Generalized Abelnus relations for an anisotropic thin film of an arbitrary dielectric tensor

The extended Jones matrix method is applied to one dielectrically anisotropic, homogeneous thin film at oblique incidence. Standard boundary conditions are imposed on resultant electric- and magnetic-field vectors at interfaces. Thus simple matricial relations are obtained for transmitted and reflected electric-field amplitudes at the two interfaces. In the limits of isotropy, they reduce to four well-known Abelès relations, and thus they may be considered as generalized Abelès relations for dielectrically anisotropic thin films. These matricial relations include multiple reflections while dealing with total fields. Thus they provide new insights into the 2 x 2 extended Jones matrix formalism.     

Shadow-angle method for anisotropic and weakly absorbing films

A method for determining the optical properties of a film on an isotropic substrate is proposed. The method is based on the existence of two specific incidence angles in the angular interference pattern of the p-polarized light where oscillations of the reflection coefficient cease. The first of these angles, theta(B1), is the well-known Abelès angle, i.e., the ambient-film Brewster angle, and the second angle theta(B2) is the film-substrate Brewster angle. In the conventional planar geometry and in a vacuum ambient there is a rigorous constraint epsilon(1) + epsilon > epsilon(1)epsilon on the film and the substrate dielectric permittivities epsilon(1) and epsilon, respectively, for the existence of the second angle theta(B2.) The limitation may be removed in an experiment by use of a cylindrical lens as an ambient with epsilon(0) > 1, so that both angles become observable. This, contrary to general belief, allows one to adopt the conventional Abelès method not only for films with epsilon(1) close to the substrate's value epsilon but also for any value of epsilon(1). The method, when applied to a wedge-shaped film or to any film of unknown variable thickness, permits one to determine (i) the refractive index of a film on an unknown substrate, (ii) the vertical and the horizontal optical anisotropies of a film on an isotropic substrate, (iii) the weak absorption of a moderately thick film on a transparent or an absorbing isotropic substrate.     

Abelès method revisited

The Abelès method is a classical method for determining the refractive index of dielectric thin films. In this paper we examine the main features of the method in a formal manner, using closed-form equations, and we show that the method is ambiguous in certain yet unreported situations.     

Elastic anisotropy effect on indentation-induced thin film interfacial delamination

Effect of elastic anisotropy on indentation-induced thin film interfacial delamination, especially, at the initiation and early growth stage, is examined. The indentation load is modeled as a constant pressure over an expanding semi-spherical cavity. The delamination process is approached by a cohesive zone model. The rest of the problem is formulated within the general anisotropic elasticity theory, and solved numerically by the boundary element method employing a special Green’s function for multilayers. The material system of a Cu(0 0 1) film on a Si(0 0 1) substrate is studied as an example. The interfacial damage initiation and crack development under indentation are captured in the simulation. By comparing the predictions with the materials being modeled as isotropic and as anisotropic (of the cubic symmetry as they are), it is shown that the elastic anisotropy of the copper film plays a significant role in determining the delamination pattern. In the isotropic model, the delamination crack fronts are circular reflecting the problem axisymmetry. In contrast, crack fronts are square with rounded corners in the anisotropic case. This significant difference necessitates a three-dimensional anisotropic stress analysis of the indentation-induced delamination of strongly anisotropic films.     

Characterizing the reflectance near the Brewster angle: a Padé-approximant approach

We characterize the reflectance peak near the Brewster angle for both an interface between two dielectric media and a single slab. To approach this problem analytically, we approximate the reflectance by a first-order diagonal Padé. In this way, we calculate the width and the skewness of the peak, and we show that although they present a well-resolved maximum they are otherwise not so markedly dependent on the refractive index. As an application of interest, we derive simple expressions for the precision of the Abelès Brewster-angle method.     

