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.

我们使用 Wigner 相位时间方法和传递矩阵方法对一维光子晶体中的能带结构和模式的电磁密度进行了建模和研究，该晶体的折射率由 Lamb 波的基本对称模式的激发来调制。绘制 Rayleigh-Lamb 色散曲线以选择所考虑的光子晶体结构的每个子层的适当厚度，该子层由二氧化硅 (SiO ₂ ) 和金红石 (TiO ₂ ) 层组成，作为晶胞的子层。兰姆波传播到所考虑的结构中为声波产生了千兆赫频率的声子带隙。此外，兰姆波传播到所考虑的结构中会导致 SiO ₂中的压缩和 TiO 中的膨胀₂或反之亦然，这可以进一步增加或减少两层的折射率。因此，折射率变化可以有三种组合：情况 1（两层都具有未受扰动的折射率）、情况 2（SiO _{2中折射率的最大变化和 TiO 2}折射率层中的最小变化），以及情况3（SiO _{2中折射率的最小变化和TiO 2}折射层中的最大变化）。为两种极化电磁波绘制了所考虑结构的带隙结构。