1. Introduction

Mode division multiplexing (MDM) has recently been demonstrated as an effective method to increase the capacity in fiber communication systems [1], as well as on-chip optical interconnections [2–4]. It can offer new degrees of freedom for the implementation of both fiber and on-chip networks. Similar as in single-mode fiber (SMF) networks, in future MDM networks combined with wavelength division multiplexing (WDM), wavelength conversion can provide high flexibility by avoiding the optical-electrical-optical conversion and overcoming the “electronic bottleneck”. Wavelength conversion based on parametric processes may also achieve optical phase conjugation (OPC) for nonlinearity mitigation, which has been demonstrated in long-haul single-mode fiber (SMF) transmission [5]. Wavelength conversion for MDM networks can be carried out with or without mode selectivity. We have recently proposed and demonstrated all-optical wavelength conversion for MDM fiber networks without addressing individual modes based on three semiconductor optical amplifiers (SOAs) with large size and high power consumption [6]. However, the scaling issue of the number of SOAs or other equivalent nonlinear elements with the number of modes has to be addressed. On the other hand, mode-selective wavelength conversion has been demonstrated for on-off keying (OOK) signal at 40 Gb/s based on integrated photonic chip [7]. MDM wavelength conversion with mode selectivity has also been proposed based on FMF in simulation [8]. However, mode-selective wavelength conversion for coherent multicarrier multilevel modulations, i.e., orthogonal frequency-division multiplexing (OFDM), has not been reported yet. Wavelength conversion of OFDM signals is highly desirable since it greatly enhance the system capacity but is particularly challenging for integrated devices because it requires higher conversion efficiency and less phase noises.

In this paper, we design and fabricate a multimode silicon waveguide to achieve mode-selective wavelength conversion for complex modulated optical signal in on-chip network. Degenerated FWM is utilized so that OPC is simultaneously realized. A TE₀&TE₁ mode multiplexer based on tapered directional coupler (DC) is used to combine the two input optical signals into the multimode silicon waveguide with two spatial modes. The mode-selective wavelength conversion can be realized using strong four-wave mixing (FWM) when pump and signal lights are on the spatial mode. FWM between different spatial modes is weak due to phase mismatch. To prove the function of mode-selective wavelength conversion using our fabricated device, we conduct an experiment by transmitting an optical OFDM signal with QPSK format at 102.6 Gb/s. After coherent detection and digital signal processing (DSP), the experimental results show 0.5 dB and 0.7 dB power penalty for the conversion of each mode taken individually, as well as 1.4 dB and 1.9 dB excess conversion penalty when both signal modes co-propagate in the multimode silicon waveguide.

2. Device fabrication and characterization

The key to achieve the on-chip mode-selective wavelength conversion based on FWM is to design a multimode waveguide so that the phase matching conditions is satisfied between the interacting waves of the same modes while the other way around for different modes, which are determined by the dispersive properties of the waveguide [9]. The dispersion properties are affected by the geometric dimension of the waveguide. The second-order dispersion ${\beta }_2$ for both TE₀ and TE₁ modes of a rib silicon-on-insulator (SOI) waveguide of H = 220 nm with different widths are calculated by a finite vectorial finite difference (FD) mode solver [10], as shown in Fig. 1. The waveguide width is chosen to be ~700 nm so that both TE₀ and TE₁ modes have similar and close to zero dispersion values over C band. We also calculate the phase matches for FWM when the pump, signal and idler are on the same and different spatial modes, respectively. By defining the phase mismatch parameter as $\Delta \beta ={\beta }_{\text{signal}}+{\beta }_{\text{idler}}-2{\beta }_{\text{pump}}$, where ${\beta }_{\text{signal}}$, ${\beta }_{\text{idler}}$ and $2{\beta }_{\text{pump}}$ are the propagation constants of the signal, idler and pump, the phase mismatches with pump light placed at 1570 nm are shown in Fig. 2. It can be seen that the phase mismatches for each individual mode is small to enhance the conversion efficiency while a large phase mismatch between the TE₀ and TE₁ modes is achieved to keep low conversion efficiency between the two modes. Pump wavelength at 1570 is chosen according to our experimental verification, which will be explained later.

 

Fig. 1 Second-order dispersion of a silicon waveguide with height of 220 nm and different widths for (a) TE0 and (b) TE1 modes.

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Fig. 2 Calculated phase mismatch as a function of signal wavelength for single-pump FWM with a pump wavelength of 1570 nm for (a) TE0 mode, (b) TE1 mode, (c) TE0 mode for the pump, TE1 mode for the signal, and TE0 mode for the idler, and (d) TE1 mode for the pump, TE0 mode for the signal, and TE1 mode for the idler.

