1. Introduction

Data traffic grooming is considered to be an attractive technique for achieving high efficiency and enhanced flexibility in robust network management [1]. Many forms can be taken in grooming techniques, such as (de)multiplexing, multicasting, add/drop, switching, and data exchange [2–7]. Data exchange is an important concept for efficiently utilizing network resources and enabling superior network performance [8–10]. Generally speaking, data exchange in the wavelength domain, which is also known as wavelength exchange or wavelength interchange, would require the swapping of data from one wavelength with the data from another wavelength. Desirable features of such data exchange would be ultrafast response, transparency to the modulation format, and capability of achieving the exchange function in a single optical element (e.g. a single waveguide).

Optical nonlinearities are promising candidates to facilitate data exchange with the aforementioned features. Previous works of optical data exchange between different wavelengths include the use of wavelength conversion of degenerate four-wave mixing (FWM) in a highly nonlinear fiber (HNLF) [5,11], parametric depletion of non-degenerate FWM in an HNLF [12–17], and parametric depletion of cascaded sum- and difference-frequency generation (cSFG/DFG) in a periodically poled lithium niobate (PPLN) waveguide [18,19]. HNLF-/PPLN-based optical data exchanges have been reported for binary on-off keying (OOK), differential phase-shift keying (DPSK), and quadrature phase-shift keying (QPSK) signals [5,11–19]. With unabated exponential growth of data traffic, advanced multi-level modulation formats, e.g. m-ary phase-shift keying (m-PSK) and m-ary quadrature amplitude modulation (m-QAM), have become of great importance to increase the capacity and spectral efficiency of communication systems [20–25]. So far some optical signal processing applications with m-PSK and m-QAM signals have been reported including high-base format conversion [26,27], optical computing [28,29] and coding/decoding [30] but not data exchange. Hence, one challenge would be to realize modulation-format-transparent optical data exchange of m-PSK/m-QAM signals. Additionally, driven by the trend of large-scale integration, it is also highly desirable to perform data exchange using compact devices. Silicon waveguide is of great interest owing to its compactness and potential for complementary metal-oxide-semiconductor (CMOS) compatibility. Recently, slot waveguide with tighter light confinement has been proposed, fabricated and demonstrated in the experiments [31–35]. Very recently, silicon-organic hybrid slot waveguide has attracted lots of interest for its capability for efficient high-speed optical signal processing and high-speed low drive-voltage modulator [36–42]. However, silicon waveguide or slot waveguide based data exchange of m-QAM signals has not yet been reported.

In this paper, we present a silicon-organic hybrid slot waveguide with tight light confinement, enhanced nonlinearity, and negligible two-photon absorption (TPA) and free-carrier absorption (FCA). By exploiting parametric depletion of non-degenerate FWM, we propose and simulate low-power (<10 mW) ultrahigh-speed data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM signals and 640 Gbaud (3.84 Tbit/s) 64-QAM signals. The error vector magnitude (EVM) and bit-error rate (BER) are analyzed for comprehensive performance evaluation. The performance dependence on the waveguide length, pump power, operation speed and waveguide propagation loss is also discussed.

2. Silicon-organic hybrid slot waveguide

Figure 1(a) depicts the 3D structure of a silicon-organic hybrid slot waveguide. It features a sandwich structure with a low-refractive-index PTS [polymer poly (bis para-toluene sulfonate) of 2, 4-hexadiyne-1, 6 diol] layer surrounded by two high-refractive-index silicon layers. The cladding is air and the substrate is silicon dioxide. The typical geometry parameters are as follows: waveguide width W = 250 nm, upper silicon height H_u = 180 nm, lower silicon height H_l = 220 nm, and slot height H_s = 25 nm. The quasi-TM mode distribution and its normalized power density along X and Y directions are shown in Fig. 1(b)-1(d), respectively. One can clearly see the tight light confinement in the nano-scale nonlinear organic slot region, which offers high nonlinearity for instantaneous Kerr response. Using the finite-element method, we calculate the effective mode area and nonlinearity to be 8.3x10⁻¹⁴ m² and 5100 w⁻¹m⁻¹, which can potentially facilitate efficient optical signal processing (e.g. data exchange).

