Enhanced backscattering in a magnetic field

By means of numerical simulations the authors study the scattering of a beam of p-polarized light from a small RMS slope one-dimensional random surface on a semi-infinite metal or n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x₃=ξ(x₁), where the surface profile function ξ(x₁) is a stationary stochastic Gaussian process. The plane of incidence is the x₁x₃ plane, and the magnetic field is directed along the x₂-axis. In the presence of the magnetic field the dispersion curve for the surface polaritons supported by the surface in the absence of the random roughness becomes non-reciprocal, i.e. the wavenumber k₊(ω) for a surface polariton of frequency ω propagating in the +x₁-direction is unequal to the (magnitude of the) wavenumber k_-(ω) for a surface polariton of the same frequency propagating in the -x₁-direction. As a consequence of this they find that the peak in the angular distribution of the intensity of the incoherent component of the scattered light that is observed in the retroreflection direction in the absence of the magnetic field—enhanced backscattering—is shifted in the direction of larger scattering angles with increasing magnetic field strength. At the same time the width of the peak increases and its amplitude decreases. When the frequency of the incident light is high enough that the dispersion curve for surface polaritons on the planar surface becomes completely non-reciprocal, i.e. the surface polariton propagates only in the +x₁-direction but not in the -x₁-direction, the enhanced backscattering is completely suppressed. These results are interpreted as being due to the breakdown of the coherency between a given light/surface polariton path that contributes to backscattering and its time-reversed partner, caused by the removal of time-reversal symmetry from the scattering system by the application of the external magnetic field. They provide strong evidence for the fundamenlal role played by surface polaritons in the enhanced backscattering of light from small RMS slope random surfaces.     

Surface phonon–polaritons in rectangular quantum wires of polar ternary mixed crystals

In this paper, the dispersion relations of surface phonon–polaritons in freestanding rectangular quantum wire systems of polar ternary mixed crystals are derived. The numerical calculations for Al_xGa_1−xAs and Zn_xCd_1−xSe quantum wire systems are performed. The results reveal that the frequencies of surface phonon–polariton modes are sensitive to the geometric structures of the quantum wires, the wave-vectors in z-direction, and the compositions of the ternary mixed crystal materials. The effects of the “two-mode” and “one-mode” behaviors of the ternary mixed crystals on the surface phonon–polariton modes are also discussed.     

Inverse Raman Scattering by Polaritons in LiNbO3 Single Crystals

Experimental studies of IRS by polaritons in LiNbO₃ are reported for the first time. In compliance with the classification of IRS-scattering geometries by polaritons in uniaxial crystals [3] for different polarisation directions of laser and anti-Stokes continuum two A₁-type polaritons and also E-type-polaritons of the upper and the lower ordinary dispersion branches, respectively, could coherently be generated. Introducing a new polariton specific excitation state instead of the mechanic vibration the shortened IRS equations without small signal approximation are solved in the stationary case and for “responseless” polariton fields. The increase of the laser field and the decrease of the anti-Stokes field show for α_px ? 1 the same behaviour as Stokes growth and laser depletion, respectively, in the case of SRS by dipole inactive levels. Model calculations show the necessity of the used intra cavity arrangement for photographic registration of IRS-polariton spectra.     

Effect of quantizing magnetic field on the spectrum and damping of polaritons in double two-dimensional electronic systems

Nonradiative (surface and bulk) polaritons in a semiconductor structure composed of two heterojunctions GaAs/Al_xGa_1?x As are investigated under the integer quantum Hall effect (IQHE) conditions. The dispersive, polarization, and energy characteristics of these polaritons are determined including energy dissipation in the two-dimensional electron semiconductor layers. The phase and group velocities of surface and bulk polaritons are shown to be quantized under the IQHE conditions. It is found that resonance coupling of two surface polariton modes may occur in double GaAs/Al_xGa_1?x As heterojunctions. Possible experimental observation of nonradiative polaritons is discussed.     

