Controlling the band structures and electromagnetic density of modes in one-dimensional photonic crystals with Lamb wave

Abstract

We have modeled and investigated band structures and the electromagnetic density of modes in one-dimensional photonic crystal whose refractive index is modulated by the excitation of the fundamental symmetric mode of Lamb wave using the Wigner phase time approach and transfer matrix method. The Rayleigh–Lamb dispersion curves are plotted to select the proper thickness of each sub-layer of considered photonic crystal structure which is comprised of silica (SiO2) and rutile (TiO2) layers as sub-layers of unit cell. The propagation of Lamb wave into the considered structures produced phononic band gaps in gigahertz frequency for acoustic waves. Also, the propagation of Lamb wave into the considered structures causes compression in SiO2 and dilation in TiO2 or vice versa, which can further increase or decrease the refractive index of both layers. Thus, there can be three combinations of change in refractive indices: case 1 (both layers have an unperturbed refractive index), case 2 (maximum change of the refractive index in SiO2 and minimum change in the refractive layer of TiO2), and case 3 (minimum change of the refractive index in SiO2 and maximum change in the refractive layer of TiO2). The band gap structures of considered structures are plotted for both polarized electromagnetic waves.