Optical characterization of thin chalcogenide films by multiple-angle-of-incidence ellipsometry

Optical properties of thin chalcogenide films from the systems As-S(Se) and As-S-Se were investigated as a function of the film composition, film thickness and conditions of illumination by light using multiple-angle-of-incidence ellipsometry. Thin films were deposited by thermal evaporation and exposed to white light (halogen lamp) and to monochromatic light from Ar⁺ — (λ = 488, 514 nm) and He-Ne- (λ = 632.8 nm) lasers. The ellipsometric measurements were carried out at three different angles of light incidence in the interval 45-55°, at λ = 632.8 nm. An isotropic absorbing layer model was applied for calculation of the optical constants (refractive index, n and extinction coefficient, k) and film thickness, d. The homogeneity of the films was checked and verified by applying single-angle calculations at different angles. It was shown that the refractive index, n of As-S-Se films is independent of film thickness in the range of 50 to 1000 nm and its values varied from 2.45 to 3.05 for thin layers with composition As₂S₃ and As₂Se₃, respectively. The effect of increasing in the refractive index was observed after exposure to light which is related to the process of photodarkening in arsenic containing layers. The viability of the method for determining the optical constants of very thin chalcogenide films with a high accuracy was confirmed.     

Quarter-wave layers with 50% reflectance for obliquely incident unpolarized light

The conditions under which light interference in a transparent quarter-wave layer of refractive index n1 on a transparent substrate of refractive index n2 leads to 50% reflectance for incident unpolarized light at an angle phi are determined. Two distinct solution branches are obtained that correspond to light reflection above and below the polarizing angle, phi(p), of zero reflection for p polarization. The real p and s amplitude reflection coefficients have the same (negative) sign for the solution branch phi>phi(p) and have opposite signs for the solution branch phior=(square root 2+1)square root n2. A monochromatic design that uses a high-index TiO2 thin film on a low-index MgF2 substrate at 488 nm wavelength is presented as an example.     

Morphological characterization of TiO2 thin films

Films prepared by reactive magnetron sputtering always present some structural and morphological heterogeneities.In this work, optical parameters, n(λ), k(λ) and E₀, of TiO₂ thin films were obtained, using only optical transmittance measurements. Films were described according to Abèles's model. Using a mono-oscillator type dispersion curve for the refractive index and a Lorentzian type curve for the absorption coefficient, we were able to demonstrate that the films were optically equivalent to a porous layer, with some dispersion in film thickness.The detailed analysis of the experimental transmittance data, fitted between 330 nm to 2200 nm, also enabled us to correlate the effective refractive index of each film with its deposition conditions.     

Laguerre-Gauss and Bessel-Gauss beams in uniaxial crystals

A simple correspondence between the paraxial propagation formulas along the optical axis of a uniaxial crystal and inside an isotropic medium is found in the case of beams with linearly polarized circularly symmetric boundary distributions. The electric fields of the ordinary and the extraordinary beams are related to the corresponding expressions in a medium with refractive index n(o) and n(e)2/n(o), where n(o) and n(e) are the ordinary and the extraordinary refractive indexes, respectively. Closed-form expressions for Laguerre-Gauss and Bessel-Gauss beams propagating through an anisotropic crystal are given.     

Optical Properties of Polyimide Films in the Infrared

The objective of this study is to determine the infrared optical constants of polyimide films in the spectral range between 2000 and 7000 cm^-1using a five-oscillator Lorentz model. Model parameters are presented, in addition to the derived values of the complex refractive index and dielectric constant. The parameters were obtained using electromagnetic theory for thin films to model reflectivity data from two film samples with different thicknesses (5.17 and 12.4 m) on gold substrates examined at two incident angles. Measurements were taken using a polarizable reflectometer device in a Fourier transform infrared (FTIR) spectrometer. The real part of the refractive index, n, is shown to be about 1.67, while the imaginary part, k, is less than 0.01 over the spectral range examined. Results are consistent with findings of other experimentalists, and new data presented here show that polarization effects on thin film layers are predictable from the proposed model.     

