A procedure is presented for the design of bilayer pellicle and bilayer-coated prism beam splitters that serve as the key optical element of the division-of-amplitude photopolarimeter (DOAP). The bilayer consists of two transparent thin films of sufficiently different refractive indices whose thicknesses are selected to achieve 50 to 50% split ratio and optimum ellipsometric parameters in reflection and transmission, such that the determinant of the DOAP instrument matrix is maximized at the proper angle of incidence. As a specific example, we present a Ge-coated nitrocellulose (NC) first-order pellicle beamsplitter for the near IR (2.0 to 2.2 µm). Visible designs include a GaP-coated NC fourth-order pellicle and a SiO2-GaP bilayer-coated glass prism at and near the 633-nm wavelength. Operation of these beamsplitters over a range of incidence angles, wavelengths, and in the presence of ±5% film thickness errors is also considered.
A high-efficiency beamsplitter for the equipartition of infrared input power using combined reflection and transmission is described. The new design does not use a back metal reflector coating, and hence is more efficient than those previously described. The beamsplitter uses a parallel slab of fused silica that is strip coated with a germanium film on the front and back sides to generate four beams of equal powers. A specific design for operation at the 1.55-µm fiber communication wavelength is presented. Power, efficiency, and polarization analysis of fractional beams in the presence of angular, film-thickness, and spectral deviations near the equipartition condition are discussed. The following results are obtained. An angular deviation of ±0.5 deg has no significant effect on power (<0.1%), efficiency (<0.02%), or polarization (ellipsometric) parameters (< 1 deg) of the fractional beams. A film-thickness deviation of ±10 nm results in a small change in power (<2%), efficiency (<0.1%), and polarization (<0.5 deg) of the fractional beams. A spectral variation of ±25 nm also has a small effect on power (<1.5%), efficiency (<0.01%), and polarization (<1 deg).
Performance of reflection polarizers using bare semiconductor substrates in the visible and UV spectral range is presented. Performance evaluation based on extinction ratio, throughput, and sensitivity to angular and spectral variations of Si and Ge reflection polarizers are considered.
We show that antireflection-coated (ARC) optical systems with numerical apertures < 1 exhibit negligible polarization aberrations of the fourth and sixth order for the retardance and di-attenuation, respectively. Results for ARC high-index optics are presented as examples.
We describe efficient beam splitters for the equi-partition of infrared input power using combined reflection and transmission by a strip-coated all-dielectric slab. Because no metal coating is used, high efficiency is achieved. The beam splitters use a fused silica parallel-slab that is strip coated with germanium on the front and back sides. Specific designs for operation at 1.55, 2.02 and 5.0 µm wavelengths are presented.
External-reflection phase retarders with high reflectance have been of interest for many years. 1-7 By selecting the angle of incidence, film thickness, and refractive indices of both the film and metallic substrate, the p- and s-polarized components of incident monochromatic light can be reflected equally and with a specified differential reflection phase shift introduced beween them. In general, these studies involved isotropic films. Azzam and Perilloux1 discussed the constraint on the optical constants of a film-substrate system such that it functions as a quarter-wave retarder (QWR) or half-wave retarder (HWR) at incidence angles of 70° and 45°, respectively.
Ellipsometry is a sensitive optical technique for non- invasive in-situ (in any optically transparent environment) and ex-situ (in air) characterization of surfaces, interfaces, and thin films which is based on measurement of the polarization of light before and after reflection from a given sample at different angles of incidence and as a function of wavelength. The spectral range of spectroscopic ellipsometry (SE) -typically 1-6eV of photon energy- has been extended to the mid and far IR on one side and to the VUV, EUV, and X-ray region on the other. Significant advances and sophistication of available instrumentation and supportive software have resulted in extensive use of ellipsometry in biology, chemistry, physics, materials science and engineering, and industrial applications over the past two decades. Fast ellipsometers are used for real- time on-line monitoring and feedback process control of various thin films and for the fabrication of pre-engineered multilayer and graded-composition structures. As a metrology tool, ellipsometry yields information on dielectric functions of layered optically isotropic or anisotropic materials, film thicknesses, interface roughnesses, and compositions (void and alloy fractions) and depth profiles of inhomogeneous thin films.
