Transverse Optical Modes Research Articles

Theoretical optimization of transverse waveguiding in oxide-confined VCSELs with internal photonic crystals

We systematically investigate transverse optical modes in oxide-confined vertical-cavity surface-emitting lasers (VCSELs) with photonic crystal (PC) structures embedded within the cavity of the VCSEL. We consider the interplay between the effective refractive index step of the oxide and the semiconductor and the oxide aperture size. The PC lattice period a, the diameter of the holes d, and the number of lattice periods around the central defect are considered. We evaluate confinement factors for the various transverse modes and consider their spatial extent in the transverse plane which we relate to the output power. Results suggest that the power of the single-mode photonic crystal vertical-cavity surface-emitting lasers (PC-VCSELs) is limited by the smaller radius of the fundamental mode of the PC-VCSEL compared to the VCSEL with no PC. We discuss various designs aimed to optimize power into the single-fundamental mode and to discriminate from power going into other modes.

Theory of fundamental microwave absorption in sapphire (α-Al2O3)

An accurate model for intrinsic dielectric loss in sapphire (α-Al2O3) is presented. The proposed model is based on a theory of electromagnetic field absorption governed by multiphonon relaxation processes influenced by a finite lifetime of thermal phonons. Expressions for anisotropic sapphire dielectric loss tangent are derived utilizing sapphire dielectric function given in terms of the quasiharmonic approximation. The frequency-dependent two- and three-phonon damping constants of each fundamental transverse optical mode were determined numerically employing the accurate anharmonic coefficient computations based on sapphire lattice-dynamical data. The results of the dielectric loss tangent calculations in microwave and millimeter-wave regions are presented. The developed sapphire dielectric loss model offers excellent agreement between the experimental and calculated magnitudes of the tan δ components and also accurately reproduces their frequency and temperature dependencies.

Infrared optical properties of calcium lanthanum sulfide

The fundamental infrared optical properties of CaLa 2S 4 were determined by specular reflectance measurements from theoretically dense, optically transparent, polycrystalline ceramics. Kramers–Kronig transformation of the reflectance spectra permitted the extraction of refractive index, and transverse and longitudinal optic modes. Five transverse modes predicted by factor group analysis were observed with the intense high wavenumber mode occurring at 142 and 205 cm − 1 . The other three modes are weak and occur at 37, 59, and 86 cm − 1 . The two high wavenumber intense modes have identifiable longitudinal modes at l51 and 318 cm − 1 .

Raman Piezospectroscopy of Phonons in Bulk 6H-SiC

Raman piezospectroscopy of high quality 6H-SiC crystals is presented. The crystals used in experiments were grown by the seeded physical vapor transport method. Uniaxial stress up to 0.9 MPa, obtained using a spring apparatus, was applied along [11–20] and [10–10] directions. It was found that the application of uniaxial stress led to different energy shifts of the observed phonon excitations in the investigated 6H-SiC crystals. The obtained pressure coefficients vary in the range 0.98–5.5 cm−1 GPa−1 for different transverse optical phonon modes. For longitudinal optic phonon modes pressure coefficients in the range 1.6–3.6 cm−1 GPa−1 were found. The data obtained could be useful in evaluation of local strain fields in SiC based structures and devices including epitaxial graphene.

Kohn anomalies in graphene nanoribbons

The quantum corrections to the energies of the $\ensuremath{\Gamma}$ point optical phonon modes (Kohn anomalies) in graphene nanoribbons (NRs) are investigated. We show theoretically that the longitudinal optical (LO) modes undergo a Kohn anomaly effect, while the transverse optical (TO) modes do not. In relation to Raman spectroscopy, we show that the longitudinal optical modes are not Raman active near the zigzag edge, while the transverse optical modes are not Raman active near the armchair edge. These results are useful for identifying the orientation of the edge of graphene nanoribbons by G band Raman spectroscopy, as is demonstrated experimentally. The differences in the Kohn anomalies for nanoribbons and for metallic single-wall nanotubes are pointed out, and our results are explained in terms of pseudospin effects.

