The optical properties of the excitons in thin crystals with surface heterolayers

Effect of the short-range near-surface exciton potential on the interference spectra of thin crystals is studied theoretically. The potential modeled by a right-angled well or step leads to a strong perturbation both of the Fabry-Perot structure and the one due to the interference of the additional waves. Several effects are discussed. The most interesting one is the correlation between the localization of the exciton in the near-surface potential well and the change by π of the exciton-wave phase. The surface exciton is displayed by a strong maximum in reflection spectra, and the phase change results in the almost entire quenching of the additional interference structure.     

Reflection and transmission of waves in pyroelectric and piezoelectric materials

The reflection and transmission theories of waves in pyroelectric and piezoelectric medium are studied in this paper. In general in an infinite homogeneous pyroelectric medium there are four bulk wave modes: quasi-longitudinal, two quasi-transversal and temperature waves. In an infinite homogeneous piezoelectric medium there are three bulk wave modes: quasi-longitudinal and two quasi-transversal waves. In the reflection and transmission problem there are five complex boundary conditions in the pyroelectric medium and four complex boundary conditions for the piezoelectric medium. In this paper, we find that the surface waves will be revealed in the reflection and transmission wave problem. The surface waves have the same wave vector component with the incident waves on the interface plane. The two dimensional reflection problem of waves at the interface between the semi-infinite pyroelectric medium and vacuum is researched in greater detail and a numerical example is given.     

Reflection and transmission of plane waves at the interface of pyroelectric bi-materials

A simple reflection and transmission theory of plane waves at the interface of pyroelectric media is studied in this paper. In an infinite homogeneous pyroelectric medium, there are four bulk wave modes: quasi-longitudinal (QL), two quasi-transversal (QT) and one temperature (T) waves, whose velocities depend on the frequency and incident angle. Simultaneously, a quasi-surface (QS) wave on each side of the interface of pyroelectric bi-materials will appear in the general reflection and transmission problem. The quasi-surface wave has the same wave vector component with the incident waves along the interface plane. So, the reflection and transmission problem is different with the propagation wave in the infinite homogeneous space, but it is still solvable. In the reflection and transmission problem, there are ten complex continuous conditions on the interface, which are satisfied by the bulk and quasi-surface waves together. Numerical calculations are performed for bi-material PZT-6B/BaTiO₃. Incidences of the quasi-longitudinal and quasi-transversal waves from the side of PZT-6B or BaTiO₃ medium are discussed. The reflection and transmission amplitude coefficients and energy flow ratios varying with the incident angle are examined.     

Comparison between the dispersion curves calculated in complex frequency and the minima of the reflection coefficients for an embedded layer

Analytical solutions of Lamb functions for symmetric and antisymmetric elastodynamic modes propagating within a solid layer embedded in an infinite medium are presented. Alternative theoretical analyses of such modes are performed, first in terms of the usual approach of harmonic heterogeneous plane waves (real frequency and complex slowness) and then in terms of transient homogeneous plane waves (complex frequency and real slowness). An example structure of a 0.1-mm-thick "alpha case" (an oxygen-rich phase of titanium that is relatively stiff) plate embedded in titanium is used for the study. A large difference between the usual dispersion curves calculated in real frequency and complex slowness and those calculated in complex frequency and real slowness is shown. Thus the choice between a spatial and a temporal parameter to describe the imaginary part of the guided waves is shown to be significant. The minima and the zeros of the longitudinal and shear plane-wave reflection coefficients are calculated and are compared with the dispersion curves. It is found that they do not match with the dispersion curves for complex slowness, but they do agree quite well with the dispersion curves for complex frequency. This implies that the complex frequency approach is better suited for the comparison of the modal properties with near-field reflection measurements.     

Multipath reflection of light from plane-parallel crystalline plates in the presence of additional exciton-polariton waves

The reflectance and transmittance of light by plane-parallel crystal plates were found in the exciton-transition spectral region upon oblique incidence of light with polarization in which two transverse and one longitudinal normal exciton-polariton wave are excited. The reflection spectra calculated for a model crystal with the parameters of the CdSe crystal are analyzed for different thicknesses of the plates, angles of incidence, and damping constants. It is shown that accounting for additional exciton-polariton waves and multiple reflections of light inside the plate results in the possibility of an abrupt change in the phase (by more than 2π) in the vicinity of the exciton transition.     

Anomalous wave interference at Z3-exciton resonance of CuCl

The transmission and the reflection spectra of a thin CuCl single crystal of 0.15μ thickness have been measured in the Z₃-exciton resonance region at 1.6K by using a weak dye-laser light as a light source. Well resolved interference fringes have been obtained over the exciton resonance. In the higher energy region than the longitudinal exciton's energy, the separation of adjacent fringes cannot be explained by interference of the lower branch polariton waves (LBP) or the upper branch polariton waves (UBP). These structures have been explained by the mutual interference effect between the UBP and LBP waves, anomalous waves. This has been confirmed by the measurements of two-photon absorption due to the excitonic molecule via respective polariton states.     

