An angle-of-incidence tunable,SiO2-Si (film-substrate) reflection retarder for the UV mercury line λ=2537Å

We present an optimum design of a SiO₂-Si film-substrate single-reflection, angle-of-incidence tunable retarder for the UV spectral line λ=2537 Å. Small changes in film thickness around the optimum value do not significantly affect the device performance. The same applies to small shifts of the wavelength of operation, neglecting the effect of dispersion.     

Separability of amplitude,phase and polarization information in the Jones calculus

The two-component Jones vector is cast in a form that achieves the separation of the information on the polarization ellipse from that on the amplitude and phase of the light wave. The shape, sense of rotation and orientation of the elliptic vibration of the electric field are described by the complex polarization variable χ while the amplitude a (size) and temporal phase ? of that vibration are described by the complex amplitude A = aexp(i?). The transformation of the complex amplitude of the wave A after passing through an optical system leads to a complex-amplitude transfer function (CATF) which is a nonanalytic function of the complex polarization variable χ. The CATF is, in turn, separable into polarization-dependent (real) amplitude and phase transfer functions (ATF and PHTF). Together with the polarization transfer function PTF (the transformation of χ), the ATF and PHTF provide a useful set of tools that complement the well-known Jones calculus.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Determination of the complex refractive index profiles in P+31 ion implanted silicon by ellipsometry

Ellipsometry was used to determine the complex refractive index profiles in silicon implanted with P⁺₃₁ ions with energies of 35, 52,5 and 70 keV. The profiles were determined both by anodization-stripping of the implanted layer and by numerical fitting of multiple-angle-of-incidence ellipsometer data taken on the as-implanted surface, assuming that the implantation would exhibit a Gaussian distribution. Good correlation was obtained between the two types of profiles, indicating that the non-destructive measurements on the as-implanted surface may be useful in process control. Good agreement with published results was also obtained on the increase in depth with energy of both the damage and the implanted species.     

Explicit solution for the optical properties of a uniaxial crystal in generalized ellipsometry

The complex ordinary (N_o) and extraordinary (N_e) refractive indices of an absorbing uniaxial crystal can be explicitly derived from the normalized diagonal (α) and off-diago-nal (β) elements of one oblique-incidence (at angle φ) reflection matrix measured by generalized ellipsometry on a crystal face that contains the optic axis at an oblique orientation (ω ≠ O or $\text{π}\text{2}$) with respect to the plane of incidence. At most four solution sets (N_o, N_e) are mathematically and physically consistent with one measurement set (α,β,φ,ω). In many cases, identification of the correct solution is feasible without additional measurements. If necessary repeated measurements at a different value of φ or ω will resolve the ambiguity; only one solution set remains invariant upon a change of φ or ω, the correct set. A single measurement of reflectance (e.g., for p-polarized light) may also be adequate. The analytic inversion method is used in an error analysis to determine optimum choices of angle of incidence (φ ? 50–70°) and crystal orientation (ω ? 45°) that lead to minimum percentage errors of N_o and N_e for several uniaxial crystals.