Frozen light in photonic crystals with degenerate band edge

Abstract

Consider a plane monochromatic wave incident on a semi-infinite periodic structure. What happens if the normal component of the transmitted wave group velocity vanishes? At first sight, zero normal component of the transmitted wave group velocity simply implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possible outcome. Instead, the transmitted wave can appear in the form of a frozen mode with very large diverging amplitude and either zero, or purely tangential energy flux. The field amplitude in the transmitted wave can exceed that of the incident wave by several orders of magnitude. There are two qualitatively different kinds of frozen mode regime. The first one is associated with a stationary inflection point of electromagnetic dispersion relation. This phenomenon has been analyzed in our previous papers. Now, our focus is on the frozen mode regime related to a degenerate photonic band edge. An advantage of this phenomenon is that it can occur in much simpler periodic structures. This spectacular effect is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in a variety of practical applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc.