Exact localization length for s-polarized electromagnetic waves incident at the critical angle on a randomly-stratified dielectric medium

The interplay between Anderson localization and total internal reflection of electromagnetic waves incident near the critical angle on randomly-stratified dielectric media is investigated theoretically. Using an exact analytical formula for the localization length for the Schr\"odinger equation with a Gaussian $\delta$-correlated random potential in one dimension, we show that when the incident angle is equal to the critical angle, the localization length for an incident $s$ wave of wavelength $\lambda$ is directly proportional to $\lambda^{4/3}$ throughout the entire range of the wavelength, for any value of the disorder strength. This result is different from that of a recent study reporting that the localization length at the critical incident angle for a binary multilayer system with random thickness variations is proportional to $\lambda$ in the large $\lambda$ region. We also discuss the characteristic behaviors of the localization length or the tunneling decay length for all other incident angles. Our results are confirmed by an independent numerical calculation based on the invariant imbedding method.Comment: 12 pages, 3 figure

Resonant absorption of electromagnetic waves in transition anisotropic media

We study the mode conversion and resonant absorption phenomena occurring in a slab of a stratified anisotropic medium, optical axes of which are tilted with respect to the direction of inhomogeneity, using the invariant imbedding theory of wave propagation. When the tilt angle is zero, mode conversion occurs if the longitudinal component of the permittivity tensor, which is the one in the direction of inhomogeneity in the non-tilted case, varies from positive to negative values within the medium, while the transverse component plays no role. When the tilt angle is nonzero, the wave transmission and absorption show an asymmetry under the sign change of the incident angle in a range of the tilt angle, while the reflection is always symmetric. We calculate the reflectance, the transmittance and the absorptance for several configurations of the permittivity tensor and find that resonant absorption is greatly enhanced when the medium from the incident surface to the resonance region is hyperbolic than when it is elliptic. For certain configurations, the transmittance and absorptance curves display sharp peaks at some incident angles determined by the tilt angle.Comment: 15 pages, 11 figure

Anderson localization and Brewster anomaly of electromagnetic waves in randomly-stratified anisotropic media

Anderson localization of $p$-polarized waves and the Brewster anomaly phenomenon, which is the delocalization of $p$-polarized waves at a special incident angle, in randomly-stratified anisotropic media are studied theoretically for two different random models. In the first model, the random parts of the transverse and longitudinal components of the dielectric tensor, between which the longitudinal component is the one in the stratification direction, are assumed to be uncorrelated, while, in the second model, they are proportional to each other. We calculate the localization length in a precise way using the invariant imbedding method. From analytical considerations, we provide an interpretation of the Brewster anomaly as a phenomenon arising when the wave impedance is effectively uniform. Similarly, the ordinary Brewster effect is interpreted as an impedance matching phenomenon. We derive the existence condition for the Brewster anomaly and concise analytical expressions for the localization length, which are accurate in the weak disorder regime. We find that the Brewster anomaly can arise only when disorder is sufficiently weak and only in the second model with a positive ratio of the random parts. The incident angle at which the anomaly occurs depends sensitively on the ratio of the random parts and the average values of the tensor components. In the cases where the critical angle of total reflection exists, the angle at which the anomaly occurs can be either bigger or smaller than the critical angle. When the transverse and longitudinal components are uncorrelated, localization is dominated by the the transverse component at small incident angles. When only the longitudinal component is random, the localization length diverges as $\theta^{-4}$ as the incident angle $\theta$ goes to zero and is also argued to diverge for all $\theta$ in the strong disorder limit.Comment: 15 pages, 4 figure

Excitation of surface waves on the interfaces of general bi-isotropic media

We study theoretically the characteristics of surface waves excited at the interface between a metal and a general bi-isotropic medium, which includes isotropic chiral media and Tellegen media as special cases. We derive an analytical dispersion relation for surface waves, using which we calculate the effective index and the propagation length numerically. We also calculate the absorptance, the cross-polarized reflectance and the spatial distribution of the electromagnetic fields for plane waves incident on a bilayer system consisting of a metal layer and a bi-isotropic layer in the Kretschmann configuration, using the invariant imbedding method. The results obtained using the invariant imbedding method agree with those obtained from the dispersion relation perfectly. In the case of chiral media, the effective index is an increasing function of the chirality index, whereas in Tellegen media, it is a decreasing function of the Tellegen parameter. The propagation length for surface waves in both cases increase substantially as either the chirality index or the Tellegen parameter increases. In Tellegen media, it diverges to infinity when the effective index goes to zero, whereas in chiral media, it does when the parameters approach the cutoff values where quasi surface waves are excited. We investigate the characteristics of quasi surface waves excited when the chirality index is sufficiently large.Comment: 15 pages, 13 figure

Giant enhancement of reflectance due to the interplay between surface confined wave modes and nonlinear gain in dielectric media

We study theoretically the interplay between the surface confined wave modes and the linear and nonlinear gain of the dielectric layer in the Otto configuration. The surface confined wave modes such as surface plasmons or waveguide modes are excited in the dielectric-metal bilayer by obliquely incident $p$ waves. In the purely linear case, we find that the interplay between linear gain and surface confined wave modes can generate a large reflectance peak with its value much greater than 1. As the linear gain parameter increases, the peak appears at smaller incident angles, and the associated modes also change from surface plasmons to waveguide modes. When the nonlinear gain is turned on, the reflectance shows very strong multistability near the incident angles associated with surface confined wave modes. As the nonlinear gain parameter is varied, the reflectance curve undergoes complicated topological changes and sometimes displays separated closed curves. When the nonlinear gain parameter takes an optimally small value, a giant amplification of the reflectance by three orders of magnitude occurs near the incident angle associated with a waveguide mode. We also find that there exists a range of the incident angle where the wave is dissipated rather than amplified even in the presence of gain. We suggest that this can provide the basis for a possible new technology for thermal control in the subwavelength scale.Comment: 11 pages, 6 figure