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An on-chip two-mode division multiplexing circuit with 3.14 mm long straight multimode silicon waveguide is designed and fabricated for experimental demonstration. As shown in Fig. 3, waveguides are fabricated on a silicon-on-insulator (SOI) wafer (top silicon layer: 220 nm, buried silicon dioxide lay: 2.0 μm). The TE₀&TE₁ mode (de)multiplexers are achieved based on tapered directional couplers (DCs) due to their simpler structure and larger fabrication tolerance than normal DCs [11,12]. In the tapered DC, the upper waveguide tapered from 500 nm to 180 nm is coupled to the wide waveguide, which is tapered from 650 nm to 930 nm with tapering length of 300 μm and coupling gap of 200 nm. The output of the mode multiplexer with width of 930 nm is connected by a straight waveguide, and then tapered to 680 nm to match the width of the multimode silicon waveguide.

 

Fig. 3 (a) Schematic of designed multimode silicon waveguide for mode multiplexing and de-multiplexing; (b) enlarged coupling area of mode multiplexer and de-multiplexer; (c) microscope image of the two-mode division multiplexing circuit.

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The total insertion losses over the wavelength at the input optical power of 7 dBm are measured in Fig. 4(a). As shown in Fig. 4(a), the insertion loss are 16 dB and 17 dB between the input/output I/I and II/II, with mode crosstalk around −18 dB and −17 dB at 1570 nm. It is noted that the insertion losses are mainly due to the propagation losses of the multimode waveguide (0.3 dB for both modes), the insertion losses of the multiplexer and de-multiplexer (2 dB for TE0 and 3 dB for TE1), and the coupling losses to the fiber grating (10 dB for both modes) and SMF (4 dB for both modes, 8-degree tilt angle), which are used to connect the chip to the laser source and photodiode. The different losses between the CH1 and CH2 are caused by the fact that the multiplexing losses of TE1 mode are higher than those of TE0 mode. We also investigate the effects of nonlinear loss caused by two-photon absorption (TPA) and TPA-induced free carrier absorption, as shown in Fig. 4(b) [13]. The nonlinear loss achieves ~1 dB when the input optical power is ~20 dBm

 

Fig. 4 (a) Measured transmission and mode crosstalk of the two channels (Ch.I and Ch.II) of the two-mode division multiplexing circuit; (b) The relationship between the input power and output power of the multimode silicon waveguide.

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3. Experimental setup and results

We conduct experiments to verify the mode-selective wavelength conversion with optical phase conjugation in optical OFDM signals. The experimental setup is illustrated in Fig. 5. The OFDM signal is generated off-line in Matlab with QPSK format. An arbitrary waveform generator (AWG, Tektronix 7122C) is used to produce OFDM signal at 12 GS/s, which is subsequently split into I & Q parts and then fed into respective I and Q ports of an optical IQ modulator. In order to enhance the net data rate, an intensity modulator is used to replicate the OFDM signal to three copies with driving sine wave signal at 10.5 GHz. The inverse fast Fourier transform size is 128 with 108 subcarriers that are filled with data. The middle 2 subcarriers are unfilled. We also use 1/32 of OFDM symbol period for cyclic prefix to avoid inter symbol interference. The signal at wavelength λ₁ = 1570 nm is split into two streams with a PC introduced for each stream to excite the TE₀ mode of the input waveguides. A length of 50-km SMF is used to de-correlate the two signal streams. The two signal streams are amplified by two erbium-doped fibre amplifiers (EDFAs). The powers of signal streams at the input of the chip are about 19.5 dBm. The pump light at wavelength λ₂ = 1570.6 nm is also split into two streams with a length of 50-km SMF for de-correlation and PC at each stream for polarization alignment followed by EDFA amplification. The powers of pump streams at the input of the chip are set at 23.8 dBm. The line-width of the two external cavity lasers (ECL) at the transmitter side is 50 kHz. The generated idlers on the TE₀ and TE₁ modes are de-multiplexed to different output ports and filtered out by an optical band-pass filter (OBPF, Santec OTF-350 with minimum bandwidth of 10GHz), and finally collected by a standard single polarization coherent receiver and local oscillator with line-width of 50 kHz. After optical-to-electrical conversion, the electrical signals are sampled by a Tektronix oscillator scope of DPO73304D operating at 50 GS/s, and processed off-line. In the experiment, 10 training symbols are used in the conventional TSs-CE followed by 300 OFDM payload symbol, and 2 pilot subcarriers in each OFDM symbol are used for carrier phase recovery. Therefore, the net rate for the two signal streams including the 7% forward error correction (FEC) code is 102.6 Gb/s. 2 million bits are collected for bit error rate (BER) calculation.

