Research On Ultrahigh-q Spherical Photonic-crystal Microcavities And Slow-light Waveguides

With the novel mechanism of guiding light by the optical band gap, the photonic crystal can manipulate light effectively. Thus it can be explored to manufacture optical devices and systems with high qualities. This dissertation focuses on four types of technologies. Firstly, we design an optical resonator cavity of ultra-high quality factor. The cavity is named spherical photonic crystal cavity, due to its structural characteristic. Secondly, we propose a two- dimensional photonic-crystal waveguide in which a frozen mode is contained. And we explore the effect of parametric amplification in such waveguide. Thirdly, we study the dispersion properties of the air-core photonic-crystal waveguides, as well as the W2 hybrid-core PhCW with Si layers inserted in. Last, the dispersion relation of the longitudinally uniform waveguides is theoretically derived and calculated and numerical simulations are given by using Matlab.This dissertation is organized as follows:Chapter One first briefly describes the definition, theoretical basis, classification and analyzing methods of photonic crystals. Then we introduce the applications and researches on optical resonators. At last, we introduce the slow-light techniques and describe the mechanisms to achieve slow light, focusing on the analysis of the material- and structure dispersions. A comparison between EIT and CRS is given.In chapter two, we propose a novel optical resonator cavity. The microcavity is composed of a serial of concentric spherical shells with periodic refractive index. We name it spherical photonic crystal microcavity. By adjusting the structural parameters, we obtain a microcavity of ultra-high optical quality factor that can achieve 109 orders. Such a cavity has a strong ability to confine light and energy.In chapter 3 we design two-dimensional dislocated photonic-crystal waveguide which can achieve the frozen mode regime. By adjusting the structural parameters, such as the radius of the airholes and the dislocation of the two claddings, we get a stationary inflection point in the dispersion diagram, where the first and second order derivatives of frequency with respect to wacevector are both equal to zero. Light of frozen mode would have a vanished velocity and enhanced amplitude. The enhanced parametric amplification is demonstrated in this paper to shown the enhancement by slow light effect.In chapter 5, we investigate the properties of the air-slotted photonic crystal waveguides. The relationship between the width of air slot and the dispersion diagram is studied. Light is confined in the narrow slot with low refractive index. The guided mode has much higher intensities than that in conventional rectangular waveguides. The decreasing of the overlap-area between light and media could cause diminishes in loss. In addition, we insert Si layers into the W2 air-slotted photonic crystal waveguides. With light is confined in the thin Si layer, loss is also under control.In chapter 6, a formalism that utilizes the analytic transfer-matrix technique is derived to investigate the longitudinally uniform waveguide with slow light mode. The analytic expression of the dispersion relation is demonstrated. The numerical calculation is realized by using Matlab.