## Abstract

We implement dispersion-tolerant and time-gating-free all-optical OFDM transmission using a photonic-integrated discrete Fourier transform (DFT) device. We show that 35-Gb/s OFDM data having near-unity spectral efficiency can be transmitted all-optically with 1-dB dispersion margin of ~1000 ps/nm. The passive-optical DFT circuit is implemented using multi-mode interference (MMI) couplers on a high index-contrast silica integrated-optic platform. We also propose a photonic DFT circuit based on an NxN MMI device capable of simultaneous channelization of OFDM signals into N subcarriers.

©2011 Optical Society of America

## 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]. It is also recognized that CO-OFDM is a powerful tool not only for tightly packing high data rate signals within the ITU grid, but also for combining multiple high data-rate coherent channels into a super-channel carrying >Tb/s traffic [2]. 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. The high-speed electronic processing, however, 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 are minimized. The fact that the discrete Fourier transform (DFT), which is the critical operation for channelizing orthogonally multiplexed subcarriers, can be all-optically performed was realized early on in the development of optical OFDM [3,4]. This can be seen from the equation for DFT in the context of demultiplexing an OFDM signal$E(t)$into subcarrier channel *E _{n}* [3]:

*N*is the number of subcarriers and

*T*(

*=*symbol period

*/N*) is equivalent to the sampling time. Thus, all-optical DFT can be implemented using essentially passive devices comprising optical delay lines with incremental temporal delay of

*T*and optical phase shifters for adjusting the optical phases of the delay lines. Several groups have reported all-optical OFDM (AO-OFDM) using all-optical DFT in various configurations including a single-stage asymmetric Mach-Zehnder interferometer (AMZI) [3,4], two-stage cascaded AMZIs [5], a 10x10 slab star coupler [6], and most recently simulation of an arrayed waveguide gratings (AWG) device for demultiplexing up to 16 OFDM channels [7].

These prior studies, however, have not investigated the tolerance of AO-OFDM against residual chromatic dispersion. In CO-OFDM with electronic processing, chromatic dispersion is compensated before channelization via electronic fast Fourier transform (FFT) [2]. Hence, it is important to verify that AO-OFDM is stable against residual chromatic dispersion with sufficient margin if it is to be practical. Otherwise, all-optical DFT is either incompatible with coherent detection in the presence of residual dispersion, or the residual dispersion needs to be fully compensated before channelization using a per-channel optical tunable dispersion compensator (TDC) but the added cost of the TDC reduces the value of all-optical DFT.

In addition, temporal gating was needed in previous work to optically filter out coherent inter-carrier crosstalk in the time domain. The time gating introduces several complications: first, temporal gating requires an optical modulator per subcarrier, which increases the optical losses and becomes impractical when *N* becomes large. Second, the duration of temporal window within which the inter-carrier cross talk is suppressed is in the order of *T* ( = symbol period/*N*). Therefore, these *N* time-gating optical modulators should have sufficient modulation bandwidth to be able to support generation of short temporal gates. Finally, the time gating needs to be synchronized with the data stream with a channel-dependent time delay, adding to the complexity.

In this paper, we report experimental demonstration of all-optically demultiplexing an OFDM signal using a compact integrated-optic DFT without resorting to optical temporal gating. In addition we demonstrate successful demultiplexing in the presence of large chromatic dispersion. We implement all-optical discrete DFT (*N* = 8) for demultiplexing near-unity spectral-efficiency (0.93 accounting for 7% FEC overhead) OFDM channels consisting of 5-Gb/s-per channel NRZ-OOK signals. The all-optical DFT is implemented using a silica planar light wave circuit (PLC). The dispersion tolerance is demonstrated by transmitting 7 x 5-Gb/s of OFDM data over 84-km standard single-mode fiber (SSMF) (D = 1430 ps/nm) without dispersion compensation, with required OSNR of 18.5 dB (3 dB penalty relative to back-to-back) for bit error rate (BER) of 10^{−3}. Finally, we propose an all-optical OFDM demultiplexer using an NxN MMI for simultaneous parallelization of OFDM signals.