Thermal Properties for Bulk Silicon Based on the Determination of Relaxation Times Using Molecular Dynamics

Molecular dynamics simulations are performed to estimate acoustical and optical phonon relaxation times, dispersion relations, group velocities, and specific heat of silicon needed to solve the Boltzmann transport equation (BTE) at 300 K and 1000 K. The relaxation times are calculated from the temporal decay of the autocorrelation function of the fluctuation of total energy of each normal mode in the ⟨100⟩ family of directions, where the total energy of each mode is obtained from the normal mode decomposition of the motion of the silicon atoms over a period of time. Additionally, silicon dispersion relations are directly determined from the equipartition theorem obtained from the normal mode decomposition. The impact of the anharmonic nature of the potential energy function on the thermal expansion of the crystal is determined by computing the lattice parameter at the cited temperatures using a NPT (i.e., constant number of atoms, pressure, and temperature) ensemble, and are compared with experimental values reported in the literature and with those computed analytically using the quasiharmonic approximation. The dependence of the relaxation times with respect to the frequency is identified with two functions that follow the functional form of the relaxation time expressions reported in the literature. From these functions a simplified version of relaxation times for each normal mode is extracted. Properties, such as group and phase velocities, thermal conductivity, and mean free path, needed to further develop a methodology for the thermal analysis of electronic devices (i.e., from nano- to macroscales) are determined once the relaxation times and dispersion relations are obtained. The thermal properties are validated by comparing the BTE-based thermal conductivity against the predictions obtained from the Green–Kubo method. It is found that the relaxation times closely resemble the ones obtained from perturbation theory at high temperatures; the contribution to the thermal conductivity of the transverse acoustic, longitudinal acoustic, and longitudinal optical modes being approximately 30%, 60%, and 10%, respectively, and the contribution of the transverse optical mode negligible.

Dynamical behavior ofSeO4tetrahedra in protonic conductorK3H(SeO4)2

Neutron powder diffraction and inelastic neutron scattering experiments were performed to clarify the mechanism of phase transition and protonic conductivity of ${\text{K}}_{3}\text{H}{({\text{SeO}}_{4})}_{2}$. A rotational ${\text{SeO}}_{4}$ tetrahedra mode at the zone boundary $L$-point accounts for the symmetrical change in space group from $R\overline{3}m$ to $C2/c$. No significantly anomaly was observed in the transversal acoustic and under-damped optical modes, while a broad spectrum was observed around 0 meV at the $L$-point above ${T}_{C}$. The spectrum depends on the temperature and the dependence is represented by the soft mode due to an over-damped phonon both $Q$ and energy space. The rotational mode of tetrahedra drives the improper ferroelastic phase transition.

Lattice dynamics of cubicNaNbO3: An inelastic neutron scattering study

The phonon-dispersion relations for cubic ${\text{NaNbO}}_{3}$ have been determined along the [100], [110], and [111] directions using inelastic neutron scattering. A simultaneous softening of transverse acoustic (TA) phonon modes occurs at the zone-boundary $M(0.5,0.5,0)$ and $R(0.5,0.5,0.5)$ points, indicating the instabilities of in-phase and out-of-phase rotations of the oxygen octahedra about the [001] direction. These zone-boundary modes exhibit an extremely gradual softening as the temperature is lowered toward ${T}_{c1}=913\text{ }\text{K}$. The inelastic diffuse scattering at the $M(0.5,0.5,0)$ point polarized along the $[1\overline{1}0]$ direction remains up to 9 meV, whereas the inelastic diffuse scattering at the $M$ point polarized along the [001] direction is suppressed. Polarization dependence shows that the inelastic diffuse scattering at the $M$ and $R$ points originates from the dynamical motion of oxygen octahedra. The transverse optic (TO) phonon modes along the [110] direction polarized with the [001] direction also soften around $\mathbf{q}=[0.15,0.15,0]$ and merge into the lower-energy TA phonon modes. This is basically similar to the waterfall phenomenon observed for Pb-based perovskite relaxor ferroelectrics. The extreme broad longitudinal acoustic (LA) and TA modes in ${\text{NaNbO}}_{3}$ contribute significantly to the inelastic diffuse scattering around Bragg points. The broadening of TA and TO modes are attributed to the anharmoic lattice potential in ${\text{NaNbO}}_{3}$. The coexistence of long-wavelength and zone-boundary phonon instabilities above ${T}_{c1}=913\text{ }\text{K}$ is closely related to the complex sequence of phase transitions in ${\text{NaNbO}}_{3}$.

