We experimentally demonstrate enhanced Kerr nonlinear effects in highly nonlinear As2Se3 chalcogenide fiber tapered down to subwavelength waist diameter of 1.2 µm. Based on self phase modulation measurements, we infer an enhanced nonlinearity of 68 W-1m-1. This is 62,000 times larger than in standard silica singlemode fiber, owing to the 500 times larger n 2 and almost 125 times smaller effective mode area. We also consider the potential to exploit the modified dispersion in these tapers for ultra-low threshold supercontinuum generation.
©2007 Optical Society of America
Highly nonlinear optical waveguides are of great interest for compact, low power, all optical nonlinear devices. Nonlinearity in waveguides can be enhanced either by modifications in the structure to reduce the effective area of the mode (Aeff), or by using materials with higher Kerr nonlinearity (n2). Tapering is a commonly used method for reducing optical fiber dimensions and engineering the waveguide dispersion. Low loss fiber tapers with sub-wavelength waist diameters have been fabricated from both standard single mode fibers (SMFs) [1, 2] and microstructured fibers . These not only serve as platforms for microphotonic device components, they also enable nonlinear process such as supercontinuum generation at low power thresholds [4, 5]. The reduction in the modal area and the subsequent enhancement of the nonlinearity is ultimately limited by the index contrast of air and silica in the case of SMFs , as well as the structural dimensions in the case of photonic crystal fibers .
Materials with higher nonlinearity include semiconductors such as silicon  and AlGaAs , and glasses such as tellurite , lead silicate , bismuth  and chalcogenides . Chalcogenide glasses are of particular interest for device applications based on Kerr nonlinearity as it exhibits very high n2 (100~1000 times greater than in silica), low two photon absorption (TPA, β) and fast response time of less than 100 fs . Chalcogenides have a good nonlinear figure of merit FOM=(n2/βλ) across the telecommunications band , making the material a suitable platform for broadband, low power, compact all optical signal processing devices, including all optical 2R regenerators . Furthermore, being a glass, chalcogenide fibers can be potentially tapered to further enhance the overall nonlinearity by combining the high nonlinearity of the material with reduced mode area.
In this paper we experimentally demonstrate enhanced nonlinearity in As2Se3 chalcogenide fiber (n2~500 times silica) by tapering down to a sub-wavelength diameter. By measuring the propagation of picosecond pulses through the taper and comparing the results with simulations we infer a nonlinear coefficient inside the taper waist of 68 W-1m-1, which is 62,000 times greater than standard SMFs, opening up new possibilities for nonlinear photonic devices with ultra-low threshold energy. We also consider exploiting the strong waveguide dispersion in these tapers for dispersion sensitive nonlinear processes.
2. As2Se3 fiber taper design and fabrication
The nonlinearity in conventional optical fibers can be characterized through the nonlinear coefficient γ=(2π/λ).(n2/A eff) , valid when the guided mode is well confined inside the fiber. In a tapered fiber, however, the mode can extend evanescently beyond the fiber boundaries into the surrounding air, particularly at diameters comparable to or smaller than the wavelength. In this case, only the field inside the fiber contributes to the nonlinearity, such that 
where S z is the longitudinal component of the Poynting vector and r is the cross sectional position vector. For small taper diameters, this integral is evaluated by making n 2=n 2(r), where n 2(r) is zero outside the fiber.
Figure 1 plots γ at 1550 nm as a function of taper diameter for As2Se3 and silica fibers, both surrounded in air, calculated using the finite element method. The calculation used n 2=1.1×10-17 m2W-1 for As2Se3  and n 2=2.2×10-20 m2W-1 for silica . For the silica taper, γ increases as the taper diameter decreases, until it reaches a peak value of 0.067 W-1m-1 when the diameter is 1.1 µm and the corresponding A eff=1.36 µm2. Similarly, the nonlinearity in As2Se3 taper also increases with decreasing diameter, but peaks at a smaller diameter of 0.6 µm, owing to the stronger mode confinement in As2Se3. The insets in Fig. 1 show the calculated mode profiles for the As2Se3 and silica tapers at a waist diameter of 0.6µm, for linearly polarized light at 1550 nm. The high index (n=2.8) of As2Se3 helps to strongly confine light inside the fiber, whereas in silica, the lower index results in a significant portion of the field guided evanescently outside the fiber. As a result, γ in As2Se3 peaks at a value of 164 W-1m-1 where the diameter is 0.6 µm and A eff=0.26 µm2. This value of γ is 149,000 times stronger than in standard untapered silica (SMF28) fibers, and 2440 times the peak γ in silica tapers. The enhancement of γ originates from the 500 times larger n 2 and the 5 times smaller A eff in As2Se3, the latter arising from the increased confinement of light associated with the higher index of the material.
