Nonlinear diffraction in spontaneous three-wave and coherent four-wave light scattering by polaritons

Spontaneous three-wave and coherent four-wave scattering by polaritons in crystalline media with periodically modulated nonlinear quadratic susceptibility have been studied both theoretically and experimentally. Phase matching conditions and an expression for the scattering spectral line shape with due account of cascade processes in nonlinear diffraction for coherent Stokes polariton light scattering have been derived. Measurements of the light intensity distribution due to the three-and four-wave scattering in a LiNbO₃:Nd:Mg crystal with a periodic domain structure are in good agreement with theoretical results. The prospects for using the effects of nonlinear diffraction in spectroscopic studies of media with periodic distributions of nonlinear optical parameters, specifically, in precision measurements of the IR refractive index dispersion and determination of the period and profile of the quadratic susceptibility distribution are discussed. Zh. éksp. Teor. Fiz. 112, 2001–2015 (December 1997)     

Parametric and polariton scattering in noncentrosymmetric crystals

The work is dedicated to studying of the somewhat nontrivial effect of parametric light scattering (also known as parametric luminescence), which could be treated as an elastic scattering of photons in noncentrosymmetric media at vacuum fluctuations. The essence of the effect is the observation of a conic scattered light spectrum, the frequency of which is connected by means of simple dependence with the angle of scattering due to conservation laws for energy ( _p = _s + _i ) and momentum (k _p=k _s+k _i). The photon which propagates in a noncentrosymmetric medium is a mixed electromagnetic-mechanical exitation called the polariton.The theory of parametric light scattering in noncentrosymmetric crystals is given. Experimentally the effect was studied by means of two methods (photoelectric and photographic ones) in single-axial crystals of ADP, KDP, LiNbO₃ and biaxial crystal of a-HIO₃. The measurements fulfilled permitted us to find the eigenvalues of the refractive indexes of the crystals in the region of deep absorption of infrared radiation, where study of these characteristics is strongly hampered or even impossible.In the -HIO₃ crystal spectrum strange-looking polariton lines (without mutual pushing away when crossing, wide and diffuse, with sharp decreasing of the intensity with increasing to the scattering angle beginning after some value of it) were observed. The theory of the effect was constructed, computer simulation in the frame of which had shown that such resonant lines could exist, if one took into account the absorption in the medium.     

Hexagonal optical structures in photorefractive crystals with a feedback mirror

A nonlinear theory is presented for the formation of hexagonal optical structures in a photorefractive medium equipped with a feedback mirror. Oppositely directed beams in photorefractive crystals are unstable against the excitation of sideband waves. It is shown here that as this instability evolves to its nonlinear stage, the three-wave interaction between weak sideband beams does not stabilize it, but rather leads to explosive growth of the amplitudes of beams whose transverse wave vectors form angles that are multiples of π/3. As a result, sideband beams at these angles are found to be correlated. A range of parameters is found in which four-wave interactions saturate the explosive instability, which explains the appearance of stable hexagons in the experiment. Outside this region, nonlinearities of higher order saturate the explosive instability, and the process of hexagon generation must be studied numerically. Matrix elements are obtained for the three-and four-wave interactions as functions of the distance to the feedback mirror, and an equation for the time evolution of the sideband wave amplitudes is derived that describes the hexagon generation. A comparison is made with experimental results for the photorefractive crystals KNbO₃ and BaTiO₃. Zh. éksp. Teor. Fiz. 113, 1122–1146 (March 1998)     

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.     

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     

Enhanced backscattering in a magnetic field

Abstract

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 x ₃=ξ(x ₁), where the surface profile function ξ(x ₁) is a stationary stochastic Gaussian process. The plane of incidence is the x ₁ x ₃ plane, and the magnetic field is directed along the x ₂-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 +x ₁-direction is unequal to the (magnitude of the) wavenumber k _?(ω) for a surface polariton of the same frequency propagating in the ?x ₁-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 +x ₁-direction but not in the ?x ₁-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.     

