The transmission-line analogy of the planar electromagnetic reflection problem is exploited to obtain a transmission-line model that can be used to design effective, robust, and wideband interference-based matching stages. The proposed model based on a new definition for a scalar impedance is obtained by using the reflection coefficient of the zeroth-order diffracted plane wave outside the photonic crystal. It is shown to be accurate for in-band applications, where the normalized frequency is low enough to ensure that the zeroth-order diffracted plane wave is the most important factor in determining the overall reflection. The frequency limitation of employing the proposed approach is explored, highly dispersive photonic crystals are considered, and wideband matching stages based on binomial impedance transformers are designed to work at the first two photonic bands.
Optical bistability provides a simple way to control light with light. We demonstrate low-power thermo-optical bistability caused by the Joule heating mechanism in a one-dimensional photonic crystal (PC) nanobeam resonator with a moderate quality factor (Q ~8900) with an embedded reverse-biased pn-junction. We show that the photocurrent induced by the linear absorption in this compact resonator considerably reduces the threshold optical power. The proposed approach substantially relaxes the requirements on the input optical power for achieving optical bistability and provides a reliable way to stabilize the bistable features of the device.
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