1. Introduction

All-optical nonlinear signal processing is seen as critical for future telecommunication networks to address the growing demand for network flexibility, low cost, energy consumption and bandwidth as they evolve from 40 Gb/s to 160 Gb/s and beyond [1]. Nonlinear devices that exploit the χ ⁽³⁾ (third-order) nonlinearity are particularly attractive since χ ⁽³⁾ is nearly instantaneous and accounts for a range of processes such as four-wave mixing (FWM), Raman gain, two-photon absorption and the Kerr nonlinear refractive index (n₂) which in turn gives rise to self and cross-phase modulation (SPM, XPM). These phenomena have been the basis of a wide range of all-optical signal processing demonstrations including all-optical regeneration [2, 3], switching [4–8], wavelength conversion [9–13], and others.

Reducing the power requirements of all-optical signal processing devices to milliwatts or below is important to achieve their widespread acceptance in commercial systems. A key approach to this has been to increase the nonlinear parameter, γ = ωn₂/c A_eff, where A_eff is the waveguide effective area. This has naturally led to a focus on highly nonlinear, high index, optical materials such as bismuth glass [7] (for fiber devices), silicon (for integrated devices) [14] and chalcogenide glasses [15] (for both fiber and waveguides). Chalcogenide glasses, in particular, exhibit extremely high optical nonlinearities (n₂) of up to 500 × silica glass. This has resulted in numerous signal processing demonstrations up to 160 Gb/s [8].

A parallel approach to increasing γ is to reduce the mode-field area. Fiber “nanowires” have attracted attention [16] with their potential for ultra-low power all-optical signal processing as well as chip-scale routing of optical signals. Silica glass nanowires [16, 17] have produced extremely tightly confined mode fields by the glass-air interface, increasing the nonlinear parameter (γ) up to 600 W^-1 km^-1 [17]. Chalcogenide glasses are even more suited to this approach because of their very high linear refractive index (up to 3 [18]). Extraordinarily high nonlinearities have been achieved in tapered arsenic selenide chalcogenide glass (As₂Se₃) nanowires (to 0.95 μm diameter) [19, 20] – as high as γ > 90,000 W^-1 km^-1 at 1550 nm – almost 10,000 times that of highly nonlinear fiber in silica. This has enabled the demonstration of ultra-low power self-phase modulation [19] and – with the added feature of waveguide dispersion engineering – ultra low power super-continuum generation [20].

However, to date fiber based photonic “wires” have not achieved the key goal of signal processing at full, ultra-high, bit rates. Whilst recent results have been reported in integrated silicon nanowire devices [21], fiber based photonic wire devices – either sub-μm scale (nanowires) or μm scale (photonic wires) have not yet achieved this. In addition to yielding extremely high γ factors, tapered fiber photonic wires have ultra low propagation losses (< 1 dB/m) – potentially over very long lengths – although not necessarily large footprints – (compared to integrated devices) [22], which would result in extremely low pump power requirements. Hence, fiber based photonic wires offer a qualitatively different approach to all-optical signal processing than photonic integrated circuit based nanowires.

In this paper we report the first demonstration of high bit rate signal processing by a fiber-based photonic wire. We achieve 160 Gb/s demultiplexing (to 10 Gb/s) at 1550 nm via four wave mixing in a 5cm long, 1.9 μm diameter, photonic wire, tapered down from a As₂S₃ chalcogenide glass single mode fiber. The 1.9 εm diameter taper yields a high nonlinearity (γ) parameter of ~7,850 W^-1 km^-1, and when combined with the very low total insertion loss of 4 dB results in an average pump power requirement of only 18 mW. This is aided by the intrinsically high nonlinear figure of merit [1] (FOM > 10) in arsenic sulphide glass which results in an enhanced power handling capability. In addition, by engineering the waveguide dispersion to compensate for the high (normal) material dispersion (present in all chalcogenide glasses in the 1550 nm wavelength range) we reduce the overall device dispersion to less than a third that of the un-tapered fiber, thus significantly improving the phase-matching condition [23]. All of these effects collectively dramatically improve the device efficiency. This demonstration of high bit rate nonlinear signal processing by a fiber photonic “wire” is the first step in their potential role in future all-optical fibre-optic telecommunication networks.