Figure 2 shows the schematic of the fabricated chalcogenide fiber taper used in our experiment. To taper the As2Se3 fiber, we use a modified version of the standard flame brushing technique  that is used to taper silica fibers. Since the melting temperature of As2Se3 is just below 200°C, we use resistive heating to heat the fiber rather than a flame. First we taper a multimoded chalcogenide fiber (with a core size of 7.5 µm, NA: 0.19) from an outer diameter of 165 µm down to 75 µm so that the fiber core becomes singlemode at wavelength of 1550 nm with a mode field diameter (MFD) of 5µm. The uniform waist section of this initial taper is then cleaved, butt-coupled and secured to high numerical aperture silica fibers using UV cured epoxy. The now singlemode waist is further tapered to 1.2 µm diameter. To further confirm our calculation for waist diameter , we examined the taper under a high resolution optical microscope and measured the waist to be 1.2 µm±0.1µm in diameter. The length of the uniform waist is 18 mm and total length of the taper is 164 mm, as shown in Fig. 2b.
The heat brushing profile determining the shape of taper profile and the length of the waist region was constrained by the length of the stages on our taper rig. As a result, we were required to compromise on the adiabaticity of the As2Se3 taper and produced tapers having tapering loss of 3dB.
3. Nonlinear experiments and analysis
3.1 Experimental Setup
Figure 3 schematically shows the experimental set up for the measurement of the nonlinear pulse propagation. We launch transform limited pulses into the chalcogenide taper from a passively modelocked fiber laser. The transform limited pulses have full width half maximum pulse duration of 1.48 ps, repetition rate of 4 MHz and wavelength of 1545 nm. The pulse peak power is varied via a variable optical attenuator, with peak power of up to 5.7 W incident on the chalcogenide fiber.
The total insertion loss through the taper is 11 dB. Approximately 8 dB of this is due to buttcoupling and propagation loss whilst tapering account for 3 dB. Note that the propagation loss of the untapered material is ~1 dB.m-1. The input and output powers are monitored using optical power meters. For the diameter of 1.2 µm, we have calculated using beam propagation method, the effective area to be A eff=0.64 µm2 and the dispersion β2=59.3 ps2/km at 1545 nm.
To characterize the nonlinear pulse propagation, we first measure the transmitted power as a function of the input power (power transfer function), which is plotted in figure 4. The average output versus input average power is not linear indicating TPA and this allows a value of β=2.5×10-12 m.W-1 to be inferred, consistent with [13–16].
Figure 5 shows the transmitted pulse spectra at the output of the taper at different power levels. The dashed lines are simulated self phase modulation (SPM) by solving the nonlinear Schrodinger equation using split step Fourier method . In the simulations, we use values n 2=1.1×10-17 m2W-1 , β=2.5×10-12 m.W-1 and include both the transition and waist regions of the taper as well as the untapered section of As2Se3 fiber. Spectral broadening due to SPM is clearly visible as we increase the peak power from 0.055 W to 5.7 W. We estimate that ~60% of the spectral broadening is due to the waist region of the taper. From these results, we infer a nonlinear coefficient, γ, in the waist to be 68 W-1m-1, which corresponds to about 62,000 times enhancement of nonlinearity compared to that of normal silica fiber (SMF28 γ~1.1×10-3 W-1m-1). Note that SPM measurements conducted on a 75 µm diameter section of fiber, prior to second stage tapering to 1.2µm, showed no appreciable spectral broadening, indicative of the enhanced nonlinearity in the taper.
In the current experiment, the pulses were not significantly affected by dispersion because the dispersion length is much longer than the length of the sample. However, by reducing the taper diameter below the current dimensions, we can exploit the strong waveguide dispersion to shift the dispersion into the anomalous dispersion regime, where we expect efficient four-wave mixing and supercontinuum generation. To consider these other nonlinear processes, we calculate the dispersion as a function of waist diameter (figure 6) at wavelength of 1550 nm. For the untapered As2Se3 fiber, the dispersion is dominated by the intrinsic material dispersion where β2~700 ps2/km (strong normal dispersion) at 1550 nm [14, 15] whilst for tapers with waist diameters below a few microns, the waveguide dispersion dominates. We can clearly see for a waist diameter of 1.2 µm, which corresponds to the current experiment, the dispersion is still in its normal dispersion regime at 1550 nm. However, by reducing the taper diameter dimensions further we can move into the anomalous dispersion regime at 1550 nm. Combining this with longer-taper lengths or higher-pulse powers, would enable ultra-low threshold phase matched nonlinear processes, such as four-wave mixing and supercontinuum generation to be produced. These two considerations are topics for future investigations.
In conclusion, we have demonstrated the enhancement of the nonlinearity in tapered As2Se3 chalcogenide fiber. We tapered the As2Se3 to 1.2 µm diameter with a waist length of 18 mm, and measured a nonlinear coefficient γ of 68 W-1m-1 which is 60 times greater than in untapered As2Se3 fibers and 62,000 times greater than in untapered silica fibers. The group velocity dispersion was also calculated to be zero near this taper diameter. Such strongly enhanced highly nonlinear fiber tapers, with careful optimization of the nonlinearity and dispersion, will open possibilities of nonlinear processes such as supercontinuum generation and parametric processes at ultra small power thresholds.
This work was produced with the assistance of the Australian Research Council (ARC). CUDOS (the Centre for Ultrahigh-bandwidth Devices for Optical Systems) is an ARC Centre of Excellence.
Dong-Il Yeom is supported by Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund, KRF-2006-214-C00029).
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