Frequency-dependent Refractive Index Research Articles

Towards functional 3D T-ray imaging

We review the recent development of T-ray computed tomography, a terahertz imaging technique that allows the reconstruction of the three-dimensional refractive index profile of weakly scattering objects. Terahertz pulse imaging is used to obtain images of the target at multiple projection angles and the filtered backprojection algorithm enables the reconstruction of the object's frequency-dependent refractive index. The application of this technique to a biological bone sample and a plastic test structure is demonstrated. The structure of each target is accurately resolved and the frequency-dependent refractive index is determined. The frequency-dependent information may potentially be used to extract functional information from the target, to uniquely identify different materials or to diagnose medical conditions.

Quantum-optical coherence tomography with dispersion cancellation

We propose a new technique, called quantum optical coherence tomography (QOCT), for carrying out tomographic measurements with dispersion-cancelled resolution. The technique can also be used to extract the frequency-dependent refractive index of the medium. QOCT makes use of a two-photon interferometer in which a swept delay permits a coincidence interferogram to be traced. The technique bears a resemblance to classical optical coherence tomography (OCT). However, it makes use of a nonclassical entangled twin-photon light source that permits measurements to be made at depths greater than those accessible via OCT, which suffers from the deleterious effects of sample dispersion. Aside from the dispersion cancellation, QOCT offers higher sensitivity than OCT as well as an enhancement of resolution by a factor of 2 for the same source bandwidth. QOCT and OCT are compared using an idealized sample.

Method of integral equations for ultrafast pulses and its application to the polariton resonance of GaAs

Instead of using a frequency-dependent refractive index, we propose to use the integrodifferential equation approach to describe reflection and transmission of an ultrashort pulse passing through the system’s boundary. This method, which is an adaptation of the extinction theorem for ultrafast pulses, explicitly follows time and space evolution without the slowly varying envelope approximation. When the duration of the pulse is comparable with the relaxation time, the results differ significantly from those given by the traditional method (Fresnel formulas), especially if the carrier frequency is close to an absorption line. We compare the two approaches, using the data of GaAs in the infrared domain where pulses of only a few cycles are available experimentally. We also work out a method that efficiently includes the background refractive index that originates from electronic transitions.

Amplifying Sommerfeld precursors and producing a discontinuous index of refraction with gains and losses.

We show that for specially designed linear dispersive media with one absorption line and one gain line the Sommerfeld precursors of a pulse can be amplified leading to an earlier detection of the signal. Also, we show that in some systems with one strong absorption line, a carefully placed gain resonance must induce a discontinuity in the imaginary part of the frequency dependent index of refraction and in the first derivative of its real part.

Determination of the optical constants of the γ-phase GdH3 thin films

We have measured the optical transmittance of thin films of gadolinium trihydride GdH3 over a broad spectral range, 0.05–6 eV. The analysis indicates that GdH3 is a wide-gap semiconductor with an energy gap of 2.55 eV. The fundamental absorption and impurity-related transitions dominate the spectra in the high-energy region, 1–6 eV. Hydrogen vibration modes dominate the spectra in the low-energy region, 0.05–0.2 eV. A strong free-carrier absorption effect is observed. In addition, the frequency-dependent refractive index, extinction coefficient, dielectric function, and optical conductivity are determined from the transmission spectra. This work also evaluates the plasma frequency associated with free carriers.

Optical properties of the γ-phase yttrium trihydride YH3−δ

The transmission spectra of thin films of γ-phase yttrium trihydride YHx, x≅2.87, are measured in the energy range 0.05–6 eV at room temperature. The measured quantities are used to determine the frequency-dependent index of refraction, extinction coefficient, dielectric function, and optical conductivity. In the energy range (E=0.2–6 eV), interband transition and impurity-related transitions dominate the optical properties. In the low-energy range (E=0.05–0.2 eV), hydrogen vibration modes dominate the optical properties. In addition, strong absorption due to free carriers is observed. This work also evaluates several parameters such as plasma frequency, effective carrier density, and donor ionization energy. The possible sources for optical features observed in the spectra are also described.

Electrodynamic properties of coplanar waveguides made from high-temperature superconducting YBa2Cu3O7−δ electrodes on nonlinear dielectric SrTiO3 substrates

We present a comprehensive study of broadband (0–2 GHz) electrodynamic properties of coplanar waveguides made from high-temperature superconducting thin-film YBa2Cu3O7−δ electrodes on nonlinear dielectric single-crystal SrTiO3 substrates. The waveguides exhibit strong dielectric nonlinearities, in addition to temperature-, dc-bias-, and frequency-dependent dissipation and refractive index. By using parameters determined from small-signal (linear) transmission characteristics of the waveguides as a function of dc bias, we develop a model equation that successfully predicts and describes large-signal (nonlinear) behavior.

