Modeling Nonlinear Optical Phenomena in Nanophotonics

Abstract

Abstract-In this paper, we review various numerical methods currently used to model nonlinear optical processes in nanophotonics. Among the different theoretical frameworks that have been used to study nonlinear photonic structures, we particularly focus on the application of both perturbation theory and coupled-mode theory to the analysis of complex nonlinear nanophotonic devices. This description is illustrated on several examples of how these techniques can be used to design photonic-crystal-based nonlinear devices. In addition, in all these examples, we show that the predictions made by the two mentioned techniques are in a good agreement with the numerical results obtained from a nonlinear finite-difference-time-domain approach to these problems.

Employing Optical Nonlinearity in Photonic Crystals: A Step Towards All-Optical Logic Gates

“…It is shown in (Bravo-Abad et al, 2007) that a  change in the dielectric constant can result in a  variation in the original eigenvalue 0  as: 2 3 00 0 00 2 3 00 0 00…”

“…But since for a waveguide / g vk    then it can be shown that (Bravo-Abad et al, 2007) the following approximation is valid:…”

“…9b), this system can be modelled using CMT by the following set of equations (Bravo-Abad et. al, 2007): where ω c is the resonant frequency of the cavity.…”

Optimal switching using coherent control

“…Material nonlinearities are typically introduced in CMT using perturbation theory, and this has been shown to provide good agreement with full numerical calculations. 8,10,16,17 We note, however, that due to the finite Q-value of any real cavity the perturbation theory should be performed in the framework of non-Hermitian eigenvalue analysis 12,18 as we do here. Although this seems to be largely ignored in the literature, we emphasize that the absolute value of the field in Fig.…”

High-efficiency degenerate four-wave mixing in triply resonant nanobeam cavities

“…Recent developments in nanofabrication are enabling fabrication of nanophotonic structures, e.g., waveguides and cavities that confine light over long times and small volumes [17][18][19][20][21], minimizing the power requirements of nonlinear devices [22,23] and paving the way for novel on-chip applications based on all-optical nonlinear effects [18,[24][25][26][27][28][29][30][31][32][33]. In addition to greatly enhancing light-matter interactions, the use of cavities can also lead to qualitatively rich dynamical phenomena, including multistability and limit cycles [34][35][36][37][38][39][40].…”