Applications of the polarization Michelson interferometer are reviewed. These include analog and binary polarization modulation, time shearing of a light pulse into a doublet of two separate pulses with orthogonal linear polarizations, creation of 'polarization-chirped' light pulses, generation of total and partial polarization states on and within the Poincare sphere, and measurement of the coherence and spectral properties of a quasimonochromatic light source.
Several recent applications in polarimetry, ellipsometry, spectropolarimetry, and multiplexed galvanometric scanners require a single compact beam splitter capable of splitting an input beam of light into four or more components. Of special interest is to design a single beam splitter to produce multiple components of equal powers. We present a specific IR design of a parallel-slab beam splitter that uses a fused silica as a slab material, and it is strip- coated with Germanium thin film on the front and with a uniform silver coat on the back. Equal powers among the first four components can be achieved when the reflectance levels on the first, second, third, and fourth strip is equal to 20 percent, 68 percent, 54 and 18 percent respectively. Specific designs at wavelengths of 1.55, 2 and 5 micrometers are presented. At a wavelength of 5 micrometers , glass shows some absorption and is replaced by another transparent slab material. The choice of varying the otpical material of the slab and metric thickness of each strip provides a great flexibility in the design and operation of the beam splitter over a wide range of applications.
In this paper we describe novel designs of IR versions of the parallel-slab division-of-amplitude photopolarimeter (IR-PS-DOAP) to measure the state of polarization of light as determined by the four Stokes parameters. The IR-PS-DOAP uses no movable parts or modulation and thus fast and simultaneous measurement is obtained. We present two different designs. The first employs a uniform, thin, transparent, film coating on the front surface of the parallel-slab. The second employs strips of thin, transparent, film coating on the front surface of the parallel-slab. A performance analysis comparison between the two will be presented. For wavelengths up to approximately 3.5 micrometers , SiO2, is totally transparent and is selected to be the slab material for the IR-PS-DOAP. For wavelengths beyond 3.5 micrometers , SiO2 becomes absorbent and will be replaced by another transparent material like Irtran2, for example. The instrument matrix of the system is non- singular; hence the state of polarization is completely determined. The IR-PS-DOAP is compact, light-weight, rugged and based on reflective optics, so that predictive theory of instrument performance is applicable.
The pair of Fresnel amplitude reflection coefficients for internal and external reflection, that apply when p- polarized light is incident on an interface between two transparent media form opposite sides at the same angle of incidence, are considered jointly and plotted together. This creates an interesting family of curves, with the angle of incidence as a parameter. Besides the well known characteristics of total reflection at the critical angle and total refraction at the Brewster angle, some unusual properties become apparent that pertain to light reflection at the special angles of 45 degrees and 51.827 degrees. The Stokes relations apply strictly at normal incidence, and approximately at other angles for nearly vanishing interfaces. The corresponding result for the Fresnel reflection coefficient for the s polarization, and for the ratio of p and s reflection coefficients, are also obtained.
Techniques for the partial or complete determination of the Mueller matrix of elastic light scattering by a given samples are reviewed. Important developments include several implementations and applications of the dual-rotating- retarder Mueller-matrix ellipsometer and the addition of imaging, scanning, and spectroscopic capabilities. The use of a multi-channel division-of-amplitude photopolarimeter as a polarization state detector, and the propose modulation of the polarization state generator have substantially increased the efficiency and speed with which the full Mueller matrix can be measured.
