Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry

We present a reflection-type terahertz time-domain spectroscopic ellipsometry (THz-TDSE) technique for measuring the complex dielectric constants of thin-film materials without replacement of the sample. THz-TDSE provides complex dielectric constants from the ratio of the complex amplitude reflection coefficients between p- and s-polarized THz waves. The measured dielectric constants of doped GaAs thin films show good agreement with predictions of the Drude model, even though the film thickness is of the order of a tenth of the penetration depth of the THz waves. In addition, we demonstrate the measurements of soft-phonon dispersion in SrTiO(3) thin films deposited on a Pt layer. The obtained dielectric constants agree well with the predictions of a generalized harmonic oscillator model.     

The effects of residual gases on optical constants of Al films

Using the attenuated total reflection technique, the effects of residual gases on optical constants of Al films have been investigated in situ during and after growth of films. It has been found that the optical constants of Al films are strongly affected by residual gases even under ultrahigh vacua (UHV) in the order of 10⁻⁶ Pa. In order to explore the origin of a variation in optical constants produced by the residual gases, the optical constants of Al films exposed to oxygen, nitrogen or hydrogen gases have been measured.     

Conformal bootstrap in Liouville field theory

We consider the recently proposed analytic expression for the three-point function in the Liouville field theory on a sphere. It is verified that in the classical limit this expression reduces to what the classical Liouville theory predicts. Using the suggested three-point function as the structure constant of the operator algebra we construct the four-point function of the exponential fields and check numerically that it satisfies the conformal bootstrap equations. The Liouville reflection amplitude which follows explicitly from the structure constants is also considered and compared with the results of the Bethe ansatz technique.     

Characterization of Reflection Positivity: Majoranas and Spins

We study linear functionals on a Clifford algebra (algebra of Majoranas) equipped with a reflection automorphism. For Hamiltonians that are functions of Majoranas or of spins, we find necessary and sufficient conditions on the coupling constants for reflection positivity to hold. One can easily check these conditions in concrete models. We illustrate this by discussing a number of spin systems with nearest-neighbor and long-range interactions.     

Coherent optical phonons in alexandrite crystal studied by Optical Kerr Effect spectroscopy

Herewith, we report on the first observation of coherent phonons in alexandrite crystal obtained by means of the femtosecond Optical Kerr Effect spectroscopy. We have managed to observe dynamics of the Raman‐active modes with high resolution and to find their lifetimes in the temperature range between 263 K and 373 K. We have used the obtained temperature dependence of phonon lifetimes and frequencies for calculation of the anharmonic coupling constants. On the basis of our results, we have also calculated the widths of homogeneously broadened Raman lines. Our results prove that, in case of transparent samples, this experimental technique is a very good alternative to the commonly used transient reflection method. Copyright © 2013 John Wiley & Sons, Ltd.     

反射干涉光谱法测量固体薄膜的光学常数和厚度

本文报道一种简单的方法,从平原介质薄膜的反射干涉光谱来计算薄膜的光学常数和厚度。当一束光照射在基板上的介质膜上时,由于膜上下界面反射光的相干,会使反射光谱的曲线有一定的波动。我们对反射相干光谱进行理论分析,给出计算公式,从测量曲线中的实验值得出薄膜的光学常数ｎ、ｋ以及厚度等参数。此种方法简单可行,而且易于编程处理。     

Thickness of SiO2 thin film on silicon wafer measured by dispersive white-light spectral interferometry

We present a white-light spectral interferometric technique for measuring the thickness of SiO₂ thin film on a silicon wafer. The technique utilizes a slightly dispersive Michelson interferometer with a cube beam splitter and a fibre-optic spectrometer to record channelled spectra in two configurations. In the first, a standard configuration with two identical metallic mirrors, the recorded channelled spectrum is fitted to the theoretical one to determine the effective thickness of the beam splitter made of BK7 optical glass. In the second configuration one of the mirrors is replaced by SiO₂ thin film on the silicon wafer and the recorded channelled spectrum is fitted to the theoretical one to determine the thin-film thickness. We consider multiple reflection within the thin-film structure, use the optical constants for all the materials involved in the set-up, and confirm very good agreement between theory and experiment. The technique is applied to four samples with various SiO₂ film thicknesses. PACS 07.60.Ly; 68.55.Jk; 78.20     

