The auxiliary differential equation finite-difference time-domain method for modeling electromagnetic wave propagation in dispersive nonlinear materials is applied to problems where the electric field is not constrained to a single vector component. A full-vector Maxwell's equations solution incorporating multiple-pole linear Lorentz, nonlinear Kerr, and nonlinear Raman polarizations is presented. The application is illustrated by modeling a spatial soliton having two orthogonal electric field components. To the best of our knowledge, the numerical technique presented here is the first to model electromagnetic wave propagation with two or three orthogonal vector components in dispersive nonlinear materials. This technique offers the possibility of modeling sub-wavelength interactions of vector spatial solitons.

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations.

Abstract-Using the finite-difference time-domain method, we model the propagation of spatial optical solitons having two orthogonal electric field vector components, and the scattering of such solitons by compact subwavelength air holes (i.e., abrupt dielectric discontinuities in the direct paths of the solitons). Our propagation and scattering studies assume a realistic glass characterized by a three-pole Sellmeier linear dispersion, an instantaneous Kerr nonlinearity, and a dispersive Raman nonlinearity. An unexpected spatial soliton scattering phenomenon is observed: the coalescence of the scattered electromagnetic field into a propagating lower-energy spatial soliton at a point many tens of wavelengths beyond the scattering air hole. Overall, our computational technique is general, and should permit future investigations and design of devices exploiting spatial soliton interactions in background media having submicrometer air holes and dielectric and metal inclusions. Index Terms-Finite-difference time-domain (FDTD), nonlinear Schrödinger (NLS), unidirectional pulse propagation equation (UPPE).

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...

This Addendum provides a revised set of figures containing converged numerical data for total scattering cross section (TSCS), replacing the figures in our recent publication [Opt. Lett. 29, 1393 (2004)]. Due to the use of an overly large time step, our original TSCS data exhibited a systematic, nonphysical diminution above 150 THz for all cases studied. We have determined that numerical convergence in the temporal sense for the pseudospectral time-domain (PSTD) algorithm employed previously requires limiting the time step to no more than 1/60th of the sinusoidal period at the maximum frequency of interest, which in the previous case was 300 THz. This is an important point that we hereby report to future users of PSTD simulations in electrodynamics and optics. Note that all our original conclusions remain valid.