Strong quadratic acousto-optic coupling in 1D multilayer phoxonic crystal cavity

Four methods are applied to calculate the acousto-optic (AO) coupling in one-dimensional (1D) phoxonic crystal (PXC) cavity: transfer matrix method (TMM), finite element method (FEM), perturbation theory, and Born approximation. Two types of mechanisms, the photoelastic effect (PE) and the moving interface effect (MI), are investigated. Whether the AO coupling belongs to linear or quadratic, the results obtained by the perturbation theory are in good agreement with the numerical results. We show that the combination method of FEM and perturbation theory has some advantages over Born approximation. The dependence of linear and quadratic couplings on the symmetry of acoustic and optical modes has been discussed in detail. The linear coupling will vanish if the defect acoustic mode is even symmetry, but the quadratic effect may be enhanced. Based on second-order perturbation theory, the contribution of each optical eigenfrequency to quadratic coupling is clarified. Finally, the quadratic coupling is greatly enhanced by tuning the thickness of the defect layer, which is an order of magnitude larger than that of normal defect thickness. The enhancement mechanism of quadratic coupling is illustrated. The symmetry of the acoustic defect mode is transformed from odd to even, and two optical defect modes are modulated to be quasi-degenerated modes. This study opens up a possibility to achieve tunable phoxonic crystals on the basis of nonlinear AO effects.