A computational investigation of third-harmonic generation in one-dimensional photonic band-gap materials with multiple-scale method

Abstract

In this paper, we present a numerical investigation of third-harmonic (TH) generation in a one-dimensional photonic band-gap material that is doped with a nonlinear χ(3)medium. For modeling harmonic generation phenomena, a multiple-scale method has been introduced to perturb the nonlinear wave equation by a small factor with appropriate scale. So, we obtain coupled-mode equations (CMEs) with different from the conventional CMEs for this phenomenon. Then, we have solved these CMEs numerically to obtain the output amplitudes of TH waves in both forward- and backward-directions, and the conversion efficiencies. Finally, the solutions show that this photonic band-gap material can generate the TH waves whose amplitudes and the conversion efficiencies may be larger than the TH wave and the efficiency produced by an equivalent length of a phase-matched, bulk medium. © 2014 Taylor & Francis Group, LLC.