Light-scattering Process Research Articles

Coupled dipole method with an exact long-wavelength limit and improved accuracy at finite frequencies

We present a new formulation of the coupled dipole method that accounts for local-field effects and is exact in the long-wavelength limit. This formulation also leads to improved accuracy of the description of light-scattering processes at finite frequencies.

A Negative Branch of Polarization for Comets and Atmosphereless Celestial Bodies and the Light Scattering by Aggregate Particles

Optical observations of comets and atmosphereless celestial bodies show that a change of sign of the linear polarization of scattered light from negative to positive at phase angles less than ≈ 20° is typical of the cometary coma, as well as of the regolith of Mercury, the Moon, planetary satellites, and asteroids. To explain a negative branch of polarization, this research suggests a unified approach to the treatment of cometary-dust particles and regolith grains as aggregate forms. A composite structure of aggregate particles resulting in the interaction of composing structural elements (monomers) in the light-scattering process is responsible for the negative polarization at small phase angles, if the monomer sizes are comparable to the wavelength. The characteristics of single scattering of light calculated for aggregates of this kind turned out to be close to the properties observed for cometary dust. Unlike the cometary coma, the regolith is an optically semi-infinite medium, where the interaction between particles is significant. To find the reflectance characteristics of regolith, the radiative-transfer equation should be solved for a regolith layer. In this case, the interaction between scatterers can be modeled to a certain extent by representing the regolith grains as aggregate structures consisting of several or many elements. Although real regolith grains are much larger than the particles considered here, laboratory measurements have shown that it is precisely the surface irregularities comparable to the wavelength that cause a negative branch of polarization. The main observed features of the phase and spectral dependence of the linear polarization of light scattered from comets and atmosphereless celestial bodies, which are due to the difference of the elementary scatterers in composition, size, and structure, can be successfully explained using the aggregate model of particles.

Investigating non-Gaussian scattering processes by using nth -order intensity correlation functions

Dynamic light-scattering techniques provide noninvasive probes of diverse media, such as colloidal suspensions, granular materials, or foams. In homodyne photon correlation spectroscopy, the dynamical properties of the medium are extracted from the intensity autocorrelation g(2)(τ) of the scattered light by means of the Siegert relation g(2)(τ)=1+|〈E(0)E*(τ)〉|2/〈EE*〉2. This approach is unfortunately limited to systems where the electric field is a Gaussian random variable and thus breaks down when the scattering sites are few or correlated. We propose to extend the traditional analysis by introducing intensity correlation functions g(n) of higher order, which allow us both to detect non-Gaussian scattering processes and to extract information not available in g(2) alone. The g(n) are experimentally measured by a combination of a commercial correlator and a custom digital delay line. Experimental results for g(3) and g(4) are presented for both Gaussian and non-Gaussian light-scattering processes and compared with theoretical predictions.

Picosecond quantum-beat spectroscopy of quadrupole polaritons in Cu2O.

Quantum beats in picosecond time-resolved resonance fluorescence are investigated in ${\mathrm{Cu}}_{2}$O for the yellow 1S quadrupole exciton polariton. In order to obtain information on the coherence of the resonant intermediate polariton states, we have studied the electric-dipole allowed light-scattering processes involving one and two ${\mathrm{\ensuremath{\Gamma}}}_{3}^{\mathrm{\ensuremath{-}}}$ phonons. A quantitative analysis provides exciton-polariton coherence times of about 1 ns at 2 K, decreasing with higher temperatures and larger wave vectors due to phonon scattering. From the magnetic-field dependence, low-field g values are determined with high accuracy. The measurements permit a clear distinction between Raman and hot-luminescence-like contributions to the scattering intensity. The strong effect of the spectral width of the excitation pulse on the time behavior of the scattering, as well as the temperature dependence of the coherence time, indicate that it is essential to take into account the polariton character.

Two-dimensional imaging of sprays with fluorescence, lasing, and stimulated Raman scattering

Two-dimensional fluorescence, lasing, and stimulated Raman scattering images of a hollow-cone nozzle spray are observed. The various constituents of the spray, such as vapor, liquid ligaments, small droplets, and large droplets, are distinguished by selectively imaging different colors associated with the inelastic light-scattering processes.

Self-induced stimulated light scattering.

The laser-induced collective rotation of molecules in a liquid crystal is treated as a novel stimulated light-scattering process in which the Stokes shift is not constant but is induced by a pump field. The solution following the usual coupled-wave approach appears as a nonlinear eigenvalue problem and exhibits bistable behavior.

