Quarter-wave retardation systems based on the Fresnel rhomb principle

Customized retarders based on waveplates

Phase control is a critical parameter in polarization measurements. It is well known that a proper combination of wave plates allows to obtain achromatic phase shift, i.e., a constant retardation in certain spectral ranges. This paper is focused on a different, but more useful, goal, as it is to achieve customized variable retarders in broad spectral ranges. To do that, a merit function was used to measure the similarity between the overall phase shift of the wave plate combinations and the desired target. The control variables are the thicknesses and orientations of the wave plates. All possible combinations with four and five wave plates of quartz and MgF₂ were analyzed, but our approach can be perfectly extended to deal with more wave plates. The result of an optimization process determines the thicknesses and orientations of the wave plates, which results in the closest retarder to the desired one. Numerical results show deviations below 10% between the target and the obtained retardation. These systems are of special interest in those fields and instruments in which polarization control plays a fundamental role.

Analysis of non-idealities in rhomb compensators

In-line rotatable rhombs that are only weakly chromatic are desired as compensators for a wide variety of applications in spectroscopic polarimetry and Mueller matrix spectroscopic ellipsometry. These devices employ multiple total internal reflections to generate differences in the phase shifts upon reflection for orthogonal fast and slow axis optical electric field components. A framework has been developed for characterization of non-idealities in the performance of rhombs due to dissipation and associated dichroism upon each reflection as well as stress-induced birefringence along each beam path. External oblique reflection measurements by spectroscopic ellipsometry for the internally reflecting interface structures has enabled characterization of the dichroic effects and retardance generated by the reflections. The framework for analysis of the effects of stress relies on simulations demonstrating that the contributions to polarization modification from each beam path depend only on the accumulated stress-induced retardance and average azimuthal angle of the fast principal stress axis along the given path. The overall approach has been applied to straight-through Mueller matrix measurements of a three-reflection rhomb in its operational configuration to establish the set of stress parameters for each of the four beam paths needed to fit the measurements. Thus, device geometry and optical structure, including layer thicknesses and component media optical properties, as well as stress-induced retardances and average stress azimuthal angles, which are all deduced in the analysis, enable a complete description of the polarization modifying properties of the rhomb when serving as a compensator.

Design of superachromatic quarter-wave retarders in a broad spectral range

A superachromatic quarter-wave retarder using an arbitrary number of waveplates in a broadband spectral range has been proposed. Their design is based on the optimization of a merit function, the achromatism degree (AcD), which represents a global behavior metric for the retardation. By means of this technique, the thickness and azimuth of each waveplate is determined. The achromatism degree is a measure of the distance between the overall retardation and a target retardation weighted by the spectrum of the incident light. We report on a particular case where all waveplates are made of quartz. As application examples, the design of a quarter-wave retarder using two, three, and four waveplates in the spectral ranges of 500-700 nm and 400-1000 nm was studied. The numerical results show that for these ranges, the best designs obtained present a maximum difference of 0.013° and 0.010° with respect to the target retardation, respectively. In addition, an analysis of their achromatic stability is presented. These results can be applied in the aerospace industry, spectroscopic ellipsometry, and spectrogoniometry, among others.

Novel achromatic single reflection quarter-wave retarder: design and measurement

In this work, we present an achromatic quarter-wave retarder whose design is based upon the reflection properties of an isotropic-anisotropic interface. In theory, it is possible to obtain a π/2 phase shift by means of a total internal reflection at an isotropic-isotropic interface. However, in order to achieve such a phase shift, it is necessary to use a medium with a particularly high refractive index. We have previously shown that these phase shifts can be achieved by means of a total internal reflection in an isotropic-uniaxial interface, which allows the use of smaller refractive index media. By means of this property, we designed, built, and characterized a novel quarter-wave retarder that makes it possible to obtain circularly polarized light from a linear polarization state. We developed some guidelines that allowed us to obtain a device of competitive performance, low cost, and manageable manufacture.

Extended broadband achromatic reflective-type waveplate

This work demonstrates the feasibility of applying a symmetrical film stack on a silver mirror, resulting in broadband phase retardation. While functioning as a reflective-type achromatic waveplate, the symmetrical film stack comprises at least one anisotropic thin film. Additionally, selecting the birefringence and thickness of the thin film allows for the design of uniform phase retardation in both the passband and stopband. A symmetrical film stack that is composed of an anisotropic Ta(2)O(5) thin film and isotropic Ta(2)O(5) thin film is investigated for its achromatic performance in phase retardation.

