S. S. Apostolov

Self-induced tunable transparency in layered superconductors

We predict a distinct nonlinear electromagnetic phenomenon in layered superconducting slabs irradiated from one side by an electromagnetic plane wave. We show that the reflectance and transmittance of the slab can vary over a wide range, from nearly 0 to 1, when changing the incident wave amplitude. Thus changing the amplitude of the incident wave can induce either the total transmission or reflection of the incident wave. In addition, the dependence of the superconductor transmittance on the incident wave amplitude has an unusual hysteretic behavior with jumps. This remarkable nonlinear effect self-induced transparency can be observed even at small amplitudes, when the wave frequency is close to the Josephson plasma frequency J.

Anomalous dispersion of surface and waveguide modes in layered superconductor slabs

Linear surface and waveguide modes with transverse magnetic polarization propagating in a slab of layered superconductor in a uniform dielectric environment are studied theoretically. It is assumed that the superconducting layers are orthogonal to the slab surface and the waves propagate perpendicular to the layers. Dispersion relations are obtained for modes that are symmetric and antisymmetric with respect to the magnetic field. It is shown that the dispersion of these modes is anomalous within a certain range of frequencies and wave numbers. The conditions under which the group velocity of these modes goes to zero are found.

Hysteretic jumps in the response of layered superconductors to electromagnetic fields

We consider here a layered superconductor subject to an externally applied moderately-strong electromagnetic field. We predict hysteretic jumps in the dependence of the surface reactance of the superconductor on the amplitude H0 of the incident electromagnetic wave. This very unusual nonlinear phenomenon can be observed in thin superconducting slabs at not very strong ac amplitudes, if the frequency of the irradiating field is close to the Josephson plasma frequency. Using the ~ � � ,

Superposition principle for nonlinear Josephson plasma waves in layered superconductors

We show that a specific superposition principle is valid for nonlinear Josephson plasma waves in layered superconductors, which is very unusual for nonlinear media. We study theoretically the reflection and transmission of terahertz waves through a finite-size superconducting slab placed inside a rectangular waveguide with idealmetal walls. We assume that the superconducting layers are parallel to the waveguide axis. We show that there exist two specific mutually orthogonal polarizations for waves which, in spite of the nonlinearity, reflect and transmit through the superconductor independently. The wave of the first polarization causes a strong shielding current along the crystallographic ab plane of the superconductor. Therefore, this wave reflects nearly completely from the superconductor and excites only an evanescent mode inside it. The wave of the other polarization does not contain the electric field component parallel to both the sample surface and the crystallographic ab plane and excites much weaker shielding currents. Therefore, it partially reflects from and partially transmits through the sample. Moreover, this wave excites the nonlinear mode in the layered superconductor, and the transmission coefficient of the superconductor depends on the amplitude of the incident wave of this polarization. However, this transmission coefficient is independent of the amplitude of the wave with first polarization. On the basis of the discussed superposition principle, we suggest a method for solving nonlinear problems of waves interacting in layered superconductors. Namely, it is reasonable to represent incident, reflected, and transmitted waves of any polarization as superpositions of the modes with the two specific polarizations considered here and then to solve the problem separately for these modes. We apply this method to the case of nonlinear interaction and mutual transformation of the transverse-electric and transverse-magnetic modes in layered superconductors.

Self-induced terahertz-wave transmissivity of waveguides with finite-length layered superconductors

We predict and study theoretically a new nonlinear electromagnetic phenomenon in a sample of layered superconductor of finite length placed in a waveguide with ideal walls. Two geometries are considered here: when the superconducting layers are parallel or perpendicular to the waveguide axis. We show that the transmittance of the superconductor slab can vary over a wide range, from nearly zero to one, when changing the amplitude of the incident wave. Thus, one can induce the total transmission or reflection of the incident wave by just changing its amplitude. Moreover, the dependence of the superconductor transmittance on the incident wave amplitude has a hysteretic behavior with jumps. The considered phenomenon of self-induced transparency can be observed even at small amplitudes, if the wave frequency

Anomalous Temperature Dependence of the Casimir Force for Thin Metal Films

\omega

Additive N-step Markov chains as prototype model of symbolic stochastic dynamical systems with long-range correlations

is close to the cutoff frequency for linear Josephson plasma waves.

Transformation of the polarization of the electromagnetic waves reflected from the layered superconductors in an external dc magnetic field

Within the framework of the Drude dispersive model, we predict an unusual nonmonotonic temperature dependence of the Casimir force for thin metal films. For certain conditions, this force decreases with temperature due to the decrease of the metallic conductivity, whereas the force increases at high temperatures due to the increase of the thermal radiation pressure. We consider the attraction of a film to: either (i) a bulk ideal metal with a planar boundary, or (ii) a bulk metal sphere (lens). The experimental observation of the predicted decreasing temperature dependence of the Casimir force can put an end to the long-standing discussion on the role of the electron relaxation in the Casimir effect.

Transformation of the polarization of THz waves by their reflection and transmission through a finite layered superconductor

A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys Rev Lett 2003;90:110601 is generalized to the biased case (non-equal numbers of zeros and unities in the chain). In the model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities (zeros) among the preceding N symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length L are obtained analytically and verified by numerical simulations. A self-similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented. The diffusion Fokker–Planck equation governing the distribution function of the L-words is explored. If the persistent correlations are not extremely strong, the distribution function is shown to be the Gaussian with the variance being nonlinearly dependent on L. An equation connecting the memory and correlation function of the additive Markov chain is presented. This equation allows reconstructing a memory function using a correlation function of the system. Effectiveness and robustness of the proposed method is demonstrated by simple model examples. Memory functions of concrete coarse-grained literary texts are found and their universal power-law behavior at long distances is revealed.

Nonlinear localized modes in a plate of a layered superconductor

The reflection of transverse-electric and transverse-magnetic polarized waves from the surface of a semi-infinite layered superconductor in the presence of external dc magnetic field is studied theoretically. The superconducting layers are assumed to be perpendicular to the boundary of the sample. Due to a strong anisotropy of the irradiated superconductor surface, a transformation of the wave polarization occurs upon the reflection. It is shown that, despite a relatively small penetration depth of the dc magnetic field, it qualitatively affects the field distribution of the electromagnetic wave and, therefore, the reflection and transformation coefficients. Thus, the external dc magnetic field can serve as an efficient tool to control the transformation of the wave polarization. The analytical expressions for the reflection and transformation coefficients are obtained and the parameters at which the most effective transformation of the transverse-electric to transverse-magnetic waves and vice versa occur...