Slow wave phenomena in photonic crystals

Abstract

Slow light in photonic crystals and other periodic structures is associated with stationary points of the photonic dispersion relation, where the group velocity of light vanishes.

Degenerate-band-edge engineering inspired by nonlocal transformation optics

“…In a series of influential studies [17][18][19][20][21], Figotin and Vitebskiy investigated the theoretical implications of stationary points in a dispersion relationship. Assuming a timeharmonic exp(Àixt) dependence, and given a general dispersion law x(b) relating the angular frequency x and the propagation constant b, a m-th order stationary point at x = x 0 is characterized by…”

“…The latter (m = 4) constitutes the DBE case of specific interest here, and differs fundamentally from the regular band edge case above, mainly due to the critical contribution of degenerate evanescent modes. The reader is referred to [17][18][19][20][21] for a thorough discussion of the theoretical details and related physical implications.…”

“…DBEs can be obtained in photonic crystals containing uniaxial media with suitably tilted optical axes, as an effect of the coupling between two modes with different polarizations [17][18][19][20][21]30]. Alternatively, they can also be engineered in optical fibers with multiple gratings [22,24,27], coupled periodic waveguides [23,25,26,28], and periodically-loaded circular waveguides [29].…”

“…Moreover, we also address the synthesis of a multilayered metamaterial implementation that suitably approximates (within a neighborhood of the DBE stationary point) such ideal blueprints. Though still based on a periodic multilayer, our implementation is substantially different from those in references [17][18][19][20][21].…”

“…Such exotic dispersion effects, first studied by Figotin, and Vitebskiy [17][18][19][20][21], are eliciting a growing attention (see, e.g., [22][23][24][25][26][27][28][29][30] and references therein) in view of their potential relevance to diverse applications including slow light, solid-state lasers, quantum-cascade lasers, sensors, optical delay lines, traveling-wave tubes, distributed solid-state amplifiers, and switches. Here, inspired by our nonlocal TO approach, we investigate an alternative metamaterial-based design, which is amenable to a multilayered implementation.…”