Resonant Brillouin Scattering Research Articles

Giant gain enhancement in surface‐confined resonant Stimulated Brillouin Scattering

AbstractThe notion that Stimulated Brillouin Scattering (SBS) is primarily defined by bulk material properties has been overturned by recent work on nanoscale waveguides. It is now understood that boundary forces of radiation pressure and electrostriction appearing in such highly confined waveguides can make a significant contribution to the Brillouin gain. Here, this concept is extended to show that gain enhancement does not require nanoscale or subwavelength features, but generally appears where optical and acoustic fields are simultaneously confined near a free surface or material interface. This situation routinely occurs in whispering gallery resonators (WGRs), making gain enhancements much more accessible than previously thought. To illustrate this concept, the first full‐vectorial analytic model for SBS in WGRs is developed, including optical boundary forces, and the SBS gain in common silica WGR geometries is computationally evaluated. These results predict that gains 104 times greater than the predictions of scalar theory may appear in WGRs even in the 100 μm size range. Further, trapezoidal cross‐section microdisks can exhibit very large SBS gains approaching 102 m−1W−1. With resonant amplification included, extreme gains on the order of 1012 m−1W−1 may be realized, which is 108 times greater than the highest predicted gains in linear waveguide systems. image

Proposed non-linear resonant brillouin scattering and reflection to detect phonoritons

The “phonoriton” is an elementary excitation constructed from an exciton-polariton and phonon in semiconductors under intense excitation near the exciton resonance. In this paper we describe its basic properties using a simple model. We propose two experiments: Non-Linear Resonant Brillouin Scattering and Non-Linear modulation reflectivity to determine the new phonoriton spectrum. Quantitative analysis shows that the phonoriton effects are expected to be measurable.

Resonant Brillouin Scattering at Bound‐Exciton States in CdS

AbstractStrong resonant Brillouin scattering (RBS) is studied occurring under high excitation densities in the bound‐exciton energy range in CdS. RBS shows pronounced resonance enhancement not only at well‐known bound‐exciton ground state energies but also for energies of various excited states of these complexes. In this energy range, RBS has not been observed under low‐excitation‐density conditions. The phonon coupling determining the Stokes or anti‐Stokes shift of the RBS line maxima allows to calculate the spatial dimensions of the excited bound‐exciton levels acting as intermediate resonance states of the scattering process. In general, high‐density RBS spectroscopy is shown to yield important information on ground and excited states of bound exciton complexes.

Frequency-dependent damping constant and the linewidth of resonant Brillouin scattering of exciton-polaritons in CdS

The linewidths of Brillouin components involving lower-branch $A$-exciton polaritons in the resonant-Brillouin-scattering (RBS) spectrum of CdS have been carefully measured and analyzed. It was found that the exciton damping constant $\ensuremath{\gamma}$ must be frequency dependent to explain the observed increase of the linewidth in the resonance region. In particular we suggest that mixing of the ${\ensuremath{\Gamma}}_{5}(A)$ polariton and ${\ensuremath{\Gamma}}_{6}(A)$ exciton states induced by the $k$-linear interaction is the most probable explanation for the observed sharp increase of the linewidth slightly above the exciton resonance frequency. Interpretation of our linewidth data based on this mechanism led to a coefficient for the $k$-linear term for the $A$ exciton of ${\ensuremath{\varphi}}_{A}=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ eV cm. The frequency-dependent damping constant $\ensuremath{\gamma}(\ensuremath{\omega})$ must also be used to analyze the intensity of RBS which is related to the additional-boundary-condition (ABC) problem. Preliminary results of intensity fitting using a generalized form of the ABC are presented.

Resonant Brillouin scattering in CdS. I. Experiment

High-resolution resonant Brillouin-scattering (RBS) experiments were performed in the vicinity of the $A$ exciton in cadmium sulfide. The spectroscopic system used in these investigations consisted of a single-mode dye laser which was frequency tuned through the exciton resonance, and a triple-pass Fabry-Perot interferometer combined with a tandem grating spectrometer which was used to analyze the scattered light. This experimental arrangement enabled Brillouin shift, linewidth, and intensity measurements to be made on several different Brillouin components which result from the scattering by acoustic phonons of both inner- and outer-branch exciton-polaritons in the crystalline medium. Very good agreement was obtained between the Brillouin shift data and theory resulting in revised values for the exciton effective mass, transverse frequency, background dielectric constant, and oscillator strength. However, the Brillouin linewidth data indicated that the exciton damping constant $\ensuremath{\Gamma}$ is not constant in value but instead increases monotonically for frequencies greater than ${\ensuremath{\omega}}_{T}$. In an attempt to identify the correct additional boundary condition (ABC) which is needed to describe the simultaneous propagation of two degenerate exciton-polariton modes, a theoretical external scattering cross-section calculation was developed (see the following paper) and compared with the measured Brillouin intensities. Although the RBS intensity measurements did not fit very well with theory for any of the three ABC's, agreement between theory and experiment was considerably better with either ABC2 or ABC3 than with ABC1. The RBS results were also checked for self-consistency by reflectivity and absorption experiments on the same CdS sample.

