Access Type

Open Access Dissertation

Date of Award

January 2019

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Electrical and Computer Engineering

First Advisor

Yang Zhao

Abstract

Optical nanostructures are heterogeneous media containing subwavelength inclusions in periodic or aperiodic fashion. The optical properties of optical nanostructure can be controlled and tuned using their constituent material properties and spatial arrangement of the inclusions. While optical nanostructures have been widely studied, controllable and tunable nanostructures using low loss transparent materials has not been studied in detail in the literature. The objective of this research is to perform efficient design and analyses of controllable and tunable optical nanostructures using low loss transparent materials.

To that end, versatile and highly accurate numerical methods like finite different tie domain and plane wave expansion methods are reviewed first. These methods and compared in terms of their speed, accuracy, and memory requirement. Different kind of optical nanostructures, consisting of low index transparent materials, are analyzed to study their controllability. For example, single scatterers are optimized to obtain highly direction forward scattering using low index materials. Then, the minimum refractive index required for establishing optical bandgap in a planar periodic nanostructure was established. Using the bandgap, highly sensitive transparent sensors are designed using low index materials. It is found that the numerical methods can analyze small or periodic nanostructure, while requiring significant computational resources.

As an alternative to numerical modelling, analytical effective medium approximations are considered. The available approximations are reviewed, and their limitations are pointed out. Using the Mie scattering theory, the Maxwell-Garnett approximation is extended so that it can account for arbitrary size, as well as different physical structures, of the inclusions. The derived effective medium approximation is tested on a wide variety of optical nanostructure, both periodic and aperiodic. Good agreement between analytical and experimental results are established. The utility of the approximation in designing controllable and tunable optical nanostructure is demonstrated by modelling the dynamic optical properties of magnetic colloids and verifying them experimentally. The effective medium approximation can be a very fast, and efficient method of modelling the controllable and tunable properties of optical nanostructure, when applied judiciously. The applicability, limits of validity, and limitation of the approximation is also discussed.

Using the analytical framework, controllable optical nanostructure that can mimic optical elements, e.g., focusing lenses, are designed. The relationship between physical structure of the inclusions and the imparted phase by the nanostructure is studied using effective medium approximation and numerical methods. The effective medium approximation can predict the imparted phase with high accuracy, while requiring a fraction of the computation resources compared to numerical methods. Based on the relationship between imparted phase and physical structure of the inclusions, it is possible to design optical nanostructure with controllable spatial phase profile. Using this property, nanostructured optical elements are designed. Their far-field properties are calculated using analytical scalar theory. The analytical results matched well with numerical and experimental results.

In conclusion, an analytical method for designing and analyzing tunable and controllable optical nanostructure is derived and verified with experimental results. The analytical method is significantly more efficient compared to numerical methods, while being similarly accurate compared to experimental results. The research in this work can lead to efficient design of optical nanostructure for many different fields.

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