Theory and Experiment of Slow-Light Coupled-Resonator Structures

Abstract

Slow light has been an inter-disciplinary topic and a rapidly growing area, especially over the last decade with the improvement of fabrication technology. The ability to slow down and control the group velocity of light may find applications such as optical buffers, optical delay lines, and enhanced light-matter interaction in optical modulator, amplifier, detectors, lasers, and nonlinear optics. The spirit of slow light is to replace a bulky device with a much shorter, compact structure. This thesis explores the design and experiment of coupled-resonator optical waveguides (CROWs), which consist of arrays of optical resonators in which light propagates through the coupling between resonators. The group velocity of light is dictated by the inter-resonator coupling strength. Light can be significantly slowed down if the inter-resonator coupling is weak. CROWs can be realized with various types of resonators. This thesis focuses on grating resonators in silicon waveguides, including grating-defect resonators and bandgap-modulated resonators. With the strong gratings, the grating resonators are only a few microns long. We control the inter-resonator coupling via the number of holes between adjacent resonators. The major limitations in the realization of CROWs have been various kinds of transmission losses, including the resonator losses, the discontinuity between CROWs and the coupling waveguides, and the fabrication disorder. These transmission losses limit the achievable group velocity and the maximum number of resonators. We address these transmission losses throughout this thesis. The resonator losses are overcome with the design and optimized fabrication of tapered grating-defect resonators and bandgap-modulated resonators. The discontinuity between CROWs and waveguides is reduced by tailoring the coupling along the CROW for adiabatic conversion. The optimization of the CROW response leads to the study of filter design based on CROW. Filter design formalism based on coupled-mode theory is presented. The effect of fabrication disorder on CROWs is analyzed, and the Butterworth filters are shown to be more robust against fabrication disorder. The fabrication and measurement of grating CROWs are presented, featuring high-Q (Q=105) grating resonators, coupling of up to 50 resonators, control of group velocity between c/13 and c/49, and Butterworth filters. Finally, an optical analog of electromagnetically induced transparency is presented. The structure consists of two co-spatial gratings imposed on a three-mode waveguide. One of the supermodes, the Dark mode, possesses a group velocity which depends on the ratio of the grating strengths. The group velocity can be nearly zero if the two grating strengths are nearly identical.