1. Introduction

Efficient, fast and tunable wavelength conversion is an essential signal processing function for the realization of robust, high speed and high capacity wavelength division multiplexed networks. All-optical wavelength converting devices able to cope with speeds far exceeding the current limit of electronics have been demonstrated using nonlinear effects in nonlinear crystals, semiconductor optical amplifiers and optical fibers. Fiber-based wavelength converting devices have particularly been considered due to their excellent noise performance, their ability to be easily integrated in optical systems and their ultrafast response [1]. Among the various nonlinear phenomena exploited for fiber-based wavelength conversion, four-wave mixing (FWM) is regarded as advantageous due to its transparency both in terms of modulation format and bit rate.

The key parameters which contribute to a broadband and highly efficient FWM process are a high effective nonlinearity per unit length γ, a low group velocity dispersion with a low dispersion slope and a short fiber length [2]. Three different fiber technologies have achieved significant advances in optimizing these parameters in the recent years, namely highly nonlinear dispersion-shifted silica-based fibers (HNL-DSFs), silica-based holey fibers (HFs) and compound glass highly nonlinear fibers (CG-HNLFs). HNL-DSFs represent the most mature technology of the three, and impressive results have been achieved in terms of the achievable dispersion profiles, leading to the demonstration of FWM-based parametric amplifiers with broad wavelength conversion bandwidths and very high conversion efficiencies [3, 4, 5, 6]. Due to the moderate values of γ that can be achieved in HNL-DSFs, several tens of meters are normally required and hence compactness and stability are an issue. Furthermore, local variations in the zero-dispersion wavelength throughout the length of the HNL-DSF arising during the fiber fabrication drastically decrease the efficiency of the FWM process [7]. The emergence of HF technology has enabled an almost four-fold improvement in the achievable values of γ, thus allowing the fiber lengths to be significantly reduced [8, 9,10]. A further drastic increase in γ by as much as three orders of magnitude relative to conventional single-mode silica fibers has been achieved using CG-HNLF technology. This has allowed the required fiber lengths to be reduced to only a few meters (limited by the much higher propagation loss and/or chromatic dispersion in such glasses), offering significant advantages for the system stability and compactness. However, the zero-dispersion point of such glasses lies typically at far longer wavelengths than the telecoms band, therefore limiting the bandwidth of the FWM devices to just a few nanometers [11].

Our approach relies on combining HF technology with highly nonlinear glasses. This has already allowed us to fabricate fibers with ultrahigh values of γ, albeit with a large anomalous dispersion at the 1.55 μm telecommunications window due to the large waveguide dispersion resulting from the extreme fiber design [12, 13]. Perhaps even more significant is the capability to accurately tailor the fiber refractive index profile, which has allowed the fabrication of compound glass HFs with low dispersion at 1.55 μm [14, 15]. In this paper we describe our experiments on FWM-based wavelength conversion in such a recently fabricated lead silicate HF. Using just 2.2 m of the fiber, we have achieved a FWM bandwidth of ~30 nm with a conversion efficiency of -6 dB. In the second part of the paper we present numerical simulations which support our experimental findings and give a useful insight on the particular implications associated with the design of short-length compound glass FWM devices.

2. Fiber properties

The HF employed in this experiment was fabricated from commercially available SF57 lead silicate glass using the structured-element-stacking (SEST) technique. The SEST approach combines the best features of extrusion and stacking, allowing for the fabrication of the complex structures required to achieve tailored dispersion properties in compound glass HFs [15]. The design of the fiber used in our experiment is described in Ref.[15] and is shown inset in Fig. 1. The core diameter of the fiber was estimated from SEM images to be ~4.3 μm. Through measurements of the spatial mode characteristics it was confirmed that the SEST-HF supported a single mode with hexagonal symmetry at 1.55 μm.

The dispersion properties of the fiber were numerically calculated using a full vector finite element method modal solver. The simulations revealed that the fiber had a dispersion slope of 0.2 ps/nm²km (Fig. 1), which, unlike the exact zero-dispersion wavelength λ₀ which was within the range 1530–1600 nm, was largely insensitive to small structural variations. It was hence expected that any uncertainties in the estimation of the sizes of either the core or the holes would affect the accurate determination of λ₀.

The optical characteristics of the SEST-HF were experimentally determined at 1.55 μm. The loss of the fiber was measured as ~3.2 dB/m by application of the cutback method. The value of γ was estimated as ~164 W^-1km^-1, from the phase shift induced through self-phase modulation (SPM) on a dual-frequency beat signal propagating through the fiber.

3. Experimental set-up and results

 

Fig. 1. The experimental set-up for the demonstration of FWM in 2.2m of SEST-HF.

