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We numerically investigate nonlinear propagation of ultrashort pulses in a one-dimensional photonic band gap structure. We find that, near the band edge, nonlinear effects cause a dynamical shift in the location of the band gap. We demonstrate that this nonlinear mechanism can induce intensity-dependent pulse transmission and reflections. In addition, pulse reshaping and pulse generation is observed. This phenomenon has important new applications in both optical limiting and optical switching.

We use numerical methods to investigate stochastic and coherence properties of the fields transverse profiles in stimulated Raman scattering. In the linear regime with diffractive coupling, the amplified signal is characterized by fluctuations that are macroscopic. We find an interesting dependence of the beam-pointing fluctuations on photon conversion efficiency. Our results for the linear regime compare well with recent experiments, and we report an increase in beam-pointing fluctuations in the nonlinear regime. We discuss the results of modeling with one and two transverse dimensions.

We performed a numerical investigation of the dynamics of the Bloch equations, extended for dense media (media having many atoms within a cubic resonance wavelength), for optical pulses whose duration is much less than an induced-dipole dephasing time. We find a signature of near dipole-dipole interaction which may provide a useful method for validating the first-principles model, for measuring the strength of the interaction, and for coherent pumping. Further, we demonstrate a new and unique optical switching mechanism which may lead to the development of important devices

The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.

It is shown, both theoretically and experimentally, that during laser pulse filamentation in air an intense ultrashort third-harmonic pulse is generated forming a two-colored filament. The third-harmonic pulse maintains both its peak intensity and energy over distances much longer than the characteristic coherence length. We argue that this is due to a nonlinear phase-locking mechanism between the two pulses in the filament and is independent of the initial material wave-vector mismatch. A rich spatiotemporal propagation dynamics of the third-harmonic pulse is predicted. Potential applications of this phenomenon to other parametric processes are discussed.

We study the effect of near dipole-dipole interactions on the electric susceptibility of a coherently prepared three-level $\ensuremath{\Lambda}$ system. We discuss the influence of atomic nonlinearities on the recently predicted enhancement of the absorptionless index of refraction and inversionless gain due to local field effects [J.P. Dowling and C.M. Bowden, Phys. Rev. Lett. 70 1421 1993] and predict a density dependent, or piezophotonic, switching between absorption and amplification.

We include the effect of density-dependent near dipole-dipole interactions in order to generalize the theory of a simple three-level system that exhibits lasing without inversion and an enhanced index of refraction at zero absorption. For certain values of atomic density, our generalized theory predicts a novel enhancement of inversionless gain and absorptionless index by more than 2 orders of magnitude.

An adiabaticlike approximation is derived for the optical Bloch equations, extended for dense media, and used to interpret recent numerical results for the resonant interaction of ultrashort pulses with dense media. It is shown that dense media can exhibit behavior analogous to adiabatic following and adiabatic inversion. In particular, we show that dense collections of two-level systems can be adiabatically inverted by intrinsic self-chirping