Theory Of Brillouin Research Articles

Theory of Brillouin scattering on a surface grating: Role of surface polaritons.

In a recent paper [W. M. Robertson et al., Phys. Rev. B 41, 4986 (1990)] an empirical and unexplained selection rule governing light scattering by surface acoustic waves on corrugated metal surfaces has been found experimentally, whenever a surface polariton acts as an intermediate state giving rise to a Rayleigh wave replica in the spectra. The replica occurs only when the scattered light is s polarized, independently of the incident polarization. In this paper the Brillouin cross section for a corrugated surface is evaluated theoretically within the extinction-theorem formalism and the above-mentioned selection rule is shown to be valid in the limit of large dielectric constant.

On the quantum theory of Brillouin scattering of dielectric layered media

The theory of Brillouin scattering of dielectric layered elastic media is formulated in a way that also treats the electromagnetic field quantum mechanically. The general expression for the cross section obtained by this approach is applied to the investigation of shear horizontal modes in the Brillouin spectrum of finite and semi-infinite dielectric superlattices.

Magnetism of neutron-damaged alpha-quartz

Abstract Static magnetic susceptibilities have been measured on an α-quartz single crystal that had been irradiated with fast neutrons. Above 65 K, the radiation-induced paramagnetism obeys the Curie law, indicating the presence of non-interacting centres. The low-temperature measurements result in a field-dependent susceptibility comparable to the effect of the Brillouin saturation of non-interfacing centres. The average moment per centre, however, is higher than the one due to the spin only of single unpaired electrons, pointing to ferromagnetically coupled electron pairs. When the calculated susceptibility values, as obtained from the derived moments and concentrations using the Brillouin theory, are subtracted from the measured data, then the differences behave—over the whole temperature range—as the susceptibility of antiferromagnetically coupled electrons. On the same sample also, low-temperature 20.9 GHz ESR measurements have been carried out. The major resonance line is attributed to the E’ centre...

Guided acoustic-wave Brillouin scattering.

Forward light scattering by the thermally excited guided acoustic modes of an optical fiber produce numerous narrow lines not predicted by the usual theory of Brillouin scattering. Optical heterodyne detection has been used to resolve the scattering spectrum which begins at about 20 MHz and extends to the detection limit. A simple theory quantitatively accounts for the frequencies, polarizations, and intensities of the components. The light scattering from these modes constitutes a thermal-noise source in optical fibers that may prove significant in other experiments.

Resolved forward Brillouin scattering in optical fibers.

Forward light scattering by the thermally excited acoustic eigenmodes of an optical fiber produce numerous narrow lines not predicted by the bulk-interaction theory of Brillouin scattering. Optical heterodyne detection has been used to resolve the scattering spectrum which begins at about 20 MHz and extends to the detection limit.

ELASTIC WAVE PROPAGATION IN THREE-DIMENSIONAL PERIODIC COMPOSITE MATERIALS

An elastodynamic theory, based on the concepts of Brillouin theory has been developed for elastic wave propagation in periodic composite materials.

Theory of Brillouin scattering from an isotropic elastic film

In the elastic plate limit of thickness L much less than the acoustic wavelength lambda a, the description of the propagating modes simplifies to a bending, or undulation, mode and a longitudinal, or peristaltic, mode. Green functions and fluctuation spectra for these modes are derived by linear response theory. The differential cross sections for Brillouin scattering off these modes by the surface ripple mechanism are calculated. For the bending mode the power spectrum increases strongly and the cross section increases with decreasing L. For the longitudinal mode both the power spectrum and the cross section decrease with decreasing L.

Theory of Brillouin scattering from surface acoustic phonons in supported films

The theory of the Brillouin scattering from the surface of a semi-infinite medium, developed previously, is extended to coated surfaces of cubic materials. The Brillouin cross section is obtained for any scattering geometry and for p and s polarisation of the incident and scattered light. The formulae for the cross section contain contributions from the ripple and the elasto-optic scattering mechanisms for the film as well as for the substrate. The theory is applied to a silica film deposited on crystalline silicon and the behaviour of the cross section against the film thickness is investigated. The authors find that there are strong interference effects among the various contributions to the cross-section, so that the intensity of the spectral lines dramatically oscillates by changing the thickness. Although in general the ripple scattering mechanism is the dominant one it is found that the elasto-optic coupling in the silica film is not negligible and sometimes is even prevailing. The discrete phonon spectrum (Rayleigh, Sezawa, Lamb modes) and the continuous spectrum (resonances, mixed modes) are both studied.

