A critical evaluation of rhomb-type quarterwave retarders

Apophyllite waveplates

We investigate the polarization characteristics of apophyllite crystals in an attempt to evaluate their potential use for achromatic waveplates. Among the 50 plates that we extracted and polished from natural apophyllite crystals, a few show the sought-for characteristic of birefringence that increases linearly with the wavelength. However, we also find that the crystals among our samples exhibit a sectored structure in their polarization properties, as well as an undesirable degree of spatial nonuniformity.

Mueller matrix ellipsometer based on discrete-angle rotating Fresnel rhomb compensators

A spectroscopic Mueller matrix ellipsometer based on two rotating Fresnel rhomb compensators with a nearly achromatic response and optimal retardance is described. In this instrument, the compensators rotate in a discrete manner instead of continuously rotating, and this allows for a well-conditioned measurement even for low intensity samples. Moreover, in this configuration, the exposure time of the CCD detector can be varied within orders of magnitude without interfering with the dynamics of the compensator rotation. An optimization algorithm determines the optimal set of discrete angles that allows the determination of the Mueller matrix in the presence of noise. The calibration of the instrument is discussed, and examples of experimentally determined Mueller matrices are provided.

Arbitrary polarization control by magnetic field variation

We propose a universal scheme for the construction of a device for arbitrary-to-arbitrary polarization transformation, which consists of two quarter-wave plates and two Faraday rotators. Using this device, one can continuously change the retardance and the rotation angle simply by changing the magnetic fields in each Faraday rotator.

Achromatic linear retarder with tunable retardance

We present a universal design and proof-of-concept of a tunable linear retarder of uniform wavelength response in a broad spectral range. It consists of two half-wave retarders (HWR) between two quarter-wave retarders (QWRs), where the uniform retardance can be tuned continuously by simply rotating one of the HWRs. A proof-of-concept of this design is built by using commercially available Fresnel rhomb retarders that provide retardation with almost wavelength uniformity in the visible and near infrared from 450 to 1550 nm. The design is universal, since other achromatic QWRs and HWRs could also be employed. The system is experimentally demonstrated to control the state of polarization of a supercontinuum laser.

Stokes-vector and Mueller-matrix polarimetry [Invited]

This paper reviews the current status of instruments for measuring the full 4×1 Stokes vector S, which describes the state of polarization (SOP) of totally or partially polarized light, and the 4×4 Mueller matrix M, which determines how the SOP is transformed as light interacts with a material sample or an optical element or system. The principle of operation of each instrument is briefly explained by using the Stokes-Mueller calculus. The development of fast, automated, imaging, and spectroscopic instruments over the last 50 years has greatly expanded the range of applications of optical polarimetry and ellipsometry in almost every branch of science and technology. Current challenges and future directions of this important branch of optics are also discussed.

Mid-infrared Mueller ellipsometer with pseudo-achromatic optical elements

The purpose of this article is to present a new broadband Mueller ellipsometer designed to work in the mid-infrared range, from 3 to 14 μm. The Mueller ellipsometer, which can be mounted in reflection or in transmission configuration, consists of a polarization state generator (PSG), a sample holder, and a polarization state analyzer (PSA). The PSG consists of one linear polarizer and a retarder sequentially rotated to generate a set of four optimal polarization states. The retarder consists of a biprism made of two identical Fresnel rhombs disposed symmetrically and joined by an optical contact, giving the ensemble a "V" shape. Retardation is induced by the four total internal reflections that the beam undergoes when it propagates through the biprism. Total internal reflection allows the generation of a quasi-achromatic retardation. The PSA is identical to the PSG, but with its optical elements mounted in reverse order. After a measurement run, the instrument yields a set of sixteen independent values, which is the minimum amount of data required to calculate the Mueller matrix of the sample. The design of the Mueller ellipsometer is based on the optimization of an objective criterion that allows for minimizing the propagation of errors from raw data to the Mueller matrix of the sample. The pseudo-achromatic optical elements ensure a homogeneous quality of the measurements for all wavelengths. The performance of the Mueller ellipsometer, in terms of precision and accuracy, is discussed and illustrated with a few examples.

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.

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.

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.

Embedded centrosymmetric multilayer stacks as complete-transmission quarter-wave and half-wave retarders under conditions of frustrated total internal reflection

A centrosymmetric multilayer stack of two transparent materials, which is embedded in a high-index prism, can function as a complete-transmission quarter-wave or half-wave retarder (QWR or HWR) under conditions of frustrated total internal reflection. The multilayer consists of a high-index center layer sandwiched between two identical low-index films with high-index-low-index bilayers repeated on both sides of the central trilayer, maintaining the symmetry of the entire stack and constituting a QWR (Delta(t)=90 degrees or 270 degrees ) or HWR (Delta(t)=180 degrees ) in transmission. A QWR design at wavelength lambda=1.55 microm is presented that employs an 11-layer stack of Si and SiO(2) thin films, which is embedded in a GaP cube prism. The intensity transmittances for the p and s polarizations remain >99% and Delta(t) deviates from 90 degrees by <+/-3 degrees over a 100 nm spectral bandwidth (1.5< or =lambda< or =1.6 microm), and by < or =+/-7 degrees over an internal field view of +/-1 degrees (incidence angle 44 degrees < or = phi(0)< or =46 degrees inside the prism). An HWR design at lambda=1.55 microm employs seven layers of Si and SiO(2) thin films embedded in a Si cube, has an average transmittance >93%, and Delta(t) that differs from 180 degrees by <+/-0.3 degrees over a 100 nm bandwidth (1.5< or =lambda< or =1.6 microm) and by <+/-17 degrees over an internal field view of +/-1 degree . The sensitivity of these devices to film-thickness errors is also considered.

