Wave propagation and imaging in structured optical media

Structured optical media, usually characterized by periodic patterns of inhomogeneities in bulk materials, provide a new approach to ultimate control of wave propagation with possible practical applications: from distributed feedback lasers by diffraction gratings, to highly nonlinear performance for super-continuum generation, to fiber-optic telecommunications by microstructured photonic crystal fibers, to invisibility cloaking, to super-resolution imaging with metamaterials etc. In particular, structured optical media allow to manipulate the wave propagation and dispersion. In this thesis, we focus on engineering the propagation phase dispersion by modulating the compositions and dimensions of the periodic elements. By tailoring the dispersion in momentum space, we can obtain new optical properties of the structured media and show applications in optical imaging. In this work, we present a novel zeroth-order transmission resonance in hyperbolic medium with a Fabry-Perot geometry, which allows to control the propagation phase by subwavelength elements. This approach can also be extended to periodic structures and be applied to improve the performance of imaging systems. In particular, we show a negative refraction lens based on the photonic hypercrystals, which possesses a nearly constant negative refractive index and can be used to substantially reduce the image aberrations. We apply similar ideas in purely dielectric photonic crystals and demonstrate the phenomenon of conical refraction, which allows a new approach to imaging. In particular, it offers a new method of optical phase retrieval that enables a single simultaneous measurement and guarantees a rapid recovery to the true solution.