Reststrahl Band Research Articles

Second harmonic generation spectroscopy in the Reststrahl band of SiC using an infrared free-electron laser

The Reststrahl spectral region of silicon carbide has recently attracted much attention owing to its potential for mid-infrared nanophotonic applications based on surface phonon polaritons (SPhPs). Studies of optical phonon resonances responsible for surface polariton formation, however, have so far been limited to linear optics. In this Letter, we report the first nonlinear optical investigation of the Reststrahl region of SiC, employing an infrared free-electron laser to perform second harmonic generation (SHG) spectroscopy. We observe two distinct resonance features in the SHG spectra, one attributed to resonant enhancement of the nonlinear susceptibility χ(2) and the other due to a resonance in the Fresnel transmission. Our work clearly demonstrates high sensitivity of mid-infrared SHG to phonon-driven phenomena and opens a route to studying nonlinear effects in nanophotonic structures based on SPhPs.

Reststrahl band-assisted photocurrents in epitaxial graphene layers

We report on the observation of the reststrahl band-assisted photocurrents in epitaxial graphene on SiC excited by infrared radiation. The peculiar spectral dependence for frequencies lying within the reststrahl band of the SiC substrate provides a direct and noninvasive way to probe the electric field magnitude at atomic distances from the material's surface. Furthermore our results reveal that nonlinear optical and optoelectronic phenomena in two-dimensional crystals and other atomic scale structures can be giantly enhanced by their deposition on a substrate with negative dielectric constant.

A heuristic approach to precisely represent optical absorption and refractive index data for photon energies below, at, and above the band gap of semiconductors: The case of high-purity GaAs. Part I

The existence of band tails even in nominally undoped and uncompensated GaAs, and the nonparabolic absorption shape above the band gap are the prime examples for the discrepancy between theory and experiments. To overcome this difficulty, we propose a heuristic approach that is guided by the fundamental theoretical aspects and the experimental facts. For this reason, we fit the available absorption data with exponential functions over a photon energy interval from below the band gap to 3eV. This analytical representation remains well within the known experimental uncertainties over a temperature range from cryogenic to room temperature and beyond. The fitting functions are interpreted to represent the absorption contributions by the band tails, the continuum, and the excitons. This descriptive absorption function implicitly results from a perturbation of the imaginary part of the dielectric function that takes a host of unspecified contributions into account. The real part of the dielectric function due to the high-energy critical points is represented by Lorentzian functions with critical energies taken at 3 and 5eV. Its square root defines the refractive index due to these critical points, nh. The refractive index, n, is represented by the sum of nh and the truncated Kramers–Krönig transformation of the absorption function. The determination of nh is made by fitting n to the precise refractive index data of Marple [J. Appl. Phys. 35, 1241 (1964)]. This procedure yields a very precise description (<0.1% below and within experimental uncertainty at and above the band gap) of the published refractive index data from 0to2.2eV (except for the narrow reststrahl band near 0.033eV) over a temperature range similar to that mentioned for the absorption function. We feel confident to predict the refractive index for temperatures as low as 4K. An analytical expression for the refractive index describes the temperature and energy dependences very precisely below the band gap. The analytic expression is also very precise in the band-gap region for a temperature range estimated from 80to400K. We also compare the form of the absorption function derived from photoluminescence spectra. We find that low quasiequilibrium carrier densities lead to important modifications of the absorption function. These experimental findings together with the fitting procedures serve as a basis for a heuristic theory to calculate the electronic and optical properties under injection.

Thickness determination of low doped SiC epi-films on highly doped SiC substrates

The room temperature infrared reflectance of low doped SiC epi-films, both 4H and 6H polytypes, deposited by chemical vapor deposition on highly doped SiC substrates has been measured. The epi-film doping levels are in the 1015 cm−3 range while the substrate doping levels are in the 1018 to 1019 cm−3 range. Interference fringes from the epi-films are often observed in the frequency region below the reststrahl band in SiC (200–600 cm−1) and they can be used to determine the thickness of these epi-films. The fringes arise due to the difference in free carrier concentration between the epi-film and substrate which causes differences in their frequency dependent dielectric functions. The epi-film thickness determinations were made by comparison of the measured infrared reflectance spectra to calculated spectra based on a frequency dependent dielectric function modeled with Lorentz oscillators using only bulk input parameters. The effects of film and substrate anisotropy and off normal incidence are included in the calculation.