The com;lex amplitude reflection and transmission coefficients for the p and s polarizations at oblique incidence are determined for a four-port solid-substrate Fabry-Perot/Michelson interferometer. The amplitude response for each of the two reflected and two transmitted waves is considered as a function of the angle of incidence and optical path length. Incidence angles for maximum back reflection and maximum back transmission are noted for both polarizations. The presence of multiple ports enables four ellipsometric functions to be measured simultaneously, which is desirable for the accurate and unambiguous characterization of deposited thin films. Results are presented for reflection and transmission ellipsometry of a growing transparent MgF2 film on the planar entrance face of a ZnS-prism interferometer.
Fast (submillisecond) measurement of the complete state of polarization (SOP) of light, as determined by the four Stokes parameters, requires instruments that have no moving parts or modulators. This is accomplished by dividing the light beam, whose SOP is to be measured, into four or more beams that are intercepted by discrete (or array) photodetectors. The output electrical signals of at least four detectors (or array pixel groups) provide four linearly independent projections of the unknown Stokes vector of the incident light. This requires judicious choices of the beam splitting and polarizing optics.
Analytical geometry and ray tracing are used to determine the calibration matrix A' of the four detector photopolarimeter (FDP) when the incident light beam deviates from theoptical axis of the instrument by small angles. Detectors of the FDP are represented by their surface equations in Cartesian coordinates. The field ofview (FOV) is calculated as a function ofthe light beam deviation (LBD) in two orthogonal planes, one ofwhich is the plane ofincidence for light reflection at the first detector.
The extinction ratio ER and the reflectance, or throughput, for the unextinguished s polarization Rs are calculated for infrared reflection polarizers that consist of a low- index transparent layer embedded in a high-index transparent substrate. Iso-ER and iso-Rs contours illustrate the dependence of the ER and Rs for a specific IR polarizer on the depth and width of a buried layer of SiO2 in Si at 3.5-micrometers wavelength and 80 degree(s) angle of incidence. Both cases of a uniform layer with sharp boundaries and a diffuse Gaussian layer are considered. The diffuse-layer model employs Bruggeman's effective medium theory and is intended to simulate devices that are fabricated by the oxygen-ion implantation of Si. The angular and wavelength sensitivities of these polarizers are determined.
Contours of constant principal angle Φ and constant principal azimuth Ψ for an in-line, symmetric, three-reflection mirror system are presented. The three mirrors are assumed to be uncoated substrates of the same homogeneous isotropic material with complex relative dielectric function ε. By assigning values to Φ from 45 to 85 deg in 5-deg steps, the constraint on complex ε is determined numerically and represented graphically. The special case of Φ = 45 deg, which applies to a right-angle parallel-mirror beam displacer, enables an analytical solution. These results have important applications for the production of circular polarization over the entire spectrum, and especially in the VUV, where transmission-type devices are not possible. The performance of the three-mirror system as a VUV quarter-wave retarder/circular polarizer using different metals is also considered.
All possible solutions for a periodic stack of 10 ZnS-ThF4 bilayers on a Ag substrate that produce 90-deg differential reflection phase shift at 45-deg angle of incidence and 3.39-μm wavelength are determined. The angular and wavelength sensitivity of several of these designs is considered. To increase the reflectance, reduce the diattenuation, and improve the sensitivity of the 20-layer reflection quarterwave retarder (QWR), we also consider quasiperiodic stacks. These designs are obtained by iteration starting from an initial high-reflectance, 10-bilayer, non-QWR, periodic structure and adjusting the thicknesses of the two films of the topmost bilayer to realize the desired 90-deg retardance. Again multiple solutions are obtained for each initial design and their angular and wavelength sensitivity are analyzed. It is found that the best sensitivity corresponds to the lowest and nearly equal optical thicknesses of the two films of the topmost bilayer. Performance comparable to that reported in the literature, obtained for more complicated stacks in which the thicknesses of all 20 films are different, is reported.
