1. Introduction

All-optical signal processing, including signal regeneration, is critical for future high bit rate communications systems [1–3] since current electronic processing speeds are approaching fundamental limits near 40 Gb/s. Further, optical regeneration based on self-phase modulation (SPM) followed by spectral filtering, as proposed by Mamyshev [4], has a number of key advantages. These include simplicity, a bandwidth limited only by the intrinsic material nonlinear (Kerr) response, and the capability of directly improving not only the Q-factor but also the bit error-ratio (BER) of input data [5–6]. Such regenerators have been demonstrated in highly nonlinear silica based fiber [4, 6–7], and have even been used to achieve a million kilometers of error free transmission without electrical conversion [8]. However, challenges still remain to improve the device compactness for practical applications, while preserving the processing performance, as represented by a step-like output versus input power transfer function [9].

Chalcogenide glass based optical waveguides offers many advantages because of its large Kerr nonlinearity (up to 1000 x silica glass [10,11]), low two-photon absorption (TPA) and an intrinsic response time of less than 100 fs [10]. These advantages have motivated a number of groups to investigate chalcogenide fiber as a nonlinear medium for SPM and Raman gain [10] and as a basis for processing devices such as all-optical switches [12–13].

In this paper, we investigate the feasibility of using As₂Se₃ chalcogenide glass fiber for all-optical signal regeneration based on SPM followed by spectral filtering. In addition to its high nonlinearity, we find that the normal dispersion of the chalcogenide glass fiber (D = -504 ps/nm/km at 1550 nm) advantageously shapes the transfer function. Whilst traditionally the relatively high dispersion of chalcogenide has been viewed as a drawback of this fiber, for optical regeneration it in fact significantly improves device performance - even for the few meters of fiber used in this experiment - by inhibiting spectral oscillations that normally appear with SPM. We exploit both the high dispersion and nonlinearity to experimentally demonstrate a near step-like power transfer function with only 2.8 m of chalcogenide glass fiber. Finally, we demonstrate that TPA advantageously affects the shape of the transfer function by flattening the upper level of the step-like function.

2. Principle of operation and device design

The operation principle of a Mamyshev regenerator is shown in Fig. 1. A noisy return to zero input signal is passed through a dispersive and nonlinear medium producing SPM induced spectral broadening. Low power noise experiences only little SPM spectral broadening, and so is filtered out by the band-pass filter, which is offset from the input centre wavelength, whereas pulses experience sufficient spectral broadening to be partially transmitted through the bandpass filter. This results in a step-like power transfer function, which has been shown [6–7] to improve the Q-factor and BER for modulated signals at 40 Gb/s. The dispersion value is critical to properly shape the transfer function. Without dispersion, large oscillations would appear on the broadened spectrum, and after filtering, manifests as oscillations on the transfer function. Instead, a small but significant amount of normal dispersion reduces the spectral oscillations and results in a step-like transfer function. A step-like transfer function cannot be obtained with anomalous dispersion.

 

Fig. 1. Principle of device operation. At low intensities, pulses experience little SPM induced spectral broadening and so are removed by the offset bandpass filter. At high intensities, input signal pulses experience large SPM induced spectral broadening and are transmitted through the (offset) bandpass filter. The resulting nonlinear transfer function can be used to regenerate the pulses. The large n ₂ in chalcogenide fiber enables operation with less than 3 m of nonlinear fiber.

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The length (L_OPT ) of the dispersive and nonlinear medium that leads to the optimal transfer function profile has been found to follow [7]

and is valid when 10 < N < 25, where N = (L_D /L_NL )½ is the soliton number. Here L_D = $T_0^2$/β ₂ and L_NL = (P ₀ γ)^-1 are the dispersion and nonlinear lengths respectively. T ₀ is the pulse half width at 1/e-intensity, β ₂ is the group velocity dispersion parameter, P ₀ is the peak power and γ=n ₂ ω ₀/(c A_eff ) is the nonlinearity coefficient. n ₂ is the nonlinear index coefficient, ω ₀ is the angular frequency, c is the speed of light in vacuum and A_eff is the mode effective area.

