Matrix Models for photonic bandgap engineering

Raul Robles^1*, Tzu-Hsien Wang², Yu-Han Chang³, Vanna Chrismas Silalahi³, Watson Kuo³, Ray-Kuang Lee^1,2

¹Institute of Photonic Technologies, National Tsing Hua University, Hsinchu, Taiwan
²Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
³Department of Physics, National Chung Hsing University, Taichung, Taiwan

* Presenter:Raul Robles, email:raulamauryrobles@hotmail.com

Matrix models for one-dimensional left-handed meta-materials based on interleaved split resonators and complementary split resonators are proposed and analyzed analytically. In resemblance to the Su-Schrieffer-Heeger (SSH) model a non-Hermitian matrix is used. The calculated eigenvalues exhibit the appearance of a band gap as a function of the ring resonators orientation angles. Controlling such band allows changing the transmittance spectrum from a single passband to split passband. The band structure of the model matches experimental and numerically calculated transmittance. Additionally, the transmittance is explored by means of a two counter-propagating waves model.

Keywords: Split Ring Resonators, Photonic lattice, SSH model, Coupled Ring Resonators