Slow-wave resonance in periodic stacks of anisotropic layers

Abstract

Abstract. We consider a Fabry-Perot resonance (a transmission band edge resonance) in periodic layered structures involving birefringent layers. In our previous publication [2] we have shown that the presence of birefringent layers with misaligned in-plane anisotropy can dramatically enhance the performance of the photonic-crystal resonator. It allows to reduce its size by an order of magnitude without compromising on its performance. The key characteristic of the enhanced slow-wave resonator is that the Bloch dispersion relation ω (k) of the periodic structure displays a degenerate photonic band edge, in the vicinity of which the dispersion curve can be approximated as ∆ω ∼ (∆k) 4 , rather than ∆ω ∼ (∆k) 2 . Such a situation can be realized in specially arranged stacks of misaligned anisotropic layers. On the down side, the presence of birefringent layers results in the slow wave resonance being coupled only with one (elliptic) polarization component of the incident wave, while the other polarization component is reflected back to space. In this paper we show how a small modification of the periodic layered array can solve the above fundamental problem and provide a perfect impedance match regardless of the incident wave polarization, while preserving the giant slow-wave resonance characteristic of a degenerate photonic band edge. Both features are of critical importance for many practical applications, such as the enhancement of various light-matter interactions, light amplification and lasing, optical and microwave filters, antennas, etc.

Degenerate-band-edge engineering inspired by nonlocal transformation optics

“…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].…”

“…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].…”

“…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.…”

“…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…”

“…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.…”