Modeling and simulating the bidirectional reflectance distribution function (BRDF) of seawater covered by oil slicks

A high-efficiency anisotropic model for bidirectional reflectance distribution function (BRDF) of seawater covered by oil slicks (SWCOS) was proposed. This model was set by combining a BRDF model for anisotropic rough sea surface whose slopes follow Gaussian distribution and the two-beam inference theory of a thin film. We have simulated the BRDFs of oil slicks by using the above model and the measured complex refractive index data of Romashkino crude oil. In addition, the relationships between the BRDF of oil slicks and the wind speed of sea surface, thickness of oil slick, complex refractive index of crude oil and the incident zenith angle were analyzed. Also, the differences between optical characteristics of clean water and of polluted water were discussed in the context of the optical contrast of SWCOS. With high simulation speed and reliable simulation precision, this model provides a theoretical basis for rapid detection of oil spill.     

Forbidden gaps in finite periodic and quasi-periodic cantor-like dielectric multilayers at normal incidence

Periodic and quasi-periodic Cantor-like bandgap structures that bordered upon a medium of refractive index n(0) are analyzed. An immersion model is used with the assumption that each layer is embedded between two identical regions of refractive index n(0) and thickness d(0), where d(0) is set equal to zero. Transmittance and group velocity are determined. Their dependence on n(0) is emphasized. Relations for the midgap value of the normalized group velocity are given. By use of these relations, diagrams are completed at different values of n(0), showing the pairs of quarter-wave-layer refractive indices at which there is an apparent superluminal tunneling through the finite periodic and quasi-periodic Cantor-like bandgap structures.     

Forbidden gaps in periodic anisotropic layered media

The general case of obliquely incident plane-wave propagation in periodic anisotropic layered media is presented. Arbitrary permittivity tensors of the two alternating anisotropic layers are considered. An immersion model is used with the assumption that each layer is embedded between two isotropic regions that have the same index of refraction as the isotropic medium of incidence and a thickness that is set equal to zero. Then explicit relations are presented for normally incident plane waves in periodic structures that consist of alternating biaxial layers of arbitrary principal-axis orientation. Specific cases of alternating isotropic and biaxial layers are also considered. Unit cell translation matrices are presented for both traveling directions, from the left to the right and vice versa. Dispersion relations that contain information regarding the propagation bands and the forbidden gaps in periodic anisotropic structures are presented.     

Optical properties of hybrid titanium chevron sculptured thin films coated with a semiconducting polymer

Optical and structural properties of a hybrid metallic chevron sculptured thin film from titanium coated with the semiconducting polymer poly(3-dodecylthiophene) (P3DDT) are reported. The nanostructured thin film with two subsequent layers of oppositely slanted nanocolumns was fabricated by glancing angle deposition and coated with P3DDT by a spin-cast process. Spectroscopic generalized ellipsometry is employed to determine geometrical structure properties and the anisotropic optical constants of the coated and uncoated film in the spectral range from 400 to 1700 nm. The nanostructured thin films before and after hybridization show highly anisotropic optical properties. The complex refractive indices along major polarizability directions of the hybridized chevrons are increased in the entire investigated spectral range with respect to the as-deposited chevrons. Changes in birefringence and dichroism upon polymer infiltration are observed.     

Influence of small inhomogeneities on the spectral characteristics of single thin films

It is well known that the spectral transmittance and reflectance of a thin film can be influenced by even small inhomogeneities or variations in its complex refractive-index profile. Formulas are derived that describe the theoretical variation of the spectral characteristics for small changes in the refractive index and the extinction coefficient of a homogeneous thin film. These formulas, accurate to the first order in the change in the complex refractive index, are compared with exact calculations for a number of different types of inhomogeneities. It is shown that specific qualitative features in the refractive-index profile of a nearly homogeneous thin film frequently can be determined from an examination of the change in the spectral transmittance and reflectance at normal incidence.     