 

Fig. 1. Principle of all-optical time-division demultiplexing an optical signal to obtain a lower bit rate tributary by four wave mixing with a pump pulse train of sub-harmonic repetition

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2. Principle of operation

Figure 1 shows the principle of FWM-based demultiplexing. A high bit rate signal (frequency f_s) is co-propagated with a sub-harmonic pump pulse train (frequency f_p ). FWM between coinciding signal and pump pulses generates idler pulses at a carrier frequency f_i = 2f_p − f_s [23] that is filtered and directed to a receiver (or re-routed) without electronic conversion or regeneration. The efficiency of the process relies on phase matching of the wave vectors of the pump (β_p), signal (β_s) and idler (β_i): ∆β = β_s + β_i – 2β_p [23]. The propagation length, L, satisfying phase matched FWM is then determined by the coherence length, L_coh [23], which is inversely proportional to the phase mismatch, k. When the phase-mismatch is dominated by dispersion, it can be approximated by ∆β ≈ β₂ ∙ Ω_s ², where β₂ is the second-order dispersion and Ω_S is the angular frequency separation between pump and signal. The coherence length is then

 

Fig. 2. FEM calculations of a) total dispersion (at 1550 nm) and b) effective mode area, A_eff, and nonlinearity coefficient, γ, versus As₂S₃ glass fiber waist diameter.

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Satisfying L ≤ L_coh for a given Ω_S requires minimizing the device dispersion – a particular challenge in chalcogenide glasses where the material dispersion is very high (and normal) near 1550 nm: for As₂S₃ chalcogenide glass it is -367 ps/nm/km (β₂ = +470 ps²/km). The effects of this large dispersion can be mitigated either by minimizing the device length, at the expense of higher power requirements, or by using dispersion-tailored waveguides. Fig. 2(a) shows that waveguide dispersion can significantly reduce the (normal) material dispersion for sub-10 μm outer diameter (OD) tapers, becoming zero near 1.65 μm OD and anomalous below this. The photonic wire reported here has an OD of 1.9 μm, resulting in a total dispersion reduced by more than two-thirds (from -367 to -85 ps/nm/km, or for β₂ from +470 to +108 ps²/km). For the wavelength separations employed in our experiments (see below), this resulted in the coherence length, L_coh, being more than tripled to 93 cm, much longer than the device length (5 cm), implying that phase-matching is not a limiting factor, with a significant benefit to the device efficiency. Increasing the nonlinearity (γ) also improves device efficiency. Figure 2b) shows the effective area and γ versus outside diameter. The initial increase in mode area down to 30 μm (OD) occurs as the mode expands out of the 5 μm index guiding core region to occupy the entire (core + cladding) fiber (see next section).

 

Fig. 3. Schematic of As₂S₃ chalcogenide glass based fiber photonic “wire”, with 1.9 μm outer diameter and 5cm in length. The central image is an SEM picture of the photonic wire.

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3. Fabrication

The fiber photonic wires were fabricated from dual-moded As₂S₃ fiber with a 5 μm core and 140.5 μm cladding (effective area A_eff = 18.4 μm², average refractive index of 2.3, and numerical aperture (NA ≈ 0.3) [24], with index guiding achieved by varying the stoichiometry slightly. The n₂ of As₂S₃ chalcogenide glass is n₂ = 3×10^-18 m²/W [15], or ~136 times silica glass, thus yielding a nonlinearity parameter of γ = 661 /W/km at 1550 nm. To fabricate the photonic wires, we employ a tapering process previously developed for As₂Se₃ fiber [19], aided by the very low transition temperature (compared to silica) of ~200 °C which permits the use of resistive heating. A short length of As₂S₃ fiber is fixed between translation stages, then a resistive heating element is rocked periodically along the fiber axis in an orchestrated heat brushing routine that tapers the fibers diameter to the desired profile [19]. The fibers were tapered in two stages – first to 70μm outer diameter (OD) to render it single-mode. Following this, a short length, spliced between two high NA fiber pigtails, was tapered to bring the fiber down to μm (OD) dimensions, where optical guiding occurs via the glass to air interface. Figure 3 shows the tapered 1.9 μm outer diameter photonic wire, uniform along a 50 mm length with a dramatically reduced mode field area ( A_eff ) of just 1.5 μm², thereby increasing the nonlinearity (γ) by more than an order of magnitude to 7850 /W/km at 1550 nm. The total insertion loss of the device was very low (4 dB), consisting of ~2.5 dB for both the silica to chalcogenide fiber splices, and 1.5 dB of excess insertion loss induced by the tapering process. Propagation losses are not significant over these lengths, at < 1 dB / m. It is remarkable that the excess tapering loss is only 1.5 dB, despite the guiding mechanism being different in the fiber and photonic wire segments. This indicates that adiabatic conversion from the fiber to wire modes is extremely efficient, similar to silica nanowires [25].

 

Fig. 5. (a) Output optical spectrum showing generation of 10 Gb/s idler at 1540 nm via FWM between 10 GHz pump and 160 Gb/s signal. (inset) 10 Gb/s signal eye diagram of idler after optical filtering, measured using a 65 GHz bandwidth detector and electrical sampling scope. (b) Optical sampling scope measurements of (top) 160 Gb/s signal at input and (lower) output of the taper showing recovery of 10 Gb/s tributary after optical filtering.

