Polarization-Resolved Wave Propagation in Uniaxial Crystals: Interface Phenomenon, Prism Geometry and Photonic Crystal Applications

Abstract

The propagation and control of electromagnetic waves in anisotropic media are governed by the tensorial nature of their dielectric response, giving rise to propagation characteristics that differ fundamentally from those in isotropic media. Phenomena such as birefringence, polarization-dependent dispersion, crystal orientation-dependent non-collinear directions of the wave vector and Poynting vector, and polarization-selective transmission offer important opportunities for the development of advanced optical and photonic devices. However, a unified understanding of these effects, particularly their dependence on optic-axis orientation, interface geometry, and external tuning, remains equally challenging and provides open research problems. This thesis addresses these challenges through a theoretical and computational investigation of anisotropic wave propagation and polarization control at interfaces, within optical systems such as uniaxial prisms, and in anisotropic defect-based periodic crystals. The first part of the thesis investigates electromagnetic-wave propagation at anisotropicisotropic interfaces, with particular emphasis on the light incident from a denser uniaxial medium onto a rarer isotropic medium. Starting with the Maxwell equations with tensorial permittivity, an analytical formulation is developed for ordinary and extraordinary waves with arbitrary optic-axis orientation. Generalized Fresnel coefficients are derived for TEand TM-polarized light waves, and the effects of anisotropy on reflection, refraction, energy flow, and polarization are systematically analyzed. The analysis establishes conditions for unconventional phenomena, including negative reflection and polarization-dependent Brewster angle. Since the assumption in this problem is that light travels from a denser medium, the conditions for the total internal reflection problem are further investigated, revealing different critical angles and reflection phase responses for ordinary and extraordinary light waves. The resulting phase control enables the generation of linearly and circularly polarized reflected light using anisotropy and interface geometry alone, without additional polarization elements or multilayer coatings. The thesis then extends the analysis to finite anisotropic optical systems. Polarizationdependent transmission through positive and negative uniaxial prisms is investigated under the condition of minimum angle deviation using a combined ray-optics and electromagnetic framework. The dependence of TE and TM transmission on incident angle and optic-axis orientation is established, providing a theoretical basis for polarization separation using single-crystal-based anisotropic prisms, particularly for high-power laser applications. The second major focus is the development of actively tunable anisotropic photonic structures. A generalized transfer-matrix formulation incorporating tensorial permittivity is developed to analyze one-dimensional photonic crystals containing electrically tunable anisotropic defects. The combined influence of optic-axis orientation and applied voltage on transmission and polarization splitting is systematically investigated for different electrode configurations. This establishes a route towards electrically reconfigurable polarization selective photonic structures. Finally, to address the intrinsically narrow operating bandwidth of conventional single defect photonic-crystal polarizers, a broadband TM polarizer based on multiple defects and CMOS-compatible materials is proposed. Multiple defect cavities are engineered to generate and control multiple polarization-selective resonances, enabling broadband operation around 1550 nm while maintaining a high polarization extinction ratio, low insertion loss, and low spectral ripple. The proposed architecture provides a pathway towards compact and integrable polarization-control devices for integrated photonics. The research presented here combines analytical theory with rigorous numerical simulations to establish a unified framework for understanding and exploiting anisotropy for polarization control in different optical systems and interfaces. The findings provide new physical insight and will be useful in devices based on anisotropic reflection, total internal reflection, polarization separation, electrically tunable polarization splitting, and broadband polarization filtering. The physics and devices designed in this thesis have potential applications in optical communications, laser systems, polarization optics, and integrated photonic technologies based on emerging anisotropic materials.