Simple recurrence matrix relations for multilayer anisotropic thin films

Generalized Abelès relations for one anisotropic thin film [E. Cojocaru, Appl. Opt. 36, 2825-2829 (1997)] are developed for light propagation from an isotropic medium of incidence (with refractive index n(0)) within a multilayer anisotropic thin film coated onto an anisotropic substrate. An immersion model is used for which it is assumed that each layer is imaginatively embedded between isotropic gaps of zero thickness and refractive index n(0). This model leads to simple expressions for the resultant transmitted and reflected electric field amplitudes at interfaces. They parallel the Abelès recurrence relations for layered isotropic media. These matrix relations include multiple reflections while they deal with total fields. They can be applied directly to complex stacks of isotropic and anisotropic thin films.     

Three polarization reflectometry methods for determination of optical anisotropy

Three novel methods for the determination of optical anisotropy are proposed and tested. The first, the special points method, may be applied to any uniaxially anisotropic medium and is based on the measurement of s- and p-polarized light reflectances under near-normal or grazing angles (or both) and of the Brewster angle. The second method is based on the use of the Azzam universal relationship between the Fresnel s- and p-reflection coefficients. For a flat surface and an isotropic medium, the Azzam combination of coefficients becomes zero and thus is independent of the incidence angle, whereas for a uniaxial or biaxial anisotropic sample it acquires a certain angular dependence, which may be used to determine the anisotropy of the sample. Finally, for those cases in which the anisotropy of the material of a film deposited on an isotropic substrate is itself of interest, a third method, the interference method, is suggested. This technique makes use of the different dependences of s- and p-polarized beam optical path-length changes on the variation of the angle of incidence.     

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.     

Inversion of reflection ellipsometric data

The dielectric constant of an isotropic homogeneous layer on an isotropic substrate is shown to satisfy a quintic equation, with the coefficients determined by |ρ|(2) and Re(ρ), where ρ = r(p)/r(s) is found ellipsometrically. This algebraic equation eliminates many (but not all) of the nonphysical roots in the inversion of ellipsometric data. A simple form is obtained if the angle of incidence is equal to the Brewster angle of the substrate. The problem of inversion for thin films is also discussed.     

Generalized Investigations into the Brewster Angle

The standard elementary theory of the Brewster angle generated by a plane interface separating two homogeneous isotropic media, through which incident and transmitted electromagnetic waves are propagating, is well known. We introduce here a more general inhomogeneous medium for which a Brewster wave and a Brewster angle can be defined. The properties of this wave are investigated, together with a model whose field can be expressed in terms of a special degenerate hypergeometric function. Other angles of incidence also yield zero reflectivity, but these are carefully distinguished from the Brewster angle.     

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.     

Cavity ringdown spectroscopy of thin films in the mid-infrared

To demonstrate the potential of the cavity ringdown technique in mid-infrared spectroscopy of thin film samples, we measured absorption losses in a C60 film on a BaF2 substrate using a tunable optical parametric amplifier source. With a Brewster angle sample geometry, we achieved a fractional loss sensitivity as small as 1.3 x 10(-7) with 1.5 cm(-1) resolution, an improvement in sensitivity of 2 orders of magnitude compared to standard Fourier transform infrared methods. At an absorption sensitivity of 5 x 10(-7), spectra of several C60 overtone lines were recorded.     

Elimination of interference effects from photoinduced-transmission decay curves of thin silicon films

The effects of interference on the photoinduced-absorption signals of thin absorbing films have been studied by recording the picosecond photoinduced-absorption decay curves of an amorphous and a polycrystalline silicon film and applying various probe-beam wavelengths and angles of incidence. The normalized decay curves measured at close to normal incidence have been found to depend strongly on the probe-beam wavelength. By contrast the decay curves obtained at the Brewster angle of incidence have shown a satisfactory coincidence. Theoretical calculations for the photoinduced changes of the transmittance of the film have been performed. These calculations prove that at normal incidence the contributions of the photoinduced changes of the absorption coefficient Δα and of the refractive index Δn to the change in the transmittance Δ T are comparable, whereas when the Brewster angle arrangement is employed, Δ T is proportional to Δα and the effect of the change in the refractive index is negligible.     