## 2. Photonic-integrated all-optical DFT device

We show a layout of the photonic-integrated all-optical DFT circuit in 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) [8]. The relative temporal delays between the delay lines are *T* = 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. We show also in Fig. 1 a transmission spectrum of the all-optical DFT circuit tuned for demultiplexing OFDM channels, wherein the experimentally measured spectrum is in good agreement with the theoretical curve expected for 8-channel discrete Fourier transform convolved with the response function of the optical spectrum analyzer (resolution = 0.016 nm). The transmission of the all-optical DFT device can be tuned to select a desired subcarrier either by tuning each phase shifters or more conveniently tuning the temperature of the entire PLC chip. We note that simultaneous demultiplexing of eight subcarriers can be achieved by using an 8 x 8 MMI for the output coupler. We will discuss the design of such a device in section 4.

## 3. Experiment

In Fig. 2
, we show a schematic of the experimental set up for transmission of OFDM signals. We generate 5-GHz spaced optical frequency combs by sinusoidally modulating DFB laser output (1554.02 nm) using a lithium-niobate (LN) Mach-Zehnder modulator (MZM) followed by a LN phase modulator [9]. The seven central combs (Ch.1-Ch. 7) have spectral flatness better than 1.5dB and are used for bit error rate testing. The generated combs are split into two sets (even and odd) using a delay line interferometer with 10-GHz FSR. Each comb set is modulated by 5-Gb/s NRZ OOK data (2^{15}-1 PRBS) that are decorrelated with each other. 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, which was then launched into standard single mode fiber (SSMF). After transmission through SSMF, the optical signal is amplified by a two-stage EDFA before being sent into the all-optical DFT circuit for channel selection. Each subcarrier is selected one at a time by tuning the optical DFT circuit thermally. 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. The optical receiver has a 3-dB electrical bandwidth of 15 GHz; note that the other electronics in the set up have electrical bandwidths narrower than 12.5 GHz. We emphasize that no temporal gating is used in the setup to filter out inter-carrier interference.

In Fig. 3(a)
, we show the back-to-back (b-t-b) BER performance of all seven subcarriers (35 Gb/s) covering 30-GHz span. The required OSNR are measured for the entire combs with 1-nm resolution and referred to 0.1-nm resolution. The required OSNR for 10^{−3} BER is on average 15 dB for the seven channels, which is comparable to 15.1 dB expected for 35-Gb/s single-carrier non-coherent NRZ-OOK. We show eye diagrams for Ch.4 and Ch.7 in Fig. 3. They exhibit ~25-ps wide clear eye opening within which the orthogonality condition is satisfied and inter-carrier interference is suppressed. The temporal duration is sufficient to allow BER measurements with 12.5-GHz bandwidth electronics without using optical gating.

We recall that it has been widely claimed that optical time gating is necessary to isolate the temporal windows with open eyes while filtering out the inter-carrier coherent cross talk. The claim is valid under a tacit assumption that the photodetector receiving the demultiplexed OFDM signal has a limited electrical bandwidth that is only comparable to the symbol rate, as the bandwidth limitation would convert the *coherent inter-carrier interference* to *inter-symbol interference* and cause penalty. However, if the photodetector and the processing electronics have sufficient electrical bandwidth to isolate and discern the temporal regions with open eyes, then the optical time gating can be obviated. Of course, the use of higher-speed electronics can be justified when the electronics technology is mature enough not to incur excess cost increase. In this paper, we provide an example where using electronics with higher bandwidth than what symbol rate requires nevertheless delivers a substantial performance enhancement over the case where optical temporal gating is used. We achieve this by judicious choice of symbol period (200 ps) and the number of subcarriers (*N* = 8). This choice should allow ~25-ps (200 ps/8) wide temporal windows free of inter-carrier interference, in agreement with the measurement. Therefore, electronics having a 3-dB bandwidth of ~12 GHz ( = 0.3/25 ps) should be sufficient to isolate the interference-free temporal regions without incurring too much inter-symbol interference. In addition, the cost increase should be minimal given the maturity of 10G electronics. The observation indicates that baud rates and the number of subcarriers need to be selected carefully to enable AO-OFDM operation without having to use costly time gating. In this regard, it will be quite challenging to pursue all-optical OFDM for high-baud rate and many subcarrier applications as this would require high-speed electronics (proportional to N x baud rate) or multiple high-speed optical modulators for time gating.