Resonant absorption and amplification of circularly-polarized waves in inhomogeneous chiral media

It has been found that in the media where the dielectric permittivity $\epsilon$ or the magnetic permeability $\mu$ is near zero and in transition metamaterials where $\epsilon$ or $\mu$ changes from positive to negative values, there occur a strong absorption or amplification of the electromagnetic wave energy in the presence of an infinitesimally small damping or gain and a strong enhancement of the electromagnetic fields. We attribute these phenomena to the mode conversion of transverse electromagnetic waves into longitudinal plasma oscillations and its inverse process. In this paper, we study analogous phenomena occurring in chiral media theoretically using the invariant imbedding method. In uniform isotropic chiral media, right-circularly-polarized and left-circularly-polarized waves are the eigenmodes of propagation with different effective refractive indices $n_+$ and $n_-$, whereas in the chiral media with a nonuniform impedance variation, they are no longer the eigenmodes and are coupled to each other. We find that both in uniform chiral slabs where either $n_+$ or $n_-$ is near zero and in chiral transition metamaterials where $n_+$ or $n_-$ changes from positive to negative values, a strong absorption or amplification of circularly-polarized waves occurs in the presence of an infinitesimally small damping or gain. We present detailed calculations of the mode conversion coefficient, which measures the fraction of the electromagnetic wave energy absorbed into the medium, for various configurations of $\epsilon$ and $\mu$ with an emphasis on the influence of a nonuniform impedance. We propose possible applications of these phenomena to linear and nonlinear optical devices that react selectively to the helicity of the circular polarization.Comment: 10 pages, 5 figures, Optics Express 24, 1794 (2016

Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media

Bi-isotropic media, which include isotropic chiral media and Tellegen media as special cases, are the most general form of linear isotropic media where the electric displacement and the magnetic induction are related to both the electric field and the magnetic intensity. In inhomogeneous bi-isotropic media, electromagnetic waves of two different polarizations are coupled to each other. In this paper, we develop a generalized version of the invariant imbedding method for the study of wave propagation in arbitrarily-inhomogeneous stratified bi-isotropic media, which can be used to solve the coupled wave propagation problem accurately and efficiently. We verify the validity and usefulness of the method by applying it to several examples, including the wave propagation in a uniform chiral slab, the surface wave excitation in a bilayer system made of a layer of Tellegen medium and a metal layer, and the mode conversion of transverse electromagnetic waves into longitudinal plasma oscillations in inhomogeneous Tellegen media. In contrast to the case of ordinary isotropic media, we find that the surface wave excitation and the mode conversion occur for both s and p waves in bi-isotropic media.Comment: 17 pages, 4 figure

Broadband wide-angle absorption enhancement due to mode conversion in cold unmagnetized plasmas with periodic density variations

We study theoretically the mode conversion and the associated resonant absorption of p-polarized electromagnetic waves into longitudinal plasma oscillations in cold, unmagnetized and stratified plasmas with periodic spatial density variations. We consider sinusoidal density configurations for which the frequency band where mode conversion occurs is well included within a transmission band of the one-dimensional plasma photonic crystal. We calculate the mode conversion coefficient, which measures the fraction of the electromagnetic wave energy absorbed into the plasma, and the spatial distribution of the magnetic field intensity for various values of the wave frequency and the incident angle using the invariant imbedding theory of mode conversion. We find that the absorption is greatly enhanced over a wide range of frequency and incident angle due to the interplay between the mode conversion and the photonic band structure. The enhancement occurs because for frequencies within a transmission band, the wave reflection is strongly suppressed and the waves penetrate more deeply into the inhomogeneous region, thereby increasing the possibility for them to reach many resonance points where the dielectric permittivity vanishes.Comment: 11 pages, 5 figure

Optical conductivity associated with solitons in the Peierls state as modified by zero-point-motion disorder

We extend previous work to consider the effect of the soliton on the density of states and conductivity of quasi-one-dimensional Peierls systems with quantum lattice fluctuations, modeled by a random static disorder. Two features have been verified over an order of magnitude variation in the disorder. (1) The soliton density of states and the leading edges of both the soliton-to-band and the band-to-band conductivities have universal scaling forms. (2) The soliton-to-band conductivity has the remarkable feature that the leading edge is accurately predicted by the joint density of states while the trailing edge tracks the rigid-lattice conductivity. Or, in other words, disorder dominates the leading edge, while matrix element effects are predominant for the trailing edge

Theory of solitons, polarons and multipolarons in one dimension: An alternative formulation

We develop an alternative formulation of the theory of solitons, polarons and multipolarons in quasi-one-dimensional degenerate and non-degenerate conducting polymers, starting from the continuum Hamiltonian introduced by Brazovskii and Kirova. Based on a convenient real-space representation of the electron Green function in one dimension, we present a simple method of calculating the Green function and the density of states in the presence of a single soliton or polaron defect, using which we derive exact expressions for the soliton, polaron and multipolaron excitation energies and the self-consistent gap functions for an arbitrary value of the electron-phonon coupling constant. We apply our results to $cis$-polyacetylene.Comment: 13 pages, 1 figure, to appear in Physical Review