FDTD Computational Study of Ultra-Narrow TM Non-Paraxial Spatial Soliton Interactions

Abstract

Abstract-We consider the interaction between two (1+1)D ultra-narrow optical spatial solitons in a nonlinear dispersive medium using the finite-difference time-domain (FDTD) method for the transverse magnetic (TM) polarization. The model uses the general vector auxiliary differential equation (GVADE) approach to include multiple electric-field components, a Kerr nonlinearity, and multiple-pole Lorentz and Raman dispersive terms. This study is believed to be the first considering narrow soliton interaction dynamics for the TM case using the GVADE FDTD method, and our findings demonstrate the utility of GVADE simulation in the design of soliton-based optical switches.Index Terms-Finite-difference time-domain method, FDTD, GVADE, nonlinear optics, spatial solitons. SPATIAL optical solitons are self-trapped optical beams balancing diffraction and self-focusing due to intensity-induced modifications in the local refractive index. One fascinating feature of solitons is their deflection behavior when in the vicinity of other solitons. This can be exploited for applications in optical routing and guiding or in switching applications in all optical-based interconnects and nanocircuits (for example, [1]).The work by Aitchison, et al. first reported experimental observations that solitons either repel or attract each other with a periodic evolution over propagation, depending on the relative phase between them [2]. Subsequent studies extended the findings and explored applications; slight variation on the launch angle and relative phase was found to cause a soliton pair to merge into one of the original trajectories [3]. More recent efforts considered interactions in semiconductor media [4], incoherent interactions [5], all-optical switching [6], long-range interactions [7], and the dynamics of interacting, self-focusing beams [8].An effective numerical technique known as the beam propagation method (BPM) can be used to model soliton interaction. It is a Fourier-based algorithm that solves the nonlinear Schrodinger equation (NLSE) for the envelope of the field. It typically requires low memory for computer implementation. Some limitations, however, are that it makes a scalar approximation, relies on paraxiality, and also depends on slowly-varying envelope conditions for validity without proper modifications Recently, a new FDTD algorithm was described, which can accommodate more than one electric-field component in media possessing both instantaneous and dispersive nonlinearities, as well as linear material dispersion. Known as the general vector auxiliary differential equation (GVADE) method [15], it has been applied to the study of soliton interactions with nanoscale air gaps embedded in glass [16]. Ultra-narrow solitons involve significant interactions between both longitudinal and transverse electric-field components [14] and the GVADE method accounts for this physics.In this study, we consider the problem of modeling interacting spatial solitons with beamwidths on the order of one wavelength using the GVADE FDTD metho...

FDTD computational study of nanoplasmonic guiding structures for non‐paraxial spatial solitons

“…These observations are similar to those presented in Ref. 11, where it was shown using GVADE FDTD that copropagating non‐paraxial TM polarized solitons can attract each other depending on relative phase and separation distance. We hypothesize this phenomenon may be attributable to the combined effects of the dual‐soliton interaction and the scattered fields from the films as suggested above.…”

“…It solves for multiple electric field components, and incorporates nonlinearities and both linear and nonlinear dispersions of the modeled media. GVADE was previously used to study the influence of scattering air holes on soliton propagation and also the interactions between a pair of copropagating non‐paraxial solitons [10, 11].…”

Electromagnetic Modeling of Third-Order Nonlinearities in Photonic Crystal Fibers Using a Vector Two-Dimensional FDTD Algorithm

“…7 h. Fig. 3 shows obtained results, which can be compared with [28] to notice that good agreement has been achieved.…”

“…For that purpose, two TM-polarized solitons separated by 1.5 μm are excited in fused silica at λ = 800 nm [28]. The solitons are excited in phase, out of phase, and in quadrature to observe well-known phase-induced differences in their mutual interaction.…”

Computationally-efficient FDTD modeling of supercontinuum generation in photonic crystal fibers

“…One of prospective candidates is the finite-difference time-domain (FDTD) method as a versatile numerical tool naturally adapted to broadband EM analysis (Taflove and Hagness 2005). Although several valuable papers focused on FDTD modelling of third-order nonlinear effects, that stay behind SC generation, have been published (Fujii et al 2004;Lubin et al 2011), large computational effort and memory requirements involved in the full-wave EM analysis of centimeter-long PCFs make the method inapplicable (Hu et al 2008). For that reason, a novel approach that takes the advantage of the accuracy of the FDTD method, while substantially alleviating its prohibitive computational requirements, is proposed in this paper.…”