Dynamics of ferroelectric thin films described by the transverse Ising model

The dynamic properties of thin films described by the Ising model in a transverse field (TIM) have been studied under the random-phase approximation. The frequencies of soft modes and surface modes have been obtained. For films with reduced surface interaction (compared to the bulk), the soft mode corresponds to a surface-like mode in the ferroelectric phase but to a bulk-like mode in the paraelectric phase. Conversely, for films with an enhanced surface interaction, the soft mode is a bulk-like mode in the ferroelectric phase and a surface-like mode in the paraelectric phase. The number of surface-like modes in the ferroelectric phase can be greater than one; the number increases as the temperature approaches the Curie temperature, and does not depend on the in-plane wavevector for a given temperature in the ferroelectric phase. However, there is only one surface-like mode in the paraelectric phase, and its character becomes bulk-like at large wavevector. The surface modes can be clearly seen from the frequency dependence of the dynamic susceptibility; the surface mode pole increases in strength with decreasing film thickness. The frequency dependences of optical reflectivity coefficients have also been obtained. The reflection peaks due to the surface modes lie below the bulk reststrahl band in the ferroelectric phase of films with reduced surface ferroelectricity, and also in the paraelectric phase of films with enhanced surface ferroelectricity; otherwise, they lie within the reststrahl band.

Contribution of longitudinal excitons to second harmonic generation in CuCl

The nonlinear reflection of the second harmonic at oblique incidence is measured in the reststrahl band of the Z 3-exciton of CuCl. Due to two-photon selection rules longitudinal excitons can be excited. The measurements show clear evidence that the longitudinal polarization wave contributes to the coherent process of second harmonic generation.

Effect of crystal anisotropy on the infrared reflectivity of 6H-SiC

Polarized infrared reflectivity spectra of 6H-SiC single crystals under different angles of incidence are reported. A new sharp line in the reststrahl band was observed in the extraordinary ray, whose line shape is dependent on the angle of incidence. It was possible to show that crystal anisotropy of 6H-SiC is the reason for the new line in the reflectivity spectrum. A numerical calculation using a Lorentz oscillator model confirmed this result. Two weak one-phonon absorption lines in the reststrahl band region for E ‖ c were observed. Furthermore, we found a new line at 859 cm−1 in the extraordinary ray and an unusual structure near wTO in the reststrahl band of parallel c-cut 6H-SiC samples, which could not be explained in terms of the classical Lorentz oscillator model.

Far-infrared measurements of the real and imaginary parts of the complex refractive index of InSb at 300 and 100 K

Measurements of the real and imaginary parts of the complex refractive index of a nominally undoped single crystal of InSb have been made by a combination of reflection and transmission dispersive Fourier transform spectroscopy in the far-infrared at 300 and 100 K. Features observed in the spectra are assigned as 2-phonon combination bands with the aid of an 11-parameter rigid ion model and good overall agreement has been found between calculated and observed frequencies. In addition, a strong bulk plasmon mode due to free carriers is observed in the low wavenumber region below the reststrahl band.

Three-photon reststrahl bands near exciton resonances.

Excitation of a KI crystal by a high-power laser in the visible (around 6930 nm) leads to «reflected» light at the third harmonic (around 210 nm). There is a pronounced structure in the spectrum between the longitudinal and the transverse excitons, which is interpreted as a nonlinear reststrahl band. Study of third-harmonic generation in transmission also reveals pronounced structure. An analysis according to Maxwell boundary conditions leads to a good fit to the experimental results

Investigation of the Infrared‐Active Lattice Vibration in SrCl2

AbstractSrCl2, single crystals were grown by the Czochralsky method. Their reflectivity at 300 K and transmission at 4.2 K were measured for frequencies from 10 to 930 cm−1 and 10 to 150 cm−1, respectively. The reststrahl band found in the reflection spectrum has been analyzed by means of a classical oscillator model. In addition, a Kramers‐Kronig analysis was performed since a satisfactory fit could not be achieved with the classical model. The frequencies of the TO‐mode and the LO‐mode were determined to be 138 and 233 cm−1, respectively. A pronounced shoulder on the reststrahl band was observed as is also the case for CaF2, BaF2 etc. Its origin is discussed in terms of multi‐phonon processes. The results of the transmission measurements show that SrCl2, is transparent in the far infrared up to 110 cm−1 where the lattice absorption starts at 4.2 K.

Ionic Raman Scattering and Ionic Frequency Mixing

AbstractTwo closely related effects based on the nonlinearity of ionic polarizability are considered, ionic Raman scattering and ionic frequency mixing. A simple model is used to make explicit calculations for quartz. Both effects have two resonances associated with each reststrahl band. In addition, antiresonances may occur due to the interference between the ionic process and the corresponding normal process. Although two resonance conditions may be satisfied simultaneously in quartz, the Raman efficiency seems to be below the present limits of observation. On the other hand, the calculation shows that resonant ionic frequency mixing should be observable in quartz.

