Complex Dielectric Tensor Research Articles

Generalized ellipsometry and dielectric tensor of rubrene single crystals

The optical spectra of rubrene single crystals are reported and compared with those of the molecule in solution. From generalized ellipsometry and a proper biaxial model, the complex dielectric tensor is deduced in the spectral region of the excitonic transitions of the crystal between 2.2 eV band 4.4 eV, where the optical bands are assigned and rationalized on the basis of the molecular and crystal symmetries.

Investigation of Local Coordination and Electronic Structure of Dielectric Thin Films from Theoretical Energy-Loss Spectra

AbstractQuantum mechanical simulations were performed to calculate the valence electron energy-loss spectra (VEELS) for hafnium oxide, hafnium silicate, silicon oxide and silicon systems using the full potential Linearized Augmented Plane Wave (LAPW) formalism within the Density Functional Theory (DFT) framework. The needed energy-loss function (ELF) was derived from the calculation of the complex dielectric tensor within the random phase approximation (RPA). The calculated spectra were compared with experimental scanning transmission electron microscopy (STEM)/EELS of atomic layer deposited (ALD) HfO2 on Si(100) to evaluate their use as a “fingerprint” method that can be used to distinguish among various polymorphs of HfO2 thin films and relate the fine structure to the electronic structure and local bonding environment. Calculated low-loss spectra are found to be in satisfactory agreement with experimental data. Also, the combination of such theoretical calculations and experimental data could be of key importance in our understanding of fundamental issues of these systems. Compared to energy-loss near edge structure (ELNES) or core energy-loss spectra, the ELF calculated for low-loss spectra is computationally less expensive and can prove useful for prompt analysis.

The optics of vertebrate photoreceptors: Anisotropy and form birefringence

The optics of vertebrate photoreceptors have been investigated with specific reference to the effect of form birefringence. The complex dielectric tensor of the lamellar-like outer segment structure has been derived, allowing the transverse spectral absorbance to be calculated for different incident polarizations. These results were used to calculate the changes in the cellular dichroic ratio as a function of both the volume occupied by the bilayers and the real and complex parts of the intrinsic birefringence of the bilayers. Physiologically realistic values of these parameters show the cellular dichroic ratio to be greater than the bilayer dichroic ratio by a factor of ≈1.3. Furthermore, the calculations of spectral absorbance indicate that form birefringence may affect measurements of optical density in transversely orientated outer segments.

Mo6S6 nanowires: structural, mechanical and electronic properties

The properties of Mo_6S_6 nanowires were investigated with ab-initio calculations based on the density-functional theory. The molecules build weakly coupled one-dimensional chains, like Mo_6Se_6 and Mo_6S_(9-x)I_x, and the crystals are strongly uniaxial in their mechanical and electronic properties. The calculated moduli of elasticity and resilience along the chain axis are c_(11) = 320 GPa and E_R = 0.53 GPa, respectively. The electronic band structure and optical conductivity indicate that the Mo_6S_6 crystals are good quasi-one-dimensional conductors. The frequency-dependent complex dielectric tensor epsilon, calculated in the random-phase approximation, shows a strong Drude peak in epsilon_parallel, i.e., for the electric field polarised parallel to the chain axis, and several peaks related to interband transitions. The electron energy loss spectrum is weakly anisotropic and has a strong peak at the plasma frequency (hbar omega_p) is approx 20 eV. The stability analysis shows that Mo_6S_6 is metastable against the formation of the layered MoS_2.

Application of algebraic invariants to full-wave simulators - rigorous analysis of the optical properties of nanowires

We show an application of four states algebraic invariants to the extraction of the main optical properties of anisotropic semiconductor thin nanowires such as the complex propagation constant of the guided modes and the reflectivity at the waveguide terminations. In order to provide a numerical example, we calculate the modal and threshold gains for the first few guided modes. This has been done in conjunction with the use of a full-wave finite-element method simulator without the isotropic approximation of passive GaN. Moreover, the device has been directly analyzed in his active state, i.e., with a complex dielectric tensor: in principle, a rigorous complex resonance for simultaneously calculating the lasing frequency and the threshold gain may be performed.