 

Fig. 1 (a) 3D structure, (b) quasi-TM mode distribution, (c)(d) normalized power density along X and Y directions of a silicon-organic hybrid slot waveguide.

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3. Concept/principle of m-QAM data exchange

Figure 2(a) depicts conceptual diagram of m-QAM data exchange between two wavelength channels (SA: λ_SA, SB: λ_SB). Such modulation-format-transparent data exchange can be realized using parametric depletion effect of non-degenerate FWM in a silicon-organic hybrid slot waveguide, as shown in Fig. 2(b). Two continuous-wave (CW) pumps (P1: λ_P1, P2: λ_P2) are employed. The non-degenerate FWM converts the photons of P1 and SA to those of P2 and SB and vice versa. By properly controlling the power of two CW pumps, SA can be consumed with its data copied onto SB, and SB can be depleted and converted to SA, resulting in the data exchange between SA and SB. Under pump non-depletion approximation, simple linear relationships of output (${A^{\prime }}_{SA}$,${A^{\prime }}_{SB}$) and input ($A_{SA}$,$A_{SB}$,$A_{P1}$,$A_{P2}$) complex amplitudes are available as follows: ${A^{\prime }}_{SA}\propto A_{SB}\cdot A_{P2}\cdot A_{P1}^{\ast }$, ${A^{\prime }}_{SB}\propto A_{SA}\cdot A_{P1}\cdot A_{P2}^{\ast }$ [26–29]. One can see that the data information carried by two signals is swapped (${A^{\prime }}_{SA}\propto A_{SB}$,${A^{\prime }}_{SB}\propto A_{SA}$). In particular, as complex amplitude contains full-field information of signal (amplitude and phase), it is implied that non-degenerate FWM based data exchange is modulation format transparent, i.e. m-QAM data exchange is available.

 

Fig. 2 (a) Concept and (b) principle of m-QAM data exchange using a silicon-organic hybrid slot waveguide.

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4. Results and discussions

The proposed silicon-organic hybrid slot waveguide based data exchange is simulated using nonlinear coupled-mode equations under the slowly varying envelope approximation. Group-velocity mismatching (GVM), group-velocity dispersion (GVD), TPA, FCA, and free-carrier dispersion (FCD) are comprehensively considered. In following simulations, two 640 Gbaud 2¹³-1 pseudorandom binary sequence (PRBS) 16-QAM/64-QAM signals (λ_SA: 1542 nm, λ_SB: 1544 nm) and two pumps (λ_P1: 1548 nm, λ_P2: 1550 nm) are sent into a 17 mm long silicon-organic hybrid slot waveguide, in which 16-QAM/64-QAM data exchange is realized based on the parametric depletion effect of non-degenerate FWM process. Note that the high-speed 640 Gbaud 16-QAM/64-QAM signal could be optical time-division multiplexed (OTDM) signal from 64 low-speed 10 Gbaud tributaries in practical applications [43]. The power of two CW pumps is 9 mW and the peak power of two signals is 0.01 mW (−20 dBm). The operation performance is evaluated by EVM and BER [44].

Figure 3 shows obtained results (symbol sequences) for 640 Gbaud (2.56 Tbit/s) 16-QAM data exchange. 10 symbol sequences are plotted for two signals before (Bef. Ex.) and after (Aft. Ex.) passing through the silicon-organic hybrid slot waveguide, which clearly confirm the successful implementation of 16-QAM data exchange. The constellations are depicted in Fig. 4 with assessed EVM under a signal-to-noise ratio (SNR) of 10 dB. Figures 4(a) and 4(b) show two input 16-QAM signals before exchange with an EVM of 12. Figures 4(c) and 4(d) show two output 16-QAM signals after exchange with an EVM of 12.1. Figures 5(a) and 5(b) plot EVM and BER performance as a function of SNR for 640 Gbaud (2.56 Tbit/s) 16-QAM data exchange. The theoretical BER curve of 16-QAM signal is also plotted in Fig. 5(b) for reference. Compared to BER curves of two signals before exchange, negligible SNR penalty after exchange is observed at a BER of 2e-3 (enhanced forward error correction (EFEC) threshold).

 

Fig. 3 Simulated symbol sequences for 640 Gbaud (2.56 Tbit/s) 16-QAM data exchange.

