In the thesis, a numerical method for the analysis of optical pulses propagation through leaky-mode/guided-mode resonance (GMR) structures is implemented by integrating a Fourier decomposition technique and the rigorous coupled-wave analysis (RCWA) method. Dispersion properties of several GMR structures such as single-grating-layer GMR filters, coupled GMR filters, and cascaded GMR filters are studied and their interaction with optical pulses investigated. For device applications, a high-Q transmission filter is formed by coupling GMR reflection filters which can withstand typical attenuation in silicon. Wavelength division multiplexing (WDM) filters are proposed by cascading a number of GMR transmission filters. Generally, a N channel DWDM filter can be realized by cascading N+1 GMR transmission filters. The channel bandwidth in this structure is sensitive to the gap width between the two neighboring GMR filters. Both the channel bandwidth and channel spacing are inversely proportional to the number of cascaded GMR filters for a given gap width. For slow light applications, a conceptual optical delay line device with desired time delay and flat-dispersion is proposed by treating double GMR transmission filters as a cavity and then cascading such cavities.
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