Magnetostatic theory for Brillouin scattering of light from surface spin waves in thin ferromagnetic films

A magnetostatic theory is presented for light scattering from surface spin waves in thin ferromagnetic films deposited on non-magnetic substrates. The calculations include multiple-reflection effects for the incident and scattered light beams, and these become important at film thicknesses which are comparable with or smaller than the optical penetration depth. The theory is applied to explain recent Brillouin scattering measurements for thin iron films on various substrates, including an enhancement observed in certain cases for the scattered intensity. Further applications of the theory to EuS films are also discussed.

Brillouin-Streuung an dichten Fluiden/ On Brillouin Scattering in Dense Fluids

Abstract It has been shown analytically that Mountain's theory of the spectral distribution of density fluctuations in fluids having an external degree of freedom (MOUXI) is equivalent to the translational hydrodynamics theory (TH) of Desai and Kapral at liquid state densities where selfdiffusion can be neglected. On the other hand, comparing TH and Mountain’s second theory of Brillouin scattering on thermal relaxing fluids involving a frequency dependent volume viscosity (MOUETA), differences are found in several spectral components, especially the intensity of the Rayleigh line, of the Brillouin spectra of CCl4 , C6H12 and C6H6 at large values of the wave vector k. This theoretical effect can be demonstrated experimentally by fitting TH and MOUETA to experimental Brillouin spectra of CCl4 at high values of k, resulting in small changes of the corresponding relaxation times.

Brillouin scattering in thin film optical waveguides. II. Scattering theory

The general theory of Brillouin scattering out of the guided optical modes by the acoustic modes of a thin film optical waveguide is formulated in terms of a total field analysis which includes the effects of both the elastooptic and corrugation scattering mechanisms. The general analytical forms for the field discontinuities at the film boundaries are given and the spectral densities are evaluated for two particular radiative geometries. The results of numerical calculations for the geometries are presented.

Surface plasmon enhanced Brillouin scattering from metal films

The theory of Brillouin scattering in a prism-metal film-air (Kretschmann) geometry is analyzed and numerical estimates are given for a LaSF9 prism-Ag film-air configuration. Signal enhancement of several orders of magnitude is predicted under conditions of coupling to surface plasmon-like fields.

Brillouin scattering in polymethyl methacrylate from 4 to 300 K: Temperature dependence of the Grüneisen constant and thermal properties

Measurements of Brillouin scattering and thermal expansion of amorphous polymethyl methacrylate (PMMA) have been carried out between about 4 and 300 K. Temperature dependence of the ratio of the anti-Stokes to Stokes intensities is measured between about 2 and 15 K. This agrees with the result calculated from the quantum theory of Brillouin scattering based on the Debye theory. The lattice Grüneisen constant γL is calculated from the above two measurements, Brillouin scattering and thermal expansion. Below about 100 K, this seems to agree with the results calculated from cell theory by Curro and independently by Simha et al. Above this temperature, there is a small deviation from the theoretical result. The thermodynamic Grüneisen constant γT is also calculated by using the bulk modulus calculated from the sound velocity obtained from Brillouin scattering. At low temperature, γT seems to coincide with γL. Using the ratio γT to γL, the intermolecular specific heat Cv (inter)is obtained. The temperature dependence of Cv(inter) agrees with the calculated one from the Debye specific heat theory. Using the results of the sound velocity and Cv(inter), the temperature dependence of the thermal conductivity is obtained, and compared with the experimental result. These nearly agree with each other.

Theory of Brillouin scattering by Stoneley waves

Presents a theory of the Brillouin scattering of light from both bulk and surface acoustic phonons in two semi-infinite media in contact. The theory incorporates both elasto-optic and surface-ripple mechanisms into the cross section. The appropriate Green functions are also derived for the displacement gradients associated with the acoustic vibrations of the elastically isotropic media. Some representative computed lineshapes which include contributions from the surface Stoneley waves and from the higher-frequency bulk acoustic waves, are presented and their features discussed.