Lateral shearing with a pair of double Fresnel rhombs for nulling interferometry

A lateral-shearing interferometer with a pair of double Fresnel rhombs is proposed. Use of Fresnel rhombs enables us to accomplish simultaneously lateral shearing and achromatic nulling. Nulling interferometry with lateral shearing is one of the basic methods for searching directly for extrasolar planets with a segmented-mirror telescope. Here the Thirty-Meter Telescope is considered as a model of a segmented-mirror telescope. Our computer simulations show high extinction for the K-band (2.0-2.4 μm). Optical experiments are conducted to verify the lateral shearing and nulling with a pair of double Fresnel rhombs.

Spectral modulation for full linear polarimetry

Linear (spectro) polarimetry is usually performed using separate photon flux measurements after spatial or temporal polarization modulation. Such classical polarimeters are limited in sensitivity and accuracy by systematic effects and noise. We describe a spectral modulation principle that is based on encoding the full linear polarization properties of light in its spectrum. Such spectral modulation is obtained with an optical train of an achromatic quarter-wave retarder, an athermal multiple-order retarder, and a polarizer. The emergent spectral modulation is sinusoidal with its amplitude scaling with the degree of linear polarization and its phase scaling with the angle of linear polarization. The large advantage of this passive setup is that all polarization information is, in principle, contained in a single spectral measurement, thereby eliminating all differential effects that potentially create spurious polarization signals. Since the polarization properties are obtained through curve fitting, the susceptibility to noise is relatively low. We provide general design options for a spectral modulator and describe the design of a prototype modulator. Currently, the setup in combination with a dedicated retrieval algorithm can be used to measure linear polarization signals with a relative accuracy of 5%.

Total internal reflection without change of polarization using a right-angle prism with half-wavelength-thick optical interference coating

Monochromatic light, which is polarized in an arbitrary state, is totally internally reflected at angle of incidence phi=45 degrees without change of polarization by a right-angle prism of refractive index n0=1+1/Square root of 2=1.70711 (e.g., N-LAK8 Schott glass at wavelength lambda=706 nm), which is coated with a transparent thin film of refractive index n1=(1+1/2)1/2=1.30656 (e.g., vacuum-deposited fluoride material) and of metric thickness equal to half of the vacuum wavelength of incident light, d=lambda/2. The ambient medium of evanescent refraction is assumed to be vacuum, air, or an inert gas. Wavelength shifts of +/-50 nm, or changes of the internal angle of incidence of +/-1 degrees around 45 degrees, cause phase errors of only a few degrees. The reflected and incident polarization states are nearly identical in the presence of such small phase errors.

In-line broadband 270 degrees (3lambda/4) chevron four-reflection wave retarders

The net differential phase shift Delta(t) introduced between the orthogonal p and s linear polarizations after four successive total internal reflections inside an in-line chevron dual-Fresnel-rhomb retarder is a function of the first internal angle of incidence phi and prism refractive index n. Retardance of 3lambda/4 (i.e., Delta(t)=270 degrees) is achieved with minimum angular sensitivity when phi=45 degrees and n=1.900822. Several optical glasses with this refractive index are identified. For Schott glass SF66 the deviation of Delta(t) from 270 degrees is < or = 4 degrees over a wavelength range of 0.55 < or = lambda < or = 1.1 microm in the visible and near-IR spectrum. For a SiC prism, whose totally reflecting surfaces are coated with an optically thick MgF(2) film, Delta(t)=270 degrees at two wavelengths: lambda(1)=0.707 microm and lambda(2)=4.129 microm. This coated prism has a maximum retardance error of approximately 5 degrees over > three octaves (0.5 to 4.5 microm) in the visible, near-, and mid-IR spectral range. Another mid-IR 3lambda/4 retarder uses a Si prism, which is coated by an optically thick silicon oxynitride film of the proper composition, to achieve retardance that differs from 270 degrees by < 0.5 degrees over the 3-5 microm spectral range.

Improved method for calibrating a Stokes polarimeter

We present a method for calibrating a polarization state analyzer that uses a set of well- characterized reference polarization states and makes no assumptions about the optics contained in the polarimeter other than their linearity. The method requires that a matrix be constructed that contains the data acquired for each of the reference polarization states and that this matrix be pseudoinverted. Since this matrix is usually singular, we improve the method by performing the pseudoinversion by singular value decomposition, keeping only the four largest singular values. We demonstrate the calibration technique using an imaging polarimeter based upon liquid crystal variable retarders and with light emitting diode (LED) illumination centered at 472 nm, 525 nm, and 630 nm. We generate the reference polarization states by using an unpolarized source, a single polarizer, and a Fresnel rhomb. This method is particularly useful when calibrations are performed on field-grade instruments at a centrally maintained facility and when a traceability chain needs to be maintained.