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Fig. 4 Simulated constellations of (a)(b) input and (c)(d) output signals for 640 Gbaud (2.56 Tbit/s) 16-QAM data exchange.

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Fig. 5 Simulated (a) EVM and (b) BER versus SNR for 640 Gbaud (2.56 Tbit/s) 16-QAM data exchange.

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We further present obtained results for 640 Gbaud (3.84 Tbit/s) 64-QAM data exchange. Figure 6 shows obtained results (symbol sequences) for 640 Gbaud (3.84 Tbit/s) 64-QAM data exchange. 10 symbol sequences are plotted for two signals before (Bef. Ex.) and after transmitting (Aft. Ex.) through the silicon-organic hybrid slot waveguide, from which one can easily confirm the successful implementation of 64-QAM data exchange.

 

Fig. 6 Simulated symbol sequences for 640 Gbaud (3.84 Tbit/s) 64-QAM data exchange.

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Figures 7(a) and 7(b) show two input 64-QAM signals before exchange with an EVM of 7.5. Figures 7(c) and 7(d) show two output 64-QAM signals after exchange with an EVM of 8.0 and 8.1, respectively. The SNR is 14 dB in Fig. 7. The EVM and BER performance for 64-QAM data exchange are plotted in Figs. 8(a) and 8(b). The theoretical BER curve of 64-QAM signal is also plotted in Fig. 8(b) for reference. Compared to BER curves of two signals before exchange, the SNR penalty after exchange is less than 2 dB at a BER of 2e-3 (EFEC threshold). The flaring of the BER curve noted in Fig. 8(b) might be caused by the nonlinear effects induced distortions (e.g. TPA, FCA, FCD).

 

Fig. 7 Simulated constellations of (a)(b) input and (c)(d) output signals for 640 Gbaud (3.84 Tbit/s) 64-QAM data exchange.

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Fig. 8 Simulated (a) EVM and (b) BER versus SNR for 640 Gbaud (3.84 Tbit/s) 64-QAM data exchange.

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Remarkably, Figs. 3-8 present results for ultrahigh-speed 640 Gbaud data exchange under optimized waveguide length (~17 mm) for a given pump power (~9 mW) without considering the waveguide propagation loss. In practical applications, there might be some deviations from the optimal working conditions. Also, data exchange might operate at low speed and the waveguide propagation loss might have impact on the operation performance.

We first investigate the data exchange performance dependence on the waveguide length. The input pump power is set to be 9 mW. Figure 9(a) shows EVM as a function of the waveguide length for 16-QAM data exchange at an SNR of 16 dB. Shown in Fig. 9(b) is EVM versus waveguide length for 64-QAM data exchange at an SNR of 22 dB. It can be clearly seen from Figs. 9(a) and 9(b) that the optimal waveguide length is 17 mm for a given pump power of 9 mW. For waveguide length offset from 17 mm, the data exchange performance degrades correspondingly. The larger the waveguide length is offset from the optimal point, the severer the operation performance is degraded. Moreover, the operation performance varies slightly as the waveguide length changes within a small range from 16.8 mm to 17.2 mm, which implies favorable performance tolerance to the waveguide length.

 

Fig. 9 Simulated EVM versus waveguide length. (a) 640 Gbaud (2.56 Tbit/s) 16-QAM data exchange. (b) 640 Gbaud (3.84 Tbit/s) 64-QAM data exchange. The input pump power is 9 mW.

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We further study the data exchange performance dependence on the input pump power. The waveguide length is set to be 17 mm. Figure 10 evaluates the simulated SNR penalty as a function of the input pump power. It is shown that the SNR penalty at a BER of 2e-3 is below 4 dB for 640 Gbaud (2.56 Tbit/s) 16-QAM data exchange with varied input pump power from 8.4 to 9.8 mW. For 640 Gbaud (3.84 Tbit/s) 64-QAM data exchange, the SNR penalty at a BER of 2e-3 is below 4 dB as changing input pump power from 8.9 to 9.2 mW. The obtained results shown in Figs. 10(a) and 10(b) indicate that the proposed data exchange also has favorable performance tolerance to the input pump power.

