Structured light in structured media
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The objective of this dissertation is to investigate fundamental optical phenomena at the interface between two emerging fields of modern optics - structured light and micro/nano-structured optical materials. Until recently, these fields were developing in parallel yet independently. A majority of researchers in the field of metamaterials and photonic crystals considered "simple" linearly or circularly polarized light or Gaussian beam propagation in "structured" materials with properties not found in nature. However, in addition to conventional polarization states, light beams can be radially or azimuthally polarized and carry orbital angular momentum (OAM). A fascinating example of a beam carrying OAM is the optical vortex--a donut-shaped beam with a helical phase front. Similarly, the structured light community largely focused on complex light propagation in rather simple homogeneous, isotropic, transparent media. In this dissertation, we explore fundamentals and applications of light-matter interactions that involve both complex light and complex media. The central question that we aim to tackle is: How may the synergy of these two fields lead to a breakthrough in modern photonics? Structured materials, including metamaterials and photonic bandgap structures, realize unprecedented control over light propagation and design flexibility. They can enable new optical properties and functionalities, including new regimes of wave guiding, negative index of refraction, magnetism at optical frequencies, and subwavelength imaging to name a few. We demonstrate how nearly unlimited possibilities in engineering the properties of structured media can be used for generation and manipulation of structured light. Also, we show how the unique properties of structured light could be used for characterization of structured media.