For a given waveguide and pulsewidth, L_D is fixed, thus defining the range of optimum device lengths. As an example, in [7] a conventional silica based highly nonlinear fiber (HNLF) with D=-0.7ps/nm/km used for SPM regeneration experiments with 6 ps pulses results in L_D ~ 14 km and (1) yields a length range of 1.4–3.4 km. In the experimental setup [7], 2.5 km of fiber was used, and optimum regeneration occurred at N = 12, which from the quoted γ = 8.4 W^-1km^-1, a P ₀~1.2 W can be inferred.

In our investigations we have utilized single mode As₂Se₃ chalcogenide glass fiber as the nonlinear medium for pulse regeneration. The fiber has a core diameter of 6 μm, a core/cladding refractive index of 2.7 and a numerical aperture of 0.18 at 1550 nm, yielding an effective area of A_eff = 37 μm². The nonlinear index of As₂Se₃ has been measured [11] to be n ₂ ~ 1.1 × 10^-13 cm²/W, or ~500 × n ₂ of silica, which results in a nonlinearity coefficient γ ~ 1200 W^-1km^-1. We measured the group delay of a 2.8 m length of As₂Se₃ fiber using the differential phase shift method, obtaining a dispersion of D = -504 ps/nm/km at 1550 nm, with an average dispersion slope of +3 ps/nm2-km. Such dispersion value is not only much larger than standard single mode fiber (+17 ps/nm-km) but the negative sign of the chalcogenide dispersion is appropriate for SPM-based regeneration.

For optical regeneration in chalcogenide glass fiber, using 5.8 ps pulses involves L_D = 18 m, and so (1) yields an optimum length range of 1.7–4.3 m, three orders of magnitude smaller than for the silica HNLF. For L_OPT ~ 3 m, a peak power of ~ 8 W provides a maximum SPM-induced phase shift of ϕ_Max =L_D /L_NL ~3π, which is sufficient for operation, and is close to practical device power levels.

 

Fig. 2. Experimental configuration for demonstrating optical regeneration. PC - polarization controller, EDFA - erbium doped fiber amplifier, VOA - variable optical attenuator, BPF -bandpass filter, OSA - optical spectrum analyzer and AC - pulse autocorrelator.

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3. Experiment

For this demonstration we employed a 2.8 m long, As₂Se₃ single mode fiber which combined with 5.8 ps FWHM transform-limited pulses from a mode-locked laser near 1550 nm yielded a nearly optimum configuration for optical pulse regeneration. Figure 2 shows the experimental configuration used to demonstrate the device performance. Pulses from the mode-locked laser with a pulse repetition rate of 9.04 MHz were passed through a polarization controller and then through a custom built amplifier designed to keep extraneous SPM induced spectral broadening to a minimum. The optical signal was then butt-coupled into the chalcogenide fiber using a short segment of NA matched fiber used to improve coupling efficiency. Input and output coupling loss was 3.4 dB and 2.4, respectively, per facet, of which 0.8 dB was due to Fresnel loss from the refractive index difference. Propagation loss in the fiber is 1.0 dB m^-1. Cladding mode coupling was minimized through input alignment while imaging the output of the chalcogenide fiber end face and coating the fiber surface with liquid Gallium near its ends [14]. The polarization controller was adjusted for maximum SPM induced spectral broadening within the chalcogenide fiber. The output of the fiber was passed through a tunable bandpass filter with a FWHM bandwidth of 0.56 nm (70 GHz), offset by 1.3 nm from the input centre frequency, and then directed either into an optical spectrum analyzer or pulse autocorrelator.