Quantum-Gravitational Diffusion and Stochastic Fluctuations in the Velocity of Light

We argue that quantum-gravitational fluctuations in the space-time background give the vacuum non-trivial optical properties that include diffusion and consequent uncertainties in the arrival times of photons, causing stochastic fluctuations in the velocity of light ``in vacuo''. Our proposal is motivated within a Liouville string formulation of quantum gravity that also suggests a frequency-dependent refractive index of the particle vacuum. We construct an explicit realization by treating photon propagation through quantum excitations of $D$-brane fluctuations in the space-time foam. These are described by higher-genus string effects, that lead to stochastic fluctuations in couplings, and hence in the velocity of light. We discuss the possibilities of constraining or measuring photon diffusion ``in vacuo'' via $\gamma$-ray observations of distant astrophysical sources.

Frequency-Dependent Molecular Polarizability and Refractive Index: Are Substituent Contributions Additive?

The frequency-dependent polarizabilities of a number of halogen-substituted benzene species are computed using ab-initio methods. The polarizability tensors are analyzed for possible additive properties. Simple group or atom additivity trivially fails (the overall polarizability is not a sum of isotropic atom or group polarizabilities). If, however, the separate polarizability tensor elements are studied, they are additive, to quite substantial accuracy, for benzene with F, Cl, Br, and I substituents. This tensorial additive property has important implications for design of controlled refractive index materials, and we present calculated refractive indices utilizing ab initio calculated polarizability tensors.

Temperature- and Frequency-Dependent Optical Constants for Nitric Acid Dihydrate from Aerosol Spectroscopy

Frequency-dependent complex refractive indices have been determined from the aerosol infrared extinction spectra of laboratory-generated nitric acid dihydrate (NAD) particles. The spectra reported here were recorded at several temperatures (160, 180, and 190 K) over the mid-infrared region of the spectrum (700−4700 cm-1). The optical constants retrieved from these spectra are overall in reasonable agreement with results from thin-film experiments conducted at 184 K, although there are significant differences in the intensities of several absorption bands located below 1500 cm-1. We attribute these to the different methods used to make the samples in the two types of experiments and consider the substrate-free aerosol results to be unperturbed NAD. The temperature dependence of the NAD aerosol optical constants was found to be quite weak between 160 and 190 K, in contrast to the strong temperature dependence observed previously for the optical constants of water ice.

Frequency and temperature dependence of the refractive index of sapphire

Because the index of refraction is temperature dependent, a temperature gradient across a window causes image blur and bore sight error. Prior to this paper, there have been no direct temperature-dependent measurements reported on the mid-infrared refractive index for sapphire, a popular infrared window material of high durability. Measurements of d n/d T are reported on the ordinary ray of sapphire in the 4 μm region for the first time. Accurate temperature and frequency dependent refractive index models can now be constructed from visible measurements of the refractive index, far-infrared reflectance measurements, thermo-optic coefficient measurements, and infrared measurements of the absorption coefficient. Visible measurements determine the contribution to the refractive index from electronic transitions. Far-infrared measurements determine the contributions from fundamental lattice vibrations (phonons). Infrared absorption data are used to determine parameters in a multiphonon sum band model. By applying the Hilbert transform to this multiphonon absorption model, a model for the multiphonon refractivity is obtained. Two- and three-phonon contributions to the refractive index are important for an accurate model that includes temperature dependence. Results for the ordinary- and extraordinary-rays are obtained.

Complex Refractive Indices of Crystalline Hydrazine from Aerosol Extinction Spectra

Reported here is the first experimental measurement of the frequency dependent refractive index of crystalline hydrazine. The method used in this study is based on the measurement of the infrared spectrum of laboratory generated aerosols. The optical constants determined here should be directly useful in remote sensing and radiative transfer models of the jovian atmosphere.

Complex refractive indices in the infrared of nitric acid trihydrate aerosols

The refractive indices of nitric acid trihydrate (NAT) have been determined from the infrared spectra of laboratory generated aerosols. The aerosols are formed via homogeneous nucleation in a flow cell with separate regions for nucleation and observation, allowing for independent control of the temperature conditions in these regions. A spectrum of small, non‐scattering particles is recorded to determine the frequency dependent imaginary refractive index, within a scaling factor. A subtractive Kramers‐Kronig routine is then used to calculate the real index. The scaling factor for the imaginary indices is determined by fitting a spectrum associated with larger, scattering particles, which depends on both the real and imaginary portions of the refractive indices. The complex refractive indices of NAT are reported over the range 700 cm−1 to 4000 cm−1. While in good qualitative agreement with previously reported results, there are significant quantitative differences which are discussed.

Asymptotically stable solitary waves in a Kerr dispersive medium in the presence of linear amplification and nonlinear losses.

