Narrow Results

We study theoretically the symmetric property and coupling efficiency of the defect modes in a two-dimensional phononic crystal by calculating band structures, field distributions and transmission coefficients of the defect modes. The results show that the point defect could act as a microcavity surrounded by the phononic crystal, and the confining ability of the phononic crystal to the resonant modes strongly depends on the thickness of the phononic crystal. By investigating the transmission spectra, we also find that the defect modes cannot be absolutely excited by the normally incident plane waves. The transmission coefficients are calculated by using the eigen-mode match theory method under the supercell technique, which is applied to the phononic crystals with the defects for the first time.

Peculiarities of the defect modes of cholesteric liquid crystals (CLCs) with an isotropic/anisotropic defect inside are investigated. The influence of the defect layer thickness and its anisotropy of refraction, the influence of the system thickness and of the defect layer position in the system, as well as the influence of the dielectric borders on the defect modes are investigated. It is shown that it is possible to change reflection at the defect modes in wide intervals and change the defect mode wavelength, by tuning the defect location and its thickness. Such a system possesses transmission asymmetry. Also, the CLC system thickness and the refraction coefficient of the medium bordering the CLC layer on its both sides have essential influence on the reflection at the defect mode and on the reflection frequency.

We discuss the transmission properties of one-dimensional quarter-wavelength stack containing an inserted array of defect layers. Using a direct integration method, we show that defect layers may cause resonances inside the bandgap, called defect modes. It is shown that defect modes are strongly dependent on the number, the sizes and the positions of defect layers as well as on the period number of the separated layers between the defects. We also show that the increasing number of defects can reduce the optical bistability threshold significantly. Based on the direct integration method, it is shown that nonlinear transfer matrix method either without or with improvement in the interface conditions can only show the bistable behavior qualitatively and not quantitatively.