4. Results

Figure 3(a)–(f) shows the output pulse spectra of the chalcogenide fiber with no filter present for different coupled input peak powers, showing good agreement between the experimental SPM induced spectral broadening (black) and theoretical calculations (dashed). The theoretical results were calculated using a split-step Fourier transform method with a value of n ₂ = 0.9×10^-13 cm²/W, and using a TPA attenuation coefficient β = 2.5 × 10^-12 W/m, in line with other measurements As₂Se₃ chalcogenide glass [9,10] and our measurements discussed below.

Also shown in Fig. 3(g) is the tunable bandpass (0.56 nm FWHM) filter transmission spectrum, offset by 1.3 nm from the input centre frequency. We did not exhaustively optimize the transfer function by varying the filter offset, and so we expect that further improvements can be made. Fig. 3 clearly illustrates the principle of operation of this device - as the peak input power increases, the SPM broadens the signal spectrum so that it overlaps more with the bandpass filter, creating a nonlinear power transfer function. Although care was taken to minimize coupling to cladding modes, the slight maxima in the power spectrum near zero frequency offset at the highest peak powers is believed to be caused by residual cladding modes that experience less SPM broadening.

Optimizing the output filter shape and bandwidth largely determines pulse width and shape, ensuring signal distortion by the device is minimized. The inset in Fig. 3(g) presents the pulse autocorrelation, with a FWHM of 5.9 ps, showing good pulse retrieval.

Figure 4 shows the resulting experimental and theoretical (with and without considering TPA) nonlinear power transfer functions as a function of coupled peak input power with the filter in place. The curves show a clear output power limiting function at ~8 W peak input power, as well as a clear threshold. The former is effective in suppressing the noise in the logical ones whilst the latter contributes to suppressing noise in the zeros. There is still a slight oscillation at high peak power levels but this is much smaller than what would result without the presence of the large normal dispersion, discussed further below. The theoretical curve calculated without TPA shows that device performance is not restricted by TPA, which appears to flatten the transfer function at higher powers.

 

Fig. 3. Regenerator spectra. (a–f) Measured and theoretical SPM broadened pulse spectra with increasing coupled peak power. (g) The bandpass filter transmission spectrum, offset by 1.3nm from the input centre wavelength, and with a 3 dB bandwidth of 70 GHz. (h) Output pulse spectrum at the same power level as in (f). Inset in (h) shows pulse autocorrelation. Pulse width was calculated to be 5.9 ps.

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Fig. 4. Regenerator transfer function for a filter offset of 1.35 nm. Experiment compared to theory, with and without two photon absorption.

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Fig. 5. (a) Fiber transfer function (average power), measured with 5.8 ps pulses, clearly showing the effects of nonlinear absorption. Theoretical curves are calculated with and without the effects of TPA considered. (b) Pulse spectra for a peak power of 63 W. Theoretical curves are calculated with and without the effects of TPA loss.

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In Fig. 5 we examine the effects of TPA on pulse propagation within the device. Figure 5(a) shows a plot of the measured transfer curve (squares), calculated transfer curve including TPA (solid line) and calculated transfer curve without including TPA (dashed line), without the filter present. These results clearly show the effects of nonlinear absorption on pulse propagation leading to output saturation, manifesting in the flattening of the regeneration transfer function shown in Fig. 4. Fig. 5(b) shows the measured output pulse spectrum for a peak power of 63 W. Dashed lines corresponding to theoretical fit, with and without taking into account the effects of TPA. Comparing the two theoretical spectra, we find an increased bandwidth and amplitude when TPA is not taken into account. We did not observe any damage for the maximum coupled peak power (63 W) in this experiment which corresponded to a maximum peak intensity of 170 MW/cm².

Table 1. Regenerator parameters

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5. Discussion

Table 1 summarizes the regenerator parameters, including parameters inferred from simulation. The device performance is dependent on both SPM and normal dispersion within the chalcogenide fiber. SPM induced spectral broadening, without the presence of linear dispersion, produces an oscillating spectrum at high peak powers. The large normal dispersion in As₂Se₃ smoothes the SPM induced chirp, which averages out the spectral oscillations, thus smoothing out the nonlinear transfer curve. To illustrate this, Fig. 6(a) shows the output pulse spectra calculated with (solid line) and without material dispersion (dashed line). Adding dispersion greatly decreases the amplitude of the oscillations that would normally be present in the SPM broadened spectrum [15]. Fig. 6(b) shows the beneficial impact of dispersion in reducing the effect of these oscillations on the transfer function.

