Research Of Light And Matter Interaction In Photonic Crystal Slow Light Waveguides

In optical communication systems, there are many applications for light-matter interaction, such as optical amplifiers, lasers and frequency converters. However, these devices require long active region and high pumping power, which makes it difficult for these devices to be extended to the compact integrated optical devices. Slow light, which lengthen interaction time between light and matter and enable high density of the electromagnetic field energy, provides the possibility to solve the problem. In this dissertation, we study several types of light-matter interactions. Using theoretical analysis and numerical simulation, we demonstrate that slow light can enhance the parametric gain, third harmonic generation (THG) efficiency and gain for four-level atomic systems in photonic crystals. Thus, to obtain same interaction intensity, the interaction length can be shortened and pumping power can be reduced, these are intriguing physical phenomena, which can be used to the integrated optical communication systems.This dissertation is organized as follows:Chapter 1 of the dissertation introduces the fundamental theories of photonic crystals, various types of optical nonlinearities and optical amplifiers and lasers. The remainder of this chapter introduces basic concepts, theory and potential applications of slow light. These concepts and theories are desirable for the following research work.In Chapter 2, we show both theoretically and numerically that slow light can enhance the parametric process of silicon in photonic crystal line-defect waveguides. Specifically, to get the desired gain, the pump power for a given gain-medium length or the gain-medium length for given pump power can be reduced by (c/vgn)2 when slow light waveguides are used. In Chapter 3, we study THG in periodic structures both theoretically and numerically. Our model for THG intensity involves both dispersion and group velocity of the structure. The results of the FDTD simulation agree quite well with the theoretical analysis. The slow-light enhancement of the THG intensity and the periodic distribution of the THG intensity along the waveguide are observed and analyzed.Chapter 4 introduces the general process of developing the simulation platform for the finite-differential time-domain (FDTD) method in waveguide doped with atomic systems. We managed to do so by modifying the C++ code of the open source (MEEP) developed at MIT.In Chapter 5, we develop a formula that relates the group velocity of slow light to the conversion rate between the electric field and potential energy of atomic system by apply the Bloch-Floquet formalism and the semiclassical physical model of harmonic oscillators that coupled to electromagnetic fields. We then demonstrates the our numerical study of the stimulated emission in fiber Bragg gratings (FBG) and non-grating fiber, a 9-fold enhancement of stimulated emission is observed in FBG over the non-grating fiber when pumping near the band edge while an enhancement of 20-fold is observed when the frequency of stimulated emission at the band edge.In Chapter 6, an atomic system is suggested to be embedded in the fiber Bragg gratings (FBG) to reduce the group velocity and to eliminate the dispersion of slow light. We demonstrate numerically that the pulse can transmit at the group velocity 0.147c dispersionlessly in the FBG, compared with 0.193c and 56% of FWHM broadening without the atomic system.Chapter 7 summarizes the results of this dissertation. Future research topics for the light -matter interaction in slow light waveguides are proposed.