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...
Spatial solitons with beamwidths on the order of a wavelength are studied numerically in the context of their propagation paths being modified by planar nanoplasmonic structures.The prospect of such media in certain configurations used as soliton guiding devices is quantitatively assessed. A finite‐difference time‐domain model is used that incorporates a Kerr nonlinearity and linear dispersion, and solves for the vector components of the fields. A soliton effective beamsplitter, collimator, and dual‐beam waveguide are demonstrated. Interesting aspects of the reflection and transmission properties of gold films is discussed, including first‐time reporting of the Goos‐Hänchen effect in the nonlinear regime for a transverse magnetic, ultra‐narrow spatial soliton incident on a gold slab. The results provided herein are significant for nonlinear switching and routing applications toward future all‐optical computing devices. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2679–2684, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27182
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