Next, we test the tolerance of the all-optical OFDM against chromatic dispersion. For this we insert SSMFs with different lengths and measure BER performance. In Fig. 4(a)
, we plot the typical required OSNR for BER of 10^{−3} as a function of the accumulated dispersion or SSMF length. It is observed that the dispersion margin for 1-dB OSNR penalty is ~1000 ps/nm. This is substantially better than ~45 ps/nm for 40-Gb/s NRZ-OOK and the OFDM channels behave effectively as ~8.5 Gb/s concerning the chromatic dispersion. This implies that the all-optical OFDM scheme we implemented is compatible with the existing 10G infrastructure; no per-channel tunable dispersion compensation will be required to demultiplex OFDM channels all-optically. Dispersion tolerance can be further enhanced with minimal cost increase using an electronic equalization technique such as MLSE detection and transmission of ~40 Gb/s data over 100-km SSMF should be feasible without dispersion compensation. We believe the dispersion tolerance is a result of the low modulation speed per subcarrier as most of the dispersion penalties would result from the interference from the nearest neighboring subcarriers. In Fig. 4(b), we plot BER of Ch. 4 after transmission through 84-km (1430 ps/nm) SSMF, whose eye diagram is shown in Fig. 4(c). The penalty relative to b-t-b case is 3 dB (6 dB) for BER of 10^{−3} (10^{−9}). The excellent dispersion tolerance and the use of 10G-compatible electronics suggest that all-optical OFDM in the configuration as we demonstrated is a good candidate for upgrading optical communication systems from 10 Gb/s to 40 Gb/s or higher data rates if the AO-OFDM transmitters and receivers including the all-optical DFT can be implemented economically, for which photonic integration is crucial.

## 4. NxN MMI-based all-optical DFT for simultaneous channelization

For practical deployment, it is essential for a single optical DFT to process demultiplexing of all *N* subcarrier channels. In this section, we give details on how to implement an all-optical DFT demultiplexer based on an NxN MMI that is capable of simultaneous channelization of all subcarriers of an OFDM signal. We demonstrate that such simultaneous channelization is possible by using an NxN MMI for combining the time-delayed OFDM signals instead of an Nx1 MMI. An NxN MMI schematically shown in Fig. 5
imparts phase shifts *ϕ _{io}* onto the signal entering into the

*i*-th input waveguide and exiting the

*o*-th output waveguide according to [10]:

The goal is to connect the optical delay lines to the MMI input waveguides and to adjust the phase of each delay arm in such a way that the phase relations of the MMI ensure that the DFT condition is simultaneously satisfied for all signals exiting the *N* output ports. Mathematically, these operations can be written as

*E*is the subcarrier having carrier frequency

_{n}*f*

_{1}+(

*n*−1)/

*NT*, Δ

*ψ*

_{m}is the phase shift to be applied by the phase shifter in the delay line having (

*m-*1)

*T*relative temporal delay, and

*ψ*

_{mn}is the phase shift applied by the MMI unto the signal originating from the

*m*-th delay line. Note that the index

*m*(

*n*) does not directly refer to the

*m*(

*n*)-th waveguide of the MMI in Fig. 5. Instead, these phase shifts

*ψ*

_{mn}and Δ

*ψ*

_{m}can be expressed using the phase matrix of the MMI, ${\varphi}_{io}$ in Eqs. (2) and (3): with a function

*μ*that rearranges the matrix elements by the rule

*m*-th delay line (with delay of (

*m*-1)

*T*) should be connected to μ(

*m*)-th input waveguide of the MMI and

*n*-th subcarrier having frequency

*f*

_{1}+(

*n*−1)/

*NT*emerge out of $\mu (n)$–th output waveguide of the MMI.

Equivalently, the frequency${f}_{o}$ of the subcarrier exiting from the *o*-th output waveguide can be expressed as

The above equations can be understood in more concrete terms using a specific example; we show a wiring diagram for the case of *N* = 8 in Fig. 6
. In Fig. 6, we denote the signal path that needs to be connected to an input waveguide of the 8x8 MMI by indicating the relative temporal delay of the path and the relative optical phase shifts Δψ. The signal in each path is a replica of the OFDM signal and the method by which the replicas are obtained is not important, whether a single 1x8 power splitter or multiple 1x2 couplers are used to split the OFDM signal. We calculate the transmittance of such-configured all-optical DFT circuit and show the spectra in Fig. 6 (right). The spectrum is consistent with that required for demultlexing an OFDM signal consisting of 8 subcarriers.

