Searcharxiv⌕ Search

arXiv subjects

Lev I. Deych

Publications and source records attributed to Lev I. Deych.

17 recordsLinked to original sources
arXiv2001

Single parameter scaling in 1-D Anderson localization. Exact analytical solution

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We derive an exact analytical criterion for the validity of the single parameter scaling in this model. According to this criterion, states with energies from the conduction band of the underlying non-random system satisfy single parameter scaling when disorder is small enough. At the same time, single parameter scaling is not valid for states close to band boundaries and those outside of the original spectrum even in the case of small disorder. The obtained results are applied to the Kronig-Penney model with the potential in the form of periodically positioned $δ$-functions with random strengths. We show that an increase in the disorder can restore single parameter scalingbehavior for states from band-gaps of this model.

cond-mat.dis-nn↗
arXiv2001

Local polariton modes and resonant tunneling of electromagnetic waves through periodic Bragg multiple quantum well structures

We study analytically defect polariton states in Bragg multiple-quantum-well structures and defect induced changes in transmission and reflection spectra. Defect layers can differ from the host layers in three ways: exciton-light coupling strength, exciton resonance frequency, and inter-well spacing. We show that a single defect leads to two local polariton modes in the photonic bandgap. These modes cause peculiarities in reflection and transmission spectra. Each type of defect can be reproduced experimentally, and we show that each of these plays a distinct role in the optical properties of the system. For some defects, we predict a narrow transmission window in the forbidden gap at the frequency set by parameters of the defect. We obtain analytical expressions for corresponding local frequencies as well as for reflection and transmission coefficients. We show that the presence of the defects leads to resonant tunneling of the electromagnetic waves via local polariton modes accompanied by resonant enhancement of the field inside the sample, even when a realistic absorption is taken into account. On the basis of the results obtained, we make recommendations regarding the experimental observation of the effects studied in readily available samples.

cond-mat.dis-nn↗
arXiv2001

Tunable local polariton modes in semiconductors

We study the local states within the polariton bandgap that arise due to deep defect centers with strong electron-phonon coupling. Electron transitions involving deep levels may result in alteration of local elastic constants. In this case, substantial reversible transformations of the impurity polariton density of states occur, which include the appearance/disappearance of the polariton impurity band, its shift and/or the modification of its shape. These changes can be induced by thermo- and photo-excitation of the localized electron states or by trapping of injected charge carriers. We develop a simple model, which is applied to the $O_P$ center in $GaP$. Further possible experimental realizations of the effect are discussed.

cond-mat.dis-nn↗
arXiv2001

Single parameter scaling in 1-D localized absorbing systems

Numerical study of the scaling of transmission fluctuations in the 1-D localization problem in the presence of absorption is carried out. Violations of single parameter scaling for lossy systems are found and explained on the basis of a new criterion for different types of scaling behavior derived by Deych et al [Phys. Rev. Lett., {\bf 84}, 2678 (2000)].

cond-mat.dis-nn↗
arXiv2000

Concept of local polaritons and optical properties of mixed polar crystals

The concept of local polaritons is used to describe optical properties of mixed crystals in the frequency region of their {\it restrahlen} band. It is shown that this concept allows for a physically transparent explanation of the presence of weak features in the spectra of so called one-mode crystals, and for one-two mode behavior. The previous models were able to explain these features only with the use of many fitting parameters. We show that under certain conditions new impurity-induced polariton modes may arise within the {\it restrahlen} of the host crystals, and study their dispersion laws and density of states. Particularly, we find that the group velocity of these excitations is proportional to the concentration of the impurities and can be thousands of times smaller then the speed of light in vacuum.

cond-mat.dis-nn↗
arXiv2000

Polariton Dispersion Law in Periodic Bragg and Near-Bragg Multiple Quantum Well Structures

The structure of polariton spectrum is analyzed for periodic multiple quantum well structures with periods at or close to Bragg resonance condition at the wavelength of the exciton resonance. The results obtained used to discuss recent reflection and luminescent experiments by M. Hübner et al [Phys. Rev. Lett. {\bf 83}, 2841 (1999)] carried out with long multiple quantum well structures. It is argued that the discussion of quantum well structures with large number of wells is more appropriate in terms of normal modes of infinite periodic structures rather then in terms of super- and sub- radiant modes.

cond-mat.dis-nn↗
arXiv2000

Polariton Local States in Periodic Bragg Multiple Quantum Well Structures

We analytically study optical properties of several types of defects in Bragg multiple quantum well structures. We show that a single defect leads to two local polariton modes in the photonic band gap. These modes lead to peculiarities in reflection and transmission spectra. Detailed recommendations for experimental observation of the studied effects are given.

