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

Z Lubin, J H Greene, A Taflove
2011 IEEE Microwave and Wireless Components Letters  
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
more » ... n 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. S PATIAL 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 Manuscript [9] . Such modifications to enhance its capability have been proposed in [10], [11] . The finite-difference time-domain (FDTD) method has been previously applied to analyzing problems in nonlinear optics, including solitons [9], [12]- [17] . FDTD accounts for the full-vector nature of the fields, and can readily accommodate inhomogeneous and dispersive media. FDTD does not rely on any simplifying assumptions such as paraxial or scalar approximations as is often employed in a typical analysis with the NLSE. Such assumptions are not appropriate when considering soliton beamwidths on the order of a wavelength. 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 method. The separation of the solitons as well as their relative phase is varied, and their influences on the propagation dynamics are qualitatively assessed. Soliton interaction has previously been modeled using FDTD, but only for the transverse electric (TE) polarization case with a single electric-field component, and the model did not incorporate dispersion [13] . To the best of our knowledge, this is the first work utilizing the GVADE FDTD method to simulate ultra-narrow soliton interactions in the transverse magnetic (TM) polarization. Our study is of interest to efforts involved with time-domain numerical techniques for electromagnetic fields, and relevant to both optical switching applications and control of microwave devices given increasing integration of microwave and optical technology. I. GVADE FDTD MODEL The GVADE method allows for multiple electric-field components to be included in the FDTD domain where a media nonlinearity is present. It also permits integration of linear and nonlinear dispersive models. GVADE has been shown to converge to previously published FDTD results, as well as reproduce known characteristics of higher-order solitons [15] . GVADE could also easily accommodate complex boundary conditions where a variety of materials exist in the propagation path, such as plasmonic nanoscale metals.
doi:10.1109/lmwc.2011.2126019 fatcat:eji5mtwhfrfzhouhzrqvuk7alu