## 5. Summary

We successfully implemented an all-optical DFT device in an integrated-optic platform that enabled demultiplexing of a 7x5-Gb/s NRZ-OOK based AO-OFDM signal, without the use of optical temporal gating and even in the presence of large chromatic dispersion. We also presented a design of all-optical DFT based on an NxN MMI capable of simultaneous channelization of an OFDM signal consisting of N subcarriers. The approach that we have demonstrated here can be scaled to higher net data rates. For example, if each subcarrier was modulated by 10-Gb/s (5 Gbaud) DQPSK signals, transport capacity approaching 100-Gb/s can be realized with dispersion tolerance comparable to that of 10G transport systems with reduced amount of computation and energy consumption. Crucial to the successful deployment of AO-OFDM is photonic integration of elements including photodetectors and we believe the level of integration that can support the optical DFT and photodetectors is within the capability of the current state of the art [11].

## References and links

**1. **W. Shieh and I. Djordjevic, *OFDM for Optical Communications* (Academic Press, 2010).

**2. **S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” ECOC '09, PD2.6 (2009).

**3. **H. Sanjoh, E. Yamada, and Y. Yoshikuni, “Optical orthogonal frequency division multiplexing using frequency/time domain filtering for high spectral efficency up to 1bit/s/Hz,” OFC 2002, ThD1 (2002).

**4. **A. Sano, H. Masuda, E. Yoshida, T. Kobayashi, E. Yamada, Y. Miyamoto, F. Inuzuka, Y. Hibino, Y. Takatori, K. Hagimoto, T. Yamada, and Y. Sakamaki, “30x100-Gb/s all-optical OFDM transmission over 1300 km SMF with 10 ROADM nodes,” ECOC 2007, PDS 1.7 (2007).

**5. **D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express **18**(9), 9324–9340 (2010). [CrossRef] [PubMed]

**6. **K. Takiguchi, T. Kitoh, A. Mori, M. Ogima, and H. Takahashi, “Integrated-optic OFDM demultiplexer using slab star coupler-based optical DFT circuit,” ECOC 2010, PD1.4 (2010).

**7. **Z. Wang, K. S. Kravtsov, Y.-K. Huang, and P. R. Prucnal, “Optical FFT/IFFT circuit realization using arrayed waveguide gratings and the applications in all-optical OFDM system,” Opt. Express **19**(5), 4501–4512 (2011). [CrossRef] [PubMed]

**8. **I. Kang, M. Rasras, M. Dinu, M. Cappuzzo, L. T. Gomez, Y. F. Chen, L. Buhl, S. Cabot, A. Wong-Foy, S. S. Patel, C. R. Giles, N. Dutta, J. Jaques, and A. Piccirilli, “All-optical byte recognition for 40-Gb/s phase-shift-keyed transmission using a planar-lightwave-circuit passive correlator,” IEEE Photon. Technol. Lett. **20**(12), 1024–1026 (2008). [CrossRef]

**9. **T. Healy, F. C. Garcia Gunning, A. D. Ellis, and J. D. Bull, “Multi-wavelength source using low drive-voltage amplitude modulators for optical communications,” Opt. Express **15**(6), 2981–2986 (2007). [CrossRef] [PubMed]

**10. **M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in N × N multimode interference couplers including phase relations,” Appl. Opt. **33**(18), 3905–3911 (1994). [CrossRef] [PubMed]

**11. **S. Corzine, P. Evans, M. Kato, G. He, M. Fisher, M. Raburn, A. Dentai, I. Lyubomirsky, R. Nagarajan, M. Missey, V. Lal, A. Chen, J. Thomson, W. Williams, P. Chavarkar, S. Nguyen, D. Lambert, T. Butrie, M. Reffle, R. Schneider, M. Ziari, C. Joyner, S. Grubb, F. Kish, and D. Welch, “10-channel x 40Gb/s per channel DQPSK monolithically integrated InP-based transmitter PIC,” OFC 2008, PDP18 (2008).