title: Modal theory of slow light enhanced third-order nonlinear effects in photonic crystal waveguides.
abstract: In this paper, we derive the couple-mode equations for third-order nonlinear effects in photonic crystal waveguides by employing the modal theory. These nonlinear interactions include self-phase modulation, cross-phase modulation and degenerate four-wave mixing. The equations similar to that in nonlinear fiber optics could be expanded and applied for third-order nonlinear processes in other periodic waveguides. Based on the equations, we systematically analyze the group-velocity dispersion, optical propagation loss, effective interaction area, slow light enhanced factor and phase mismatch for a slow light engineered silicon photonic crystal waveguide. Considering the two-photon and free-carrier absorptions, the wavelength conversion efficiencies in two low-dispersion regions are numerically simulated by utilizing finite difference method. Finally, we investigate the influence of slow light enhanced multiple four-wave-mixing process on the conversion efficiency.
authors.affiliation: Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China.
authors.forename: Tao
authors.initials: T
authors.lastname: Chen
authors.forename: Junqiang
authors.initials: J
authors.lastname: Sun
authors.forename: Linsen
authors.initials: L
authors.lastname: Li
mesh_terms: D003198:Computer Simulation; D008027:Light; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D017785:Photons; D012542:Scattering, Radiation; D020349:Surface Plasmon Resonance / Q000379:methods*