In assessing chalcogenide fiber based regenerators and their potential advantage over silica based devices, we find that it is both the large nonlinearity and high dispersion that contribute to device performance. Although the total dispersion of 1.4 ps/nm present in the device is comparable to silica HNLF based regeneration experiments [7], the key is that for chalcogenide glass, this level of dispersion is present in short lengths. Furthermore, the dispersion slope for HNLF is large in comparison to the dispersion, resulting in a significant variation in the dispersion length versus wavelength, leading to performance degradation in wide bandwidth operation. This is not so for the chalcogenide glass fiber, where the dispersion slope is relatively small compared to the dispersion, allowing for operation over a wide spectrum.

From experimentally measured data and theoretical fits, we were able to infer values of n ₂ and β. We calculate a nonlinear figure of merit (FOM = n ₂/βλ) of 2.3, in line with other measurements in fiber [10] and in bulk [11]. Interestingly, this level of TPA improved the transfer function shape of the regenerator.

 

Fig. 6. Pulse spectra at 8 W peak power (a) and regenerator transfer function (b) calculated with and without the effect of dispersion.

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For this proof of concept demonstration, low duty cycle pulses were used. Ultimately, this device would have to operate on a high duty cycle signal (such as 8.3 ps pulses at 40 Gb/s) at practical power levels. Our results already demonstrate device operation at power levels commensurate with typical powers achievable for such systems [6]. Fig. 4 indicates that our device performs at peak power levels of 8 W, corresponding to 0.9 W of average power for a signal composed of 5.8 ps pulses at 40 Gb/s. We note that apart from the filter, which is intrinsic to SPM regenerator devices, the main source of device loss is the chalcogenide fiber. Although the propagation loss is high (total 2.8 dB propagation loss) it is still comparable to silica HNLF based devices (1.5 dB reported in [7]) and this is expected to improve. Improving fiber coupling losses (cleave quality and AR coatings) would also assist. In addition, whilst our device operates at power levels comparable with silica based devices, there is a wide scope for further power reductions by reducing the mode field diameter below the current value of ~6.7 μm (such has been achieved in [16]), and possibly increasing the intrinsic nonlinearity of the chalcogenide glass by optimizing stoichiometry.

Finally, a key goal for optical regenerators is to operate at ultrahigh bit rates. Our initial proof of concept was performed with 5.8 ps pulses, suitable for 40 Gb/s systems. For operation at 160 Gb/s, device performance with 2 ps pulses would need to be demonstrated. Spectral broadening has already been reported for femtosecond pulses in chalcogenide fiber [14]. SPM-based regeneration is therefore conceivable with 2 ps pulses and shorter. From (1), the optimum device length for 2 ps pulses is 0.2–0.5 m, and calculations show this will require smaller mode areas to maintain operation at practical power levels.

6. Conclusions

We investigate the potential for optical regeneration in single mode chalcogenide fiber, operating on the principle of SPM induced spectral broadening. We find that the large material dispersion in chalcogenide fiber is ideal for optical regeneration, allowing for a reduction of required fiber lengths from kilometers to meters, while maintaining device performance and that the relative dispersion slope potentially provides capability for operation across multiple wavelength channels. By optimizing device parameters, we demonstrate a near optimum nonlinear power transfer curve with 5.8 ps optical pulses, with peak powers of <10 W, and with no signal distortion in 2.8 m of single mode As₂Se₃ fiber. The effect of two photon absorption on device performance was investigated and was not found to be an impediment. System test measurements for device operation on high duty cycle signals will be reported in future work.