Longitudinal and angular dispersions in photonic crystals: a synergistic perspective on slow light and superprism...

The slow-light effect and the superprism effect are two important effects in photonic crystal structures. In this paper, we will review some of our recent works on the fundamental physics and device applications of these two effects. We will present a synergistic perspective that examines these two effects as a whole. Apparently, the slow light effect is due to the dispersion of a photonic crystal along the direction of light propagation, namely the longitudinal direction, and the superprism effect is related to angular dispersion. However, a deep analysis will show that the superprism effect has an elusive dependence on the longitudinal dispersion as well. Some subtle connections and distinctions between the slow-light effect and the superprism effect will be revealed through our physical analysis. This allows us to treat these two effects under a common theoretical framework. As an example, we will apply this framework to make a direct comparison of the slow-light optical phase array approach and the superprism approach to beam steering applications. Dispersive effects are frequently accompanied by high optical loss and/or narrow bandwidths. We will discuss these issues for both longitudinal and angular dispersions. For the slow light effect, we will give a simple proof of the scaling of fabrication-imperfection related random scattering losses in a slow-light photonic crystal waveguide. Similar to the bandwidth-delay product for the longitudinal dispersion, we will introduce a simple, yet fundamental, limit that governs the bandwidth and angular sensitivities of the superprism effect. We will also discuss the application of the slow-light effect to making compact silicon optical modulators and switches.