cond-mat.dis-nn↗
arXiv2000

Single parameter scaling in one-dimensional localization revisited

The variance of the Lyapunov exponent is calculated exactly in the one-dimensional Anderson model with random site energies distributed according to the Cauchy distribution. We find a new significant scaling parameter in the system, and derive an exact analytical criterion for single parameter scaling which differs from the commonly used condition of phase randomization. The results obtained are applied to the Kronig-Penney model with the potential in the form of periodically positioned $δ$-functions with random strength.

cond-mat.dis-nn↗
arXiv1999

Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap

We consider tunneling of electromagnetic waves through a polariton band gap of a 1-D chain of atoms. We analytically show that a defect embedded in the structure gives rise to the resonance transmission at the frequency of a local polariton state associated with the defect. Numerical Monte-Carlo simulations are used to examine properties of the electromagnetic band arising inside the polariton gap due to finite concentration of defects.

cond-mat.dis-nn↗
arXiv1999

Raman Scattering Due to Disorder-Induced Polaritons

The selection rules for dipole and Raman activity can be relaxed due to local distortion of a crystalline structure. In this situation a dipole-inactive mode can become simultaneously active in Raman scattering and in dipole interaction with the electromagnetic field. The later interaction results in disorder-induced polaritons, which could be observed in first-order Raman spectra. We calculate scattering cross-section in the case of a material with a diamond-like average structure, and show that there exist a strong possibility of observing the disorder induced polaritons.

cond-mat.dis-nn↗
arXiv1999

Local Polariton States in Polar Crystals with Impurities

We show that an impurity embedded in an ionic crystal can give rise to a novel kind of local states. These states exist within a polariton gap of a material and are a mix of excitations of the crystal, such as phonons or excitons, and the transverse electromagnetic field. The electromagnetic component of the states along with the corresponding excitations of the material are localized in the vicinity of an impurity.

cond-mat↗
arXiv1999

Statistics of Lyapunov exponent in 1-D random periodic-on-average systems

By means of Monte Carlo simulations we show that there are two qualitatively different modes of localization of classical waves in 1-{\em D} random periodic-on-average systems. States from pass bands and band edges of the underlying band structure demonstrate single parameter scaling with universal behavior. States from the interior of the band gaps do not have universal behavior and require two parameters to describe their scaling properties. The transition between these two types of behavior occurs in an extremely narrow region of frequencies. When the degree of disorder exceeds a certain critical value the single parameter scaling is restored for an entire band-gap.

cond-mat.dis-nn↗
arXiv1998

Resonant tunneling of electromagnetic waves through polariton gaps

We consider resonant tunneling of electromagnetic waves through an optical barrier formed by dielectric layers with the frequency dispersion of their dielectric permiability. The frequency region between lower and upper polariton branches in these materials presents a stop band for electromagnetic waves. We show that resonance tunneling through this kind of barriers is qualitatevely different from tunneling through other kind of optical barriers as well as from quantum mechanic tunneling through a rectangular barrier. We find that the width of the resonance maxima of the transmission coeffcient tends to zero as frequency approach the lower boundary of the stop band in a very sharp non-analytical way. Resonance transmission peaks give rise to new photonic bands inside the stop band if one considers periodical array of the layers.

cond-mat↗
arXiv1998

Resonance tunneling of polaritons in 1-D chain with a single defect

We consider propagation of coupled waves (polaritons) formed by a scalar electromagnetic wave and excitations of a finite one dimensional chain of dipoles. It is shown that a microscopic defect (an impurity dipole) embedded in the chain causes resonance tunneling of the electromagnetic wave with the frequency within the forbidden band between two polariton branches. We demonstrate that resonance tunneling occurs due to local polariton states caused by the defect.

cond-mat.dis-nn↗
arXiv1998

Local polariton states in impure ionic crystals

We consider the dynamics of an ionic crystal with a single impurity in the vicinity of the polariton resonance. We show that if the polariton spectrum of the host crystal allows for a gap between polariton branches, the defect gives rise to a novel kind of local states with frequencies within the gap. Despite the atomic size of the impurity we find that new local states are predominated by long-wavelength polaritons. The properties of these states are shown to be different from the properties of the well-known vibrational local states. The difference is due to the singular behavior of the density of states of polaritons near the low-frequency boundary of the polariton gap. Assuming cubic simmetry of the defect site we consider a complete set of the local states arising near the bottom of the polariton gap.

cond-mat↗
arXiv1997

Wave localization in generalized Thue-Morse superlattices with disorder

In order to study an influence of correlations on the localization properties of classical waves in random superlattices we introduce a generalized random Thue-Morse model as a four-state Markov process with two parameters that determine probabilities of different configurations. It is shown that correlations can bring about a considerable change in the transmission properties of the structures and in the localization characteristics of states at different frequencies.

cond-mat↗