Władysław A. Woźniak

Phase retardation measurement in simple and reverse Senarmont compensators without calibrated quarter wave plates

Summary The modification of the Senarmont compensator is presented. It uses standard simple and reverse Senarmont setups, however, the phase retardances of unknown medium as well as the element used as a quarterwave plate in classical setups could be measured. It leads to conclusion that retardations of two unknown elements could be obtained and no calibrated quarter wave plate is needed.

Singularities of interference of three waves with different polarization states

We presented the interference setup which can produce interesting two-dimensional patterns in polarization state of the resulting light wave emerging from the setup. The main element of our setup is the Wollaston prism which gives two plane, linearly polarized waves (eigenwaves of both Wollastons wedges) with linearly changed phase difference between them (along the x-axis). The third wave coming from the second arm of proposed polarization interferometer is linearly or circularly polarized with linearly changed phase difference along the y-axis. The interference of three plane waves with different polarization states (LLL - linear-linear-linear or LLC - linear-linear-circular) and variable change difference produce two-dimensional light polarization and phase distributions with some characteristic points and lines which can be claimed to constitute singularities of different types. The aim of this article is to find all kind of these phase and polarization singularities as well as their classification. We postulated in our theoretical simulations and verified in our experiments different kinds of polarization singularities, depending on which polarization parameter was considered (the azimuth and ellipticity angles or the diagonal and phase angles). We also observed the phase singularities as well as the isolated zero intensity points which resulted from the polarization singularities when the proper analyzer was used at the end of the setup. The classification of all these singularities as well as their relationships were analyzed and described.

Compact spatial polariscope for light polarization state analysis

A new setup established to measure the light polarization state and the birefringent media parameters is proposed. The described setup consists of two pairs of the linear Wollaston compensators and circular compensators which form a set of two spatially modulated elliptical compensators. These compensators could be used separately as a spatial generator of polarization states and as an analyzer. Using them together allows us to establish a polariscopic setup in which the birefringent media parameters could be measured. When analyzing both the light polarization state and the birefringent media parameters the singular points in the output light intensity appear. The coordinates of these points depend linearly on the azimuth and ellipticity angles of the examined light or on the eigenvectors of the birefringent medium, while the measured light maximum value corresponds to the phase shift for the measurements of the birefringent medium parameters. Neither movable parts nor active elements are needed and no complicated analysis of output light should be made to calculate the desired quantities.

Geometric phase: two triangles on the Poincaré sphere

The method of obtaining the dynamic and geometric part of the phase introduced by a birefringent medium in two kinds of interferometric experiments is presented. The mathematical formulas for the phases obtained using Jones formalism are visualized with the specific triangles on the Poincaré sphere. Generally, these triangles are similar to those used in the Pancharatnams original construction developed by Courtial to calculate the Pancharatnam geometric phase for the light passing through a single birefringent plate. In these graphical constructions following Courtials idea, we used the points representing both of the birefringent mediums eigenvectors. This allowed the most intuitive explanation of the mechanism of dividing the whole phase shift introduced by the birefringent plate into two different parts: dynamical and geometrical. The considered constructions were used as a description of two simple experiments with a birefringent medium in a Mach-Zehnder interferometer and a polariscopic setup. The experimental verifications of our theoretical predictions should convince the reader of the correctness of the assumed model.

Adjustment method of an imaging Stokes polarimeter based on liquid crystal variable retarders

The description of adjustment of an imaging Stokes polarimeter constructed and tested in our laboratory is presented. Our polarimeters operation is based on six fast intensity distribution measurements realized in six different configurations of linear and circular analyzers. Using liquid crystal variable retarders (LCVRs) makes this construction compact and mechanically simple. However, new problems arise with proper azimuthal alignment as well as with proper LCVR voltage adjustment. Three basic steps of the adjustment procedure adapted to the specific construction of our polarimeter are described in detail. Some remarks concerning the critical parameters of the used CCD cameras parameters are also presented, as well as experimental verifications of the setups accuracy acquired due to the proper adjustment process.

Dynamic polarization states and birefringence distributions measurements in spatial elliptical polariscope using Fourier analysis method

A new method to measure the light polarization state and the birefringent media parameters is proposed. We have used the setup described previously, consisting of two pairs of the linear Wollaston and circular compensators which form a set of two spatially modulated elliptical compensators. We have modified this setup introducing some carrier frequencies in all compensators and assuming that the second linear one would introduce the frequency which is a multiplicity of the basis frequency of the first linear compensator. Both of these modifications allow calculating all polarization parameters of polarized light or birefringent medium from only one measured intensity distribution of the light outcoming the described setup. They allow measuring not only the parameters of homogeneous beams/mediums but also x,y-distributions of all desired parameters, like azimuth and ellipticity angles of the light or first medium eigenvector and the phase difference introduced by this medium. The proposed calculation method comprises of Fourier analysis of obtained intensity distribution with some manipulation of coordinate system and filtration of obtained data. This method is claimed to be simple and fast enough to be treated as a real-time method.

Measurements of the small wave tilt using the optical vortex interferometer with the Wollaston compensator

A classical Mach-Zehnder two-beam interferometer was modernized using the Wollaston compensator, which allowed obtaining a stable set of specific optical markers--optical vortices. This new interferometer setup that generated optical vortices was used to measure small angle tilt. The theoretical basis of setups behavior has been described. The value of the described setup was confirmed by practical experiments.

Superposition rule for the magneto-optic effects in isotropic media

Summary The two well-known magneto-optic phenomena: the Faraday and Cotton-Mouton effects describe behavior of optically isotropic medium in the external magnetic field which is parallel or perpendicular to the wave propagation direction, respectively. In this paper a superposition rule for both magneto-optic effects as a generalization of Faraday and Cotton-Mouton effects for any orientation of external magnetic field with regard to the wave propagation direction is presented.

Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator

The classical Mach?Zehnder two-beam set-up has been modernized with the use of polarization elements to generate a set of optical vortices. The main element of these set-ups is the Wollaston compensator, which allows us to obtain a specific phase distribution (with polarization singularities) in one of the arms of our interferometer. We have confirmed the practical value of this set-up by developing a method of birefringent media properties measurement. In the present paper we have started with developing the method for linearly birefringent media only: however, we hope that this method can be extended to elliptically birefringent media. The numerical analysis has confirmed our theoretical predictions. The mutual displacement measurements of the two OV sublattices of different topological charges allowed us to calculate the basic birefringent media parameters: the azimuth angle of its first eigenvector and the phase difference between their eigenwaves. We also carried out some experiments which convinced us about the practical value of the proposed set-ups.

Effect of multiple reflections in retardation plates with elliptical birefringence

The theory of elliptical retardation plates that takes into account a phenomenon of multiple reflections is presented. An analytical form of a transition matrix for a normally incident plane wave is shown. Sample calculations of phase shift introduced by quartz retardation plates and of the output-beam parameters as a function of plate thickness and optical axis orientation are done.