Light scattering by electrons in the excitonic absorption region of GaAs

A study has been made of the effect of the additional generation of photoexcited electrons on the excitonic absorption and luminescence spectra of ultrapure GaAs samples at T=2 K. The observed increase in the absorption coefficient for the ground (n=1) excitonic state is shown to originate from the polariton character of the energy spectrum of this state and to be due to an increase of polariton damping. The increased damping observed under electron generation is caused by polariton scattering from hot electrons as the latter undergo thermalization. As a result, the polaritons are heated. The changes observed in the luminescence spectra are produced by the reverse effect of electron heating and polariton cooling. Fiz. Tverd. Tela (St. Petersburg) 39, 1011–1016 (1997)     

Anomalous light diffusion in ferroelectrics having a diffuse phase transition

It has been shown by using the statistical approach that the angular dependence of intensity I(θ) in multiple small-angle light scattering can be described by Lévy’s universal distribution functions. The fundamental property of the stability of these distributions permits one to extract information on the characteristics of fractal media as complete as it is possible in the simple single-scattering case. In particular, an analysis of the polarization characteristics of I(θ) in disordered PST reveals that the surface fractals observed in these crystals are of the heterophase rather than domain origin. Fiz. Tverd. Tela (St. Petersburg) 40, 1537–1541 (August 1998)     

Polariton parametric amplifier pump dynamics in the coherent regime

We studied the pump coherent dynamics in a II-VI microcavity parametric amplifier, using angle-resolved four-wave mixing. The polariton parametric amplification is found to result in a strong quenching and saturation of the pump coherence lifetime above the threshold. For the polariton scattering processes that remain below the amplification threshold, we find an angle-dependent collision broadening associated with the efficiency of the polariton scattering towards the excitonic reservoir.     

Resonant Mandelstam-Brillouin light scattering and Raman scattering in semiconductors with intermediate exciton states belonging to discrete exciton bands and the continuous spectrum

The results of a theoretical and experimental investigation of resonant Mandelstam-Brillouin light scattering by thermal acoustic phonons with k=0 near the direct absorption edge (in the case of ZnSe crystals) are analyzed. The appearance of a new type of resonant increase in the intensity of Raman scattering by optical phonons with k≠0, which corresponds to resonance with the scattered light in the output channel, near the indirect absorption edge (in the case of semi-insulating GaP:N crystals) is also reported. The resonant gain reaches ∼4×10³ at frequencies corresponding to overtone scattering assisted by LO(X) and LO(L) phonons. Exciton states belonging to both discrete exciton bands and to the continuous spectrum are considered as the intermediate states involved in the scattering processes in calculations of the resonant scattering tensors. In addition, all the intraband transitions, as well as the interband transitions between the conduction band, the valence bands, and the spin-orbit split-off band are taken into account, and good agreement with the experimental results is obtained. Fiz. Tverd. Tela (St. Petersburg) 40, 938–940 (May 1998)     

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.     

Electric-field-induced tetragonal phase in [Pb(Mg1/3Nb2/3)O3]0.68–[PbTiO3]0.32 by Raman scattering

ABSTRACT

The paper describes investigation of the electric-field-induced phase transition in PMN-xPT single crystals with x = 0.32 by means of detailed polarized Raman scattering measurements. Field-induced tetragonal state was reached by applying an electric field up to 30 kV/cm along pseudo-cubic direction at a temperature slightly below that of the zero-field rhombohedral–tetragonal phase transition (T_RT). In this field-induced tetragonal state, the angular dependencies of the polarized Raman spectra were recorded and compared with the similar data available for the rhombohedral single-domain and multidomain states.     

Counterpropagating Four-Wave Mixing in Ghost Imaging

Journal of Experimental and Theoretical Physics - The advantages of counterpropagating four-wave mixing in ghost imaging compared to three-wave parametric scattering in terms of an increase in the...     

Transmission spectra of thin CdS and CdSe crystals near higher-order isotropic points

Summary For photon energies below the absorption edge in CdS, CdSe and other II–VI crystals the polariton dispersion curves forE⊥c andE‖c (c-axis in a wurtzite crystal) corss at some points called isotropic points (IP). The occurrence of isotropic points provides the possibility of mode coupling between ordinary and extraordinary waves. Since the consequences of mode coupling on the optical properties for photon energies near the lowest IP lying much below the first excitonic state were widely discussed in recent years, more attention is now paid to isotropic points lying near the band gap and related to then=2,3, … excitonic states (?higher isotropic points?). Making use of Stahl's real density matrix approach we derive the polariton dispersion relationsk _⊥ (ω), andk _‖ (ω), for CdS and CdSe bulk crystals and determine the positions of IP's due to the crossing of theB-polariton with higherA-excitonic resonances. By the method of multiple internal reflection we calculate the transmission spectra for various crystal thicknesses (between 3 μm and 0.5 mm) and coupling mechanisms. The calculated transmission shows sharply peaked structures centred at the isotropic points.     

