Second-Order Raman Scattering Research Articles

Second-Order Raman Scattering in Ferroelectric Ceramic Solid Solutions LiNbxTa1−xO3

In the second-order Raman spectra of ceramic solid solutions, LiNbxTa1−xO3 weak overtone bands of fully symmetric fundamental polar excitations were observed for the first time. The frequencies of the two bands exceeded the value of the overtone frequency corresponding to the fully symmetrical vibration 4A1(z). The possibility of the existence of phonon bound states of the antipolar type in the vibrational spectrum of LiNbxTa1−xO3 ceramics is predicted.

Second-Order Raman Scattering in Exfoliated Black Phosphorus.

Second-order Raman scattering has been extensively studied in carbon-based nanomaterials, for example, nanotube and graphene, because it activates normally forbidden Raman modes that are sensitive to crystal disorder, such as defects, dopants, strain, and so forth. The sp2-hybridized carbon systems are, however, the exception among nanomaterials, where first-order Raman processes usually dominate. Here we report the identification of four second-order Raman modes, named D1, D1', D2 and D2', in exfoliated black phosphorus (P(black)), an elemental direct-gap semiconductor exhibiting strong mechanical and electronic anisotropies. Located in close proximity to the Ag1 and Ag2 modes, these new modes dominate at an excitation wavelength of 633 nm. Their evolutions as a function of sample thickness, excitation wavelength, and defect density indicate that they are defect-activated and involve high-momentum phonons in a doubly resonant Raman process. Ab initio simulations of a monolayer reveal that the D' and D modes occur through intravalley scatterings with split contributions in the armchair and zigzag directions, respectively. The high sensitivity of these D modes to disorder helps explaining several discrepancies found in the literature.

Triply resonant Raman scattering in perovskite semiconductor CsSnI3

We report on the first-order and second-order Raman scattering (SORS) by longitudinal optical (LO) phonons in perovskite semiconductor CsSnI3. The intensity of SORS is stronger than that of the first order. The spectral line shape of SORS is asymmetric and much broader than that of the first order. It is identified that the strong SORS intensity is attributable to the triply enhanced resonant process, which is naturally implemented through the peculiar band structure of this semiconductor compound having two adjacent parallel conduction bands with a separation close to the energy of two LO phonons. Copyright © 2012 John Wiley & Sons, Ltd.

Impulsive excitation of phonon-pair combination states by second-order raman scattering

The excitation of (100)-oriented KTaO3 with 25-fs laser pulses impulsively drives phonon-pair combination states via second-order Raman scattering. Oscillations in the phonon-amplitude covariance at the sum and difference frequency of the two involved phonons are observed in a spectrally and temporally resolved pump-probe experiment. Transmission changes of the sample are dominated by contributions of wave vector conserving phonon-pair combinations from the entire Brillouin zone that have maxima in their combined density of states. For low temperatures the temperature dependence of the covariance oscillations of different phonon combinations is reproduced by a quantum-mechanical model.

Phonon Squeezed States Generated by Second-Order Raman Scattering

We study squeezed states of phonons, which allow a reduction in the quantum fluctuations of the atomic displacements to below the zero-point quantum noise level of coherent phonon states. We investigate the generation of squeezed phonon states using a second-order Raman scattering process. We calculate the expectation values and fluctuations of both the atomic displacement and the lattice amplitude operators, as well as the effects of the phonon squeezed states on macroscopically measurable quantities, such as changes in the dielectric constant. These results are compared with recent experiments.

Microscopic model for the two-phonon Raman spectra of alkali halides.

