INTRODUCTION

Laser pulses are continuing to be utilized in a variety of advanced commercial, civilian, and military systems. Their bandwidth and intensity have been increasing, to the point at which the materials they interact with no longer respond in a linear fashion. The material response is nonlinear and the properties of the materials depend on the shape of the pulse propagating in them. Moreover, the materials have memory effects so that trains of multiple pulses can produce effects similar to those occurring from one large pulse. Despite the increase in complexity of the associated physical properties, these nonlinear effects offer the potential for a variety of novel device and systems applications.

Nonlinear optical (NLO) devices are currently being explored for their applications in various systems associated with communications, remote sensing, optical computing, and so on. However, as the size of optical devices such as microcavity lasers is pushed to the size of an optical wavelength and less, the need for more exact materials and response models is paramount to the successful design and fabrication of those devices. Most current simulation models are based on known macroscopic, phenomenological models that avoid issues dealing with specific microscopic behavior of the materials in such NLO devices. Inaccuracies in the simulation results are then exacerbated as the device sizes shrink to subwavelength sizes and the response times of the excitation signals surpass the response times of the material. There are laser sources currently under development with submicron wavelengths that are pushing the boundaries of the subfemtosecond regime. Phenomenological nonresonant models lose their ability to describe the physics in this parameter regime; hence, they lose their accuracy there. Quantum mechanical effects begin to manifest themselves; the simulation models must incorporate this behavior to be relevant.

Until recently, the modeling of pulse propagation in and scattering from complex nonlinear media has generally been accomplished with one-dimensional, scalar models. These models have become quite sophisticated; they have predicted and explained many of the nonlinear as well as linear effects in present devices and systems. Unfortunately, they cannot be used to explain many observed phenomena; and expectations are that they are not adequately modeling multidimensional nonlinear phenomena. It is felt that vector and higher dimensional properties of Maxwell's equations that are not currently included in existing scalar models in addition to more detailed material and device structure models may significantly impact the scientific and engineering results. The associated propagation and scattering issues have a direct impact on a variety of applications, particularly on the design and engineering of integrated photonic components that have immediate utility to nonlinear soliton fiber optical communications systems currently under development. It is believed that the successful development of semi-classical simulators that combine numerical quantum mechanical models of materials and macroscopic Maxwell's equations solvers will significantly affect the concept and design stages associated with novel nonlinear optics phenomena.

The problem of accurate numerical modeling of the propagation of ultrafast pulses in nonlinear media and their use in NLO optical devices has been subject to increasing interest in recent years. Since the most interesting nonlinear phenomena are transient and superposition is not available, it is natural to try to carry out this modeling directly in the time-domain. For this reason the finite-difference time-domain (FDTD) method is receiving intensive study for modeling linear and nonlinear optical phenomena. In contrast to the case for frequency-domain linear analysis, a single value of permittivity ε is completely inadequate to describe nonlinear time-dependent phenomena, and it is essential to model the interaction of the electromagnetic field with the material medium.

Initial simulations of these ultrafast optical pulse interactions have been based upon several well-known phenomenological material models (Ziolkowski and Judkins, 1993a,b, 1994; Judkins and



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