Study of Si-based three-dimensional photonic crystals infiltrated with liquid crystal within a one-dimensional effective model

Abstract

In this work, we study Si-based three-dimensional photonic crystals infiltrated with liquid crystal (LC), within a one-dimensional effective medium model. Two specific systems of diamond crystal structure compatible with the mature Si technology are considered, namely, (i) diamond-1 which is composed of LC spheres embedded in the Si background, and (ii) diamond-2 which is the inverse of the foregoing structure, with Si spheres immersed in the LC background. For each system, the study is carried out with the LC being in the isotropic/nematic phase. The one-dimensional effective medium model employed in the study is an improved version of the conventional mean field theory (MFT). While retaining partially the typical advantage of MFT, e.g., physical transparency, analytical capability, and computational efficiency, it goes beyond the conventional MFT by taking into account the modulation of dielectric constant in the direction of wave propagation. As such, it improves greatly the poor numerical accuracy inherent in the MFT. We find a partial gap between the 2nd and 3rd bands, with the gap-to-midgap ratio being a few percents. Moreover, the edge of partial gap may be shifted by about 1% (in relative unit) when optical, thermal, or electrical means are applied to alter the phase of LC or rotate the axis of nematic molecules.