Fractional rotational diffusion of rigid dipoles in an asymmetrical double-well potential

The longitudinal and transverse components of the complex dielectric susceptibility tensor of an assembly of dipolar molecules rotating in an asymmetric double-well potential are evaluated using a fractional rotational diffusion equation (based on the diffusion limit of a fractal time random walk) for the distribution function of orientations of the molecules on the surface of the unit sphere. The calculation is the fractional analog of the Debye theory of orientational relaxation in the presence of external and mean field potentials (excluding inertial effects). Exact and approximate (based on the exponential separation for normal diffusion of the time scales of the intrawell and overbarrier relaxation processes associated with the bistable potential) solutions for the dielectric dispersion and absorption spectra are obtained. It is shown that a knowledge of the characteristic relaxation times for normal rotational diffusion is sufficient to predict accurately the anomalous dielectric relaxation behavior of the system for all time scales of interest. The model explains the anomalous (Cole-Cole-like) relaxation of complex dipolar systems, where the anomalous exponent differs from unity (corresponding to the normal dielectric relaxation), i.e., the relaxation process is characterized by a broad distribution of relaxation times (e.g., in glass-forming liquids).

Microscopic calculation of axial dispersion for quaterthiophene crystals

We present a microscopic calculation of the axial dispersion for the quaterthiophene crystal in a spectral region including the first and higher molecular excited states. After evaluating the complex dielectric tensor near the corresponding Frenkel excitons we observe that two of the principal axes referring to the upper Davydov states rotate with energy within the reflection plane of the monoclinic unit cell. In particular, we show the role of this dispersion in understanding the relationship between the transverse dielectric tensor and the measured optical spectra.

Fractional rotational Brownian motion in a uniform dc external field

The longitudinal and transverse components of the complex dielectric susceptibility tensor of an assembly of dipolar particles subjected to a dc bias field are evaluated in the context of a fractional noninertial rotational diffusion model. Exact and approximate solutions for the dielectric dispersion and absorption spectra are obtained. It is shown that a knowledge of the effective relaxation times for normal rotational diffusion is sufficient to predict accurately the anomalous dielectric relaxation behavior of the system for all time scales of interest. Simple equations for the characteristic frequencies of the dielectric loss spectra are obtained in terms of the physical model parameters (dimensionless field and fractional exponent). The model explains the anomalous (Cole-Cole like) relaxation of complex dipolar systems, where the anomalous exponent differs from unity (corresponding to the normal dielectric relaxation), i.e., the relaxation process is characterized by a broad distribution of relaxation times.

Optical anisotropy of nanotube suspensions.

A semimacroscopic model of an optically anisotropic nanotube suspension is derived perturbatively from Maxwell's equations in a dielectric medium. We calculate leading-order expressions, valid in the dilute and semidilute limits, for the intrinsic and form contributions to the complex dielectric tensor in terms of the volume fraction, mean orientation, aspect ratio, optical anisotropy, and optical contrast of the nanotubes. The birefringence and dichroism are derived explicitly to leading order in fluctuations, and the connection with depolarized light scattering is established. The results are generalized to include tube deformation.

Absorption effects in liquid crystal waveguides.

An analytical and numerical study of the propagation of optical fields through a nematic hybrid slab is developed. We take into account explicitly the absorption of radiation by the liquid crystal by introducing a complex dielectric tensor. For a low intensity beam we first derive the eikonal equation and from it we calculate the ray trajectories in the optical limit. We show that in the presence of absorption, there are no caustics within the slab. Then we consider the WKB limit and calculate the field transverse magnetic modes, their number and their cutoff frequencies. We show that for both limits the agreement between our analytical and numerical results for the propagation constants is excellent, while there are larger differences in the analytically and numerically calculated field amplitudes. These differences show that absorption effects are important for this quantity and have their origin in the fact that the chosen parameter values in our exact numerical calculations, strictly speaking, do not lie within the limits of validity of the WKB approximation. Although a more precise comparison between these approaches requires the use of different sets of values of the relevant parameters, our analysis shows the effects and complications arising from the inclusion of absorption. Finally, we discuss the scope and limitations of our approach.

