Optical Negative Index Metamaterials.

Abstract

Research of metamaterials focuses on unprecedented optical properties that may be obtained from composite media, and has attracted great attention since the seminal paper “Negative Refraction Makes a Perfect Lens”. The theory underpinning this field treats electromagnetic composites using homogenization and effective medium theory (EMT). This thesis discusses negative index metamaterials (NIMs) that exhibit negative refraction. The results can be summarized as follows: 1. The refractive index and maximum unit cell size of an arbitrary NIM can be determined from its photonic band structure in the zero-loss limit. 2. A unified, quantitative explanation can be given to negative refraction observed in both lossy NIMs and lossless photonic crystals. 3. A near-infrared subwavelength NIM is demonstrated. 4. There is no theoretical basis for constructing a superlens. We first derive a general relationship between the bulk index of an arbitrary NIM and its photonic band structure and a maximum unit cell size in the zero-loss limit. Based on discrete translational symmetry, we generalize Bloch’s theorem to a phase matching condition with a complex transverse wavevector, which provides a unified explanation of negative refraction observed in lossless photonic crystals and lossy NIMs. A near-infrared NIM using paired metallic strips is also designed and fabricated using electron beam lithography. It operates at a wavelength of 1μm, and has a ratio of wavelength to periodicity of 7, to our knowledge the highest yet achieved among experimental optical NIMs. The NIM is characterized by scanning electron and atomic force microscopies. Optical transmission and interferometric measurements are also consistent with a bulk negative index derived from band structure. Finally, a model NIM is designed based on Mie resonances, resulting in an effective medium with ε=µ=-1 after homogenization. EMT predicts that such a material is capable of perfect lensing, but is found to substantially overestimate the range of recoverable evanescent waves due to neglect of the microstructure. This result explains the fact that the perfect lens has not been demonstrated after a decade of experimental effort. This dissertation emphasizes the physical behavior of composites, as well as the importance of microscopic models and experiment in metamaterials research.