The effect of formation of asymptotically stable solitary waves (ASSW) in an amplifying dispersive medium with frequency-dependent linear amplification, nonlinear losses, and nonlinear refractive index is predicted. All the parameters of the ASSW are invariants of the medium. The method developed is based on formalism of the Fokker-Planck equation describing a pulse dynamics in the presence of noise. The stability is proved by Lyapunov's method. It was found that the ASSW is described by the Euler-Lagrange equation defined by a minimum of the effective potential being the Lyapunov function. It was found that the bright solitary wave is unstable whereas the dark solitary wave is asymptotically stable.

Interband absorption due to dipole coupling and interference in isolated quantum-wire structures.

We present a self-consistent field theory and numerical calculations for a set of temperatures and electron densities for the interband absorption coefficient and the frequency-dependent refractive index for an array of isolated quantum wires. The peaks in the absorption coefficient correspond to interband transitions, resulting in the resonant absorption of light. The peaks in the refractive index are slightly redshifted from those in the absorption coefficient because the former involve both the real and imaginary parts of the response function, whereas the latter is directly proportional to the imaginary part of the response and inversely proportional to the refractive index. There is interference between the real and imaginary parts when the derivative of the absorption coefficient is taken with respect to frequency, which greatly modifies the line shape in the absorption spectrum. The oscillations in the derivative spectrum are due to the quantization of the energy levels related to the in-plane confining potential for such reduced dimensional systems. There are appreciable changes in the absorption spectrum when the electron density or temperature is increased. One interband transition peak is suppressed in the high electron density limit and the thermal depopulation effect on the electron subbands can be easily seen when the temperature is high. We also find that the exciton coupling weakens the shoulder features in the absorption spectrum. This paper is relevant to optical characterization techniques.

Propagation through nonuniform grating structures

We consider linear propagation through shallow, nonuniform gratings, such as those written in the core of photosensitive optical fibers. Though, of course, the coupled-mode equations for such gratings are well known, they are often derived heuristically. Here we present a rigorous derivation and include effects that are second order in the grating parameters. While the resulting coupled-mode equations can easily be solved numerically, such a calculation often does not give direct insight into the qualitative nature of the response. Here we present a new way of looking at nonuniform gratings that immediately does yield such insight and, as well, provides a convenient starting point for approximate treatments such as WKB analysis. Our approach, which is completely within the context of coupled-mode theory, makes use of an effective-medium description, in which one replaces the (in general, nonuniform) grating by a medium with a frequency-dependent refractive index distribution but without a grating.

Effective Dielectric Function of Porous Silicon: the Transverse Component

ABSTRACTA self-consistent many-body theory is developed to study the effect of temperature and electron density on the interband absorption coefficient and the frequency-dependent refractive index for an array of isolated quantum wires. The peaks in the absorption coefficient correspond to interband transitions resulting in the resonant absorption of light. The oscillations in the derivative spectrum are due to the quantization of the energy levels related to the in-plane confining potential for such reduced dimensional systems. There are appreciable changes in the absorption spectrum when the electron density or temperature is increased. One interband transition peak is suppressed in the high electron density limit and the thermal depopulation effect on the electron subbands can be easily seen when the temperature is high. We also find that the exciton coupling weakens the shoulder features in the absorption spectrum. This study is relevant to optical characterization of the confining potential and the areal density of electrons using photoreflectance. By using incident light with tunable frequencies in the interband excitation regime, contactless photoreflectance measurements may be carried out and the data compared with our calculations. By fitting the numerical results to the peak positions of the photoreflectance spectrum, the number of electrons in each wire may be extracted.

Ruby laser‐induced frequency dependent refractive index change in KCl:Li+ FA crystal

Ruby laser‐induced frequency dependent refractive index change in KCl:Li⁺ F_A crystal

A study of the far-infrared optical properties of rexolite?

The far-infrared optical properties of Rexolite™ 1422 were characterized at the University of Lowell Research Foundation using Fourier transform spectroscopy. The spectroscopic transmission measurements were performed on a 0.0236″ thick sample of material over the submillimeter wavelength region from 10 cm−1 to 360 cm−1. Using multiple reflection theory for transmission through an etalon, the frequency dependent complex refractive index of Rexolite™ is reported.

Electronic structure and optical properties of LiB3O5.

The band structure and the interband optical conductivity of a ${\mathrm{LiB}}_{3}$${\mathrm{O}}_{5}$ crystal with excellent nonlinear optical properties are studied by means of a first-principles method. The electronic structure is characterized by highly localized bands with a direct gap of 7.37 eV at \ensuremath{\Gamma} and a very low static dielectric constant of 2.7. The optical absorption curve shows several prominent structures but with very small directional anisotropy. The calculated frequency-dependent refractive index is in good agreement with experimental data.