Recombination of hydrogen atoms via free-to-bound Raman transitions

The recombination of atomic hydrogen to form ${\mathrm{H}}_{2}$ in its electronic ground state $X^{1}\ensuremath{\Sigma}_{g}^{+}$ via a Raman light-scattering process is considered. A rate coefficient is obtained in two approximations. For wavelengths of light much above that of Lyman $\ensuremath{\alpha}$, the polarizability theory is used to compute a recombination rate coefficient, which amounts to \ensuremath{\cong} ${10}^{\ensuremath{-}39}$ ${\mathrm{cm}}^{6}$/s at a wavelength of $\ensuremath{\lambda}=2000$ \AA{} and features a $\frac{1}{{\ensuremath{\lambda}}^{4}}$ dependence. For wavelengths approaching that of Lyman-$\ensuremath{\alpha}$ a sum over states, suitably truncated, is used. For wavelengths from 1220 to 1600 \AA{}, where resonance behavior occurs, values for the rate coefficient of \ensuremath{\cong} ${10}^{\ensuremath{-}34}$ ${\mathrm{cm}}^{6}$/s and greater are obtained nearly independent of temperature (100- 10 000 K).

Brillouin scattering of light by spin waves in thin ferromagnetic films (invited)

The new technique of Brillouin scattering from spin waves has been applied to thin ferromagnetic films. Scattering from standing spin waves and the Damon Eshbach (DE) surface wave is observed. The interaction of both types of waves at a mode crossing in Fe films under variation of the thickness d is investigated. The results suggest the absence of surface anisotropy and pinning. For d≲20 nm scattering from standing modes becomes too weak to be observed. In contrast to this, for the DE mode there is a strong increase in the scattering intensity when the films have been evaporated onto the proper substrates. It is shown that this is due to both an increase in the thermal DE mode amplitudes and multiple interference effects in the lightscattering process. Very strong scattering is obtained from films with d≊5 nm. There is also a remarkable Stokes-Antistokes asymmetry, which persists down to d≲3 nm. It comes from the elliptical spin-precession characteristic for such small values of d and the strong metallic attenuation of the light. The technique has also been applied to an investigation of the coupling of DE modes in double layer systems.

Role of elastic exciton-defect scattering in resonant Raman and resonant Brillouin scattering in CdSe

We report a detailed resonant Brillouin and Raman study in the wurtzite semiconductor CdSe in the vicinity of its lowest-energy $A$ exciton. By using a spectrometer and laser system with a combined spectral resolution of 0.16 ${\mathrm{cm}}^{\ensuremath{-}1}$ we were able to measure the widths and line shapes of Raman and Brillouin modes. In a nominally undoped CdSe sample we found that wave vector is conserved in the light-scattering process only for incident photon frequencies below the longitudinal exciton frequency. For incident laser frequencies above the longitudinal exciton frequency, scattering processes which do not conserve wave vector became dominant. We propose that this breakdown in wave-vector conservation is due to elastic exciton-defect scattering, and our results are in qualitative agreement with the predictions of the elastic exciton-defect scattering theory of Gogolin and Rashba. In another CdSe sample doped with Li, we found that its Raman and Brillouin spectra are always dominated by wave-vector-nonconserving modes even for incident photon frequencies below the $A$-exciton frequency. From the Brillouin spectra we deduced the following parameters for the $A$ exciton in CdSe: ${M}_{\ensuremath{\perp}} (\mathrm{exciton}\mathrm{mass}\mathrm{perpendicular}\mathrm{to}\mathrm{the} c \mathrm{axis})=0.40{m}_{0}$ (free electron mass), ${M}_{\ensuremath{\parallel}}\ensuremath{\sim}1.3{m}_{0}$, ${\ensuremath{\omega}}_{T} (\mathrm{transverse}\mathrm{exciton}\mathrm{frequency})=14713$ ${\mathrm{cm}}^{\ensuremath{-}1}$ (at \ensuremath{\sim}10 K), and the splitting between longitudinal and transverse exciton frequencies is 4 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Static and dynamic Kerr-effect studies of glycerol in its highly viscous state

Static and dynamic Kerr-effect studies have been made for glycerol in the range 205–255 K. The static measurements indicate extensive association of the molecules and that this increases with decreasing temperature, in accord with the results of dielectric studies. The dynamic Kerr effect shows one, near single-relaxation time, process at all temperatures with the rise and decay correlation times being related according to τK,r=(1.45 ± 0.20)τK,d. Dielectric relaxation measurements made concurrently with the Kerr-effect relaxation measurements show that τD≈(½)τK,d. The relationships between the relaxation of the Kerr effect, dielectric ultrasonic and dynamic light-scattering processes are discussed in terms of the structural relaxation mechanism and cross-correlation functions which appear for each technique. The Kerr-effect relaxation is slower than that for dielectric relaxation at a given temperature which is, in turn, slower than that for the light-scattering relaxation. The importance of mixed Rayleigh and Mountain relaxation for the latter is discussed in relation to the theory of Demoulin and co-workers.