The Magneto-Optical Response of Diluted Magnetic Semiconductor CdTe-Cd1-xMnxTe Multi Quantum Wells in the Voigt Configuration

We have calculated the s- and p-polarized far infrared magnetoplasmon spectra of doped CdTe‐Cd1ixMnxTe multi quantum wells in the presence of a static magnetic field up to 20 T parallel to the surface of the layers using a macroscopic model based on eective medium theory, using a novel approach which gives a good account of the data together with a clear physical interpretation of the various spectral features, such as the free carrier and optical phonon properties. The results show that the transverse optical modes (for the whole composition range, x = 0 to 1) are sensitive and change linearly with respect to the composition parameter. In p-polarized reflectivity the cyclotron resonance experiences a blue shift when the magnetic field strength increases. Also, the analysis of the dielectric tensor function and the Voigt dielectric function is used to determine the carriers’ cyclotron eective masses (for both holes and electrons) as a function of composition. Furthermore, a modified random element iso-displacement approach has been extended for the multi layers to analyze the influence of the composition on the optical phonon response in the barrier layer.

Optical nanocrystallography with tip-enhanced phonon Raman spectroscopy

Conventional phonon Raman spectroscopy is a powerful experimental technique for the study of crystalline solids that allows crystallography, phase and domain identification on length scales down to approximately 1 microm. Here we demonstrate the extension of tip-enhanced Raman spectroscopy to optical crystallography on the nanoscale by identifying intrinsic ferroelectric domains of individual BaTiO(3) nanocrystals through selective probing of different transverse optical phonon modes in the system. The technique is generally applicable for most crystal classes, and for example, structural inhomogeneities, phase transitions, ferroic order and related finite-size effects occurring on nanometre length scales can be studied with simultaneous symmetry selectivity, nanoscale sensitivity and chemical specificity.

Study of phase transformation dynamics in Na1/2Bi1/2TiO3 by Mandelstam-Brillouin scattering

The results of the study of Mandelstam-Brillouin light scattering in single-crystal Na1/2Bi1/2TiO3 within a broad temperature interval covering successively the cubic, tetragonal, and rhombohedral phases are reported. Measurements conducted within the range 820–300 K have revealed quasi-elastic scattering and distortion of the phonon spectra in shape, which suggests possible coupling between the low-frequency transverse optical and acoustic modes. These two observed phenomena are believed to be closely interrelated.

Renormalization of the phonon spectrum in semiconducting single-walled carbon nanotubes studied by Raman spectroscopy

In situ Raman experiments together with transport measurements have been carried out in single-walled carbon nanotubes as a function of electrochemical top gate voltage (Vg). We have used the green laser (EL=2.41 eV), where the semiconducting nanotubes of diameter ~1.4 nm are in resonance condition. In semiconducting nanotubes, the G−- and G+-mode frequencies increase by ~10 cm−1 for hole doping, the frequency shift of the G− mode is larger compared to the G+ mode at the same gate voltage. However, for electron doping the shifts are much smaller: G− upshifts by only ~2 cm−1 whereas the G+ does not shift. The transport measurements are used to quantify the Fermi-energy shift (EF) as a function of the gate voltage. The electron-hole asymmetry in G− and G+ modes is quantitatively explained using nonadiabatic effects together with lattice relaxation contribution. The electron-phonon coupling matrix elements of transverse-optic (G−) and longitudinal-optic (G+) modes explain why the G− mode is more blueshifted compared to the G+ mode at the same Vg. The D and 2D bands have different doping dependence compared to the G+ and G− bands. There is a large downshift in the frequency of the 2D band (~18 cm−1) and D (~10 cm−1) band for electron doping, whereas the 2D band remains constant for the hole doping but D upshifts by ~8 cm−1. The doping dependence of the overtone of the G bands (2G bands) shows behavior similar to the dependence of the G+ and G− bands.

