R. M. A. Azzam

Multiple determination of the optical constants of thin-film coating materials

The seven participating laboratories received films of two different thicknesses of Sc2O3 and Rh. All samples of each material were prepared in a single deposition run. Brief descriptions are given of the various methods used for determination of the optical constants of these coating materials. The measurement data are presented, and the results are compared. The mean of the variances of the Sc2O3 refractive-index determinations in the 0.40–0.75-nm spectral region was 0.03. The corresponding variances for the refractive index and absorption coefficient of Rh were 0.35 and 0.26, respectively.

Simple and direct determination of complex refractive index and thickness of unsupported or embedded thin films by combined reflection and transmission ellipsometry at 45° angle of incidence

Measurements of the polarization states (represented by complex numbers χr and χt, respectively) of light reflected and transmitted by an unsupported or embedded thin film, for totally polarized light (with nonzero p and s components) incident at 45°, permit simple, direct, and explicit determination of the film’s complex refractive index N1independently of film thickness or input polarization. If α = χr/χt, we find that α = rs + rs−1, where rs is Fresnel’s complex reflection coefficient of the ambient–film interface for the s polarization at 45° incidence. From α, rs is determined, and from rs we get N1 = N0(1 + rs2)1/2/(1 + rs), where N0 is the refractive index of the transparent medium surrounding the film. Knowledge of the incident polarization χi allows the film thickness to be determined, also explicitly, by using either of the ratios χi/χr or χi/χt.

Maximum minimum reflectance of parallel-polarized light at interfaces between transparent and absorbing media

The pseudo-Brewster angle ϕpB, of minimum reflectance ℛpm for the parallel (p) polarization, of an interface between a transparent and an absorbing medium is determined by Im{(∊ − u)[1 − (1 + ∊−1)u]2} = 0, where ∊ is the complex ratio of dielectric constants of the media and u = sin2ϕpB. It is shown that, for a given value of the normal-incidence amplitude reflectance |r|, there is an associated normal-incidence phase shift, δ = δmm, that leads to maximum minimum parallel reflectance, ℛpmm. We determine δmm, ℛpmm, ϕpBmm as functions of |r|. We find that, as |r| increases from 0 to 1, δmm decreases from 90° to 0, ℛpmm/|r|2 increases from 0 to 1, and the associated ϕpBmm decreases from 45° to 0, all monotonically.

Stationary property of normal-incidence reflection from isotropic surfaces

The complex reflection coefficients for the parallel (p) and perpendicular (s) polarizations of light that are normally incident upon an isotropic surface are proved to be stationary with respect to small changes of the angle of incidence in the neighborhood of zero. This is true not only for a single interface between isotropic media but also for any one-dimensionally inhomogeneous or multilayer reflecting structure that is stratified in the direction of the surface normal. For incident light of certain intensity, phase, and polarization, the intensity, phase, and polarization of the reflected light all remain stationary with respect to small near-normal angle-of-incidence variations to first order. A second-order analysis is carried out to determine the parabolic (quadratic) variation of various reflection parameters of an interface with an angle near normal incidence.

Constraint on the optical constants of a film–substrate system for operation as an external-reflection retarder at a given angle of incidence

Given a transparent film of refractive index n1 on an absorbing substrate of complex refractive index n2-jk2, we examine the constraint on n1, n2, and k2 such that the film–substrate system acts as an external-reflection retarder of specified retardance Δ at a specified angle of incidence ϕ. The constraint, which takes the form f(n1,n2,k2;ϕ,Δ) = 0, is portrayed graphically by equi-n1 contours in the n2,k2 plane at ϕ = 45, 70° and for Δ = ±90 and ±180°, corresponding to quarterwave and halfwave retarders (QWR and HWR), respectively. The required film thickness as a fraction of the film thickness period and the polarization-independent device reflectance ℛ are also studied graphically as functions of the optical constants. It is found that as n2 → 0, ℛ → 1, so that a metal substrate such as Ag is best suited for high-reflectance QWR (ϕ > 45°) and HWR (ϕ ≤ 45°). However, films that achieve QWR at ϕ ≤ 45° are excellent antireflection coatings of the underlying dielectric, semiconductor, or metallic substrate.

Extinction of the p and s polarizations of a wave on reflection at the same angle from a transparent film on an absorbing substrate: applications to parallel-mirror crossed polarizers and a novel integrated polarimeter

The p- and s-polarized components of light can be suppressed on reflection at the same angle of incidence from an absorbing substrate coated by a transparent thin film if the wave is refracted in the film at 45° and the constraint Re[(∊2 − α)/(1 − α)]1/2 = α + |∊2 − α| is satisfied, where 2α and ∊2 are the ratios of dielectric constants of the film and substrate, respectively, to that of the ambient. For high-reflectance metal substrates (|∊2| ≫ 1), α ≃ 1, the ratio of film to ambient refractive index approaches 2, and the unextinguished reflectances approach 1. The least film thicknesses required to suppress the p and s polarizations are in the ratio 2:1. The analysis is applied to Si and Al substrates in the near UV-visible-near-IR spectral range. It is found that the film refractive index and thickness should be controlled to within ±0.01 and ±5 A, respectively, for an Al substrate at 550 nm. Significant applications are proposed that include parallel-mirror crossed polarizers, a novel polarimeter that integrates the polarization-analysis and photodetection functions, high-reflectance crossed thin-film reflection polarizers integrated on the same substrate, and division-of-wavefront polarizing beam splitters.

