Graded circular Bragg reflectors: a semi-analytical retrieval of approximate pitch profiles from Mueller-matrix data

Abstract

Abstract Graded pitch profiles are found in structurally chiral materials like cholesteric liquid crystals (CLC) and in the cuticle of some scarab beetles. In most cases, the pitch profile is determined from electron microscopy techniques. Recently, it was shown that approximate pitch profiles in the cuticle of scarab beetles can be retrieved through an analysis of the spectral dependence of maxima and minima in normalized Mueller-matrix data. The analysis relies on basic concepts of interference in thin films, properties of optical modes in chiral systems, and the condition for circular Bragg reflection. In this work, the consistency of the procedure is demonstrated by analysis of normalized Mueller matrices of circular Bragg reflectors calculated for three predefined pitch profiles with (1) a stepwise decrease, (2) a stepwise increase and, (3) an exponential increase. The procedure does not require knowledge of the full Mueller matrix and can be used for non-destructive analysis of pitch in CLC, beetle cuticle and similar structures.