Effective-medium approach for surface-localized magnetic polaritons in magnetic (ferromagnetic and antiferromagnetic) superlattices

The general effective-medium dispersion relations are derived for surface-localized magnetic polaritons which propagate parallel to the surface between a superlattice and semi-infinite bulk material, as applied to ferromagnetic and antiferromagnetic superlattices, in the situation when a static magnetic field is applied in the plane of the layers and parallel to the magnetization. The dependence of the energy of the surface waves on the volume fraction of the ferromagnetic superlattice component and the influence of the external magnetic field on the spectrum of the surface magnetic polaritons for the antiferromagnetic superlattice are investigated. The spectrum of the surface-localized magnetic polaritons which appear at the junction of the magnetic (ferromagnetic and antiferromagnetic) superlattice with the magnetic material are more complex, in contrast to the cases of semi-infinite magnetic material or semi-infinite magnetic SL. It is essential that in all cases in the presence of the external magnetic field the spectrum of the magnetic polaritons are non-reciprocal. The properties of surface polaritons are discussed in detail for the system ferromagnetic superlattice (YIG/non magnet)/YAG and the antiferromagnetic superlattice (MnF₂/ZnF₂)/FeF₂.     

Enhanced backscattering in a magnetic field

By infinite-order perturbation theory the authors study the scattering of p-polarized light from a small-amplitude random grating ruled on the surface of a metal or an n-type semiconductor to which a constant magnetic field is applied. The surface is defined by the equation x₃=ζ(x₁), where the surface profile function ζ(x₁) is a stationary, stochastic, Gaussian process. The plane of incidence is the x₁x₃ plane, and the magnetic field is directed along the x₂ axis. We find that the position of the peak in the angular distribution of the intensity of the incoherent component of the scattered light that is observed in the retroreflection direction in the absence of the magnetic field—enhanced backscattering—is shifted in the direction of larger scattering angles from the retroreflection direction with increasing magnetic field strength. At the same time the width of the peak increases and its amplitude decreases. This is interpreted as due to the breakdown of the coherency between the contribution to backscattering from a given light/surface polariton path and from its time-reversed partner, caused by the removal of time reversal symmetry from the scattering system by the application of the external magnetic field. The latter is manifested by the non-reciprocity of the surface polariton dispersion relation in the presence of the magnetic field.     

Four-wave polariton scattering of light in LiNbO3

Four-wave Stokes k-spectra for light scattering on polaritons in lithium niobate crystals with an Mg impurity are studied experimentally. The mechanisms for direct, cascade, coherent, and incoherent four-wave mixing of light are discussed in the course of interpreting the angular dependences of the scattered light intensity. It is shown that the dispersion of the real part of the polariton wave vector and the refractive index of the crystals at the polariton frequencies can be measured with an order of magnitude greater accuracy than by spontaneous three-wave polariton light scattering. A significant discrepancy is found between determinations of the polariton absorption coefficient from the angular spectra of three-wave scattering and four-wave scattering in terms of the model employed here. Zh. éksp. Teor. Fiz. 112, 441–452 (August 1997)     

Raman scattering by hot and thermal polaritons in crystal quartz

Summary Nonlinear mixing of IR and visible radiation,i.e. coherent Raman scattering by polaritons driven by a CO₂ laser, has been used to obtain the dispersion curve and its width inq-space of the polariton associated to theE-phonon at 1065 cm⁻¹ in crystal quartz. It is shown in this paper that a direct method to determine indipendently, with high precision, the refractive index and absorbance of a crystal can be obtained in this way. The results are compared with accurate data obtained from Raman scattering by polaritions in thermal equilibrium and very good agreement is found between the two measurements. It is finally shown that nonlinear-mixing techniques turn out to be completely consistent with the simple picture of scattering of light by hot polaritons. This work was supported by the Italian Consiglio Nazionale delle Ricerche del Ministero della Pubblica Istruzione.     