Spectral interferometric technique to measure the relative phase change on reflection from a thin-film structure

A two-step white-light spectral interferometric technique to measure the relative phase change on reflection from a thin-film structure is presented. The technique is based on recording of the channeled spectra at the output of a Michelson interferometer and their processing by using a windowed Fourier transform to retrieve the phase functions. In the first step, the phase difference between the beams of the interferometer with a thin-film structure is retrieved. In the second step, the structure is replaced by a reference sample of known phase change on reflection and the corresponding phase difference is retrieved. From the two phase differences, the relative phase change on reflection from the thin-film structure is obtained. The feasibility of the simple method is confirmed in processing the experimental data for a SiO₂ thin film on a Si wafer of known optical constants. Four samples of the thin film are used and their thicknesses are determined. The thicknesses obtained are compared with those resulting from reflectometric measurements, and good agreement is confirmed.     

The spherical sector of the Calogero model as a reduced matrix model

We investigate the matrix-model origin of the spherical sector of the rational Calogero model and its constants of motion. We develop a diagrammatic technique which allows us to find explicit expressions of the constants of motion and calculate their Poisson brackets. In this way we obtain all functionally independent constants of motion to any given order in the momenta. Our technique is related to the valence-bond basis for singlet states.     

椭偏精确测定透明衬底上吸收薄膜的厚度及光学常数

椭偏仪难以精确测量透明衬底上吸收薄膜光学常数的原因:1)衬底的背面反射光为非相干光, 它的存在会极大的增加拟合难度; 2)衬底光学常数(折射率和消光系数)的差异会影响测量的准确性, 而且会在吸收薄膜的光学常数中表现出来, 需要单独测量其光学常数; 3)厚度与光学常数之间呈现强烈的关联性. 针对以上三个问题, 选择石英玻璃、载玻片、盖玻片和普通浮法玻璃作为研究对象. 采用折射率匹配法消除上述衬底背面反射光的影响. 结果显示, 折射率匹配法能够有效消除折射率在1.43-1.64、波长范围为190-1700 nm波段的石英、浮法玻璃等透明衬底的背面反射光. 之后, 通过拟合椭偏参数ψ和垂直入射时的透过率T₀ 分别得到以上衬底的折射率和消光系数. 拟合得到的结果与文献报道的趋势一致. 最后, 采用椭偏参数和透过率同时拟合的方法(SE+T法)得到类金刚石薄膜(沉积在石英玻璃上)和非晶硅薄膜(沉积在载玻片、盖玻片上)光学常数和厚度的准确解.     

White-light spectral interferometric technique to measure a nonlinear phase function of a thin-film structure

We present a new two-step white-light spectral interferometric technique to measure a nonlinear phase function of a thin-film structure. The technique is based on recording of channeled spectra at the output of a Michelson interferometer and their processing by using a windowed Fourier transform to retrieve the phase functions. First, the phase function including the effect of a thin-film structure is retrieved. Second, the structure is replaced by a reference sample of known phase change on reflection and the corresponding phase function is retrieved. From the two functions, the nonlinear phase function of the thin-film structure is obtained. The feasibility of this simple method is confirmed in processing the experimental data for a SiO₂ thin film on a Si wafer of known optical constants. Four samples of the thin film are used and their thicknesses are determined. The thicknesses obtained are compared with those resulting from reflectometric measurements, and a good agreement is confirmed.     

Data reduction from critical angle reflection measurements

This paper describes the use of a computer programme for the evaluation of elastic moduli of solid media, from data obtained using the critical angle reflection technique. The moduli are expressed in terms of the longitudinal modulus K = λ + 2μ, where λ and μ are the Lamé constants, since this is a quantity readily obtained experimentally.     

Design and development of low-cost room temperature electric field poling system for the fabrication of quasi-phase matching devices

Based on density functional theory, we perform first-principles investigations to study the optical properties of the O-, F- and H-terminated SiC nanoribbons with armchair edges (ASiCNRs). By irradiating with an external electromagnetic field, we calculate the dielectric function, reflection spectra, energy loss coefficient and the real part of the conductance. It is demonstrated that the optical constants are sensitive to the low-energy range, different terminal atoms do not make much difference in the shape of the curves of the optical constants for the same-width ASiCNR, and the optical constants of wider nanoribbons usually have higher peaks than that of the narrower ones in low energy range. We hope that our study helps in experimental technology of fabricating high-quality SiC-based nanoscale photoelectric device.     

