Reststrahlen Region Research Articles

Infrared dielectric function of GaAs1−xPx semiconductor alloys near the reststrahlen bands

The infrared dielectric function of thick GaAs1−xPx alloy layers grown on (001) GaAs substrates by hydride vapor phase epitaxy was investigated in the reststrahlen region using Fourier-transform infrared ellipsometry. The spectra are influenced by the Berreman artifact at the longitudinal optical phonon frequency of the GaAs substrate and by interference fringes due to the finite layer thickness. The ellipsometric angles were analyzed to determine the dielectric function of the alloy layer. Two-mode behavior, including strong GaAs-like and GaP-like optical phonons, was observed, confirming the results of Verleur and Barker [Phys. Rev. 149, 715 (1966)]. Due to the increased sensitivity of ellipsometry in the reststrahlen region, several weak phonon features could also be seen. The lattice absorption peaks are asymmetric and show side bands at the lower and higher frequencies. A single additional peak, as suggested by the percolation model, does not describe the spectra. The cluster model proposed by Verleur and Barker is a better fit to the data. Due to the broadening of the phonon absorption peaks, the authors were unable to find a unique decomposition into multiple components.

The effect of strongly nonreciprocal reflected phase behavior on waveguiding structures containing antiferromagnets

We investigate how nonreciprocal waveguiding structures using antiferromagnets in the terahertz range should be possible within the magnon reststrahl region of such materials. Application of a external magnetic field should make these structures nonreciprocal. In particular, we relate this nonreciprocity to strong nonreciprocity in the phase of radiation reflected off an antiferromagnet at oblique incidence. We confirm the effect using simulations for a copper–vacuum–MnF2 waveguide structure at low temperature, and show that only a small applied field is necessary to induce nonreciprocal propagation in the waveguide. We consider how such a waveguide may be used as a two-way optical switch or a reversible optical diode, and show how damping effects may be minimized.

Surface phonon polaritons for infrared optoelectronics

In recent years, there has been significant fundamental research into surface phonon polaritons, owing to their ability to compress light to extremely small dimensions, low losses, and the ability to support anisotropic propagation. In this Perspective, after briefly reviewing the present state of mid-infrared optoelectronics, we will assess the potential of surface phonon polariton-based nanophotonics for infrared (3–100 μm) light sources, detectors, and modulators. These will operate in the Reststrahlen region where conventional semiconductor light sources become ineffective. Drawing on the results from the past few years, we will sketch some promising paths to create such devices and we will evaluate their practical advantages and disadvantages when compared to other approaches to infrared optoelectronics.

Polaritonic quantization in nonlocal polar materials.

In the Reststrahlen region, between the transverse and longitudinal phonon frequencies, polar dielectric materials respond metallically to light, and the resulting strong light-matter interactions can lead to the formation of hybrid quasiparticles termed surface phonon polaritons. Recent works have demonstrated that when an optical system contains nanoscale polar elements, these excitations can acquire a longitudinal field component as a result of the material dispersion of the lattice, leading to the formation of secondary quasiparticles termed longitudinal-transverse polaritons. In this work, we build on previous macroscopic electromagnetic theories, developing a full second-quantized theory of longitudinal-transverse polaritons. Beginning from the Hamiltonian of the light-matter system, we treat distortion to the lattice, introducing an elastic free energy. We then diagonalize the Hamiltonian, demonstrating that the equations of motion for the polariton are equivalent to those of macroscopic electromagnetism and quantize the nonlocal operators. Finally, we demonstrate how to reconstruct the electromagnetic fields in terms of the polariton states and explore polariton induced enhancements of the Purcell factor. These results demonstrate how nonlocality can narrow, enhance, and spectrally tune near-field emission with applications in mid-infrared sensing.

Structures for surface-enhanced nonplasmonic or hybrid spectroscopy

Abstract Absorption, scattering, and fluorescence are processes that increase with electric field intensity. The most prominent way to enhance electric field intensity is to use localized or propagating surface plasmon polaritons (SPPs) based on metallic particles and nanostructures. In addition, several other, much less well-known, photonic structures that increase electric field intensity exist. Interference enhancement provided by thin dielectric coatings on reflective substrates is able to provide electric field intensity enhancement over the whole substrate and not only at certain hotspots, thereby being in particular suitable for the spectroscopy of thin surface layers. The same coatings on high refractive index substrates may be used for interference-enhanced total internal reflection-based spectroscopy in much the same way as Kretschmann or Otto configuration for exciting propagating SPPs. The latter configurations can also be used to launch Bloch surface waves on 1D photonic crystal structures for the enhancement of electric field intensity and thereby absorption, scattering, and fluorescence-based spectroscopies. High refractive index substrates alone can also, when nanostructured, enhance infrared absorption or Raman scattering via Mie-type resonances. As a further method, this review will cover recent developments to employ phonon polaritons in the reststrahlen region.

