Frozen light in periodic metamaterials

Wave propagation in spatially periodic media, such as photonic crystals, can be qualitatively different from any uniform substance. The differences are particularly pronounced when the electromagnetic wavelength is comparable to the primitive translation of the periodic structure. In such a case, the periodic medium cannot be assigned any meaningful refractive index. Still, such features as negative refraction and/or opposite phase and group velocities for certain directions of light propagation can be found in almost any photonic crystal. The only reservation is that unlike hypothetical uniform left-handed media, photonic crystals are essentially anisotropic at frequency range of interest. Consider now a plane wave incident on a semi-infinite photonic crystal. One can assume, for instance, that in the case of positive refraction, the normal components of the group and the phase velocities of the transmitted Bloch wave have the same sign, while in the case of negative refraction, those components have opposite signs. What happens if the normal component of the transmitted wave group velocity vanishes? Let us call it a "zero-refraction" case. At first sight, zero normal component of the transmitted wave group velocity implies total reflection of the incident wave. But we demonstrate that total reflection is not the only possibility. Instead, the transmitted wave can appear in the form of an abnormal grazing mode with huge amplitude and nearly tangential group velocity. This spectacular phenomenon is extremely sensitive to the frequency and direction of propagation of the incident plane wave. These features can be very attractive in numerous applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc

Magnetic Faraday rotation in lossy photonic structures

Magnetic Faraday rotation is widely used in optics and MW. In uniform magneto-optical materials, this effect is very weak. One way to enhance it is to incorporate the magnetic material into a high-Q optical resonator. One problem with magneto-optical resonators is that along with Faraday rotation, the absorption and linear birefringence can also increase dramatically, compromising the device performance. Another problem is strong ellipticity of the output light. We discuss how the above problems can be addressed in the cases of optical microcavities and a slow wave resonators. We show that a slow wave resonator has a fundamental advantage when it comes to Faraday rotation enhancement in lossy magnetic materials

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 photonic frequency band

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.Comment: text and 9 figure

Band structure and Bloch states in birefringent 1D magnetophotonic crystals: An analytical approach

An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in magneto-optic thin film devices. Full analytical expressions are obtained for the dispersion relation and Bloch modes in a layered stack photonic crystal and their properties are analyzed. It is shown that other models recently discussed in the literature are contained as special limiting cases of the formulation presented herein

Spectral Theory of Time Dispersive and Dissipative Systems

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system -- which we show is essentially unique. We illustrate the method by applying it to the spectral analysis of time dispersive dielectrics and the damped oscillator with retarded friction. In particular, we obtain a conservative extension of the Maxwell equations which is equivalent to the original Maxwell equations for a dispersive and lossy dielectric medium.Comment: LaTeX, 57 Pages, incorporated revisions corresponding with published versio

Slow wave resonance in periodic stacks of anisotropic layers

We consider transmission band edge resonance in periodic layered structures involving birefringent layers. Previously we have shown that the presence of birefringent layers with misaligned in-plane anisotropy can dramatically enhance the performance of the photonic-crystal Fabry-Perot resonator. It allows to reduce its size by an order of magnitude without compromising on its performance. The key characteristic of the enhanced photonic-crystal cavity is that its Bloch dispersion relation displays a degenerate photonic band edge, rather than only regular ones. This can be realized in specially arranged stacks of misaligned anisotropic layers. On the down side, the presence of birefringent layers results in the Fabry-Perot 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 transmission resonance, characteristic of a degenerate photonic band edge. Both features are of critical importance for a variety of practical applications, including antennas, light amplification, optical and microwave filters, etc.Comment: To be submitted to Phys. Rev.

Lagrangian Variational Framework for Boundary Value Problems

A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is implemented through a Lagrangian framework that allows to account for (i) a variety of forces including dissipative acting at the boundary; (ii) a multitude of features of interactions between the boundary and the interior fields when the boundary fields may differ from the boundary limit of the interior fields; (iii) detailed pictures of the energy distribution and its flow; (iv) linear and nonlinear effects. We provide a number of elucidating examples of the structured boundary and its interactions with the system interior. We also show that the proposed approach covers the well known boundary value problems.Comment: 41 pages, 3 figure

Open Systems Viewed Through Their Conservative Extensions

A typical linear open system is often defined as a component of a larger conservative one. For instance, a dielectric medium, defined by its frequency dependent electric permittivity and magnetic permeability is a part of a conservative system which includes the matter with all its atomic complexity. A finite slab of a lattice array of coupled oscillators modelling a solid is another example. Assuming that such an open system is all one wants to observe, we ask how big a part of the original conservative system (possibly very complex) is relevant to the observations, or, in other words, how big a part of it is coupled to the open system? We study here the structure of the system coupling and its coupled and decoupled components, showing, in particular, that it is only the system's unique minimal extension that is relevant to its dynamics, and this extension often is tiny part of the original conservative system. We also give a scenario explaining why certain degrees of freedom of a solid do not contribute to its specific heat.Comment: 51 page