“Right-handed” and “left-handed” polaritons in material media

The dispersion law for polariton waves is deduced from analysis of Maxwell equations in a dielectric medium characterized by the presence of resonance in the frequency range of lattice vibrations or exciton transitions. The theory considers polariton waves with right- and left-oriented vectors $\vec E,\vec H,\vec k$ , corresponding to “right-handed” and “left-handed” polaritons. Dispersion dependences of group velocity of polariton waves and effective mass are established for “right-handed” and “left-handed” polaritons. Expressions are obtained for the effective refractive index and reflection coefficient in a wide spectral range including the resonance region. The specific features of lattice reflection spectra in alkali halide crystals are explained using the proposed theory.     

The interference of additional waves of forbidden polaritons excited by allowed polaritons in CuGaS2

Additional waves of exciton polaritons are studied in thin (1.5–1.8 μm) CuGaS₂ crystals at 9 K. The reflectivity spectra show a fine structure related to the interference of Fabry–Perot and additional waves which is a consequence of the polariton spatial dispersion. The main parameters of the exciton polaritons were determined from the spectra calculations. The Γ₄ excitons of big oscillator strength are shown to excite the additional polariton waves of the Γ₅ excitons of small oscillator strength, which interfere determining the fine structure in exciton resonance optical spectra.     

The lattice Boltzmann phononic lattice solid

I present a Boltzmann lattice gas-like approach for modeling compressional waves in an inhomogeneous medium as a first step toward developing a method to simulate seismic waves in complex solids. The method is based on modeling particles in a discrete lattice with wavelike characteristics of partial reflection and transmission when passing between links with different properties as well as phononlike interactions (i.e., collisions), with particle speed dependent on link properties. In the macroscopic limit, this approach theoretically yields compressional waves in an inhomogeneous acoustic medium. Numerical experiments verify the method and demonstrate its convergence properties. The lattice Boltzmann phononic lattice solid could be used to study how seismic wave anisotropy and attenuation are related to microfractures, the complex geometry of rock matrices, and their couplings to pore fluids. However, additional particles related to the two transverse phonons must be incorporated to correctly simulate wave phenomena in solids.     

Formation of plasmon pulses in the cooperative decay of excitons of quantum dots near a metal surface

The formation of pulses of surface electromagnetic waves at a metal–dielectric boundary is considered in the process of cooperative decay of excitons of quantum dots distributed near a metal surface in a dielectric layer. It is shown that the efficiency of exciton energy transfer to excited plasmons can, in principle, be increased by selecting the dielectric material with specified values of the complex permittivity. It is found that in the mean field approximation, the semiclassical model of formation of plasmon pulses in the system under study is reduced to the pendulum equation with the additional term of nonlinear losses.     

Complex conjugate media: Alternative configurations for miniaturized lasers

We show that complex conjugate materials, in which the ratio of the complex electrical permittivity and the complex conjugate magnetic permeability is real, are characterized by a real refractive index and thus allow non-attenuated propagation of electromagnetic waves. Although complex conjugated media obey the same Snell law as common right-handed non-magnetic materials with the same refractive index, they differ from the latter through the reflection and transmission coefficients of electromagnetic waves. The complex conjugate materials could have important applications in miniaturized optical amplifiers and lasers.     

Specific features of the spectral properties of a cholesteric liquid crystal with a resonance defective nanocomposite layer

This paper reports on studying the spectral properties of a cholesteric liquid crystal with a defective layer of a nanocomposite consisting of metallic nanoballs dispersed in a transparent matrix and characterized by an effective resonance dielectric permittivity. The transmission, reflection, and absorption spectra of waves of both circular polarizations have been calculated, and the spectral splitting of the defective mode when its frequency coincides with the resonance frequency of the nanocomposite has been studied. An essential dependence of the splitting on the nanoball concentration in the defect has been established. It has been shown that, depending on the position of the resonance frequency with respect to the boundaries of the cholesteric band gap, an additional passband appears in the transmission spectrum, which corresponds to waves of the diffracting circular polarization, or an additional band gap for waves of both circular polarizations, which are substantially modified with variations of both the incidence angle of light and the cholesteric helix pitch.     

单轴各向异性手征介质平板的反射和透射特性研究

研究了光轴平行于界面的单轴各向异性手征介质平板对平面电磁波的反射和透射特性, 推导出了反射和透射系数(功率)公式; 按介电常数的正负分4种情形给出了反射和透射功率曲线; 讨论了手征参数对反射和透射特性的影响, 特别是给出了伪布儒斯特角与手征参数的变化关系曲线. 关键词： 单轴各向异性手征介质 手征参数 伪布儒斯特角 反射和透射     

Measurements of Building Construction Materials at Ka-Band

Millimeter waves is expected to be used for indoor broadband wireless access for its rich frequency spectrum resources. To implement the indoor MMW wireless system, it is important to know its propagation characteristics in building, which are governed by the transmission properties of construction materials. This paper focuses on the measurements of reflection characteristics and refractive indices of some interior construction materials (such as glass, brick, plasterboard, silencing board, etc.) at Ka–band. The free–space reflection method was used to measure the reflection and transmission coefficients. Then the complex refractive indices of various materials could be calculated by using the Fresnel's formula.     

