COMPUTATIONAL MODELING OF MAXIMUM LENGTH SEQUENCE (MLS) MULTILAYER AND GRATING STRUCTURES

Abstract

This thesis describes a variety of projects computing the optical response of periodic and aperiodic structures. The projects include the design of dielectric multilayer, grating, frequency selective surface and antennas, Mostly, this 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 multi- layer 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 struc- ture 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. The study of Bloch surface waves (BSWs) in dielectric multilayers has been useful in many applications in the fields of optics, photonics, and bio-sensing. BSW excitation can be achieved by the addition of a grating on the top of dielectric multilayer which provides phase matching between incident light and BSWs. However, grating coupling only provides coupling over a narrow angular range for incident monochromatic radiation. This paper reports work on realizing broadband coupling using maximum length sequence (MLS) grating structures. An MLS grating contains all possible combinations of a binary sequence save one; thus a grating with an MLS profile contains a superposition of a broad range of periods. We hypothesize that such a surface structure will permit coupling of a broad angular range of monochromatic light or a wide spectral range of collimated light into Bloch surface wave on a multilayer. We investigate the comparative spectral characteristics of MLS grating coupling with other single period counterparts. We believe our investigation provides a method to achieve efficient coupling of a higher fraction of incident light into BSWs than a single period grating or by using prism coupling. We analyze periodic arrays of frequency selective surfaces (FSSs) built from the split ring resonators (SRRs) and CSRRs. FSSs are two-dimensional periodic structures that behave like either passband or stop band filters in the microwave frequency band. SRRs are ar- tificially created structures with non-magnetic loops and small gaps between them. Using COMSOL Multi-physics, we investigate the transmission characteristics of such structures with variation of the physical parameters gap width, dielectric constant, gap separation, and incident angle. This analysis offers a new approach in the design of meta-material based radio frequency(RF) devices. We present a metamaterial-based design of large scale antennas for massive multiple input and multiple output (MIMO) communication systems. The reliable data link and better per- formance over modern fifth generation (5G) wireless communication systems is possible with large numbers of such adaptive antennas. The miniature metamaterial antennas are best for practical implementation of such large antenna arrays. We investigate the design of meta- material antennas and analyze the S-parameter, radiation pattern, and define mathematical relationship to find the correlation coefficient and diversity gain.