4 × 4 Transfer Matrix T _p for Dielectric Helical Films

Abstract

Dielectric helical thin films (DHTF’s) are described by a homogeneous rotation of an arbitrarily oriented symmetric dielectric function tensor ɛ assuming that all other linear response dyadics are zero, and that the permeability tensor μ₀μ has its scalar vacuum value μ₀ [1, 2, 3, 4, 5, 6, 7]. Such material properties are well-known from chiral liquid crystals [8], and which require ellipsometry for appropriate optical characterization [9, 10]. A new class of designed matter is about to emerge upon sculpturing solid-state materials in thin film form. Such designs involve physical deposition techniques in three-dimensional growth regimes, where, depending on growth parameters and appropriate substrate rotation, “zick-zack” pattern, “S”-shapes or helices can be deposited [11, 12, 13, 14]. Design dimensions can be well within the nanometer region, providing interesting grounds for new applications such as micro-filters, micro-antenna arrays, micro-springboards, or “frozen” chiral liquid crystals for optical filters. Crucial for design is the choice of the right dimensions, because electrical and optical properties will depend on confinement effects leading to form birefringence. Due to the complexity of such films, optical characterization is a challenge. The generalized ellipsometry approach allows for nondestructive characterization of helical dielectric materials [15] . The mathematical description of the transfer matrix T_p for dielectric helical films is therefore included here.