We present a theory of the Fano resonance for optical resonators, based on a temporal coupled-mode formalism. This theory is applicable to the general scheme of a single optical resonance coupled with multiple input and output ports. We show that the coupling constants in such a theory are strongly constrained by energy-conservation and time-reversal symmetry considerations. In particular, for a two-port symmetric structure, Fano-resonant line shape can be derived by using only these symmetry considerations. We validate the analysis by comparing the theoretical predictions with three-dimensional finite-difference time-domain simulations of guided resonance in photonic crystal slabs. Such a theory may prove to be useful for response-function synthesis in filter and sensor applications.

We introduce a new all-optical mechanism that can compress the bandwidth of light pulses to absolute zero, and bring them to a complete stop. The mechanism can be realized in a system consisting of a waveguide side coupled to tunable resonators, which generates a photonic band structure that represents a classical analogue of the electromagnetically induced transparency. The same system can also achieve a time-reversal operation. We demonstrate the operation of such a system by finite-difference time-domain simulations of an implementation in photonic crystals.

Abstract-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 multimode cavities. Using this theory, we prove a general criterion that governs the existence of nonorthogonal modes. The presence of nonorthogonal modes creates interesting transport properties which can not be obtained in normal resonator systems. We validate our theory by comparing its predictions with first-principles finite-difference time-domain simulations and obtaining excellent agreement between the two.

We introduce a mechanically tunable photonic crystal structure consisting of coupled photonic crystal slabs. Using both analytic theory, and first-principles finite-difference time-domain simulations, we demonstrate that a strong variation of transmission and reflection coefficients of light through such structures can be accomplished with only a nanoscale variation of the spacing between the slabs. Moreover, by specifically configuring the photonic crystal structures, high sensitivity can be preserved in spite of significant fabrication-related disorders. We expect such structures to play important roles in micromechanically tunable optical sensors and filters.

It was recently demonstrated that a photonic crystal slab can function as a mirror for externally incident light along a normal direction with near-complete reflectivity over a broad wavelength range. We analyze the angular and polarization properties of such photonic crystal slab mirror, and show such reflectivity occurs over a sizable angular range for both polarizations. We also show that such mirror can be designed to reflect one polarization completely, while allowing 100% transmission for the other polarization, thus behaving as a polarization splitter with a complete contrast. The theoretical analysis is validated by comparing with experimental measurements.