Absolute cross sections for collision-induced depolarized scattering of light in krypton and xenon

Depolarized Raman spectra of binary collisional pairs of atoms in krypton and xenon are obtained at gas densities of 1–10 amagat. Absolute intensities relative to a known rotational transition of nitrogen are determined. For light of 4880 Å wavelength incident in the x-direction, polarized in the z-direction and scattered in the y-direction of a cartesian frame x, y, z, at a frequency shift of -12 cm^-1, the differential scattering cross section per unit wavenumber band times volume, is found to be 1·10 × 10^-52 cm⁶ ± 10 per cent for krypton, and 4·76 × 10^-52 cm⁶ ± 10 per cent for xenon, if the sum of both polarizations is considered. Wave-mechanical and classical computations reproduce both the shape and the intensity of the experimental spectra if the so-called point-dipole model of the anisotropy of the polarizability of collisional pairs of atoms is used. Other models of the anisotropy are seen to be overcorrected by these criteria.     

Resonant and surface polaritons in quantum wells

Summary We show how the breaking of the translational invariance in a quantum well modifies the concept of polariton with respect to that defined for bulk material. Polaritons in quantum wells result from the combination of the exciton states with the radiation field. They are here obtained as the solutions of Maxwell equations with retardation, provided an appropriate nonlocal response function is used for the electric susceptibility, and Maxwell boundary conditions are imposed. We find two types of polaritons depending on the values of the in-plane wavevectork _II: those atk _II<ω/v (wherev=c/n is the velocity of light in the sample) are resonant with the radiation field in the barrier and those atk _II>ω/v cannot be coupled to waves in the barrier. In both cases explicit expressions are given for radiative shifts and radiative broadenings as functions ofk _II. Numerical results are obtained for GaAs-Ga_1−x Al _x As and for CuCl quantum wells and new experiments are suggested. The existence of resonant and surface polaritons justifies an interpretation of the temperature dependence of the radiative lifetime suggested by the same authors. It also decreases the radiative efficiency in the direction perpendicular to the planes and increases the radiative efficiency parallel to the planes with increasing temperature. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces

Abstract

Using the unitarity and reciprocity preserving formulation of Brown et al a perturbation treatment, correct to fourth order in the surface profile function, is given for the scattering of electromagnetic waves from a weakly rough, two-dimensional, random metal surface. In this formulation the boundary conditions on the electromagnetic fields are satisfied using the extinction theorem in conjunction with the Rayleigh hypothesis and the vector equivalent of the Kirchhoff integral. The theory is applied to, and results are presented for, several different types of rough surfaces which are characterized by power spectra that are extensions to two-dimensional random surfaces of the power spectrum of some one-dimensional random surfaces recently fabricated by West and O'Donnell. These surfaces, which can be realized experimentally, favor coherent, interferent, multiple scattering of electromagnetic waves via surface plasmon polaritons in intermediate states, and clearly exhibit enhanced backscattering caused by the surface plasmon polariton mechanism. Theoretical results are presented for silver surfaces at optical wavelengths.     

Observation of magnetoplasma type surface polaritons on n-InSb

Surface polariton dispersion curves have been obtained for an n-InSb—air interface in a magnetic field using the ATR method and are found to be in qualitative agreement with theory. In particular the curves show the predicted non-reciprocal nature of the surface polariton propagation, and the appearance of virtual excitation type branches of the dispersion curves. On the basis of data obtained in zero magnetic field on etched surfaces, the quantitative differences between experimental and theoretical dispersion curves are attributed to surface damage.     

Diamagnetism of microcavity polaritons induced by spin-dependent polariton–polariton interactions

Diamagnetism of condensed microcavity polaritons in a vertically applied magnetic field is theoretically studied by using the density of free energy of polaritons. The magnetic dependence of polariton–polariton interactions and spin polarization degree of polaritons are derived, and are used to show the diamagnetic behavior of the polariton spin polarization, which is discussed for GaAs-based microcavities. We show that for strong magnetic field the spin polarization of the polaritons is paramagnetic as usual, while around positive exciton–photon detuning and special Rabi splitting, the spin polarization of the polaritons could be diamagnetic. In addition, weak magnetic field and high polariton density are beneficial to observe the polariton diamagnetism.     

Surface polaritons in a dielectric at a boundary with a metal in crossed electric and magnetic fields

AbstractThe spectrum of surface polaritons in a dielectric at a boundary with an ideal metal or a super-conductor in crossed constant electric and magnetic fields is studied. It is shown that the polariton spectrum possesses strong nonreciprocity (polaritons with fixed frequency propagate only in one direction; this is the rectification effect) and depends strongly on the directions of the external fields and their ratios H ₀/E ₀.     