Infrared reflectance characterization of porous GaN thin films on sapphire substrate using factorized-Rayleigh model

The surface morphology dependence of porous gallium nitride (PGaN) thin film on infrared (IR) dielectric response was investigated using s-polarized IR reflectance technique. Porosity-induced resonances, namely, Fröhlich modes, were observed in the reststrahlen region of PGaN. Several phenomenological effective medium theories (EMTs), i.e., Maxwell Garnett, Bruggeman, Looyenga, Lichtenecker, and Rayleigh (Ra) models, were used to simulate the dielectric function and Fröhlich modes of PGaN. Among the EMTs, only the Ra model successfully predicts all resonant features that originated from Fröhlich modes. Finally, the Ra model is reformulated in factorized form to take into account the damping of Fröhlich modes and Fröhlich-plasmon coupling. Given the good fitness of experimental and simulated spectra and with the reasonable prediction of Fröhlich modes, factorized-Ra model is determined to be the most appropriate EMT to describe the IR dielectric response of PGaN with cylindrical air hole.

Relative merits of phononics vs. plasmonics: the energy balance approach

Abstract The common feature of various plasmonic schemes is their ability to confine optical fields of surface plasmon polaritons (SPPs) into subwavelength volumes and thus achieve a large enhancement of linear and nonlinear optical properties. This ability, however, is severely limited by the large ohmic loss inherent to even the best of metals. However, in the mid- and far-infrared ranges of the spectrum, there exists a viable alternative to metals – polar dielectrics and semiconductors, in which dielectric permittivity (the real part) turns negative in the Reststrahlen region. This feature engenders the so-called surface phonon polaritons, capable of confining the field in a way akin to their plasmonic analogs, the SPPs. Since the damping rate of polar phonons is substantially less than that of free electrons, it is not unreasonable to expect that phononic devices may outperform their plasmonic counterparts. Yet a more rigorous analysis of the comparative merits of phononics and plasmonics reveals a more nuanced answer, namely, that while phononic schemes do exhibit narrower resonances and can achieve a very high degree of energy concentration, most of the energy is contained in the form of lattice vibrations so that enhancement of the electric field and, hence, the Purcell factor is rather small compared to what can be achieved with metal nanoantennas. Still, the sheer narrowness of phononic resonances is expected to make phononics viable in applications where frequency selectivity is important.

Effects of crystal anisotropy on optical phonon resonances in midinfrared second harmonic response of SiC

We study the effects of crystal anisotropy on optical phonon resonances in the second harmonic generation (SHG) from silicon carbide (SiC) in its Reststrahl region. By comparing experiments and simulations for isotropic 3C-SiC and anisotropic 4H-SiC in two crystal cuts, we identify several pronounced effects in the nonlinear response which arise solely from the crystal anisotropy. Specifically, we demonstrate that the axial and planar transverse optical phonon resonances selectively and exclusively appear in the corresponding tensor elements of the nonlinear susceptibility, enabling observation of an intense SHG peak originating from a weak phonon mode due to zone-folding along the c-axis of 4H-SiC. Similarly, we identify an anisotropy factor $\zeta \equiv \epsilon_\perp/\epsilon_\parallel$ responsible for a steep enhancement of the transmitted fundamental fields at the axial longitudinal optical phonon frequency, resulting in strongly enhanced SHG. We develop a general recipe to extract all these features that is directly applicable to all wurtzite-structure polar dielectrics, where a very similar behavior is expected. Our model study illustrates the opportunities for utilizing the crystal anisotropy for selectively enhancing nonlinear-optical effects in polar dielectrics, which could potentially be extended to built-in anisotropy in artificially designed hybrid materials.

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.

Two-phonon absorption in LiF and NiO from infrared ellipsometry

Using Fourier-transform infrared spectroscopic ellipsometry, the infrared lattice absorption of LiF and NiO was studied in the reststrahlen region. The transverse optical (TO) and longitudinal optical phonon energies, broadenings, and amplitudes were determined. Both materials also show a weak two-phonon absorption, which modifies the shape of the reststrahlen bands. The authors did not find any evidence of a splitting of the TO phonon in NiO due to antiferromagnetic ordering and place an upper limit of 17 cm−1 on this splitting.