Antireflecting and polarizing transparent bilayer coatings on absorbing substrates at oblique incidence

The condition of zero reflection of p- and s-polarized light by a transparent bilayer on an absorbing substrate is derived in the form |gν(ϕ, Ni)| ≤ 1, where gν is a function of the angle of incidence ϕ, the refractive indices Ni (i = 0,1,2,3) of the system, and the polarization state ν (= p or s). As an application, the air–Si3N4–SiO2–Si system is considered at two laser wavelengths λ = 6328 and 3250 A. The thicknesses of the two films of the bilayer and the unextinguished reflectance are determined as functions of ϕ, and the results appear graphically and in tables. Extinction of the s polarization is accompanied by low overall residual reflectance (e.g., for incident unpolarized light, it is 1.6% for λ = 6328 A at ϕ = 45°). On the other hand, suppression of the p polarization at a high incidence angle is accompanied by high s reflectance (e.g. = 96% for λ = 3250 A at ϕ = 83°). This demonstrates that efficient bilayer reflection polarizers are possible.

Single-reflection film–substrate half-wave retarders with nearly stationary reflection properties over a wide range of incidence angles

The complex reflection coefficient for the p polarization of a transparent film on an absorbing or transparent substrate can be made equal to the negative of that for the s polarization, and hence the film–substrate system acts as a half-wave retarder (HWR), by proper selection of film refractive index N1, film thickness d, and angle of incidence ϕ.This condition, which generally holds only at normal incidence, becomes possible at oblique incidence also if N1 is within a certain range, 1<N1<N1. For a given substrate and given N1, a procedure is described to determine ϕHWR and dHWR that achieve a HWR. As N1 is increased from 1 to the upper limit N1, ϕHWR decreases from 90° to 0 monotonically. dHWR approximately equals (exactly equals when the substrate is a perfect dielectric or a perfect conductor) an odd multiple of half of the film-thickness period evaluated at ϕHWR. Significantly, we find that the film–substrate HWR retains nearly the same characteristics of normal-incidence reflection over the range of angle from 0 up to (and beyond) ϕHWR. Detailed data are presented of HWR’s that use transparent films on metallic (Al and Ag), semiconducting (Si), and dielectric (glass) substrates at two laser wavelengths (0.6328 and 10.6 μm). Film–substrate HWR’s permit the realization of simple polarization-insensitive parallel-mirror beam displacers, 90° rooftop reflectors, and biconical axicons and waxicons.

Pseudo-Brewster and second-Brewster angles of an absorbing substrate coated by a transparent thin film

The pseudo-Brewster angle of minimum reflectance for the p polarization, the corresponding angle for the s polarization, and the second-Brewster angle of minimum ratio of the p and s reflectances are all determined as functions of the thickness of a transparent film coating an absorbing substrate by numerical solution of the exact equations that govern such angles of the form Re(Z′/Z) = 0, where Z = Rp, Rs, or ρ represent the complex amplitude-reflection coefficients for the p and s polarizations and their ratio (ρ = Rp/Rs), respectively, and Z′ is the angle-of-incidence derivative of Z. Results that show these angles and their associated reflectance and reflectance-ratio minima are presented for the SiO2–Si film–substrate system at wavelength λ = 0.6328 μm and film thickness of up to four periods (≃1.2 μm). Applications of these results are proposed in film-thickness measurement and control.

Three-reflection halfwave and quarterwave retarders using dielectric-coated metallic mirrors

A design procedure is described to determine the thicknesses of single-layer coatings of a given dielectric on a given metallic substrate so that a specified net phase retardance (and/or a net relative amplitude attenuation) between the p and s polarizations is achieved after three reflections from a symmetrical arrangement of three mirrors that maintain collinearity of the input and output beams. Examples are presented of halfwave and quarterwave retarders (HWR and QWR) that use a ZnS–Ag film–substrate system at the CO2-laser wavelength λ = 10.6 μm. The equal net reflectances for the p and s polarizations are computed and found to be high (above 90%) for most designs. Sensitivity of the designs (deviation of the magnitude and phase of the ratio of net complex p and s reflection coefficients from design specifications) to small film-thickness and angle-of-incidence errors is examined, and useful operation over a small wavelength range (10–11 μm) is demonstrated.