Optimization of Optical Soliton self-Frequency Shifting Towards the Mid-Infrared Alaa M. AI-kady and Matin Rochete Department of Electrical and Computer Engineering McGill University Montreal, Canada alaa.al-kadry@mail.mcgill.ca Abstract- We propose an approach to design microwire waveguides that maximize wavelength-shit from 2.29 1m up to wavelengths in the mid infrared. The model is based on the optimization of soliton self-frequency shit and avoiding dispersive waves emission. Keywords-component; soliton pulse; optical iber; nonlinear optics; I. INTRODUCTION Solitons are nonlinear waves that maintain their shape as they propagate. Near the zero-dispersion wavelength (ZDW) of optical ibers, solitons are strongly perturbed by third-order dispersion (TOD) where their dynamics is modelled by the perturbed nolinear Shrodinger equation (NLS) [1]. The key question to soliton is whether perturbation compels it into instability which manifests through emission of radiation ields [2]. The standard approach for answering this question goes back to Elgin [3], who accurately measured soliton perturbation strength due to TOD. The ield's amplitude and requency-position were then expressed analytically by Anediev et al. [4] through dimensionless parameters. A more recent study has extended the analytic expressions and provided a thorough study of the inluence of higher order effects on the ield's characteristics [5]. When ultrashort solitons propagate in optical iber, they gradually shit to longer wavelengths, a mechanism known as soliton self-requency shit (SSFS). The SSFS stems rom the nonlinear intrapulse Raman scattering process. Considering a constant pulse width, the SSFS increases with soliton input energy and inherent material nonlinearity. Chalcogenide glasses with low intrinsic losses at wavelengths above 2 11m, allow the shiting of ultrashort pulses toward mid-inrared (IR) spectral range. Moreover, chalcogenide As2Se3 microwires [6], with convex dispersion proiles, are considered optimal for soliton shiting as they exhibit high waveguide nonlinearity. The microwires are here coated with PMMA cladding to provide mechanical strength for practical applications [7]. However, as soliton propagates closer to the long ZDW, it becomes signiicantly unstable as it sheds energy into the normal dispersion regime. Nonuniform microwires with varying ZDW along the propagation length avoid the DW generation. With the pupose of optimizing the shiting in these microwire proiles, several methods were proposed for a given soliton energy and duration [8, 9]. Here, we propose an approach to design PMMA- As2Se3 nonuniform microwires which provides a maximum wavelength shit at �3150nm with large wavelength tunability in the mid-IR wavelength. The proposed design is based on reducing the inluence of TOD. Following this approach, the microwire design is expected to be less sensitive on initial soliton parameters in generating DWs at the output. Numerical solutions reveal enhancement to soliton shiting rate at low TOD. II. ADIABATIC APPROXIMATION THEORY To describe the soliton propagation near the ZDW, we considered included only the inluence of TOD. In the normalized form, the perturbed NLSE is given as: au sgn( 3 2 ) (1) i a( -i 2 a ; U (( , T) + i N 2 U (( , T) IU (( , T) 1 2 E = i 6 a1u((,T) Where (, T and E are dimensionless variables given as: � _ Z _ t-z/vg _ J3 > - - T- -E- - LD ' LD ' IJzlTo' (2) Here, LD is the dispersion length, 32 is the group velocity dispersion (GVD), To and Po represent the width and peak power of the input pulse. N is the soliton order, and 33 is the TOD parameter of the iber. The E parameter in Eq. (2) quantiies the inluence of �3 on soliton dynamics. Owing to perturbation of soliton by higher-order dispersion and nonlinearity, dispersive waves are generated in the normal dispersion regime of the iber. This phenomenon dictated by the phase matching condition, leads to a transfer of energy rom the soliton to the DW at a speciic requency. The rate of energy transfer is proportional to the amplitude of the soliton at the resonance requency. The phase matching condition arises rom the equality of the soliton and DWs propagation constant expressed in Taylor expansion. However, in the vicinity of the ZDW, the soliton propagation is mainly inluenced by the TOD, and thus the Taylor expansion can just retain up to the third-order term. Under this situation the resonance requency can be approximated as: ' �n = 3 13 2 1 13 3 1 T (3) where lQ is the dimensionless spectral offset between soliton and the DW. Based on this concept, two approaches were