Scattering approach to the von Klitzing effect

Earlier results of the scattering theoretical approach to the quantum Hall effect are simplified and generalized. Finite size corrections to the plateau values are found to be not of order (l/L _x ) but (l ² /L _x L _y )²,l,L _x ,L _y being the magnetic length, and the sample dimensions inx andy-direction respectively. An expression for the current parallel to the electric field in terms of a scattering matrix is derived. In the weak scattering regime this expression leads to a vanishing diagonal conductivity _xx .     

Quantum optical effects in semiconductor microcavities

Investigations of quantum effects in semiconductor quantum-well microcavities interacting with laser light in the strong-coupling regime are presented. Modifications of quantum fluctuations of the outgoing light are expected due to the non-linearity originating from coherent exciton–exciton scattering. In the strong-coupling regime, this scattering translates into a four-wave mixing interaction between the mixed exciton–photon states, the polaritons. Squeezing and giant amplification of the polariton field and of the outgoing light field fluctuations are predicted. However, polariton–phonon scattering is shown to yield excess noise in the output field, which may destroy the non-classical effects. Experiments demonstrate evidence for giant amplification due to coherent four-wave mixing of polaritons. Noise reduction below the thermal noise level was also observed. To cite this article: E. Giacobino et al., C. R. Physique 3 (2002) 41–52     

Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces

Using the unitarity and reciprocity preserving formulation of Brown et al a perturbation treatment, correct to fourth order in the surface profile function, is given for the scattering of electromagnetic waves from a weakly rough, two-dimensional, random metal surface. In this formulation the boundary conditions on the electromagnetic fields are satisfied using the extinction theorem in conjunction with the Rayleigh hypothesis and the vector equivalent of the Kirchhoff integral. The theory is applied to, and results are presented for, several different types of rough surfaces which are characterized by power spectra that are extensions to two-dimensional random surfaces of the power spectrum of some one-dimensional random surfaces recently fabricated by West and O'Donnell. These surfaces, which can be realized experimentally, favor coherent, interferent, multiple scattering of electromagnetic waves via surface plasmon polaritons in intermediate states, and clearly exhibit enhanced backscattering caused by the surface plasmon polariton mechanism. Theoretical results are presented for silver surfaces at optical wavelengths.     

Microcavity polariton scattering probed by coherent control experiments

We present coherent control experiments which simultaneously probe both the coherence and the population dynamics of the exciton–photon polariton states in a semiconductor microcavity. The coherent manipulation of either the spin orientation or the density of polaritons is demonstrated leading to the measurement of the optical dephasing time. The polariton scattering by acoustical phonons or by mutual collision processes are investigated by a simultaneous measurement of both the optical dephasing time T₂and the decay time T₁of the radiant states. These results clearly evidence a quenching of the different scattering processes at resonance.     

Multiple light scattering from metal and dielectric rough surfaces

Abstract

A numerical study is done on light scattering from one-dimensional random rough surfaces supporting both dielectrics and metals. The influence of the corrugation on the Brewster angle as well as on the angular distribution of transmitted intensity into the dielectric is investigated. The authors also obtain enhanced backscattering in the light reflected from metallic surfaces. Finally they discuss the influence of roughness on the drop of reflectance due to polariton absorption.     

Dispersion of Exciton Polaritons in Terbium Nitrate Hexahydrate

The dispersion relations of exciton polariton waves in terbium nitrate hexahydrate are determined based on the model of the interaction of electromagnetic waves with resonant electronic states of Tb³⁺ ions at the ⁵D₄–⁷F₆ transition. Frequencies of unitary polaritons characterized by refractive indices equal to unity are determined. It is shown that the group velocity of electromagnetic waves in the region of unitary polaritons is lower than the speed of light in vacuum by several orders of magnitude. A sharp increase in the efficiency of photoluminescence and Raman scattering is predicted in the case where the excitation radiation frequency approaches the unitary polaritons frequency.