Calculated Optical Absorption of Anthracene under High Pressure

Starting from the crystalline structure optimized with respect to the internal geometry we investigate the optical properties of anthracene up to 10.2 GPa within density functional theory. Using the random phase approximation we calculate the frequency-dependent complex dielectric tensor for several pressure values. We observe a red-shift of the absorption spectrum as a function of pressure, which is in good agreement with literature data.

Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs

We report on the time-domain terahertz (THz) magneto-optical Kerr spectroscopy in the frequency range from 0.5 to 2.5 THz. The developed technique employs reflection geometry, enabling high-frequency noncontact Hall measurements in opaque samples. We also present a method to reveal the off-diagonal component of the complex dielectric tensor from the measured polarization-dependent THz wave forms. At a static magnetic field of 0.48 T, a large Kerr rotation over 10° originating from magnetoplasma resonance is observed in an n-type undoped InAs wafer at room temperature. This indicates the strong potential of this material for the polarization modulator in the THz regime.

Directional magnetization effects in magnetic circular dichroism spectra of Fe

Magnetic circular dichroism (MCD) spectra exhibit distinctively different spectral and angular variations that depend strongly on the interacting geometry defined by the propagation vector of the radiation, the direction of magnetization $\mathbf{M},$ and the angle of incidence ${\ensuremath{\theta}}_{i}.$ Two extreme cases for MCD measurements around the Fe ${M}_{2,3}$ region, where the magnetization is either parallel (longitudinal geometry) or perpendicular (polar geometry) to the surface, are presented and compared with theoretical predictions based upon the classical Fresnel formalism for reflections. The magnetic properties of Fe were modeled by a frequency-dependent, complex dielectric tensor $\ensuremath{\epsilon}(\ensuremath{\omega}).$ Agreement between the model predictions and the reflection MCD measurements performed in both polar and longitudinal geometries demonstrates the validity of this approach.

Optical functions and electronic structure ofCuInSe2,CuGaSe2,CuInS2,andCuGaS2

We report on the complex dielectric tensor components of four chalcopyrite semiconductors in the optical energy range (1.4-5.2 eV, from 0.9 eV for CuInSe2) determined at room temperature by spectroscopic ellipsometry. Our results were obtained on single crystals of CuInSe2, CuGaSe2, CuInS2, and CuGaS2. Values of refractive indices n, extinction coefficients k and normal-incidence reflectivity R in the two different polarizations are given and compared with earlier data where available. We analyze in detail the structures of the dielectric function observed in the studied energy region. Critical-point parameters of electronic transitions are obtained from fitting of numerically calculated second-derivative spectra. Experimental energies and polarizations are discussed on the basis of published band structure calculations.

Optical properties of CuAlSe2

We have determined the complex dielectric tensor components of the chalcopyrite semiconductor CuAlSe2 in the energy range between 1.4 and 5.2 eV, at room temperature, using spectroscopic ellipsometry. We present results obtained on two single crystals grown by the traveling-heater method using In solvent. Values of refractive indices n, extinction coefficients k and normal-incidence reflectivity R in the two independent polarizations are reported. The structures observed in the energy region studied are analyzed by fitting the second-derivative spectra d2ε(ω)/dω2 to analytic critical-point line shapes. The obtained energies are assigned to certain electronic interband transitions by comparison with existing band structure calculations.

