Resonance enhancement of magnetic Faraday rotation

Magnetic Faraday rotation is widely used in optics. In natural transparent materials, this effect is very weak. One way to enhance it is to incorporate the magnetic material into a periodic layered structure displaying a high-Q resonance. One problem with such magneto-optical resonators is that a significant enhancement of Faraday rotation is inevitably accompanied by strong ellipticity of the transmitted light. More importantly, along with the Faraday rotation, the resonator also enhances linear birefringence and absorption associated with the magnetic material. The latter side effect can put severe limitations on the device performance. From this perspective, we carry out a comparative analysis of optical microcavity and a slow wave resonator. We show that slow wave resonator has a fundamental advantage when it comes to Faraday rotation enhancement in lossy magnetic materials

Giant Slow Wave Resonance for Light Amplification and Lasing

We apply the idea of giant slow wave resonance associated with a degenerate photonic band edge to gain enhancement of active media. This approach allows to dramatically reduce the size of slow wave resonator while improving its performance as gain enhancer for light amplification and lasing. It also allows to reduce the lasing threshold of the slow wave optical resonator by at least an order of magnitude.Comment: Preliminary version of the manuscrip

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.

Giant Gain Enhancement in Photonic Crystals with a Degenerate Band Edge

We propose a new approach leading to giant gain enhancement. It is based on unconventional slow wave resonance associated to a degenerate band edge (DBE) in the dispersion diagram for a special class of photonic crystals supporting two modes at each frequency. We show that the gain enhancement in a Fabry-Perot cavity (FPC) when operating at the DBE is several orders of magnitude stronger when compared to a cavity of the same length made of a standard photonic crystal with a regular band edge (RBE). The giant gain condition is explained by a significant increase in the photon lifetime and in the local density of states. We have demonstrated the existence of DBE operated special cavities that provide for superior gain conditions for solid-state lasers, quantum cascade lasers, traveling wave tubes, and distributed solid state amplifiers. We also report the possibility to achieve low-threshold lasing in FPC with DBE compared to RBE-based lasers.Comment: 14 pages, 7 figures, version 3, Published in Physical Review B, 201

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 publications. Now, our focus is on the frozen mode regime related to a degenerate photonic band edge. An advantage of this new 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 practical applications, such as higher harmonic generation and wave mixing, light amplification and lasing, highly efficient superprizms, etc

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 appears to be proportional to forth 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 N^2. Thus, the anisotropy allows to drastically reduce the size of the resonance cavity with similar performance. The key characteristic of the periodic arrays with the gigantic transmission resonance is that the dispersion curve omega(k)at the photonic band edge has the degenerate form Delta(omega) ~ Delta(k)^4, rather than the regular form Delta(omega) ~ Delta(k)^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.Comment: To be submitted to Phys. Re

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 loosing 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 to slow 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.Comment: 96 pages, 12 figure

Band-Gap Structure Of Spectra Of Periodic Dielectric And Acoustic Media. I. Scalar Model

. We investigate the band-gap structure of the spectrum of second-order partial differential operators associated with the propagation of waves in a periodic two-component medium. The medium is characterized by a real-valued position-dependent periodic function "(x) that is the dielectric constant for electromagnetic waves and mass density for acoustic waves. The imbedded component consists of a periodic lattice of cubes where "(x) = 1. The value of "(x) on the background is assumed to be greater than 1. We give the complete proof of existence of gaps in the spectra of the corresponding operators provided some simple conditions imposed on the parameters of the medium. Key words: propagation of electromagnetic and acoustic waves, band-gap structure of the spectrum, periodic dielectrics, periodic acoustic media. AMS subject classification. 35B27, 73D25, 78A45. 1. INTRODUCTION. One of the main observations in the quantum theory of solids is that the energy spectrum of an electron in a ..

Giant Slow Wave Resonance for Light Amplification and Lasing

We apply the idea of giant slow wave resonance associated with a degenerate photonic band edge to gain enhancement of active media. This approach allows to dramatically reduce the size of slow wave resonator while improving its performance as gain enhancer for light amplification and lasing. It also allows to reduce the lasing threshold of the slow wave optical resonator by at least an order of magnitude