 

Fig. 5 Experimental setup of the wavelength conversion of optical OFDM signal at 102.6 Gb/s with coherent detection.

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In the off-line DSP for signal recovery, most steps are similar as those for conventional OFDM signal [14]. The only difference is that subcarrier re-ordering is required after discrete Fourier transform de-modulation. We take 8 OFDM subcarriers as an example. This can be explained in Fig. 6, which shows the schematic of spectrum in FWM process, where the spectra of original signal and idler are symmetrical to the pump. Considering the effect of OPC, the relationship between the original signal and idler at the kth subcarrier can be expressed as $\text{S}\left(k\right)={\text{I}}^{\text{*}}(N+1-k)$, where N is the number of subcarriers. Therefore, the subcarriers of the received signals should be re-ordered for the following channel estimation and equalization.

 

Fig. 6 Spectrum of the signal after FWM considering 8 OFDM subcarriers.

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Figures 7(a) and 7(b) show the measured FWM spectrum at output ports I and II, respectively. It can be seen that strong FWM is obtained when signal and pump lights are injected into the same multiplexing port. However, very weak residual FWM is observed if the pump and signals are input from different multiplexing ports. As shown in Fig. 7, the modal crosstalk on the idlers remains −18dB and −17dB for the two modes. The modal crosstalk is caused by the multiplexer, where the signal stream at TE₀ (TE₁) mode is leaked to the TE₁ (TE₀) mode in the multimode waveguide. From Fig. 7(a) and 7(b), the spectrum peak at ~1569.2 nm can be viewed as satellite light in FWM, where the optical OFDM signal can be seen as pump light and previous pump light can be seen as signal light. We also study the conversion bandwidth of the two modes by changing the wavelength differences between the pump and signal (without modulation OFDM signal). It is shown in Fig. 7(c) that the 3-dB bandwidth is only 1.2 nm for both modes if both the positive and negative values of wavelength difference are considered. This may due to the fact that the dispersion properties of mode (de)multiplexers have not been taken into account. As shown in Fig. 7(d), the conversion efficiency (at wavelength difference of 0.6 nm) can be increased with the pump power. However, even at the pump power of 23.8 dBm, the conversion efficiency is only −33 dB. Higher FWM conversion efficiency can be achieved with longer waveguide and optimized dispersion characteristic of waveguide [15].

 

Fig. 7 (a) Spectrum measured at output port I for pump input from port I and signal input from port I and II, respectively; (b) Spectrum measured at output port II for pump input from port II and signal input from port I and II, respectively; (c) Conversion bandwidth for both TE₀ and TE₁ modes; (d) Conversion efficiency versus pump power for both TE₀ and TE₁ modes

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Figure 8 shows the BER performances of the two idlers obtained at output port I (corresponding to idler on the TE₁ mode) and output port II (corresponding to idler on the TE₀ mode). As shown in Fig. 8, in the absence of crosstalk, power penalties of 0.5 dB and 0.7 dB compared to the back-to-back case are observed at 7% FEC threshold [14] for the idlers output from port I and II, respectively. In the presence of crosstalk, where the two pump streams and two signal streams are input to the ports I and II simultaneously, additional 1.4 dB and 1.9 dB power penalties are observed in Fig. 8. The constellations of the recovered signals with and without the crosstalk at the OSNR of 14.6 dB are also shown in the in Fig. 8. The performance is mainly limited by the OSNR of the idlers or low conversion efficiency. Based on the designed structure, mode-selective wavelength conversion for higher-order modulation formats can also be expected with optimized dispersion properties and longer length of straight waveguide, which can further increase the conversion efficiency.

 

Fig. 8 BER vs. OSNR for the TE₁ and TE₀ idlers output from demultiplexing port I and II, respectively, with and without crosstalk. Inset: constellation at OSNR of 14.6 dB for (I) TE₀ idler w/o crosstalk; (II) TE₁ idler w/o crosstalk; (III) TE₀ idler w/ crosstalk; (IV) TE₁ idler w/ crosstalk.

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4. Conclusion

We have reported the first experimental demonstration of on-chip mode-selective wavelength conversion based on FWM for optical OFDM-QPSK signals. Mode-selective FWM is achieved in a multimode silicon waveguide using a two-mode division multiplexing circuit. Experimental results show the power penalties of 0.5 dB and 0.7 dB for the conversion of each mode taken individually, as well as 1.4 dB and 1.9 dB excess conversion penalties with crosstalk. The method has the potential to realize high-speed optical switching in future few-mode fiber transmission networks.