The second-order Raman-scattering (SORS) cross section of alkali halides has been evaluated by using the Buckingham expansion for the induced polarizability. This ab initio approach leads to a microscopic expression of the SORS cross section without free parameters. The first two nonzero contributions of the expansion, namely, the dipole-induced dipole (DID) coming from the first-order dressed polarizability and the BTQ (second-dipole hyperpolarizability \ifmmode\times\else\texttimes\fi{} dipole propagator \ifmmode\times\else\texttimes\fi{} effective charge) coming from the second-dipole--quadrupole polarizability, have been considered. The short-range contribution to the induced polarizability coming from the electronic overlap has not been included in the present work. The SORS spectra are expressed in terms of the dynamical quantities of the crystal (eigenvectors and eigenfrequencies) and in terms of some bare ionic susceptibilities, namely, the ions' bare polarizabilities ${\mathrm{\ensuremath{\alpha}}}^{+}$ and ${\mathrm{\ensuremath{\alpha}}}^{\mathrm{\ensuremath{-}}}$ and the second-dipole--quadrupole bare polarizabilities ${\mathit{B}}^{+}$ and ${\mathit{B}}^{\mathrm{\ensuremath{-}}}$. As an example the results are shown in the case of KBr. Considerations on the long-range nature of the DID spectrum and on the short-range nature of the BTQ spectrum are made. The relative weights of the two contributions to the SORS in the whole class of alkali halides are also discussed.

Microscopic theory of second-order Raman scattering in silicon under uniaxial stress.

A microscopic calculation of the second-order Raman-scattering efficiency of silicon, with special emphasis on the effects of uniaxial stress, is presented. Employing diagrammatic perturbation theory, the scattering efficiency is obtained for incident- and scattered-photon energies either on or off resonance. A numerical evaluation employs realistic models for the electronic band structure and phonon spectra, and sums over all two-, three-, and four-band scattering channels. The scattering efficiency is normalized by the integrated first-order efficiency, and the results of the calculation are quantitatively compared with experimental data for second-order Raman scattering in crystalline silicon under [001] stress, taken with an incident laser energy of 2.34 eV.

Second-Order Raman Scattering in Graphite Intercalation Compounds

ABSTRACTThe stage dependence of various second-order Raman features observed for acceptor (FeCl3, SbCl5) and donor (Rb) Graphite Intercalation Compounds is reported and discussed in terms of recent Born-von Kármán lattice dynamics calculations of Al-Jishi and Dresselhaus.

Second-Order Raman Scattering and Its Resonant Behavior in Thallium Halide Crystals

Second-order Raman scattering spectra have been measured in TlBr and TlCl single crystals at 77 K. In both crystals, the resonant behavior of the overtone band of LO phonon with q ∼0 (the 2LO(\(\varGamma\)) band) is explained by the theory of Ganguly and Birman. Combination bands of two phonons with large wave vector have been observed in the spectra. The dependence of their intensities on the incident photon energy has been found to be different from that of the 2LO(\(\varGamma\)) band, which shows that the scattering processes are different.

Resonant First- and Second-Order Raman Scattering in GaP

The dependence on laser frequency of the scattering cross section for allowed and forbidden first-order Raman scattering and for second-order scattering is presented. The measurements were performed in the vicinity of the ${E}_{0}$ and ${E}_{0}+{\ensuremath{\Delta}}_{0}$ gaps. It is shown that the ${\ensuremath{\Gamma}}_{15}$ components of the Raman tensor exhibit a sharp resonance at ${E}_{0}$ while ${\ensuremath{\Gamma}}_{1}$ components resonate both at ${E}_{0}$ and ${E}_{0}+{\ensuremath{\Delta}}_{0}$. The results are interpreted in terms of a theory which assumes parabolic bands extending to infinity. The second-order scattering is produced mainly by electron-two-phonon interaction vertices, except for the strongly resonant sharp peaks which correspond to the creation of two LO phonons with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\simeq}0({\ensuremath{\Gamma}}_{1})$ and one LO plus one TO phonon with $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\simeq}0({\ensuremath{\Gamma}}_{15})$. From these measurements, values for the electron-two-phonon deformation potentials are obtained.

Temperature Dependence of Second-Order Raman Scattering in Potassium and Rubidium Halides

Temperature Dependence of Second-Order Raman Scattering in Potassium and Rubidium Halides

First- and Second-Order Raman Scattering of SrTiO3

First- and Second-Order Raman Scattering of SrTiO3