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Fig. 4. Experimental set-up for optical time-division demultiplexing a 160 Gb/s signal to 10 Gb/s via FWM in a As₂S₃ photonic wire.

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4. Experiment

The experimental setup for 160 Gb/s demultiplexing is shown in Fig. 4. The 160 Gb/s signal was generated from a 40 GHz mode-locked fiber laser emitting 1.4 ps, 1.8 nm bandwidth pulses at λ = 1560 nm. A Mach-Zehnder electro-optic modulator encoded data on the pulses at 40 Gb/s with a 2³¹-1 pseudo random bit sequence, and a two-stage multiplexer (MUX) of 2⁷-1 bit delay-length interleaved the signal up to 160 Gb/s (pulse width 1.9 ps, 30% duty cycle). The pump pulse train was sourced from a 10 GHz MLFL (2.3 ps long, 1.1 nm bandwidth at 1550 nm, average power = 18 mW, peak power ≈ 0.45 W, energy = 1.8 pJ inside the taper) synchronized to the 160 Gb/s signal (by using the same 40 GHz RF clock), prescaled to 10 GHz (in place of using a 10 GHz clock recovery circuit). The signal and pump were combined with a 50:50 coupler and amplified by an erbium-doped fiber amplifier (EDFA) before launching into the waveguide with polarizations aligned via polarization controllers (PC). An optical delay line (∆T) aligned the pump pulses with the channel of the 160 Gb/s signal to be demultiplexed. The average signal power was 7 mW (in fiber, or ~30 mW peak incident) for a combined launch average power of just 25 mW, which is an order of magnitude lower than for As₂S₃ planar rib waveguides of similar length [1].

5. Results and discussion

The optical spectra at the waveguide output (Figure 5a) shows the pump and signal spectra (> 10 nm wavelength separation) as well as the idler spectra at 1540 nm generated by FWM. Figure 5b shows the optimized eye diagrams of both the 160 Gb/s input signal and 10 Gb/s idler, extracted by tunable bandpass optical filters, highlighting the effective demultiplexing operation that has been achieved. The power conversion efficiency from the pump to the idler (G_c) of the FWM process for an un-depleted pump power (P_p), ignoring propagation loss and differences in mode profile overlap integrals is [23],

where g is the parametric gain coefficient

A plot of G_c versus taper diameter (Fig. 6) (for our experimental conditions) predicts an efficiency of ~2.9% for our device dimensions (1.9 μm diameter), an increase of more than two orders of magnitude compared to the un-tapered fiber, and in reasonable agreement with our measured conversion efficiency of 1.2 %. Figure 6 shows that decreasing the taper diameter to 1μm or even further (peak gamma occurs at ~ 0.7 μm) substantially increases the device efficiency. This is aided by the dispersion becoming anomalous below 1.65 μm where, according to Eq. 2, idler growth becomes exponential with both pump power and taper length. Therefore, by lengthening the taper [22] and optimising its width, sub-milliwatt powers can be achieved. The maximum pump intensity in these experiments was only 30MW/cm², far below the damage threshold of ~2GW/cm² in As₂S₃ glass [1], and so reducing the diameter would not significantly increase the risk of damage. Finally, a FOM of >10 for As₂S₃ glass implies that two-photon pump absorption is negligible (at < 0.02dB/cm) in our experiments. In summary, the broadband low dispersion of this device combined with the large ultra-fast Kerr nonlinearity will allow scaling to much higher data-rates and broader bandwidths for future wavelength conversion applications.

 

Fig. 6. Conversion efficiency from signal to idler wavelengths via FWM in a lossless 5 cm length waveguide (Eq. [2]) using data from Fig. 2 for γ and β₂ at the pump wavelength, for a 10 nm pump and signal wavelength separation and different pump powers of 0.45 W (solid curve), 2 W (dashed curve) and 4 W (dotted curve)

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5. Conclusion

We report all-optical signal processing of high bit rate data by a fiber photonic wire. We achieve time-division demultiplexing at 160 Gb/s (to 10 Gb/s) via FWM in a 5 cm long, 1.9 μm diameter As₂S₃ fiber photonic wire with an average optical pump power of 18mW (peak power = 0.45W), enabled by a dramatically enhanced nonlinearity (γ ~ 7,850 W^-1 km^-1) and reduced dispersion. These results raise the possibility of extremely tapered photonic wires to perform low power nonlinear signal processing at ultra-high bit-rates for future telecommunications networks.