Engineering gold alloys for plasmonics

We demonstrate the formation of metal alloys in Au–Ag, Au–Cu and Au–Pd systems and the experimental determination of their optical properties using optical transmission and reflection spectroscopy. The optical constants define the plasmon resonance wavelength and electromagnetic field local intensity. However, the optical constants behavior cannot be precisely modeled based on the data of pure metals due to unknown morphology and composition of the alloy. It has to be determined experimentally. We demonstrate the surface-enhanced Raman scattering using alloy metals. Depending on the metal to which molecules are adsorbed, we observe enhancement of different Raman modes. It is mainly due to the chemical enhancement effect between metal and molecules.     

The role of the polarization in ATIR proximity sensing

The proximity sensing based on the attenuated total internal reflection (ATIR) is a technique that allows us to control the separation between two planes—the attenuating media surface and dielectric boundary, in the neighborhood of which the total internal reflection (TIR) takes place. This measurement supposes known optical constants of all media. An effect of lateral fringe shift and variations in intensity distribution of the interferometrical signal were observed during the measurements by an angular sheering polarization interferometer. The simple theory here proposed explains these effects. For that reason the relationship between the polarization effects, accompanying the ATIR and the output interferometrical signal had to be taken into account. To explain the variations of interference fringes intensity topography, the evolution of the Stokes parameters as a function of the gap width for Si attenuator is studied numerically.     

二苯甲酮晶体的红外反射光谱研究

室温下记录了有机非线性光学晶体二苯甲酮三种不同偏振的红外反射光谱（２００－４０００ｃｍ＾－１）。利用Ｋ－Ｋ变换确定了晶格振动模的模，纵频率。根据由Ｋ－Ｋ变换得到的介电常数和折射率的色散曲线外推得到晶体的静态介电常数，高频介电常数和近红外波段的折射率。还对反射带进行了认定。研究表明该晶体二苯甲酮分子间不存在氩键，只以弱的范德华键相结合。结合晶体结构对强反射带出现的原因作了解释。     

Über die bestimmung der optischen konstanten dünnster oberflächenschichten und das problem der schichtdicke

The Fresnel reflection coefficients of a phase boundary disturbed by values of the optical constants differing from the values in the adjacent phases (boundary phase) are derived. The derivation on the basis of Maxwells' theory uses integral boundary conditions. The deviations from the ideal reflection properties, caused by a boundary phase with uniaxial symmetry, are proportional to the difference of the dielectric constants (for the tangential component) and to the difference of the reciprocal values of the dielectric constants (for the normal component) to the value in the undisturbed case, integrated over the boundary phase. An optical thickness of the boundary phase can not be determined by means of ellipsometry or reflection spectroscopy.     

Use of surface plasmon excitation for determination of the thickness and optical constants of very thin surface layers

We present a method using attenuated total reflection (ATR) with excitation of surface plasma waves at different wavelengths and angles of incidence, which allows an accurate determination of the thickness and optical constants of absorbing surface layers from optical measurements only. This method is applied to the case of very thin Au surface layers on (111)Ag, and the results are discussed.     

Coupled-mode analysis of fiber-optic add drop filters for dense wavelength-division multiplexing

We present a coupled-mode theory of fiber-optic add-drop filters, which involve directional coupling between two fibers combined with fiber Bragg gratings defined inside the coupling region. The analysis self-consistently accounts for both the directional and the reflection coupling, and the propagation constants and structure of the supermodes of the combined structure are derived. We present a detailed analysis of a filter design based on identical fibers. The calculated device parameters satisfy the requirements for dense wavelength-division multiplexing applications.     

REFLECTION TIME AND THE GOOS-HÄNCHEN EFFECT FOR REFLECTION BY A SEMI-INFINITE RECTANGULAR BARRIER

The reflection time, during which a particle is in the classically forbidden region, is described by the trajectory representation for reflection by a semi-infinite rectangular barrier. The Schrödinger wave function has microstates for such reflection. The reflection time is a function of the microstate. For oblique reflection, the Goos-Hänchen displacement is also a function of the microstate. For a square well duct, we develop a proposed test where consistent overdetermination of the trajectory by a redundant set of observed constants of the motion would be beyond the Copenhagen interpretation.