| In this dissertation, we introduce a new mechanism for controlling the free space propagation of light using photonic crystal slabs in an extremely compact form. Each slab consists of a periodic lattice of air holes introduced into the dielectric slab. These structures exploit guided resonance effects which give rise to strong variation of transmission for normally incident light.; Importantly, when the size of the air holes is large, the guided resonance is not a narrow band phenomenon. Consequently, over 99% reflection can be achieved with a wavelength range of 30nm around 1.55mum, enabling us to develop a new class of dielectric mirrors.; Having two slabs introduces new opportunities for displacement sensing and various filter applications. First, when the two slabs are separated apart by a few wavelengths, such a coupled slab structure behaves as a miniaturized Fabry-Perot cavity with two photonic crystal slabs acting as highly reflecting mirrors. Therefore, the transmission through the structure is highly sensitive to the spacing between the slabs. Furthermore, when the two slabs are in proximity to each other, the evanescent tails of the resonance start to overlap. Exploiting the evanescent tunneling, we introduce a new type of displacement sensor structures that can sense both the vertical and lateral displacements in the nanometer regime.; In addition, we develop a general temporal coupled-mode theory for multimode optical resonators. This theory incorporates a formal description of a direct transmission pathway, and is therefore capable of describing Fano interference phenomena in multi-mode cavities, including those in photonic crystal slab structures. Using the theory, we demonstrate that these photonic crystal slab structures can be readily designed to support multiple resonances and to form tunable filters with various filter functions that are useful in optical communication systems. They include optical all-pass filters which exhibit near complete transmission for both on and off resonant frequencies and yet generate large resonant group delay, and flat-top reflectors which reflect a narrow spectral range of light with a sharp transition sidewall. Thus, we expect the coupled photonic crystal slab structures to play important roles in micro-mechanically tunable optical sensors and filters. |
