We investigate the nonlinear response of GaAs-based photonic crystal cavities at time scales which are much faster than the typical thermal relaxation rate in photonic devices. We demonstrate a strong interplay between thermal and carrier induced nonlinear effects. We have introduced a dynamical model entailing two thermal relaxation constants which is in very good agreement with experiments. These results will be very important for Photonic Crystal-based nonlinear devices intended to deal with practical high repetition rate optical signals.

Self-phase modulation effects in 1D optical slow-wave structures made of Fabry-Pérot cavities coupled by Distributed Bragg Reflectors (DBRs) are discussed. The nonlinear response of the structure is investigated by a comparative analysis of several numerical methods operating either in time or frequency-domain. Time-domain methods include two Finite-Difference Time-Domain approaches, respectively, optimized to compensate for numerical dispersion and to model nonlinearity at any order. In the frequency-domain an efficient method based on a numerical integration of Maxwell’s equations and an iterative nonlinear extension of the Eigenmode Expansion method are discussed. A Nonlinear Equivalent Circuit of DBRs is also presented as a useful model to reduce computational efforts. Numerical results show that bistable effects and self-pulsing phenomena can occur when either the optical power or the number of coupled cavities of the structure are sufficiently increased

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Numerical integration schemes of time-domain Maxwell equations in optical dispersive and nonlinear media are considered. In this context, we study quantitatively the impact of numerical dispersion on a typical nonlinear parametric conversion process, comparing the widely used finite difference (FDTD) approach and pseudo-spectral (PSTD) methods. Our results show that, unless using very dense grid, only fourth-order PSTD gives results in good quantitative agreement with standard coupled-mode theory

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We investigate forward and backward second-harmonic generation by means of FDTD method. We show that numerical dispersion of the method can strongly affect the generation process. Nevertheless FDTD captures complex dynamical phenomena such as separatrix crossing.Introduction. Frequency conversion processes and in particular second-harmonic generation, both in forward (FSHG) and backward (BSHG, requiring a QPM grating) configuration, are usually described in the framework of the coupled-mode theory (CMT) [1]. Beyond the undepleted regime, CMT predicts complex phenomena such as controllable qualitative changes of the dynamical field behavior accompanied by quantitative changes of the conversion. These phenomena are associated with separatrix crossing in a suitable reduced phase-space, and can occur both in FSHG and BSHG, though driven by different mechanisms: competition between quadratic and unavoidable cubic nonlinearities in the former case [2], and due to intrinsic nonlinear feedback in the latter one [3]. However, no experimental evidence for these phenomena has been reported so far, and one naturally wonders whether they are expected to persist when full Maxwell equations are considered, thereby going beyond the intrinsic approximations of CMT (slowly-varying, rotating-wave, other generated frequencies neglected). To this end one can apply nonlinear and dispersive finite-difference time-domain (FDTD) methods [4], which imply no other approximation than discretization, and are suitable to describe nonlinear frequency conversion in complex (non-homogeneous and/or anisotropic) structures [5,6] as well as self-pulsing and hysteresis phenomena characteristic of nonlinear distributed feedback structures [7]. In order to emphasize basic limitations and advantages of the method, and to compare with CMT, we run FDTD simulations of FSHG and BSHG both in homogeneous media and QPM gratings, keeping complexity to the minimum by considering the 1D quasi-scalar case, and mainly continuous wave excitation.