Calculated optical properties of ppp-oligomers

Abstract We have calculated the frequency dependent complex dielectric tensor for bi-and terphenyl within the framework of density functional theory. The good agreement with experimental data confirms that the anisotropy in the optical absorption can be well understood within the band picture. We predict the absorption behavior of ordered films with various chain orientations with respect to the substrate surface. We compare the optical properties of the molecular and the crystal phase. Furthermore, we show differences between the absorption spectra of poly( p -phenylen) (PPP) and its oligomers, respectively.

Transverse magneto-optical Kerr effect at the 2p threshold of 3d magnets

The transverse magneto-optical Kerr effect (T-MOKE) was investigated for thin epitaxial films of Fe grown on Ag(100) in the region of the 2p excitation threshold. The experimental reflectivity and asymmetry spectra are compared to those derived from the complex dielectric function tensor. The T-MOKE asymmetry is a mixture of both the real and imaginary parts of the off-diagonal elements of the dielectric function tensor, depending sensitively on the relative magnitudes between the real and imaginary parts of the diagonal elements. We demonstrate the possibility to determine the exchange coupling between a ferromagnetic thin film and an adsorbed monolayer by T-MOKE.

Dielectric tensor for magneto-optic NiMnSb

The diagonal component « xx and off-diagonal component « xy of the complex dielectric tensor for the ferromagnetic compound NiMnSb are determined using ex situ spectroscopic ellipsometry and magneto-optic analysis over the spectral range from 0.7 to 6.2 eV. The effects of the overcoat on the raw data are removed by the analysis. First, the complex « xx of thin-film NiMnSb were determined byex situ spectroscopic ellipsometry; then « xy was determined by analyzing Kerr rotation and ellipticity data using the determined « xy data. Lorentz oscillators were used to model peaks seen in the « xx spectra. The diagonal dielectric component « xx is dominated by free-carrier effects below 1.15 eV, and dominated by interband transitions above 2.0 eV. The center energies of the Lorentz oscillators are consistent with the calculated band structure and minority-spin optical conductivity of NiMnSb. Joint density of states and optical conductivity calculated from « xx(2) data with free-carrier effects removed shows onset energies at ;0.6 and ;0.2 eV, respectively. From a study of the « xx and « xy spectra, the Kerr rotation peak at lower energy is determined to be due to combined contributions from: ~1! a crossover between the free-carrier effect and interband transitions, and ~2! transitions involving spin-orbit coupling. The high-Kerr rotation peaks at higher energies result exclusively from transitions involving spin-orbit coupling. @S0163-1829~99!13615-4#

Transverse magneto-optical Kerr effect of Fe at the 2p excitation threshold

The transverse magneto-optical Kerr effect (T-MOKE) was investigated for thin epitaxial Fe films grown on Ag(0 0 1) in the region of the 2p excitation threshold. The experimental reflectivity and asymmetry spectra are compared to those derived from the complex dielectric function tensor calculated by using the first-principles spin-polarized relativistic band theory. We found that the T-MOKE asymmetry in general is a mixture of both the real and imaginary parts of the off-diagonal element of the dielectric function tensor, depending sensitively on the relative magnitudes of real and imaginary parts of the diagonal element. For angles of incidence larger than about 5° the influence of the Ag-substrate is significant. The major features in experimental and calculated reflectivity and asymmetry spectra are in agreement.

Analytical solutions for rotational diffusion in the mean field potential: application to the theory of dielectric relaxation in nematic liquid crystals

A theory of dielectric relaxation in nematics is developed for a molecular dipole moment directed at an arbitrary angle to the molecular long axis. Both exact and simple approximate analytical formulae for the longitudinal and transverse components of the complex dielectric permittivity tensor are obtained for the non-inertial rotational Brownian motion of a molecule in the mean field potential of Maier and Saupe. It appears that both longitudinal and transverse relaxation processes are effectively described by two Debye type mechanisms with corresponding relaxation times and dielectric strengths expressed in terms of the order parameter. The generalization of the theory for an arbitrary axially symmetric mean field potential is given.