Photonic band-gap and defect modes of a one-dimensional photonic crystal under localized compression

Abstract

The rupture of periodicity caused by one defect (defect layer) in a one-dimensional photonic crystal (1DPhC) results in a narrow transmission spectral line in the photonic band-gap, and the field distribution shows a strong confinement in the proximity of the defect layer. In this work, we present a theoretical model to calculate the frequency of defect modes caused by defect layers induced by localized mechanical stress. Two periodical arrangements were studied: one with layers of poly(methyl-methacrylate) (PMMA) and polystyrene (PS), PMMA-PS; the other with layers of PMMA and fused silica (SiO2), PMMA-SiO2. The defect layers were induced by localized compression (tension). The frequencies of the defect modes were calculated using elasto-optical theory and plane wave expansion and perturbation methods. Numerical results show that the frequency of the defect mode increases (decreases) when the compression (tension) increases. Based on the theoretical model developed, we show that compression of n layers of a 1DPhC induces n defect modes whose frequencies depend on the compression magnitude in the case of normal incidence of electromagnetic waves, in accordance with the results reported for other types of defect layers. The methodology shows the feasibility of the plane wave expansion and perturbation methods to study the frequency of the defect modes. Both periodical arrangements are suitable for designing mechanically tunable (1DPhC)-based narrow pass band filters and narrow reflectors in the (60, 65) THz range.