Contours of constant principal angle (Phi) and constant principal azimuth (Psi) for an in-line, symmetric, three-reflection mirror system are presented. The three mirrors are assumed to use uncoated substrates of the same homogeneous isotropic material with complex relative dielectric function (epsilon) . By assigning values to (Phi) from 45 degree(s) to 85 degree(s), the constraint on complex (epsilon) is determined numerically and represented graphically. The special case of (Phi) - 45 degree(s), which applies to a right-angle parallel-mirror beam displacer, permits an analytical solution. These results have important applications for the production of circular polarization over the entire spectrum, and especially in the VUV where transmission-type devices are not possible. The performance of the three-mirror system as a VUV quarter-wave retarder/circular polarizer using different methods is also considered.
This paper reviews recently obtained results related to Fresnel's reflection coefficients which play a central role in the optics of light reflection by surfaces and thin films. Topics include conjugate and reciprocal interfaces between transparent media, reflectance matching between normal and oblique incidence, and reflectance switching. For light reflection at interfaces between transparent and absorbing media, contours of constant pseudo-Brewster angle and of constant principal angle are presented in the complex plane, along with a discussion of a condition of maximum minimum parallel reflectance at oblique incidence. Conformal mappings that describe the transformation of the Fresnel coefficients between normal and oblique incidence, and between the s and p polarizations at the same angle, are included. Reflectance for incident light of arbitrary polarization is also considered. Finally, trajectories that describe the evolution of the Fresnel coefficients with angle of incidence are presented.
All possible solutions for a periodic stack of 10 ZnS-ThF4 bilayers on a Ag substrate that produce 90 degree(s) differential reflection phase shift at 45 degree(s) angle of incidence and 3.39- micrometers wavelength are determined. The angular and wavelength sensitivity of several of these designs is considered. To increase the reflectance, reduce the diattenuation, and improve the sensitivity of the 20-layer reflection quarter-wave retarder (QWR), we also consider quasiperiodic stacks. These designs are obtained by iteration starting from an initial high- reflectance 10-bilayer, non-QWR, periodic structure and adjusting the thicknesses of the two films of the topmost bilayer to realize the desired 90 degree(s) retardance. Again multiple solutions are obtained for each initial design and their angular and wavelength sensitivity are analyzed. It is found that the best sensitivity corresponds to the lowest and nearly equal optical thicknesses of the two films of the topmost bilayer. Performance comparable to that reported in the literature, obtained for more complicated stacks in which the thicknesses of all 20 films are different, are reported.
IR reflection quarter-wave retarders (QWR5) are described that maintain the collinearity of the transmitted and incident beams. One QWR uses a symmetric prism of Ge (refractive index n = 4) with an apex angle of 119 deg. Light incident parallel to the base of the prism is totally refracted, without change of polarization, at the side faces of the prism that are coated with an appropriate transparent bilayer. Total internal reflection at the prism base produces the desired 90-deg retardance. The second QWR uses a right-angle Ge prism with its base coated with a PbTe layer (n = 5.1) to introduce the required phase shift at a 55.18-deg angle of incidence. The entrance and exit faces are antireflection coated with a polarization-preserving bilayer. Both QWRs are reasonably insensitive to small (±8 deg) angle-of-incidence errors.
Considerable progress has been achieved recently in the development of new ellipsometric and polarimetry sensors that meet the requirements of an industrial environment. In particular, multidetector instruments, such as the four-detector photopolarimeter (FDP or Stokes meter), are particularly suited for fast, on-line, and real-time monitoring of industrial processes because of their simplicity, ruggedness, and absence of moving parts. We review some of these recent developments with reference to the semiconductor, steel-making, and optical- coating industries as examples.