<Emphasis Type="Italic">SH</Emphasis>-wave intromission concept

The existence of an SH-wave incidence angle for which the reflected amplitude is zero (SH-wave intromission angle) is established for the case of plane-wave scattering by a planar interface joining two homogeneous, isotropic, and linearly elastic half-spaces. Such an incidence angle is numerically shown to exist for two combinations of bimaterial interface properties. The SH-wave intromission angle is roughly parallel to the electromagnetic Brewster angle and the acoustic P-wave intromission angle, and the concept should find new applications for non-intrusive characterization of interfaces.     

Contours of the constant third Brewster angle in the complex plane of a dielectric constant

Three special angles associated with the external reflection of light at the surface of an absorbing medium are well known: the principal angle, the pseudo-Brewster angle, and the second Brewster angle. Another significant angle has been identified recently by Azzam and El-Saba [Appl. Opt. 28, 1365 (1989)]. At this angle, the slope of the differential reflection phase shift with respect to the angle of incidence is maximum negative. For convenience it is called the third Brewster angle. The nature of the contours of the constant third Brewster angle in a complex dielectric constant plane is considered both analytically and graphically in comparison with the other constant special-angle contours.     

Analytical study of the principal angle used in optical experiments

An analytical method has been developed for directly calculating the principal angle theta(p) at which the phase difference between the two reflection coefficients is equal to 90 degrees and at which the ratio of /r(p)/ to /r(s)/ is equal or close to a minimum. The equations given here can be used in many optical applications. For example, ellipsometric data measured at an incidence angle theta(p) will have higher precision than data measured at other incidence angles. theta(p) is the principal angle. Instead of three principal angles, there is only one principal angle, which can be found in the region of 0 < or = theta(p) < or = 90 degrees for most metallic materials used in applications. Results show good agreement between the measured and the calculated spectra of delta(p) and rho(po).     

Reflection of light in the vicinity of the Brewster angle from a multilayer system of ultrathin inhomogeneous dielectric films

An analysis of the influence of nanoscopically stratified dielectric overlayer on the reflection parameters of linearly polarized light from transparent substrates is carried out. The second-order formulas for characteristic Brewster angles are derived and their accuracy is estimated by using exact numerical methods for the solution of the inhomogeneous reflection problem. The possibilities are discussed for determining the parameters of nanometre-scale dielectric layers by means of characteristic reflection angles. A novel scanning angle differential reflectance method in the vicinity of the classical Brewster angle, whose sensitivity is in principle the same as that of ellipsometry, is developed.     

Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide

Values of the transmittance T(s) and the phaseretardation D were recorded in situ at two angles duringthe growth of thin films of tantalum oxide, titanium oxide, andzirconium oxide for deposition angles theta(nu) in the range40 degrees -70 degrees . Column angles for the same films were determinedex situ from scanning electron microscopy photographs ofdeposition-plane fractures. We show that the experimental columnangles are smaller than the corresponding values predicted by thetangent-rule equation psi = tan(-1)(0.5 tan theta(nu)) and that the experimental values fit a modifiedform of the equation psi = tan(-1)(E(1) tan theta(nu)) where E(1) is less than 0.5. We also show that theprincipal refractive indices are represented well by quadraticfunctions of the deposition angle, for example, n(1)(theta(nu)) = A(0) + A(2) theta(nu)(2).     

Thickness measurements on transparent substrates based on reflection ellipsometry. I. Optical effects of high-refractive-index additional layers

Theoretical studies were conducted for thickness measurements using transparent substrates on the external and internal reflection configurations. For three-phase systems consisting of ambient, film, and substrate, the refractive index of the substrate could be optimized to obtain the high sensitivity of an ellipsometric quantity delta to the film thickness and the small susceptibility of delta to errors in the incident angle. It was shown that the combination of an ordinary glass substrate and an additional dielectric layer with an appropriate layer thickness works as a synthetic high-index single substrate (SHIS). The optical effect of the combination was approximately described by use of the effective refractive index of SHIS. A method to select the refractive index of the additional layer was also given.     