Optimal design of achromatic true zero-order waveplates using twisted nematic liquid crystal

Phase retarders usually show strong wavelength dependence. A novel and simple configuration with the combination of two twisted nematic liquid-crystal cells is proposed for the design of a true zero-order achromatic quarter-wave plate. The present optimization method considers the material dispersion. Simulation computations show a good achromatic behavior of the optimized waveplate. Compared with other types of broadband quarter-wave plates, the present device is compatible with classical liquid-crystal displays and can be expected to be used in precision polarimeters with low cost and enhanced light efficiency.

Design and performance of a stable linear retarder

The National Institute of Standards and Technology (NIST) has developed a nominally quarter-wave linear retarder for wavelengths near 1.3 mum that is stable within +/-0.1 degrees retardance over a range of wavelength, input angle, temperature, and environmental variations. The device consists of two concatenated Fresnel rhombs made from a low stress-optic-coefficient glass that minimizes the residual birefringence from machining and packaging. Device machining, assembly, and antireflection coating tolerances are discussed, and the theoretical performance is compared with measurements. Humidity can modify retardance of the total-internal-reflection surfaces; we discuss packaging that mitigates this effect and provides an estimated 10-year lifetime for the device. Several measurement methods were intercompared to ensure that the device retardance can be measured with an uncertainty less than 0.1 degrees . Similar retarders will be certified by NIST and made available as Standard Reference Materials.

Phase retarders with variable angles of total internal reflection

Results for three λ/4 phase retarders are reported. One of them is achromatic to within ± 0.06° of 90° in the visible region. It is shown that, under certain conditions, oblique incidence on the entrance face of total internal reflection phase retarders can greatly improve the achromaticity.

Measurement of spectral, directional reflectivities of solids at high temperatures between 9 and µm

A new apparatus to measure spectral,<directional reflectivities of solids for temperatures up to 1100 °C is developed. Reflectivities of two ceramic materials, silicon nitride (Si(3)N(4)) and silicon carbide α-SiC, are measured at wavelengths between 9 and 11 µm (the operating range of tunable CO(2) lasers) for various temperatures, angles of incidence, and for two types of polarization, the electric vector perpendicular and parallel to the plane of incidence. Reflectivities are measured by comparing the power of the beam reflected from the sample (heated in the furnace) with that of the incident beam. This experimental setup is limited to relatively specular surfaces (with a collection half-angle of 15°). The measurements show that the reflectivity of α-SiC at room temperature rises sharply near ~10.2 µm because of the presence of a 12.6-µm reflection band (restrahlen band), and the occurrence of this phenomenon gradually shifts to longer wavelengths as the temperature is raised to 1000 °C. At 10.6 µm, where most CO(3) lasers operate, the reflectivity of SiC diminishes rapidly as the temperature is raised. Si(3)N(4) has two restrahlen bands on both sides of 9.9 µm at room temperature that gradually shift to longer wavelengths with temperature. However, the decrease in reflectivity of Si(3)N(4) with temperature at 10.6 µm is very small.

Wavelength-scanning polarization-modulation ellipsometry: some practical considerations

A discussion is presented of the practical considerations involved in wavelength-scanning polarization-modulation ellipsometry. Emphasis is placed on factors affecting accuracy and precision and on the alignment of the optical elements. The system described is used to measure the optical properties of air-cleaved KCI and of clean and tarnished Ag surfaces in ultrahigh vacuum in the 250-650-nm range.

A critical evaluation of rhomb-type quarterwave retarders

The most achromatic quarterwave plates appear to be rhomb-type devices. General relations are given for calculating the phase retardation of these devices and are used to determine the variation of the phase retardation with wavelength and with acceptance angle for different rhomb designs. Length-to-aperture ratio, beam deviation, surface coatings, effect of strain birefringence, and other parameters are also considered. The classical version of the Fresnel rhomb can be optimized to improve its performance, and several of the more recent rhomb designs have excellent characteristics. The choice of which type of rhomb to use depends on the requirements of the particular optical system.

Opticsat the naional physical laboratory

Optics is spread widely in the National Physical Laboratory, anda condensed account is given of some of the highlights.

Some applications of thin films to polarization devices

In the first application of thin films discussed, a multilayer stack is enclosed in a cemented cube to form a polarizing beam splitter. Polarizing efficiencies exceeding 99.8% have been achieved in both reflected and transmitted beams at the design wavelength. In the second application, the deposition of thin films on the totally reflecting surfaces of silica phase retarding systems has resulted in a substantial improvement in achromatism of these devices. Measured phase retardations of one of the two devices described were within 0.5 degrees of 90 degrees over the visible and uv to wavelengths down to 200 nm.