Alexander B. Shvartsburg

Optics of subwavelength gradient nanofilms

Propagation and tunneling of light through subwavelength photonic barriers, formed by dielectric layers with continuous spatial variations of dielectric susceptibility across the film are considered. Effects of giant heterogeneity-induced non-local dispersion, both normal and anomalous, are examined by means of a series of exact analytical solutions of Maxwell equations for gradient media. Generalized Fresnel formulae, visualizing a profound influence of gradient and curvature of dielectric susceptibility profiles on reflectance/transmittance of periodical photonic heterostructures are presented. Depending on the cutoff frequency of the barrier, governed by technologically managed spatial profile of its refractive index, propagation or tunneling of light through these barriers are examined. Nonattenuative transfer of EM energy by evanescent waves, tunneling through dielectric gradient barriers, characterized by real values of refractive index, decreasing in the depth of medium, is shown. Scaling of the obtained results for different spectral ranges of visible, IR and THz waves is illustrated. Potential of gradient optical structures for design of miniaturized filters, polarizers and frequency-selective interfaces of subwavelength thickness is considered.

Superluminal tunneling of microwaves in smoothly varying transmission lines.

Tunneling of microwaves through a smooth barrier in a transmission line is considered. In contrast to standard wave barriers, we study the case where the dielectric permittivity is positive, and the barrier is caused by the inhomogeneous dielectric profile. It is found that reflectionless, superluminal tunneling can take place for waves with a finite spectral width. The consequences of these findings are discussed, and an experimental setup testing our predictions is proposed.

Reflectionless tunneling of light in gradient optics

We analyze the optical (or microwave) tunneling properties of electromagnetic waves passing through thin films presenting a specific index profile that provides a cutoff frequency when the films are used below this frequency. We show that, contrary to the usual case of a square index profile, where tunneling is accompanied by a strong attenuation of the wave due to reflection, such films present the possibility of reflectionless tunneling, where the incoming intensity is totally transmitted.

Broadband antireflection properties of thin heterogeneous dielectric films.

New exactly solvable flexible models of inhomogeneous thin film with smooth and deep variations of dielectric susceptibility epsilon(z) are presented. Formation of cutoff frequencies of such films (as well as the broadband antireflection), controlled by the profiles epsilon(z), is shown. The crucial role of gradients of epsilon(z) in the optics of strongly inhomogeneous media is emphasized.

Polarization-dependent tunneling of light in gradient optics

Reflection-refraction properties of photonic barriers, formed by dielectric gradient nanofilms, for inclined incidence of both S - and P -polarized electromagnetic waves are examined by means of exactly solvable models. We present generalized Fresnel formulas, describing the influence of the nonlocal dispersion on the reflectance and transmittance of single- and double-layer gradient photonic barriers for S and P waves and arbitrary angles of incidence. The nonlocal dispersion of such layers, arising due to a concave spatial profile of dielectric susceptibility across the plane film, is shown to result in a peculiar heterogeneity-induced optical anisotropy, providing the propagation of S (P) waves in tunneling (traveling) regimes. The results obtained indicate the possibility of narrow-band nonattenuated tunneling (complete transmittance) of oblique S waves through such heterogeneous barriers, and the existence of spectral areas characterized by the strong reflection of P waves and profound contrast between transmitted S and P waves. The scalability of obtained exact analytical solutions of Maxwell equations into the different spectral ranges is discussed and the application potential of these phenomena for miniaturized polarizers and filters is demonstrated.

Instantaneous optics of ultrashort broadband pulses and rapidly varying media

Publisher Summary This chapter discusses the instantaneous optics of ultrashort broadband pulses and rapidly varying media. The chapter focuses on the physical fundamentals and mathematical basis of the optics of waveforms whose parameters vary in the course of propagation. The dynamics of instantaneous optical fields, travelling in free space and continuous media, opens many new opportunities for controlled spatiotemporal reshaping of these fields. The investigation of coupled spatial and temporal deformations of localized waveforms is discussed and the waveforms used in modeling such processes are described. Both frequency- and time-domain models are presented. The chapter reviews how such waveforms are produced, and measured experimentally. The chapter focuses on the spatiotemporal dynamics of localized electromagnetic (EM) pulses interacting with stationary dielectric media. The reshaping of harmonic CW trains interacting with non-stationary media is discussed.

Reflectionless tunneling of infrared radiation through subwavelength slit in a waveguide

A new effect of resonant tunneling of a fundamental mode of optical radiation through a subwavelength slit formed by smoothly shaped narrowing of a waveguide is examined. An effective energy transfer by evanescent waves is shown to be determined by the geometry of curvilinear narrowing. Spectra of reflectionless transmittance for waves 2.5–3 times longer than the width of the slit are found. Dependence of resonant tunneling on the geometrical parameters of narrowing and splitting of resonant maxima resulting in formation of two peaks of tunneling transmittance are demonstrated. An additional insight into the properties of narrowed waveguides has been obtained through the visualization of the variation of the field patterns associated with the modes for a specific configuration and the wavelength.

Transverse-electric polarized surface solitons

Abstract It is shown that transverse electric (TE) polarized waves can propagate along the surface of a nonuniform plasma. A nonlinear theory for such waves is presented. It turns out that long-wavelength surface perturbations can develop into soliton structures.

Propagation of microwaves in gradient transmission lines: exactly solvable model

Propagation of microwaves along the transmission line with smoothly continuously distributed capacitance and inductance (gradient transmission line) is considered in the framework of an exactly solvable model. The appearance of strong heterogeneity-induced plasma-like dispersion in gradient transmission line determined by the sizes and shapes of these distributions, is visualized by means of this model. Owing to this dispersion the energy transport in the line discussed can be ensured by both travelling and evanescent microwave modes, characterized by the real and imaginary wave numbers, respectively. The reflectance spectra for microwaves, incident on this heterogeneous transition section located between two homogeneous sections of transmission line are presented, the antireflection properties of this section are demonstrated. The interference of evanescent and anti-evanescent microwave modes is shown to provide the effective weakly attenuated energy transfer in the tunneling regime. The analogy between this microwave system and gradient nano-optical photonic barrier in revealed.

Dynamics of electrons in gradient nanostructures (exactly solvable model)

AbstractA flexible multi-parameter exactly solvable model of potential profile, containing an arbitrary number of continuous smoothly shaped barriers and wells, both equal or unequal, characterized by finite values and continuous profiles of the potential and of its gradient, is presented. We demonstrate an influence of both gradient and curvature of these potentials on the electron transport and spectra of symmetric and asymmetric double-well (DW) potentials. The use of this model is simplified due to one to one correspondence between the algorithms of calculation of the transmittance of convex barriers and energy spectra of concave wells. We have shown that the resonant contrast between maximum and minimum in over-barrier reflectivity of curvilinear barrier exceeds significantly the analogous effect for rectangular barrier with the same height and width. Reflectionless tunneling of electrons below the bottom of gradient nanostructures forming concave potential barriers is considered. The analogy between dynamics of electrons in gradient fields and gradient optics of heterogeneous photonic barriers is illustrated.