Simple optical method to determine the porosity of porous silicon films

A simple optical method to estimate the porosity of microporous silicon films is described. The technique relies upon determination of film refractive index via measurement of the incident (Brewster) angle corresponding to a minimum in the intensity of light reflected from the air-film interface. The sample porosity is then obtained using an effective medium model. Porosities obtained using this method show general agreement with those obtained using gravimetric means and, where comparison was possible, excellent agreement with those of similarly-prepared films found by low angle X-ray reflectivity. These results confirm the general applicability of this technique to the determination of microporous silicon film porosity.     

Scattering of light from the random interface between two dielectric media with low contrast

We calculate the coherent and incoherent scattering of p- and s-polarized light incident from a dielectric medium characterized by a real, positive, dielectric constant epsilon0 onto its one-dimensional, randomly rough interface with a dielectric medium characterized by a real, positive, dielectric constant epsilon. We use a perturbation theory with a new small parameter, namely, the dielectric contrast eta = epsilon0 - epsilon between the medium of incidence and the scattering medium. The proper self-energy entering the expression for the reflectivity is obtained as an expansion in powers of eta through the second order in eta, and the reducible vertex function in terms of which the scattered intensity is expressed is obtained as an expansion in powers of eta through the fourth. The roughness-induced shifts of the Brewster angle (in p polarization) and of the critical angle for total internal reflection (epsilon0 > epsilon) are obtained. The angular dependence of the intensity of the incoherent component of the scattered light displays an enhanced backscattering peak, which is due to the coherent interference of multiply scattered lateral waves supported by the interface and their reciprocal partners. Analogs of the Yoneda peaks observed in the scattering of x rays from solid surfaces are also present. The results obtained by our small-contrast perturbation theory are in good agreement with those obtained in computer simulation studies.     

Evaluation of the elastic modulus of thin film considering the substrate effect and geometry effect of indenter tip

A method using finite element method (FEM) is proposed to evaluate the geometry effect of indenter tip on indentation behavior of film/substrate system. For the nanoindentation of film/substrate system, the power function relationship is proposed to describe the loading curve of the thin film indentation process due to substrate effect. The exponent of the power function and the maximum indentation load can reflect the geometry effect of indenter and substrate effect. In the forward analysis, FEM is used to simulate the indentation behavior of thin film with different apex angles of numerical conical indenter tip, and maximum indentation load and loading curve exponent are obtained from the numerical loading curves. Meanwhile, the dimensionless equations between the loading curve exponent, the maximum load, elastic properties of film/substrate system and apex angle of indenter are established considering substrate effect. In the reverse analysis, a nanoindentation test was performed on thin film to obtain the maximum indentation load and the loading curve exponent, and then the experimental data is substituted into the dimensionless equations. The elastic modulus of thin film and the real apex angle of indenter can be obtained by solving the dimensionless equations. The results can be helpful to the measurement of the mechanical properties of thin films by means of nanoindentation.     

Diffraction of horizontally polarized ultrasonic plane waves on a periodically corrugated solid-liquid interface for normal incidence and Brewster angle incidence

The theory, and the use at normal incidence, of shear-vertically polarized waves (with polarization vector in the plane containing the incident wave vector and the normal on the interface) using the mode conversion method has been tackled by others. Here we develop the theory for shear-horizontally polarized incident waves (with polarization vector perpendicular to both the normal on the interface and the incoming wave vector). We take into account normal incidence as well as oblique incidence. For normal incidence, we discover the generation of Love waves. If oblique incidence is considered, we discover the existence of a Brewster angle of incidence, comparable with the Brewster angle in optics, in which a diffraction grating can be used as a polarization filter.     

仿生超疏水聚丙烯薄膜的制备与性能

采用简单溶剂/非溶剂法制备出超疏水性聚丙烯薄膜。该薄膜表面与水的接触角为160°,滚动角小于4°。pH值为1～14的水溶液在其表面都有很高的接触角。通过对表面进行扫描电子显微镜分析可知,薄膜具有类鸟巢状多孔微纳米复合微观结构,这种结构可捕获空气,形成水与基底之间的气垫,对表面超疏水性的产生起到了关键的作用。用Cassi...     

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.