Resonant Raman study of phonons in high-quality colloidal CdTe nanoparticles

We report on a resonant Raman scattering study of colloidal CdTe nanoparticles (NPs). The perfect crystallinity and narrow size distribution of the NPs allowed at least three additional spectral features near the main longitudinal optical phonon peak to be resolved at 50 K. We assign these features to scattering by transverse (145 cm−1) and surface (159 cm−1) optical phonon modes as well as to a combined optical-acoustic phonon mode(s) (180–200 cm−1). Both the transverse and combined optical-acoustic phonon modes were not reported previously for CdTe NPs.

Femtosecond laser excitation of coherent optical phonons in ferroelectricLuMnO3

We have used femtosecond pump-probe spectroscopy to excite and probe coherent optical phonon vibrations in single crystals of hexagonal ferroelectric ${\text{LuMnO}}_{3}$. An optical phonon mode of ${A}_{1}$ symmetry was coherently excited with 25 fs pump-laser pulses $(\ensuremath{\lambda}\ensuremath{\approx}800\text{ }\text{nm})$. The phonon mode, involving Lu ion motion along the $c$ axis, was identified as the soft mode driving the ferroelectric transition. The excitation mechanism was determined to be purely displacive in nature due to resonant excitation of a narrow intra-atomic ${d}_{xy,{x}^{2}\ensuremath{-}{y}^{2}}\ensuremath{\rightarrow}{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ transition in Mn. The lifetime of the $\text{Mn}\text{ }{d}_{xy,{x}^{2}\ensuremath{-}{y}^{2}}\ensuremath{\rightarrow}{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ excitation was measured to be 0.8 ps. A remarkable reversal of the sign of the oscillation amplitude ($\ensuremath{\pi}$ phase shift) of the reflectivity curve was observed upon comparing longitudinal-optical (LO) with transverse-optical (TO) mode geometries. The phase reversal is attributed to the macroscopic electric depolarization field accompanying infrared-active longitudinal phonon modes but absent in TO modes. In addition to the direct effect of the ion motion on the optical properties, which is the same in LO and TO modes, the longitudinal depolarization field of the LO mode gives rise to an additional modulation of the refractive index via the linear electro-optic effect which dominates the optical response.

Hydrogenated Amorphous Silicon Layer Formation by Inductively Coupled Plasma Chemical Vapor Deposition and Its Application for Surface Passivation of p-Type Crystalline Silicon

The satisfactory surface passivation properties of hydrogenated amorphous silicon (a-Si:H) prepared by inductively coupled plasma chemical vapor deposition (ICP-CVD) at a low temperature (400 °C) on p-type crystalline silicon wafers are reported. Certain parameters, such as SiH4/H2 ratio, annealing temperature, film thickness, and substrate temperature, were varied to determine their optimal levels. Completely amorphous layers with a broad transverse optic (TO) mode peak at approximately 480 cm-1 were identified by Raman spectroscopy, and an optical band gap of approximately 1.6 eV was determined from optical absorption data. A maximum carrier lifetime of 53 µs for an a-Si:H thickness of 15 nm and an annealing temperature of 450 °C was measured for 525-µm-thick p-type crystalline silicon (c-Si) substrates with a resistivity in the range of 1–20 Ω cm by the quasi-steady-state photoconductance (QSSPC) method. The lowest value of interface trapped charge density (Dit) of approximately 3.34 ×1011 cm-2 eV-1 was estimated by capacitance–voltage (C–V) measurement using a metal–insulator–semiconductor (MIS) structure. Furthermore, simple processing with satisfactory results can be achieved with substrate heating at 400 °C during deposition. The optimal conditions of a SiH4/H2 gas ratio of 1/1 and a substrate temperature of 400 °C were implemented for a passivation layer thickness of 5 nm.

