COMPUTATIONAL MODELING OF BLOCH SURFACE WAVES IN ONE-DIMENSIONAL PERIODIC AND APERIODIC MULTILAYER STRUCTURES

Abstract

Photonic crystals and their use in exciting Bloch surface waves have received immense attention over the past few decades. This interest is mainly due to their applications in bio-sensing, wave-guiding, and other optical phenomena such as surface field enhanced Raman spectroscopy. Improvement in numerical modeling techniques, state of the art computing resources, and advances in fabrication techniques have also assisted in growing interest in this field. The ability to model photonic crystals computationally has benefited both the theoretical as well as experimental communities. It helps the theoretical physicists in solving complex problems which cannot be solved analytically and helps to acquire useful insights that cannot be obtained otherwise. Experimentalists, on the other hand, can test different variants of their devices by changing device parameters to optimize performance before fabrication. In this dissertation, we develop two commonly used numerical techniques, namely transfer matrix method, and rigorous coupled wave analysis, in C++ and MATLAB, and use two additional software packages, one open-source and another commercial, to model one-dimensional photonic crystals. Different variants of one-dimensional multilayered structures such as perfectly periodic dielectric multilayers, quasicrystals, aperiodic multilayer are modeled, along with one-dimensional photonic crystals with gratings on the top layer.

Applications of Bloch surface waves, along with new and novel aperiodic dielectric multilayer structures that support Bloch surface waves are explored in this dissertation. We demonstrate a slow light configuration that makes use of Bloch Surface Waves as an intermediate excitation in a double-prism tunneling configuration. This method is simple compared to the more usual techniques for slowing light using the phenomenon of electromagnetically induced transparency in atomic gases or doped ionic crystals operated at temperatures below 4K. Using a semi-numerical approach, we show that a 1D photonic crystal, a multilayer structure composed of alternating layers of TiO2 and SiO2 , can be used to slow down light by a factor of up to 400. The results also show that better control of the speed of light can be achieved by changing the number of bilayers and the air-gap thickness appropriately.

The existence of Bloch surface waves in periodic dielectric multilayer structures with a surface defect is well-known. Not yet recognized is that quasi-crystals and aperiodic dielectric multilayers can also support Bloch-like surface waves. We numerically show the excitation of Bloch-like surface waves in Fibonacci quasi-crystals, Thue-Morse aperiodic dielectric multilayers using the prism coupling method. We report improved surface electric field intensity and penetration depth of Bloch-like surface waves in the air side in such structures compared to their periodic counterparts.

Bloch surface waves have also demonstrated significant potential in the field of bios-ensing technology. We further extend our study into a new type of multilayer structure based on Maximal-length sequence, which is a pseudo random sequence. We study the characteristics of Bloch surface waves in a 32 layered Maximal-length sequence multilayer and perform angular, as well as spectral sensitivity analysis for refractive index change detection. We demonstrate numerically that Maximal-length sequence multilayers significantly enhance the sensitivity of Bloch surface waves.

Another type of structure that support Bloch surface waves are dielectric multilayer structures with a grating profile on the top-most layer. The grating profile adds an additional degree of freedom to the phase matching conditions for Bloch surface wave excitation. In such structures, the conditions for Bloch surface wave coupling can also be achieved by rotating both polar and azimuthal angles. The generation of Bloch surface waves as a function of azimuthal angle have similar characteristics to conventional grating coupled Bloch surface waves. However, azimuthal generated Bloch surface waves have enhanced angular sensitivity compared to conventional polar angle coupled modes, which makes them appropriate for detecting tiny variations in surface refractive index due to the addition of nano-particles such as protein molecules.