Stress in Thin Films;Diffraction Elastic Constants and Grain Interaction

Untextured bulk polycrystals usually possess macroscopically isotropic elastic properties whereas for most thin films transvers isotropy is expected,owing to the limited dimenionlity .The usually applied models for the calculation of elstic constants of polycrystals from single crystal elastic contants(so-called grain interaction models)erroneously predict macroscopic isotropy for an(untextured) thin film.This paper presents a summary of recent work where it has been demonstrated for the first time by X-ray diffraction analysis of stresses in thin films that elastic grain interaction can lead to macroscopically anisotropic behaviour (shown by non-linear sin^2φ plots).A new grain interaction model,predictin the macroscopically anisotropic behaviour of thin films,is proposed.     

Determination of properties of wedged, nonuniformly thick, and absorbing thin films by using a new numerical method

Nonuniformity in the thickness of thin films can severely distort their transmission spectra as compared with those of flat, smooth films. Methods that extract properties such as refractive index, thickness, and extinction coefficient of such films can suffer inaccuracies when they are applied to wedged or nonuniformly thick films. To accurately extract optical properties of nonuniform films, we have developed a novel numerical method and efficient constitutive relations that can determine film properties from just the transmission spectrum for films that are locally smooth with negligible scattering loss. This optimum parameter extraction (OPE) method can accommodate films with two-dimensional thickness variation that would result in significant errors in the values of refractive index and film thickness if not considered. We show that for carefully chosen test cases and for actual pulsed-laser-deposition AlN thin films, properties such as refractive index, extinction coefficient, and film thickness were very accurately determined by using our OPE method. These results are compared with previous techniques to determine the properties of thin films, and the accuracy of and applicable conditions for all these methods are discussed.     

Modeling of the refractive index and extinction coefficient of binary composite films

Southwell's analysis of optical multilayers within the limits of very thin films has been extended to include absorption in the multilayer for predicting the effective values of the refractive index n(e) and extinction coefficient k(e) of mixed-composition binary homogeneous films over a wide spectral region, including the high-absorption (k > 10(-2)) region. It has been found that n(e) in general is a complicated function of the optical parameters (n(1), k(1), n(2), k(2)) and volume fractions (f(1), f(2)) of the component materials in a homogeneous layer, and the expression for n(e) becomes the same as that predicted by the Drude model in the spectral region where the layers are transparent. Moreover, according to the present analysis, the volume fractions of the product of the refractive index and the extinction coefficient of the component materials of a binary composite film are additive and the sum equals the product of the effective refractive index and extinction coefficient of the composite film.     

Omnidirectional reflection from finite periodic and Fibonacci quasi-periodic multilayers of alternating isotropic and birefringent thin films

Omnidirectional reflection from periodic and Fibonacci quasi-periodic multilayers that are embedded in an isotropic medium is further analyzed. Besides the isotropic structures, birefringent structures are considered that comprise uniaxial layers in the principal-axis system, alternating with isotropic layers so that the refractive index of isotropic layers is equal to the principal extraordinary refractive index of the uniaxial layers. The transfer-matrix method is applied, and the same formalism is used forboth the isotropic and the uniaxial media in the principal-axis system. Simple and original relations are obtained for the invariant of the one-dimensional Fibonacci sequences at oblique incidence. Numerical examples are given comparatively for the isotropic and the birefringent structures in the case of periodic and Fibonacci quasi-periodic sequences at different values of the refractive indices.     

PECVD方法用于梯度薄膜材料的研究

本文研究了ＰＥＣＶＤ方法制备Ｓｉ－Ｏ－Ｍ系梯度薄膜材料，并运用计算机控制技术成功地制备了涂层折射率随膜深成正弦波形式连续变化的Ｒｕｇａｔｅ单通带滤波器样品。结果表明，采用ＰＥＣＶＤ方法可以制备性能上乘、结构复杂的梯度薄膜材料，ＰＥＣＶＤ方法在研究、开发高级光学涂层领域有着宽广的应用前景。