 

Fig. 10 Simulated SNR penalty versus input pump power. (a) 640 Gbaud (2.56 Tbit/s) 16-QAM data exchange. (b) 640 Gbaud (3.84 Tbit/s) 64-QAM data exchange. The waveguide length is 17 mm.

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For a given pump power, there exists an optimal waveguide length. When the waveguide length is offset from its optimal value, the operation performance is degraded, which however could be improved again by appropriately adjusting the pump power. Figure 11 depicts simulated results for 640 Gbaud 16-QAM/64-QAM data exchange under reduced waveguide length of 5 mm and 10 mm. Correspondingly, the pump power is changed to 30.6 mW and 15.4 mW to achieve favorable operation performance for 5 mm and 10 mm long waveguide, respectively. It is shown that longer waveguide offers better operation performance. The SNR in Fig. 11 is 16 dB for 16-QAM and 22 dB for 64-QAM.

 

Fig. 11 Simulated results for 640 Gbaud 16-QAM/64-QAM data exchange under reduced waveguide length of 5 mm and 10 mm and optimized pump power of 30.6 mW and 15.4 mW.

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In addition to ultrahigh-speed data exchange operation, we also simulate 16-QAM/64-QAM data exchange operating at a relatively lower speed. Figure 12 plots simulated results for 20 Gbaud 16-QAM/64-QAM data exchange with calculated EVM values. The waveguide length is 17 mm and the input pump power is 9 mW. One can clearly see that the proposed data exchange also works well at low speed with favorable operation performance. The SNR in Fig. 12 is 16 dB for 16-QAM and 22 dB for 64-QAM.

 

Fig. 12 Simulated results for 20 Gbaud 16-QAM/64-QAM data exchange under a waveguide length of 17 mm and pump power of 9 mW.

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We finally simulate 16-QAM/64-QAM data exchange when considering the propagation loss. Shown in Fig. 13 are simulated results for 640 Gbaud 16-QAM/64-QAM data exchange with propagation loss of 3 dB/cm, waveguide length of 17 mm, and optimized input pump power of 15.5 mW. The SNR is 16 dB for 16-QAM and 22 dB for 64-QAM. It can be clearly seen that the proposed silicon-organic hybrid slot waveguide based data exchange works well even considering the waveguide propagation loss. However, the required pump power increases to compensate the propagation loss.

 

Fig. 13 Simulated results for 640 Gbaud 16-QAM/64-QAM data exchange under a waveguide length of 17 mm and pump power of 15.5 mW. Waveguide propagation loss of 3 dB/cm is considered.

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The adopted silicon-organic hybrid slot waveguide enables compact, ultrahigh-speed, and low power operations for 16-QAM/64-QAM data exchange. The required power is less than 10 mW, which is more than one order of magnitude lower than traditional approaches. The impacts of waveguide length, pump power, operation speed and waveguide propagation loss are analyzed, showing favorable performance with good tolerance. Future improvements would be comprehensive optimization of waveguide design (dispersion, nonlinearity, etc) to further reduce the required pump power and achieve superior data exchange performance.

5. Conclusion

In this paper, we present modulation-format-transparent data exchange for m-QAM signals using a single silicon-organic hybrid slot waveguide with tight light confinement and enhanced nonlinearity. By exploiting the parametric depletion effect of ND-FWM process in the slot waveguide, we propose and simulate low-power (<10 mW) ultrahigh-speed optical data exchange of 640 Gbaud (2.56 Tbit/s) 16-QAM and 640 Gbaud (3.84 Tbit/s) 64-QAM signals. The operation performance is characterized by EVM and BER. The calculated SNR penalties of data exchange are negligible for 2.56 Tbit/s 16-QAM signals and less than 2 dB for 3.84 Tbit/s 64-QAM signals at a BER of 2e-3. The proposed m-QAM data exchange offers good performance tolerance to the slight variation of waveguide length (16.8 mm to 17.2 mm) and pump power (8.4 mW to 9.8 mW for 2.56 Tbit/s 16-QAM, 8.9 mW to 9.2 mW for 3.84 Tbit/s 64-QAM). Additionally, m-QAM data exchange operating at low speed (e.g. 20 Gbaud) or considering waveguide propagation loss is also analyzed with favorable performance.