Theory of Raman light scattering by nanocrystal acoustic vibrations

A theory of Raman scattering of light by acoustic phonons in spherical nanocrystals of zinc-blende and wurtzite semiconductors has been developed with the inclusion of the complex structure of the valence band. The deformation-potential approximation was used to describe the exciton-phonon interaction. It is shown that this approximation allows only Raman scattering processes involving spheroidal acoustic phonons with a total angular momentum F=0 or 2. The effect of phonon quantum confinement on linewidth in Raman scattering spectra and scattered polarization is analyzed. An expression for the shape of the spectral line corresponding to nonresonant scattering from F=0 phonons was obtained. Fiz. Tverd. Tela (St. Petersburg) 41, 1473–1483 (August 1999)     

Dispersion and damping of a surface plasmon polariton on a one-dimensional randomly rough metal surface

Abstract

By the use of the reduced Rayleigh equation for the amplitude of a surface plasmon polariton on a one-dimensional randomly rough metal surface that is in contact with vacuum, we calculate the dispersion and damping of the surface electromagnetic wave to the lowest nonzero order in the rms height of the surface. It is found that the frequency of the surface plasmon polariton is depressed by the surface roughness. The attenuation of the surface plasmon polariton in the long wavelength limit is due primarily to its scattering into other surface plasmon polaritons, while in the short wavelength limit it is due primarily to its roughness-induced scattering into volume electromagnetic waves in the vacuum. The energy mean free path of the surface plasmon polariton is shorter on a randomly rough metal surface than it is on a lossy planar metal surface, and the surface plasmon polariton is more tightly bound to a rough surface than to a planar one.     

Excitonic polariton dispersion in CuBr determined by resonant Raman scattering under two-photon excitation of excitonic molecules

The excitonic polariton dispersion in wide k-space for k∥[111] is measured through the two-photon-resonant Raman scattering with the use of the double beam excitation technique. The k-linear effect, the heavy and light masses and the polariton effect of the Z_1,2 exciton are clarified.     

Torque equations for spin and orbital angular momenta of radiation fields and Faraday effect

The spin angular momentum S of light has never been linked to the Faraday rotation of light traveling in an optically active medium possessing a rotational invariance of a crystal, because there was no helicity term associated with the phase shift in the previous torque equation for S. In order to relate the change in S with time to the Faraday rotation, therefore, we derived an exact torque equation for S. As a result, a magnetic helicity term appeared in a new torque equation for S, so that one-half of the phase shift derived from the helicity term was equivalent to the Faraday rotation angle. However, the orbital angular momentum L had no relation to the Faraday rotation. It was thus clarified that the change in S with time is related to the Faraday rotation angle of light traveling in an optically active medium, owing to the appearance of the helicity term without a rotational invariance around the optical axis. It was also demonstrated theoretically that the Faraday rotation is accompanied by a torque acting on the crystal so that the total angular momentum of light and matter is conserved.     

Quantum theory of polaritons with spatial dispersion: Exact solutions

Summary We give the exact solution of the quantum polariton problem with spatial dispersion. The exact polariton eigenstates are obtained in terms of photon and polariton states. For all values ofk a nonlinear contribution of the photon and polarization states is present in the polariton wave function. Two- and three-photon components are explicitly singled out.

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Riassunto Si presentano le soluzioni esatte del problema quantistico del polaritone con dispersione spaziale. Gli autostati polaritonici esatti sono ottenuti come combinazioni di stati fotonici e di stati di polarizzazione. Contributi non lineari di fotoni e di quanti di polarizzazione sono presenti a tutti i valori dik. Componenti a due fotoni e a tre fotoni sono date in forma esplicita.