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The experimental setup for the demonstration of FWM in the SEST-HF is shown in Fig. 1. Two continuous-wave (CW) lasers, tunable inside the C-band, were used as the pump and signal sources. In order to achieve peak pump powers of the order of a few Watts with a moderate average-power fiber amplifier, the pump was modulated using a LiNbO₃ Mach-Zehnder modulator with 100 ps rectangular pulses at a duty cycle of 1:64. The modulated pump and the CW signal beams were amplified by two separate fiber amplifiers and combined through a 3-dB coupler. This configuration allowed us to independently control the power of the two beams, and also ensured that nonlinear interaction of the two signals occurred only in the SEST-HF. The resulting beam was free-space coupled into 2.2 m of the SEST-HF with an estimated coupling efficiency of ~28% (note that we envisage that a more appropriate selection of lenses should enable a higher coupling efficiency). The peak power of the pump into the fiber was ~6.2 W, while the power of the signal was 2.4 mW. At the output of the system, the strong FWM process between the pump and the signal in the SEST-HF gave rise to a clear idler (wavelength converted) beam, as shown in Fig. 2(a). By appropriate adjustment of the polarization controllers in the signal and pump ports, both beams were aligned to one of the principal polarization axes of the fiber, in which case the wavelength conversion efficiency was optimized.

The conversion efficiency of the FWM process was measured for two different pump wavelengths, namely 1559.7 nm and 1563.0 nm, and for several signal wavelengths in each case, thus giving us a measurement of the bandwidth of the FWM process. Note that the conversion efficiency here is defined as the ratio of the peak power of the generated idler at the output of the fiber to the power of the input signal (i.e. propagation losses in the fiber are taken into account) [11]. The accuracy of the measurement was improved by subtraction of the leakage amplified spontaneous emission (ASE) power at the signal and idler wavelengths induced by the two EDFAs used in the experiment. Since the pump, and hence the idler too, were modulated at a duty cycle of 1:64, the peak power of the idler was ~18dB greater than the average power recorded on the optical spectrum analyzer (OSA). The conversion efficiency curves were then obtained from OSA traces after taking into account the attenuation of the signal due to propagation through the fiber (~7 dB in total). The results of our measurements are summarized in Fig. 2(b), and show that a maximum conversion efficiency of -6 dB was achieved with a 3-dB bandwidth of ~30 nm.

 

Fig. 2. (a) Typical spectral trace obtained at the output of the SEST-HF; (b) Experimental (symbols) and fitted numerical (solid lines) conversion efficiency curves for a pump power of 6.2 W and two different pump wavelengths (1563.0 and 1559.7 nm).

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The fact that the conversion efficiency decreases monotonically when the idler and pump are close in wavelength suggests that the SEST-HF has normal dispersion at these wavelengths [2]. The small variation of the FWM bandwidth with the pump wavelength prompted us to estimate the zero-dispersion wavelength λ₀ of the fiber using numerical simulations of the FWM process, which are presented in the following section. Fitting of the numerical results to the experimentally obtained values yielded an estimated value for λ₀ of ~1582 nm.

4. Numerical simulations

For our numerical simulation of the FWM system we used the power-phase form of the coupled equations presented in [16, 17]. We initially used the same parameters as in our experiments for the pump power, signal power, fiber length, propagation loss and nonlinear coefficient, and fitted the numerical results to our experimental measurements by using the second-order dispersion of the fiber as the free parameter (a third-order dispersion of 0.2 ps/nm²km was assumed). The λ₀ value of 1582 nm that we obtained from this process fits in well with the values predicted from the SEM characterization of the SEST-HF profile and the associated modeling.

We next extended our studies, in order to gain a better understanding of how the various performance parameters of the FWM-based system can be optimized for this type of fiber. Due to the predicted linear dispersion slope of the fiber in the range 1500-1620nm, the fourth-order dispersion term was not considered in these simulations. First, the relation between the fiber length L and the conversion efficiency and 3-dB conversion bandwidth was investigated. The simulations were carried out for a pump wavelength of 1563 nm and for the same pump power as used in our experiments. It can be seen from Fig. 3(a) that the high propagation loss of the SEST-HF sets an optimum value of L for maximum conversion efficiency, which does not depend on the applied pump power but solely on the loss of the fiber. For the fabricated fiber, this optimum length L is ~1.5 m and corresponds to a ratio L/L_eff of 1.7, where L_eff is the effective fiber length. For our experimental pump conditions, the use of the optimum fiber length corresponds to a maximum conversion efficiency of -5.5 dB. With regard to the achievable 3-dB bandwidth of the FWM process, a reduction in the fiber length improves the phase matching condition and therefore, drastically increases the operational bandwidth. Thus, the use of just ~0.5 m of SEST-HF in the experiments described in Section 3 would result in a FWM bandwidth of ~79 nm, which would be enough to cover the entire C-band, however the conversion efficiency in this case would be reduced down to -9 dB. On the other hand, we also observe that the use of ~0.9 m of fiber would result in the same conversion efficiency as we achieved in our experiments, but with an even broader 3-dB bandwidth of ~53 nm.