Complete dispersion analysis of single crystal neodymium gallate

A single crystal of neodymium gallate was investigated by FTIR-spectroscopy in the reststrahlen region between 100–1000cm−1. The three spectra of the crystal in principal orientations were analyzed by dispersion analysis and the dispersion parameters and the dielectric tensor function were obtained. This allows to properly characterize and quantitatively analyze films of this important substrate material by IR-optical methods.

Impact of dielectric parameters on the reflectivity of 3C–SiC wafers with a rough surface morphology in the reststrahlen region

A layer-on-substrate model is used to obtain the infrared reflectance for 3C–SiC with a rough surface morphology. The effect of varying dielectric parameters of the “damaged layer” on the observed reflectivity of the 3C–SiC in the reststrahlen region is assessed. Different simulated reflectance spectra are obtained to those if the dielectric parameters of the “substrate” were varied. Most notable changes in the shape of the simulated reststrahlen peak are observed for changes in the high frequency dielectric constant, the phonon damping constant, the phonon frequencies and “thickness” of damaged surface layer.

Infrared reflectance studies of hillock-like porous zinc oxide thin films

We investigated the infrared (IR) reflectance characteristics of hillock-like porous zinc oxide (ZnO) thin films on silicon substrates. The IR reflectance spectra of the porous samples exhibited an extra resonance hump in the reststrahlen region of ZnO compared with the as-grown sample. Oscillation fringes with different behaviors were also observed in the non-reststrahlen region of ZnO. Standard multilayer optic technique was used with the effective medium theory to analyze the observations. Results showed that the porous ZnO layer consisted of several sublayers with different porosities and thicknesses. These findings were confirmed by scanning electron microscopy measurements.

The origin of a peak in the reststrahlen region of SiC

A peak in the reststrahlen region of SiC is analyzed in order to establish the origin of this peak. The peak can be associated with a thin damaged layer on the SiC wafers, and a relation is found between surface roughness and the height of this peak, by modeling the damaged layer as an additional layer when simulating the reflectivity from the wafers.

Infrared reflectance of GaP nanorods

The reflectance of GaP nanorods on GaP substrates was investigated in the frequency range of 300–500 cm –1 by Fourier transform infrared (FTIR) reflectance spectroscopy. GaP nanorods were fabricated by the anodic electrochemical etching technique. The structure of nanorods, formed by using galvanostatic and potentiostatic etching regimes was studied by the SEM technique. The correlation between particular features in the infrared reflection spectra in the reststrahlen region and the morphology of nanorods was analysed and discussed.

Mineralogy and thermal properties of V-type Asteroid 956 Elisa: Evidence for diogenitic material from the Spitzer IRS (5–35 μm) spectrum

We present the thermal infrared (5–35 μm) spectrum of 956 Elisa as measured by the Spitzer Infrared Spectrograph (“IRS”; Houck, J.R. et al. [2004]. Astrophys. J. Suppl. 154, 18–24) together with new groundbased lightcurve data and near-IR spectra. From the visible lightcurve photometry, we determine a rotation period of 16.494 ± 0.001 h, identify the rotational phase of the Spitzer observations, and estimate the visible absolute magnitude ( H V ) at that rotational phase to be 12.58 ± 0.04. From radiometric analysis of the thermal flux spectrum, we find that at the time of observation 956 Elisa had a projected radius of 5.3 ± 0.4 km with a visible albedo p V = 0.142 ± 0.022, significantly lower than that of the prototype V-type asteroid, 4 Vesta. (This corresponds to a radius of 5.2 ± 0.4 km at lightcurve mean.) Analysis with the standard thermal model (STM) results in a sub-solar temperature of 292.3 ± 2.8 K and beaming parameter η = 1.16 ± 0.05. Thermophysical modeling places a lower limit of 20 J m - 2 K - 1 s - 1 2 on the thermal inertia of the asteroid’s surface layer (if the surface is very smooth) but more likely values fall between 30 and 150 J m - 2 K - 1 s - 1 2 depending on the sense of rotation. The emissivity spectrum, calculated by dividing the measured thermal flux spectrum by the modeled thermal continuum, exhibits mineralogically interpretable spectral features within the 9–12 μm reststrahlen band, the 15–16.5 μm Si–O–Si stretching region, and the 16–25 μm reststrahlen region that are consistent with pyroxene of diogenitic composition: extant diogenitic pyroxenes fall within the narrow compositional range Wo 2±1En 74±2Fs 24±1. Spectral deconvolution of the 9–12 μm reststrahlen features indicates that up to ≈20% olivine may also be present, suggesting an olivine-diogenite-like mineralogy. The mid-IR spectrum is inconsistent with non-cumulate eucrite as the major component on the surface of 956 Elisa, although cumulate eucrite material may be present at abundances lower than that of the diogenite component. Analysis of new near-IR spectra of 956 Elisa with the Modified Gaussian Model (MGM; Sunshine, J.M., Pieters, C.M., Pratt, S.F. [1990]. J. Geophys. Res. 95 (May), 6955–6966) results in two pyroxene compositions: 75% magnesian low-Ca pyroxene and 25% high-Ca pyroxene. High-Ca pyroxene is not evident in the mid-IR data, but may belong to a component that is underrepresented in the mid-IR spectrum either because of its spatial distribution on the asteroid or because of its particle size. High-Ca pyroxenes that occur as exsolution lamellae may also be more evident spectrally in the NIR than in the mid-IR. In any case, we find that the mid-IR spectrum of 956 Elisa is dominated by emission from material of diogenite-like composition, which has very rarely been observed among asteroids.

