which in principle should mitigate the part of the nonlinear penalty that is due to the inter-subcarrier XPM. In Fig. 5(a), we show an eye diagram of Ch. 4 after 1320-km transmission with the pre-compensation in place, where both even and odd channels are modulated by NRZ-OOK. The measured BER is 2x10⁻⁵. When the odd-channels are modulated by NRZ-BPSK, we observe that the eye quality improves and BER is reduced to 7x10⁻⁷. In Fig. 5(c), we show similar BER improvement for transmission after 990 km from 2x10⁻⁷ to 2x10⁻⁹ by switching from NRZ-OOK to NRZ-BSPK. For the case of transmission without the pre-compensation (shown with circular symbols), however, we observe much reduced improvement by the change of the modulation formats. We surmise that the nonlinear penalty caused by the inter-subcarrier XPM can be effectively dealt with by adjusting the dispersion map such that the inter-channel collision is minimized. Alternatively, one can choose to use constant amplitude modulation formats such as BPSK or quadrature PSK (QPSK) with similar benefits.

 

Fig. 5 (a) Eye diagram of Ch. 4 after 1320-km transmission with the pre-compensation and both even and odd channels NRZ-OOK modulated. (b) Same as (a) except that the odd channels are NRZ-BPSK modulated. (c) BER of Ch. 4 measured with the pre-compensation (pre-comp) and all-channels NRZ-OOK modulated (solid squares), BER measured with the pre-comp and odd-channels NRZ-BPSK modulated (hollow squares), BER measured without the pre-comp and all-channels NRZ-OOK modulated (solid circles), and BER measured without the pre-comp and odd-channels NRZ-BPSK modulated (hollow circles).

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5. Summary

We have demonstrated an implementation of all-optical OFDM that is suitable for long-haul transmission that uses fixed dispersion compensation devices. The dispersion tolerance afforded by the tight OFDM channel plan allowed us to transmit 35-Gb/s data over ~2000-km without using per-channel tunable dispersion compensation. This suggests that AO-OFDM with a suitable channel plan and photonic-integrated optical DFT-based receivers is an excellent alternative for upgrading the existing 10-Gb/s long-haul systems for higher-rate applications. The 35-Gb/s data rate was limited by the flatness of the optical frequency comb and the capacity can be increased by increasing the number of spectral lines and using more spectrally efficient formats, such as DQPSK; 100-Gb/s over 50-GHz spectral width, for example. We expect that adoption of formats resistant to nonlinear penalties such as DPSK or DQPSK for sub-carrier modulation may further enhance the transmission performance.

Photonic-integration is critical for cost-effective deployment in order to overcome the increased complexity of the OFDM transmitter and receiver; for example, photo-detectors integrated with optical DFT and photonic-integrated optical OFDM transmitter. The required degree of complexity in integration is indeed challenging yet is well within the capability of the current state of the art photonic integration technology [12]. Relatively low baud rate in our implementation of all-optical OFDM may afford the use of silicon photonics as a promising and potentially reduced-cost platform for integration and is a subject of future study.