Diffusing droplet model for Rayleigh linewidth studies on critical fluids

Measurements of the intensity autocorrelation of light scattered from diffusing micropheres suspended in a normal fluid show that if the particle radii satisfy the condition $l\ensuremath{\lesssim}{\ensuremath{\lambda}}_{0}$ where ${\ensuremath{\lambda}}_{0}$ is the wavelength of the incident light, and if the suspension is polydisperse (a finite-width particle-size distribution), the experimental diffusion constant displays a dependence upon the scattered wave number $k$ which is qualitatively the same as that for a critical fluid system in the nonhydrodynamic ($k\ensuremath{\xi}\ensuremath{\gtrsim}1$) regime. These experimental observations have led us to propose a model of a critical fluid in which the order-parameter fluctuations are considered as spherical molecular clusters, or droplets, performing Brownian motion in a normal host fluid. The droplets are assumed to have a Gaussian index of refraction spacial profile, and a particle-size distribution $N(l)$ characterizing the suspension determined from the requirement that the scattered light intensity be of the modified Ornstein-Zernike form. In a first approximation, the droplets are assumed to diffuse without changing size for times of the order of the characteristic diffusion time. The intensity-autocorrelation function of light scattered by our model system of diffusing droplets is evaluated, and the effective Rayleigh linewidth is found to agree to within a constant factor of order 1 with the ansatz for the critical part of the Rayleigh linewidth chosen by Perl and Ferrell. The resulting line-shape function is nearly Lorentzian, except in the wings where experimental detection of a departure from Lorentzian behavior becomes extremely difficult. Our droplet-size distribution is very similar to that which results from the static droplet model of Fisher which has been applied successfully to describe static critical phenomena in fluids below the critical temperature. In the diffusing droplet model, the $k$ dependence of the diffusion constant extracted from light-scattering measurements on critical fluids is seen to be an artifact introduced by the light-scattering process, and introduces no new physical information concerning the critical fluid behavior which is not contained in the droplet-size distribution function.

Fluctuations and light scattering in superionic conductors

We present a theory of the dynamics of the coupled crystalline-cage-charged-liquid fluctuations in superionic conductors. The dispersion relations of the coupled modes are obtained together with the imaginary parts of their self-energies, which determine, among other things, the acoustic attenuation. The light-scattering process due to these fluctuations is studied and we show that it can provide unique information about local site symmetries and hopping times. The nature of the thermal fluctuations is discussed near a critical point.

Linewidths and Two-Electron Processes in Spin-Flip Raman Scattering from CdS and ZnSe

We present inelastic-light-scattering data and analyses for spin-flip scattering from conduction electrons in CdS and ZnSe. Cross sections, linewidths, and line shapes are studied as functions of magnetic field, temperature, scattering angle, and donor concentration. Both free-conduction-electron spin-flip processes and spin-flip processes involving conduction electrons bound to shallow donors are observed. These processes exhibit different selection rules and temperature dependences; the free-electron spin-flip processes exhibit only ${\ensuremath{\alpha}}_{\mathrm{ij}}$ scattering in which $i\ensuremath{\ne}j$ and $i$ or $j\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ as expected, while the bound-electron spin-flip processes also exhibit strong ${\ensuremath{\alpha}}_{\mathrm{xx}}$ and ${\ensuremath{\alpha}}_{\mathrm{yy}}$ scattering ($z$ is the [0001] optic axis), in agreement with the selection rules calculated for shallow donors at ${C}_{3V}$ Cd sites by Thomas and Hopfield. For right-angle scattering, the free-electron linewidth increases from 0.05 ${\mathrm{cm}}^{\ensuremath{-}1}$ (half-width at half-height) at 2 \ifmmode^\circ\else\textdegree\fi{}K to about 4 ${\mathrm{cm}}^{\ensuremath{-}1}$ at \ensuremath{\sim} 150 \ifmmode^\circ\else\textdegree\fi{}K in both ZnSe and CdS. This broadening is not due to a decrease in spin lifetime, but rather to a spin diffusion, as directly confirmed by the angular dependence of the spin-flip linewidth. The linewidth is observed to vary as ${q}^{2}$, where $q$ is the momentum transfer in the light-scattering process. Bound-electron scattering exhibits a linewidth which is independent of scattering angle and nearly independent of temperature over the 2-150 \ifmmode^\circ\else\textdegree\fi{}K range. The spin-diffusion model is thus not applicable to bound-electron scattering. The double spin-flip process observed involves two interacting electrons with an apparent attractive energy of 0.25 \ifmmode\pm\else\textpm\fi{} 0.05 ${\mathrm{cm}}^{\ensuremath{-}1}$. Selection rules, relative cross sections, field dependence, and binding energy of the double spin-flip transition are discussed. At sufficiently high input powers (\ensuremath{\ge}3 MW/${\mathrm{cm}}^{2}$) the CdS single spin-flip scattering becomes stimulated, resulting in a tunable, visible, spin-flip laser.

Visibility and small-ion density

The similarity of the light-scattering process to the process of ion attachment on airborne scatterers is examined. Under the assumption that particle concentration and size are the main factors influencing visibility and ion-density fluctuation in the lower atmosphere, it is shown by analysis that a correlation exists between electrical and optical properties of a turbid atmosphere. Experiments led to the derivation of an empirical formula. Correlation coefficients in the viability range of 2 km to 100 km and over periods up to 8 hours were in the range of 0.90 to 0.95. Deviations occurred when triboelectric charges were being generated by strong winds and during the dissipation of fog. It appears that the rate of production for negative small ions is increased by at least a factor of 2 during fog dissipation.