Theoretical study of Lorentz non-reciprocal cylinder gratings

Abstract

Non-reciprocal devices are devices which behave differently when input and output is reversed. For example diode is an non-reciprocal device due to different resistance for forward and backward current. In this thesis we consider optical non-reciprocal devices such devices have different optical properties when direction of the incident electromagnetic field is reversed. There are different designs to achieve this non-reciprocal properties but they have some drawbacks such as thick and require high field intensity. In this thesis we aim to develop optical non-reciprocal devices using cylinder arrays with Lorentz non-reciprocal materials. Non-reciprocal cylinder arrays have benefit such as thin and high performance. We first review the anisotropic properties of Yttrium iron garnet (YIG) and the mechanism of being anisotropic. Then we review Mie's theory for single cylinder scattering. Mie's theory is an analytical description of scattered field from cylinders. We also develop multiple scattering theory which expand the field near cylinder into cylindrical harmonics to investigate scattering properties of multiple cylinders. We also explain two reciprocal theory, Lorentz reciprocity and energy conservation for two port system, which will ensure reciprocal transmittance. We then use multiple scattering theory to calculate transmission properties of different cylinder arrays including arrays with non-reciprocal transmission. As an example, a dimer array with lossy dielectric and YIG can achieve transmittance different about 70%. Topological approach is also employed to analysis special phenomenon. First special phenomenon we analyze is reciprocal point where at that specific parameter both transmittance and reflectance are reciprocal even in a non-reciprocal system. Second special phenomenon we analyze is isolation point where at that specific parameter the transmittance difference is unity. Robustness and annihilation of these special points are also demonstrated. We believe this thesis could lead to novel high performance non-reciprocal devices.