Maximum length sequence dielectric multilayer reflector

Abstract

This paper explores the wavelength-dependent reflectivity of alternating high and low refractive index multilayers with a thickness profile defined by a pseudo-random, maximum length sequence (MLS). An MLS contains all possible combinations of a binary sequence save one; thus, a multilayer with an MLS profile contains a superposition of a broad range of periods. The range of periodicities in an MLS multilayer should make these systems more effective broad wavelength reflectors as compared to purely periodic counterparts. We compute the reflection characteristics of MLS and periodic dielectric sequences at visible wavelengths over a range of incident angles using the transfer matrix method (TMM), a recursive multilayer calculation method. The materials SiO2 and TiO2 are chosen as the low and high refractive index materials, respectively, because these materials are commonly used in optical multilayers and because their wavelength-dependent refractive index is well known. Our results show that it is possible to create an MLS structure with high average reflectivity across the entire visible spectrum (400 nm – 700 nm) at all incident angles and polarizations. Finally, we compare the reflection characteristics of dielectric multilayers with metallic reflectors whose refractive index is based on a Brendel-Bormann (BB) model. The comparison shows that a seventh order MLS aperiodic multilayer exhibits slightly higher average reflectivity over the visible spectum than silver or aluminum metallic reflectors.