The influence of various dielectric parameters on the reststrahlen region of SiC

The reststrahlen region of SiC is analysed with the goal of establishing the origin of different shapes of this band, by varying the dielectric parameters involved when simulating the reststrahlen region as obtained by infrared reflectance.

IR reflection, attenuated total reflection, and Raman scattering of porous polar III–V semiconductors

AbstractOptical properties of porous III–V compounds (GaAs, GaP, InP) in the far infrared (IR) reststrahlen region have been studied by IR reflection and attenuated total reflection (ATR). Comparison of obtained data with Raman scattering (RS) spectra have been performed. Porous layers on III–V compounds wafers were obtained by electrochemical etching. Morphology of porous layers was investigated by methods of atomic force microscopy (AFM) and scanning electron microscopy (SEM), including cross‐section measurements. The ATR measurements allow to study dispersion and damping of surface phonon polaritons (SPPs) in λ = 20–50 µm spectral region. The ATR measurements were carried out in Otto geometry under frequency‐scanning regime at several constant angles of incidence of light. The reflection spectra of porous samples demonstrate change of the reststrahlen band shape due to direct excitation of surface polaritons. It was enabled to excite mixed plasmon–phonon surface modes for semiconductors with free electron concentrations of 1017–1018 cm−3. Frequencies of bulk TO‐, LO‐phonons, surface phonons, and coupled plasmon–phonon modes in the case of high doped semiconductors have been obtained and compared for three spectroscopic methods – reflectance, ATR, and RS.

Localized interface phonon polaritons in superlattice with a structural defect consisting of ternary mixed crystal

Abstract Using a transfer matrix method, we investigate the existence and characteristics of the localized interface phonon-polariton modes (IPPMs) in superlattice (SL) with a structural defect consisting of ternary mixed crystal (Al x Ga 1− x As). The results show that the introduction of two-mode behavior of the ternary mixed crystal leads to the rich and varied localized IPPMs spectra with new features. The characteristics and positions of the localized IPPMs in the Reststrahlen region are strongly dependent on the concentration x of the ternary mixed crystal. Moreover, it is found that the localized IPPMs are sensitive to the thicknesses of the defect and constituent layers as well as to the transverse wavenumber q ∥ .

Angular dependence of the reflectance from an isotropic polydomain medium: experimental verification

Based on average reflectance and transmittance theory (ARTT) it has been shown recently that randomly oriented polydomain materials with optically large domains can exhibit an unusual behaviour of the dependence of reflectance on the angle of incidence. In contrast to isotropic polydomain media with optically small domains it was found, for example, that Rp can exceed Rs at certain angle of incidences ranges if the domains are optically uniaxial. This theoretically predicted behaviour has been proved by experimental spectra of randomly oriented polycrystalline fresnoite recorded at an angle of incidence of 70° at the high-wavenumber side of the reststrahlen region. While the correspondence between simulated Rp and Rs spectra based on the single-crystal data and the experimental spectra is quite acceptable, it was necessary to refine these single-crystal data in order to obtain a satisfactory resemblance between the simulated and experimental cross-polarization terms.