Theory of Brillouin scattering by Love waves

Green functions are derived for the displacement gradients associated with transverse acoustic vibrations polarised parallel to the surface of a sample consisting of a plane parallel isotropic film deposited on an isotropic semi-infinite substrate. The frequency dependence of the corresponding Brillouin scattering cross section is calculated for arbitrary scattering angle. The spectrum includes contributions from the surface Love waves and from the higher-frequency bulk acoustic waves. Numerical calculations of Brillouin spectra are presented for a sample in which the substrate material is inactive in light scattering.

Surface Brillouin scattering from acoustic phonons. II. Application to semiconductors

The theory of Brillouin scattering from corrugated surfaces developed previously has been applied to semiconductors. The available spectra measured with 5145 AA light has been used for evaluating the elasto-optic constants (k11, k12, k44) of the medium. For GaAs k11=42.5, k12=51 and k44=25.5. This is the first determination of these constants in GaAs at this wavelength, where other techniques are not applicable. For silicon k11=53, k12=25 and k44=23. It is also shown that in opaque semiconductors the elasto-optic coupling depends strongly on the surface orientation.

Surface Brillouin scattering from acoustic phonons. I. General theory

The theory of Brillouin scattering from the surface of a semi-infinite medium is presented. The electromagnetic field is calculated to first order in the phonon displacements using the Rayleigh method. Both s and p polarisations are considered and the scattering geometry is not limited to the plane of incidence. The cross-section formulae can be interpreted in terms of the ripple and elasto-optic mechanisms. The effects on the displacement field due to the surface are investigated in both the discrete and the continuous part of the frequency spectrum. In particular, a detailed analysis of the so-called 'mixed modes' belonging to the continuum is analytically given for the isotropic medium. The application of the theory to GaAs and the comparison with experimental data (including A1 coated surfaces) will be discussed in paper II.

Theory of normal-incidence Brillouin scattering by acoustic phonons in a supported thin film

The theory of Brillouin scattering by acoustic phonons in a thin film on a substrate is investigated. Only the back scattering of normally incident light is considered. The calculations start with the evaluation of the Green functions for the displacement-gradient components of the acoustic vibrations, and proceed to the differential cross section. It is shown that for isotropic or cubic symmetry of the film and substrate, scattering is by longitudinal vibrations only. Various limiting cases are included, in particular an unsupported film and a semi-infinite medium, and the results obtained for these agree with those derived previously. A detailed discussion is given of the special case in which the scattering takes place only in the film, which is taken to be transparent. The line is broadened because of the finite thickness of the film, and the lineshape is modulated by a periodic factor which arises from partial reflection of the phonons at the film-substrate interface. The results obtained give the first full expressions for these effects.

Surface response of exchange- and dipolar-coupled ferromagnets: Application to light scattering from magnetic surfaces

We present the theory of the surface response of a semi-infinite ferromagnet in the presence of both exchange and dipolar coupling, within a continuum theory. The results are applied to a detailed study of the spectral density of surface spin fluctuations. From this we analyze the influence of exchange coupling and surface spin pinning on the frequency, linewidth, and line shape of the Damon-Eshbach surface spin wave, for a number of propagation angles, and for wavelengths sufficiently short that the exchange contribution to the energy of the wave is comparable to the Zeeman and dipolar energies. We also develop the theory of Brillouin scattering from spin waves near magnetic surfaces, and calculate the spectum of scattered light for experimentally interesting geometries, with recent light scattering studies of ferromagnetic surfaces in mind.

Theory of Brillouin scattering from opaque media

The general theory of Brillouin scattering from the surfaces of opaque media is developed using a total field solution approach. Acoustical modes appropriate to a stress-free surface are found from solutions to the acoustical-wave equation and boundary conditions for a finite isotropic medium. Two light-scattering mechanisms, namely, the surface corrugation and bulk elasto-optical effects, were analyzed by deriving optical fields which satisfy both the acousto-optically driven wave equation and the electromagnetic boundary conditions. The special case for a metal of scattering by acoustically created conductivity fluctuations was also investigated in a similar way. The Brillouin spectrum was obtained by summing the scattering from the individual acoustical modes over the density of phonon states. Excellent agreement was obtained with experiment for Brillouin scattering from the metals gallium (liquid) and aluminum (solid).