Phonon Dispersion and Thermodynamics Properties of CaF2 via Shell Model Molecular Dynamics Simulations

The phonon and thermodynamics properties of face-centered cubic CaF2 at high pressure and high temperature are investigated by using the shell model interatomic pair potential within General Utility Lattice Program (GULP). The phonon dispersion curves and the corresponding density of state (PDOS) in this work are consistent with the experimental data and other theoretical results. The transverse optical (TO) and longitudinal optical (LO) mode splitting as well as heat capacity at constant volume CV and entropy S versus pressure and temperature are also obtained.

Role of Covalent Defects on Phonon Softening in Metallic Carbon Nanotubes

We have examined how electrical characteristics and charging dependent Raman G-band phonon softening in individual metallic carbon nanotubes are influenced by covalent defects. In addition to decreasing electrical conductance with increasing on/off current ratio eventually leading to semiconducting behavior, adding covalent defects reduces the degree of softening and broadening of longitudinal optical (LO) phonon mode of the G-band near the charge neutrality point where the bands cross. On the other hand, the transverse optical (TO) mode softening is enhanced by defects. Implications on the interpretation of Raman G-band phonon softening and on utilizing Raman spectroscopy to examine covalent functionalization are discussed.

Raman scattering of polycrystalline GaSb thin films grown by the co-evaporation process

This paper reports that GaSb thin films have been co-deposited on soda-lime glass substrates. The GaSb thin film structural properties are characterized by Raman spectroscopy. The Sb–A1g/GaSb–TO ratio decreases rapidly with the increase of substrate temperature, which suggests a small amount of crystalline Sb in the GaSb thin film and suggests that Sb atoms in the thin film decrease. In Raman spectra, the transverse optical (TO) mode intensity is stronger than that of the longitudinal optical (LO) mode, which indicates that all the samples are disordered. The LO/TO intensity ratio increases with increasing substrate temperature which suggests the improved polycrystalline quality of the GaSb thin film. A downshift of the TO and LO frequencies of the polycrystalline GaSb thin film to single crystalline bulk GaSb Raman spectra is also observed. The uniaxial stress in GaSb thin film is calculated and the value is around 1.0 GPa. The uniaxial stress decreases with increasing substrate temperature. These results suggest that a higher substrate temperature is beneficial in relaxing the stress in GaSb thin film.

A tetragonal phase of superhard BC2N

Based on first-principles calculation, we predict a tetragonal phase of BC2N (t-BC2N), which matches the experiment well because the estimated Vickers hardness and the simulated X-ray diffraction (XRD) and Raman patterns are in excellent agreement with the experimental results besides the low total energy and formation energy. In particular, we acquire the underlying physics behind the apparent lack of the transverse optical mode in the measured Raman spectrum and find the interesting electronic structure transition among the polymorph of superhard BC2N compounds.

Raman scattering intensities in BaTiO3 and PbTiO3 prototypical ferroelectrics from density functional theory

Nonlinear optical susceptibilities and Raman scattering spectra of the ferroelectric phases ofBaTiO3 andPbTiO3 are computed using a first-principles approach based on density functional theory and takingadvantage of a recent implementation based on the nonlinear response formalism and the2n+1 theorem. These two prototypical ferroelectric compounds were chosen to demonstrate theaccuracy of the Raman calculation based both on their complexity and their technologicalimportance. The computation of the Raman scattering intensities has been performed notonly for the transverse optical modes, but also for the longitudinal optical ones. Theagreement between the measured and computed Raman spectra of these prototypicalferroelectrics is remarkable for both the frequency position and the intensity ofRaman lines. This agreement presently demonstrates the state-of-the-art in thecomputation of Raman responses on one of the most complex systems, ferroelectrics,and constitutes a step forward in the reliable prediction of their electro-opticalresponses.