Infrared Generation by Coherent Excitation of Polaritons

The work presents a transient theory of the propagation in a cubic crystal of a polariton wave excited by a three-wave nonlinear parametric interaction. The coupling coefficient of the mixing process is calculated using a quantum-mechanical perturbation approach in the second-quantization formulation and including explicitly in the theory the phase and momentum mismatches of the interaction. The solution of the partial differential equations describing the evolution of the driving optical pulses leads to a complete formulation of the transient problem for the polariton pulse propagation. The transient problem is fully solved in the case in which the duration of the driving pulse $f(z,t)$ of the polariton wave is larger than the damping parameter ${\ensuremath{\Gamma}}^{\ensuremath{-}1}$: a case of general physical relevance including the optical behavior of short pulses generated by mode-locked lasers. In particular the solution of the problem leads to the definition of a characteristic interaction length and time depending on the initial conditions and affecting in a critical way the efficiency of the excitation process. The Raman mixing process is briefly discussed as a particular case of the polariton process. The process of infrared generation is then taken into account on a semiclassical basis, with particular emphasis on the discussion of the propagation effects of the boundary conditions. In particular, the inhomogeneous character of the free solutions of the propagation equations is discussed. The theory is further extended to a brief discussion of the nonlinear optical behavior of the reststrahl band, leading to the consideration of an infinite nonlinear backward reflectivity at $\ensuremath{\omega}={\ensuremath{\omega}}_{\mathrm{LO}}$. An experiment is then described in which the coherent infrared generation in a crystal of gallium phosphide is applied to a series of accurate measurements of the linear and nonlinear optical parameters in the polariton region. The angular distribution of the emitted infrared intensity at wavelengths $\ensuremath{\lambda}=29.2, 29.9, \mathrm{and} 34.6$ \ensuremath{\mu} and the spatial evolution of the polariton field in the quasicollinear kinematical configuration lead to the determination of the index of refraction of the crystal at these wavelengths and to the first direct measurement of the absorption coefficient in the zone of large polariton dispersion. On the basis of our results, we could verify the correctness of the multiple-oscillator theoretical model proposed by Barker in order to describe the lattice oscillation in GaP. Finally, the infrared intensity at the various frequencies leads to the determination of the dispersion of the modulus of the nonlinear optical susceptibility $|d|$ of the crystal. Assuming in first approximation a single-oscillator model for the lattice in the nonlinear regime, we could measure the characteristic nonlinear parameter $C=S(\frac{{d}_{Q}^{\ensuremath{'}}}{{d}_{E}^{\ensuremath{'}}})$. We found $C=\ensuremath{-}0.48\ifmmode\pm\else\textpm\fi{}0.01$. The experimental methods described in the present work are of general interest for the nonlinear spectroscopy of solids in the optical and infrared range of frequencies.

Measurement of the dispersion of the nonlinear optical polarizability in gap by coherent ir generation in the polariton region

The i.r. generation process allows the study of the dispersion of the nonlinear response of GaP near the Reststrahl band. The frequency dependence of the i.r. intensity leads to consider the effect of two different polariton damping regimes.

Difference frequency generation in the polariton region

We report the i.r. generation by coherent excitation of polaritons in GaP. The angular distribution and the frequency dependence of the emitted intensity allows the study of the dispersion of the linear and non-linear optical susceptibility near the reststrahl band.

Coherent Excitation of Polaritons in Gallium Phosphide

The coherent excitation of polaritons has been achieved in the III-V semiconductor GaP for the first time by a nonlinear, optical parametric process. We are able to describe the polariton dispersion curve in the $\ensuremath{\omega}\ensuremath{-}k$ space and to measure the absorption coefficient of the crystal near the Reststrahl band. The results are discussed on the basis of recent theories on the polariton disperson and damping in GaP.

Dispersion in the Nonlinear Susceptibility of GaP near the Reststrahl Band

This paper describes a continuation of earlier work, in which we reported measurements of the intensities of mixed frequencies from a 6328 \AA{} beam and various infrared frequencies near the lattice reststrahl resonance, and in which we gave a theory for the dispersion of the nonlinear susceptibility which governs the mixing process near the reststrahl resonance. With more infrared frequencies, with data on the anti-Stokes side as well as on the Stokes side, and with improved techniques, we can now give a more meaningful comparison with theory. These new data provide additional confirmation of the theory for the dispersion of the nonlinear susceptibility. We also describe the apparatus more fully, and we demonstrate some incidental features of the mixing.

Anomalous Reststrahl Structure from Slight Surface Roughness

Extremely small bumps or pits on the surface of an ionic crystal will result in anomalous reststrahl measurements. Structure appears in each reststrahl band that could easily be mistaken for two-phonon structure on top of the primary bands, at frequencies slightly below the longitudinal-optic-mode frequencies of the crystal. This secondary structure is caused by localized resonances of the ionic vibrations in the immediate neighborhood of the bumps or pits. This effect is derived from a strictly local dielectric theory, by solving Maxwell's equations with appropriate boundary conditions. Such anomalies in reflectance occur in any material when the imaginary part of the dielectric constant is small, and when the real part falls in the interval roughly between -4 and -\textonequarter{}. Thus they might also be important in metals near plasma frequencies. The effect is independent of other types of anomalies that may arise from differences between dielectric properties in the bulk of the material and those near the surface.