A reflective division-of-wavefront polarizing beam splitter is described that uses a dual- thickness transparent thin-film coating on a metal substrate. A previous design that used a partially clad substrate at the principal angle of the metal [Azzam, JOSA A 5, 1576 (1988)] is replaced by a more general one in which the substrate is coated throughout and the film thickness alternates between two non-zero levels. The incident linear polarization azimuth is chosen near, but not restricted to, 45 degree(s) (measured from the plane of incidence), and the angle of incidence may be selected over a range of values. The design procedure, which uses the two-dimensional Newton-Raphson method, is applied to the SiO2-Au film- substrate system at 633 nm wavelength, as an example, and the characteristics of the various possible coatings are presented.
A near-ideal, all-dielectric, reflection polarizer is described that employs selective totally destructive interference for the p polarization and constructive interference for the s polarization in a buried low-index (BLIND) film embedded in a high-index substrate near (within 10 degree(s) of) grazing incidence. A specific design is presented of an infrared polarizer that uses a film of refractive index 1.35 embedded in a Ge substrate of refractive index 4.1. Such a polarizer has a throughput for the s polarization of 92% and 99%, when operated at incidence angles of 80 degree(s) and 85 degree(s), respectively.
The intrinsic multiple-beam-splitting and polarization-altering properties of a diffraction grating are combined with linear photodetectors to achieve a simple and versatile photopolarimeter for the simultaneous and nearly instantaneous measurement of the four Stokes parameters of light in an arbitrary state of partial elliptical polarization. For spectroscopic applications the dispersive property of the grating is also employed with photodetector arrays to obtain Stokes parameter spectra.
An automatic ellipsometer that uses a four-detector photopolarimeter (FDP) to measure the state of polarization of light reflected from an optically isotropic or anisotropic, depolarizing or nondepolarizing sample surface is described. For conventional ellipsometry on specular isotropic surfaces, the incident light is polarized (at least partially) in one stable state (e.g., using a linear polarizer that need not be perfect), and the reflectance and ellipsometric parameters of the surface are encoded onto and, hence, can be retrieved from, the Stokes parameters of the reflected light. The latter are measured, virtually instantaneously, by the FDP. The FDP also greatly simplifies generalized Mueller-matrix ellipsometry on anisotropic or nonspecular surfaces. In this case, the polarization ofthe incident light is controlled by a linear polarizer followed by a quarterwave retarder (QWR) with a rotationally adjustable fast axis azimuth C. Fourier analysis of the output current vector of the FDP as a function of C yields a series of five terms whose vectorial coefficients determine the Mueller matrix column-by-column. In such an analysis, we account for the small inevitable imperfections of the QWR. Results are presented for measurements at the 633-nm wavelength of the ellipsometric parameters of a Au surface and the zeroth-order Mueller matrix of the 1200 G/mm Alcoated holographic grating for three different orientations of the grooves relative to the plane of incidence.
An automatic effipsometer that uses a four-detector photopolarimeter (FDP) to measure the state of polarization of light reflected from an optically isotropic or aniotropic, depolarizing or nondepolarizing, sample surface is described. For conventional effipsometry on specular isotropic surfaces, the incident light is polarized (at least partially) in one stable state (e.g., using a linear polarizer which need not be perfect), and the reflectance and ellipsometric parameters of the surface are encoded onto, hence can be retrieved from, the Stokes parameters of the reflected light. The latter are measured, virtually instantaneously, by the FDP. The FDP also greatly simplifies generalized Mueller-matrix ellipsometry on amisotropic or nonspecular surfaces. In this case, the polarization of the incident light is controlled by a linear polarizer followed by a quarter-wave retarder (QWR) with rotationally adjustable fast axis azimuth C. Fourier analysis of the output current vector of the FDP as a function of C yields a series of five terms whose vectorial coefficients determine the Mueller matrix column-by-column. In such an analysis, the small inevitable imperfections of the QWR are accounted for. Results are presented for measurements at 633 nm wavelength of the ellipsometric parameters of a Au surface and the zeroth-order Mueller matrix of a 1200 G/mm Al-coated holographic grating for three different orientations of the grooves relative to the plane of incidence.
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