Ilya Vitebskiy

Electromagnetic Unidirectionality in Magnetic Photonic Crystals

Magnetization, either spontaneous or field-induced, is always associated with nonreciprocal circular birefringence which breaks the reciprocity principle and qualitatively changes electrodynamics of medium. In magnetic photonic crystals and other periodic structures involving magnetic components, broken reciprocity can result in electromagnetic unidirectionality, when the traveling waves can only propagate in one the two opposite directions. The unidirectional wave propagation can only occur if both time reversal and space inversion symmetries of the periodic structure are broken. During the last decade there have been numerous publications devoted to this kind of phenomenon. Our goal is to present some of those ideas.

Gigantic transmission band-edge resonance in periodic stacks of anisotropic layers

We consider Fabry-Perot cavity resonance in periodic stacks of anisotropic layers with misaligned in-plane anisotropy at the frequency close to a photonic band edge. We show that in-plane dielectric anisotropy can result in a dramatic increase in field intensity and group delay associated with the transmission resonance. The field enhancement turns out to be proportional to fourth degree of the number N of layers in the stack. By contrast, in common periodic stacks of isotropic layers, those effects are much weaker and proportional to N2 Thus, the anisotropy allows one to drastically reduce the size of the resonance cavity with similar performance. The key characteristic of the periodic arrays with gigantic transmission resonance is that the dispersion curve omega(k) at the photonic band edge has the degenerate form Deltaomega approximately (Deltak)4, rather than the regular form Deltaomega approximatley (Deltak)2. This can be realized in specially arranged stacks of misaligned anisotropic layers. The degenerate band-edge cavity resonance with similar outstanding properties can also be realized in a waveguide environment, as well as in a linear array of coupled multimode resonators, provided that certain symmetry conditions are in place.

Slow light in photonic crystals

The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without losing a significant portion of the incident light energy to absorption, reflection, etc. We show that the so-called frozen mode regime offers a unique solution to the above problem. Under the frozen mode regime, the incident light enters the photonic crystal with little reflection and, subsequently, is completely converted into the frozen mode with huge amplitude and almost zero group velocity. The linearity of the above effect allows the slowing of light regardless of its intensity. An additional advantage of photonic crystals over other methods of slowing down light is that photonic crystals can preserve both time and space coherence of the input electromagnetic wave.

PT-symmetric Talbot effects.

We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern has to respect specific periodicities dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter, thus allowing one to control the imaging process.

Frozen light in photonic crystals with degenerate band edge

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.

Oblique frozen modes in periodic layered media.

We study the classical scattering problem of a plane electromagnetic wave incident on the surface of semi-infinite periodic stratified media incorporating anisotropic dielectric layers with special oblique orientation of the anisotropy axes. We demonstrate that an obliquely incident light, upon entering the periodic slab, gets converted into an abnormal grazing mode with huge amplitude and zero normal component of the group velocity. This mode cannot be represented as a superposition of extended and evanescent contributions. Instead, it is related to a general (non-Bloch) Floquet eigenmode with the amplitude diverging linearly with the distance from the slab boundary. Remarkably, the slab reflectivity in such a situation can be very low, which means an almost 100% conversion of the incident light into the axially frozen mode with the electromagnetic energy density exceeding that of the incident wave by several orders of magnitude. The effect can be realized at any desirable frequency, including optical and UV frequency range. The only essential physical requirement is the presence of dielectric layers with proper oblique orientation of the anisotropy axes. Some practical aspects of this phenomenon are considered.

RF propagation in finite thickness unidirectional magnetic photonic crystals

This paper presents an analysis of a new class of magnetic photonic crystals (MPCs) constructed from periodic arrangements of available (possibly anisotropic) homogeneous material layers. Earlier, analytical studies of semi-infinite versions of these crystals demonstrated that they exhibit the phenomena of minimal reflection at their interface, large amplitude growth of the harmonic wave within the crystal, and concurrent group velocity slow-down. These characteristics are associated with the so called frozen mode and occur at a specific frequency associated with a stationary inflection point within the Bloch diagram. In this paper, we present a characterization of these phenomena for a practical, finite thickness crystal slab and propose a realizable combination of materials consisting of available ferrite and dielectric media. The existence of significant wave amplitude growth and slow down are verified for materials with realistic losses. In addition, we identify and characterize the bandwidth of the magnetic photonic crystals and examine its relationship to the amplitude growth.

Frozen light in periodic stacks of anisotropic layers

We consider a plane electromagnetic wave incident on a periodic stack of dielectric layers. One of the alternating layers has an anisotropic refractive index with an oblique orientation of the principal axis relative to the normal to the layers. It was shown recently that an obliquely incident light, upon entering such a periodic stack, can be converted into an abnormal axially frozen mode with drastically enhanced amplitude and zero normal component of the group velocity. The stack reflectivity at this point can be very low, implying nearly total conversion of the incident light into the frozen mode with huge energy density, compared to that of the incident light. Supposedly, the frozen mode regime requires strong birefringence in the anisotropic layers--by an order of magnitude stronger than that available in common anisotropic dielectric materials. In this paper we show how to overcome the above problem by exploiting higher frequency bands of the photonic spectrum. We prove that a robust frozen mode regime at optical wavelengths can be realized in stacks composed of common anisotropic materials, such as YVO(4), LiNbO(3), CaCO(3), and the like.

Absorption suppression in photonic crystals

We study electromagnetic properties of periodic composite structures, such as photonic crystals, involving lossy components. We show that in many cases a properly designed periodic structure can dramatically suppress the losses associated with the absorptive component, while preserving or even enhancing its useful functionality. As an example, we consider magnetic photonic crystals, in which the lossy magnetic component provides nonreciprocal Faraday rotation. We show that the electromagnetic losses in the composite structure can be reduced by up to two orders of magnitude, compared to those of the uniform magnetic sample made of the same lossy magnetic material. Importantly, the dramatic absorption reduction is not a resonance effect and occurs over a broad frequency range covering a significant portion of the respective photonic frequency band.

Inverse Borrmann effect in photonic crystals

The Borrmann effect, which is related to the microscopic distribution of the electromagnetic field inside the primitive cell, is studied in photonic and magnetophotonic crystals. This effect, well-known in x-ray spectroscopy, is responsible for the enhancement or suppression of various linear and nonlinear optical effects when the incidence angle and/or the frequency change. It is shown that by design of the primitive cell this effect can be suppressed and even inverted.