Resonant Brillouin Scattering in HgI2 Investigated by Acoustic Domain Injection Method

AbstractResonant Brillouin scattering by the transverse acoustic phonons is investigated for the first time in red HgI2 single crystal at room temperature by using the acoustic domain injection method. The measured results in the spectral region 579 to 800 nm show a non‐dispersive feature at the longer wavelength region and a decrease in the region very close to the fundamental absorption edge. The analysis based on the resonant Brillouin scattering theory and piezobirefringence theory shows excellent agreement with the present observation and predicts a resonant cancellation of the scattering cross section at 574 nm.

Phonon selectivity in resonant brillouin scattering (RBS) from multi-component polaritons

Phonon selectivity in resonant Brillouin scattering (RBS) from multi-component polaritons in the back scattering geometry is discussed for the deformation and piezo-electric potential interactions in the long wavelength limit. An explicit calculation of RBS intensities is also presented for the parallel (eies) and cross (ei⊥es) polarized back scatterings from CuBr[Z1,2] for k[111], with assumed ABC's in a generalized Pekar form.

Resonant Brillouin Scattering in GaAs under uniaxial stress

Resonant Brillouin Scattering experiments on GaAs employing multipass Fabry-Perot interferometry are reported for k | [100], [110] and [111]. Peaks due to forbidden TA scattering and weak structure attributed to processes involving the intermediate polariton branch are observed. From measurements under [110] uniaxial stress, a predicted small decrease in exciton mass with stress is observed and the singlet-triplet splitting is verified to be very small (δ ⪡ Δ LT).

Intensities of resonant brillouin scatterings from multicomponent exciton-polaritons

To reduce the arbitrariness in the current analysis of resonant Brillouin scattering (RBS) from multicomponent polaritons, the intensities of scattering peaks are theoretically studied. The interaction among the multicomponent excitons may contain linear and quadratic terms in translational wave vector, electron-hole exchange interaction, and any other terms that retain translational symmetry. As the scattering mechanisms due to TA and LA phonons, we consider various deformation and piezoelectric potentials. In certain cases, this theory leads to a “selection rule”, which can solve the controversy between the two different dispersion curves for CuBr obtained from RBS and two photon resonant Raman scattering, in favor of the latter. The theory also provides a basis to discuss the problem of additional boundary conditions for multicomponent polaritons in terms of the relative intensities of scattering peaks.

Contribution of the Imaginary Part of Photoelastic Constants to Resonant Brillouin Scattering in CdS

A deep but finite minimum in the dispersion of the Brillouin scattering cross section has been found in the wavelength region of the resonant cancellation at 562.4 nm ( T =300 K) in CdS. This minimum is interpreted as arising from the contribution of the imaginary part of photoelastic constant P 66 , whose existence has been overlooked so far. The lifetime broadening is introduced to obtain the imaginary part by replacing the photon energy \(\hbar\omega\) with \(\hbar\omega+i\varGamma\) (\(\varGamma\): damping energy) in the piezobirefringence theory. The damping energy is found to be \(\varGamma{=}0.5\) meV at 300 K from the best fitting of the theoretical curve to the experimental results.

Note on the Selection Rule of Resonant Brillouin Scattering in CdS at Room Temperature

The resonant Brillouin scattering has been investinated in CdS at room temperature by using monochromatic acoustic waves generated by ZnO thin film transducer. Resonant cancellation and enhancement are observed in the allowed configuration, whereas no signals are found in the forbidden configuration in contrast to the results observed by the acoustoelectric domains.

Anisotropic polariton dispersion in red HgI2

Abstract We have measured resonant Brillouin Scattering near the A-exciton region of a layer-semiconductor, red-HgI2. The Brillouin shift is interpreted in terms of a scattering process between the two polariton states by an acoustic phonon. The estimated exciton masses for the translational motion are (0.68 ± 0.1)m0 and (1.2 ± 0.1)m0 for the (100 and (001) directions, respectively.