Interference of polariton waves in structures with wide GaAs/AlGaAs quantum wells

The optical reflection spectra of semiconductor GaAs/AlGaAs structures with wide quantum wells are studied experimentally. A theoretical analysis of the spectra is performed in terms of the exciton-polariton model in the approximation of quantum confinement of the exciton center of mass with regard to the contributions of both heavy and light excitons to the crystal polarization. The applicability range of the theory of the center-of-mass confinement for GaAs/AlGaAs heterostructures is estimated. It is established that, for quantum wells more than 180 nm wide, the interference effects observed in the reflection spectra of polariton waves are reproduced, to a good accuracy, by theoretical calculations based on the quantum confinement of the exciton center of mass. For quantum-well widths less than 150 nm, the experimental results are described better by the model of quantum confinement of electrons and holes.     

Propagation of waves and chaos in transmission line with strongly anharmonic dangling resonator

Delayed differential equation of motion with multiple lags is derived for an anharmonic stub resonator coupled to a monomode transmission line. Transmission and reflection coefficients are found analytically in the harmonic approximation. Nonlinear response of the system is analysed by an electric circuit obeying the same equations of motion. Enhanced second harmonic generation is found at the frequencies, which in the harmonic approximation correspond to the zeros of transmission. An aperiodic (chaotic) response is found mainly in the frequency range close to the resonance of the dangling resonator. Zeros of transmission and total transmissions are shown to be lifted by the anharmonicity nearly in the same frequency region. Higher harmonics are preferentially transmitted at the zero transmission points in the presence of anharmonicity. Received 14 March 2002 / Received in final form 25 November 2002 Published online 14 March 2003     

Phase of reflection of very low energy electrons at crystal surfaces

The amplitude coefficients of electron reflection at crystal surfaces are complex numbers, each of which may be characterized by a reflection intensity (the squared modulus of the coefficient) and a phase. The phase of reflection of very low energy (? 10 eV) electron reflection is described on the basis of existing theory, and experimental approaches to phase determination are reviewed. Theoretical properties of the phase are described on the basis of the two-beam dynamical theory of diffraction. The model considered is an idealized substrate crystal with an attached selvedge (surface region). The indirect effect of inelastic scattering (absorption) is included by going to complex values of the electron energy or of the surface-normal component K of the propagation vector. In the absence of a selvedge the phase is determined solely by the band structure of the substrate crystal. If a selvedge is present there are large additional effects on the phase associated with zeros of the amplitude coefficient of reflection on the complex K plane. The experimental approaches considered are: (1) measurement of the kinetic energy distributions of ions produced in the field ion microscope, and (2) measurement of the periodic deviations from the Schottky line in field-assisted thermionic emission and photo-emission. Recent results of phase determination for W (011) surface by method (1) are summarized and compared with theoretical expectations.     

Phase,zeros and poles of the transmission in quantum waveguides with an attached resonator and waveguide superlattices

This work reports on a study of electron transport in two-dimensionally-defined waveguide superlattices modeled by a lateral quantum waveguide with different numbers of attached quantum stubs. It is found that for the system with a single stub, the transmission amplitude exhibits pairs of zeros and poles in the complex-energy plane and the phase of the transmission coefficient drops sharply by π when the transmission passes a zero. This co-occurrence phenomenon of the transmission zero and the phase discontinuity is identical to the feature observed in a recent double-slit-like experiment by Schusteret al.[Nature385, 417 (1997)]. When two or more quantum stubs are attached to the quantum waveguide, each transmission zero seen in the single-stub structure develops into a group of zeros and the phase of the transmission coefficient shows, in correspondence to the group of zeros, a multiple-drop structure. However, not all poles of the waveguide superlattices are found to be paired with zeros and poles that are not paired with zeros are found to be located, in the complex energy plane, at the two sides of a multiple-zero region.     

Nodal lines,ergodicity and complex numbers

This article reviews two rigorous results about the complex zeros of eigenfunctions of the Laplacian, that is, the zeros of the analytic continuation of the eigenfunctions to the complexification of the underlying space. Such a complexification of the problem is analogous to studying the complex zeros of polynomials with real coefficients. The first result determines the limit distribution of complex zeros of `ergodic eigenfunctions' such as eigenfunctions of classically chaotic systems. The second result determines the expected distribution of complex zeros for complexifications of Gaussian random waves adapted to the Riemannian manifold. The resulting distribution is the same in both cases. It is singular along the set of real points.