Figotin Alex, Vitebskiy Ilya
Department of Mathematics, University of California, Irvine, California 92697, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Dec;74(6 Pt 2):066613. doi: 10.1103/PhysRevE.74.066613. Epub 2006 Dec 28.
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.
考虑一个平面单色波入射到一个半无限周期结构上。如果透射波群速度的法向分量消失会发生什么？乍一看，透射波群速度的法向分量为零仅仅意味着入射波的全反射。但我们证明全反射不是唯一可能的结果。相反，透射波可以以一种冻结模式的形式出现，其具有非常大的发散幅度以及零或纯切向能流。透射波中的场振幅可以比入射波的场振幅大几个数量级。存在两种性质不同的冻结模式状态。第一种与电磁色散关系的一个驻点拐点相关。这种现象在我们之前的论文中已经分析过。现在，我们关注的是与简并光子带边相关的冻结模式状态。这种现象的一个优点是它可以在简单得多的周期结构中出现。这种显著的效应对于入射平面波的频率和传播方向极其敏感。这些特性在各种实际应用中可能非常有吸引力，例如高次谐波产生和波混频、光放大和激光发射、高效超棱镜等等。