Analysis of Resonant Brillouin Scattering in GaAs

AbstractThe dispersion curves of the resonant Brillouin scattering cross sections in GaAs measured by Garrod and Bray are analyzed on the basis of the resonant Brillouin scattering theory and piezobirefringence theory. The resonant enhancement and cancellation are found to be well interpreted in terms of the sign reversal of the Brillouin amplitude (or photoelastic constant). A good agreement is found between the experimental data and the present analysis. In addition the present analysis predicts a cancellation of the Brillouin scattering at Λ = 0.976 μm for the scattering by the slow transverse (Tl) acoustic phonons. This prediction is supported by the analysis of the photoelastic constant made by using piezobirefringence theory.

Effect of Lifetime Broadening on Resonant Brillouin Scattering in ZnTe and ZnSe

Resonant Brillouin scattering by fast-TA phonons in ZnTe and ZnSe has been studied by using an acoustic domain injection method. Two kinds of ZnTe and ZnSe crystals have been used to investigate some effects of the crystalline imperfections on the dispersion of the Brillouin scattering cross sections. The measurements have been made at room temperature and 77 K. It has been found that the Brillouin scattering cross sections are affected strongly by the damping of the intermediate electronic states and that the damping energy does not depend on the temperatures but on the kinds of the crystals. The damping energy of the high-quality ZnTe (ZnSe) determined from resonant Brillouin scattering is \\varGamma=26 meV (44 meV) at 77 K, which is very large compared with the value of \\varGamma≃2 meV (3 meV) obtained from reflectance spectrum. The result are interpreted in terms that the damping is caused mainly by an interaction of the intermediate electronic states with the high-intensity acoustic phonon domains and the crystalline imperfections.

Resonant Brillouin Scattering by LA Phonons in CdS

Resonant Brillouin scattering by longitudinal acoustic phonons has been observed for the first time in CdS by using mode converted phonons generated by partial reflection of acoustoelectric domains. Analysis based upon resonant Brillouin scattering theory and piezobirefringence theory shows a good agreement with the present observation, and predicts a weak cancellation at 750 nm.

Polariton effect in degenerate valence band semiconductors

We present a model which describes excitonic polariton effect for direct gap semiconductors where the valence band is degenerate, so that two (“light” and “heavy”) exciton dispersion curves exist and give rise to three polariton branches. It is shown that the quantity δ = Δ − 1 3 E LT is an important parameter in this case, Δ and E LT being respectively the exchange energy and the longitudinal transverse splitting. A comparison with the available data, extracted from Resonant Brillouin Scattering in GaAs, is carried out. It is shown that when only the uppermost and lowest polariton branches can be detected, the measured separation Δ exp between these two branches is equal to the longitudinal transverse splitting with a good approximation. In the general case the exact relation between Δ, E LT and Δ exp is derived.

Resonant Brillouin Scattering in CdS by Piezoelectrically Inactive TA Phonon Domains

Resonant Brillouin scattering in CdS has been studied at room temperature by making use of piezoelectrically inactive T A phonon domains obtained by mode conversion upon partial reflection of acoustoelectrically amplified T A phonon domains at the end surface. It has been found that the dispersion of Brillouin scattering efficiency shows a new scattering maximum at a photon energy very close to the ground-state discrete exciton energy. A damping effect on the scattering mechanism has been discussed to explain the observed dispersion. The theoretical prediction based upon Loudon's light scattering theory has shown a quite good agreement with the present results when the damping effect is taken into account. The dispersion of photoelastic constant ( P 66 ) has been determined from the present data and compared with the piezobirefringence analyses.

Study of Resonant Brillouin Scattering in ZnSe by Injected Acoustic Waves

Resonant Brillouin Scattering in semi-insulating ZnSe is investigated at room temperature by using two kinds of injected acoustic waves; fast transverse and slow transverse modes. The observed dispersions in scattering cross section show the resonant enhancement and cancellation near the fundamental absorption edge, which are explained by theoretical analyses based upon Loudon's theory. Calculated dispersions taking account of exciton virtual states agree well with the experimental results. Resonant cancellation is explained in terms of the relevant photoelastic constants undergoing a sign reversal near the band edge, which was confirmed by the analyses of piezobirefringence theory.

Resonant Brillouin Scattering by Acoustoelectrically Amplified Phonons in CdS

Resonant Brillouin Scattering by Acoustoelectrically Amplified Phonons in CdS

Spatial Dispersion Effects in Resonant Polariton Scattering. II. Resonant Brillouin Scattering

Inelastic scattering of light near an exciton resonance is considered, using a polariton description of the scattering process. We obtain the following results: for incident frequency approaching the resonance from below, the Brillouin shift increases; very near and above resonance, extra lines are predicted with intensities comparable to the usual lines. They form an octet instead of the familiar Brillouin doublet. Numerical calculations of the Brillouin scattering for CdS are given: The shifts and extra lines seem to be observable.