 

Fig. 3. Dependence of the conversion efficiency (solid lines) and the 3dB-wavelengh conversion bandwidth (dashed lines) on: (a) the SEST-HF length for a 6.2W pump placed at 1563nm; (b) the pump power for a 2.2m long SEST-HF and a pump wavelength of 1563nm; and (c) the pump wavelength for a 2.2m long SEST-HF and pump powers of 6.2 W (blue and red lines) and 2W (pink and cyan lines). (d) Conversion efficiency curves of the optimized SEST-HF for a pump placed at 1547.5nm and pump powers of 1.5W (dashed line) and 2W (solid line). The experimentally measured values of conversion efficiency and bandwidth are also presented (symbols).The insets depict the microstructrure design and the dispersion profile of this fiber. The following color convention applies to all graphs: red and pink lines – >fabricated 3.2dB/m loss SEST-HF, blue and cyan lines-> 2.0dB/m loss SEST-HF, black line->optimized SEST-HF.

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Since the FWM conversion efficiency is a function of the square of the pump power, it can be improved by increasing the input pump power. However, this increase in conversion efficiency comes at the expense of reduced bandwidth, as shown in Fig. 3(b). This behavior is due to the operation of the wavelength converter in the normal dispersion regime, where both the linear phase mismatch and the nonlinear power-dependent phase mismatch have the same sign.

Naturally, the bandwidth of the FWM process would be greatly improved if the pump wavelength was chosen to lie closer to the fiber’s zero-dispersion wavelength λ₀. This is demonstrated in Fig. 3(c). For pump wavelengths in the vicinity of λ₀ (<3nm), simulations have shown that the fourth-order dispersion term significantly affects the obtained conversion efficiency curves [18], thus it is difficult to define a 3dB conversion efficiency bandwidth.

The fabrication of SF57 HFs with much smaller core diameters compared to the HF used here and a propagation loss as low as 2 dB/m has already been reported [12]. It is therefore reasonable to expect that improvements in the fabrication process can result in similar loss performance for SF57 HFs fabricated using the SEST method. For this reason, we repeated our wavelength conversion simulations for a fiber with similar characteristics to the one used in our experiments but a propagation loss of 2.0 dB/m. For the same fiber length and experimental conditions, an improvement of ~4.8 dB in the conversion efficiency could be achieved compared to our experimental results. Note that the optimum length for such a fiber is ~2.4 m (also corresponding to L/L_eff=1.7) is very close to the actual length used in our experiments. For this fiber, a conversion efficiency of 0 dB could be achieved for a pump power of 7.2 W. With regard to the 3-dB conversion efficiency bandwidth, the performance of this lower loss fiber would be only slightly degraded compared to the one used in the experiments for the same pump power and wavelength (Fig. 3(a), 3(c)). This is because for the lower loss fiber and for the same dispersion characteristics, the nonlinear phase becomes larger, therefore the phase mismatch deteriorates in the normal dispersion regime.

By small modifications of the structural parameters of the fiber design compared to the fabricated SEST-HF, fibers with a λ₀ wavelength inside the C-band, a low dispersion slope and higher values of nonlinearity per unit length can be realized. Using an inverse design procedure, we were able to identify several such SEST designs. A good compromise between dispersion slope and nonlinearity was offered by a fiber with a design similar to the fabricated one but with a hole-to-hole distance Λ equal to 1.15 μm and a hole size d of 0.65 μm. This fiber has a zero dispersion wavelength at 1550 nm, a dispersion slope of -0.2 ps/nm²km, a dispersion profile as shown in the inset of Fig. 3(d), and a γ value of 763 W^-1km^-1. Numerical simulations were performed to assess the performance of this fiber assuming a loss of 2 dB/m and a length of 2.2 m. Higher order dispersion terms were more significant in this case, and hence they were taken into account in these simulations. For a 2 W pump placed at 1547.5 nm, a positive conversion efficiency up to 7.2 dB could be achieved over a bandwidth sufficiently broad to cover the entire C-band (Fig. 3(d)). Such a fiber could be used both in wavelength conversion and parametric signal amplification applications, enabling the realization of compact broadband nonlinear devices.

5. Conclusions

In conclusion, we have numerically and experimentally studied the potential of dispersion tailored lead-silicate-based holey fibers in FWM-based wavelength conversion applications. Using a 2.2 m-long SF57-HF fabricated following the SEST technique, we experimentally demonstrated a -6 dB conversion efficiency over a 3-dB bandwidth of ~30 nm. Simulations revealed that by careful selection of parameters such as the fiber length, the pump power and the pump position, optimization of the FWM performance in terms of bandwidth and conversion efficiency can be achieved. Further improvements in the fabrication process of SEST fibers, leading to decreased fiber loss and accurate manipulation of the fiber structural parameters, would enable the realization of fiber designs that combine a high nonlinearity with a low dispersion slope and a zero-dispersion wavelength shifted inside the C-band, or even designs exhibiting two closely spaced zero-dispersion wavelengths. Numerical simulations performed for a design with a zero-dispersion wavelength at 1550 nm and a higher effective nonlinearity of 763 W^-1km^-1 revealed that SF57-HFs can become an excellent candidate for the realization of broadband, highly efficient and compact parametric devices.