Achromatic angle-insensitive infrared quarter-wave retarder based on total internal reflection at the Si-SiO2 interface

An achromatic infrared (lambda = 1.2-4 microm), Si-prism quarter-wave retarder (QWR) is described that uses total internal reflection at a buried Si-SiO2 interface at an angle of incidence phi near 33 degrees, where deltaDelta/deltaphi = 0. The retardance delta deviates from 90 degrees by < +/- 2 degrees within a field of view of +/- 10 degrees (in air) over the entire bandwidth. Because the SiO2 layer at the base of the prism is optically thick, this QWR is unaffected by environmental contamination.

Phase retarders highly insensitive to the input angle

In the few exceptional cases of total internal reflection phase retarders that are weakly sensitive to variations in the input angle of incidence i, the devices are of increasingly larger size; deviate or translate the emergent beam; are difficult to align in optical systems; or, in coated rhombs, have an impermanent stability of the retardance. Based on new compensating effects, novel devices of high retardance stability and advantageous characteristics are presented. One device is stable to within 0.09 degrees of 90 degrees for i ? 3 degrees . It is a two-reflection quarter-wave retarder that does not alter the path of the compact size light beam, is of compact size (one seventh the size occupied by the achromatic device AD-1 for equal aperture lengths), and can be easily aligned in optical systems or used as a rotating element. The path length of the beam inside the device is less than one third the corresponding length inside the achromatic device AD-1.

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.

Rotating-polarizer polarimeter for accurate retardance measurement

We demonstrate an automated polarimeter based on a rotating polarizer for the measurement of linear retardance independent of laser power and detector gain. The retardance is found when a curve is fitted to a unique normalization of the intensity response of the polarimeter over a range of input polarizer orientations. The performance of this polarimeter is optimal for measurements of quarter-wave retardance and minimal for half-wave retardance. Uncertainties are demonstrated by measurements on six stable double Fresnel rhombs of nominal quarter-wave retardance, yielding expanded uncertainties between 0.031 degrees and 0.067 degrees . The accuracy has also been verified by blind comparisons with interferometric and modified null retardance measurement techniques.

Theory of oblique-incidence phase retarders

Phenomenological and mathematical analyses of oblique incidence in total-internal-reflection phase retarders and the procedure for constructing extremely achromatic quarter-wave retarders are presented. It is shown that the retardance can assume the same value twice at two definite spectral lines. As an example, a quarter-wave phase retarder is described that introduces a retardance of exactly 90 degrees at two He-Ne laser lines of 632.8 and 1150 nm with a maximum deviation of 0.007 degrees for other wavelengths between these two lines. This application is advantageous in conjunction with two-line and multiline lasers where the radiation is usually pumped in a state of circular polarization.

Achromatic wave retarder by phase subtraction

We analyze the method of phase subtraction in two identical optical structures to build an achromatic phase retarder. The two structures are made of right-angle prisms and are aligned orthogonal to each other. They are also made of materials of different refractive indices so that dispersion compensation can be taken advantage of. Essentially the phase retardation between the s and p waves in the first structure is subtracted from the phase retardation in the second structure. This can be done by reversing the roles of the s and p waves. By choosing the materials of the prisms properly, the phase retardation can be made to be constant over a broad spectral range. Indeed, calculations made with commercial optical glasses show that phase errors in the visible and near-infrared regions can be rather small. For example, for a 90° phase retarder (quarter-wave plate), a phase error of 0.35° can be obtained from 0.35 to 0.81 μm and from 0.59 to 1.26 μm.

Optimization of a rhomb-type quarter-wave phase retarder

Apreviously reported two-reflection, undeviating-beam total internal reflection (TIR) quarter-wave phase retarder is optimized. The specifications and characteristics of the device are sensitive to the refractive index n of the rhomb material. In particular, the size of the rhomb can be reduced by a factor of 11 for the same aperture size if a glass with n = 1.70 is used instead of one with n = 1.53. Optimal conditions are in the refractive-index interval n = 1.68-1.71. Coated rhombs of this type are mentioned.

Scanning ellipsometer by rotating polarizer and analyzer

A new type of scanning photometric ellipsometer with polarizer and analyzer both rotating synchronously at rotation rates of omega(0)/2 and omega(0) (f(0) = 51 Hz), has been designed and constructed. The mechanical and electrical design, alignment, calibration, and error reduction of the system are discussed in detail. Through measuring the amplitudes of the three ac components from the photomultiplier, at frequencies of 51, 102, and 153 Hz, respectively, complex dielectric function spectra have been obtained for test samples of Au and CdTe in the 1.5-5.5-eV range and shown to be in agreement with the results of others.

Four-channel polarimeter for time-resolved ellipsometry

A new four-channel partial polarimeter was designed for use in time-resolved ellipsometry measurements. The device outputs four parallel, equispaced beams from a single input beam. By detecting and digitizing the intensities of these four beams, the intensity, as well as two of the three elements of the reduced Stokes vector can be determined. Since there are no moving parts to the polarimeter, time resolution is limited only by the response time of the photodetectors and the digitizers. The linear array of output beams is ideal for streak-camera detection, yielding a potential time resolution of ~1 psec. A beam splitter is described that separates the input beam into two beams, which are parallel to the input beam and whose polarizations are nearly the same as the input beam. In addition, the polarimeter is achromatic, operating in the wavelength region from 220 to 1100 nm.