Monika Borwińska

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.

Generation of vortex-type markers in a one-wave setup

What we believe to be a new arrangement of an optical vortex interferometer (OVI) is presented. In the proposed configuration the optical vortex lattice is generated in a one-wave setup by use of birefringent elements--Wollaston compensators. The obtained vortex lattice is regular and stable, which is necessary for predicted applications. The new OVI configuration allows the measurement of waves and optical media properties.

Reconstruction of a plane wave’s tilt and orientation using an optical vortex interferometer

The application of the optical vortex interferometer (OVI) to small-angle rotation measurements is presented. The OVI is based on a regular lattice of optical vortices. In our experimental setup a regular lattice of optical vortices is produced by the interference of three plane waves. The vortex points are stable, pointlike structures within the interference field. Distortion of one, two, or three of the interference waves results in a characteristic vortex lattice deformation. This deformation can be measured and related to the physical quantities being investigated. We show the ability of the OVI to measure the deflection angle and the orientation of the wave vector in a single measurement. Two different methods that allow comparing the geometry of the vortex lattice are used to analyze the results of the experiment. They are compared with the method based on standard two-beam interferograms. The results show that the OVI system can be successfully used to measure the deflection and orientation of the wave vector. The vortex methodology is more accurate than classical two-beam interferometry for rotation angles in the range of a few arcseconds.

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.

Measurements of birefringent media properties using optical vortex birefringence compensator

We present some applications of the optical vortex birefringence compensator, based on the C polarization type singularities generated using two Wollaston compensators. The theory and experimental results of birefringent media properties measurements are presented. The possibility of the simultaneous measurement of both the azimuth angle and the phase retardance has been analyzed and experimentally verified.

Method of residual birefringence measurements in interferometer with increased sensitivity

We present a new method for the measurement of a residual birefringence in a polariscopic interferometer. Measured medium inserted into the setup can cause the changes in the polarization state of the propagated beam. Specific orientation of the elements (i.e. the analyzer and the phase retarder) modifies the setup response to the small changes of the azimuth and ellipticity angles of the propagated beam - the sensitivity of the setup is highly increased within the limited measuring range. The sensitivity and the measuring range of the setup can be adjusted by proper mutual orientation of the setup elements. Even though the measurement requires the analysis of the low contrast interferograms, what can be difficult, the application of the Fourier analysis allows the calculations for the interferogram contrast lower than in case of classical interference pattern shift tracking. In the present paper both theoretical considerations and experimental results taken from the experimental model setup are presented. Hundredfold increase in sensitivity was obtained in the presented experiments, which allowed the measurement of phase difference introduced by the birefringent medium with an accuracy of one hundredth degree.

Determination of the birefringent medium phase difference order in the optical vortex birefringence compensator

In this paper the two-wavelength procedure for determining of the birefringence medium phase retardance order using the optical vortex birefringence compensator (OVBC) is presented. The OVBC generates regular optical vortex lattice which moves if the measured birefringent medium is placed into the compensator setup. Due to the vortex lattice regularity, tracing the lattice shift after the measured medium is inserted, there is no possibility to determine the absolute phase retardance in the monochromatic light. This is an analogy to the well known problem in the classical fringe interferometry. Having recorded interferograms for two waves with slightly different wavelengths, one can identify the centers of the two pairs of interferogram images (with and without the examined medium in the setup) and hence in that way the absolute shift of the vortex lattice. In the paper the theoretical considerations, numerical simulations, as well as the analysis of the interferograms taken from the experiment are presented.

Reconstruction of the wave tilt and orientation of tilt axis using OVI

In this work the application of the Optical Vortex Interferometer (OVI) to small-angle rotation measurements is presented. OVI is based on the regular net of optical vortices. In our experimental setup a regular net of optical vortices is produced by the interference of three plane waves. Distortion of one, two or three of the interference waves results in a characteristic vortex net deformation. This deformation can be measured and related to the physical quantities being investigated. In the given paper we present the ability of the OVI to measure the deflection angle of the wave vector and its orientation in a single measurement. Two different methods which allow for comparing the geometry of the vortices net were used to analyze the results of the experiment. They were compared with the method based on the standard two beam interferogram analysis. The results show that the OVI system can be successfully used to measure the deflection and orientation of the wave vector. The vortex methodology is more accurate than classical two beam interferometry in the case of the rotation angles in the range of few arcseconds.

High sensitivity wave tilt measurements with Optical Vortex Interferometer

Optical Vortex Interferometer (OVI) is a new type of interferometer which is based on the regular net of optical vortices (OV)1,2,3. The net is generated by the interference of three plane waves. The idea of the measurement with the OVI is as follows: if one of the interfering waves is distorted then the geometry of the vortex net is changed. In our case one of the wavefronts was tilted. We can calculate the tilt of the wave by tracking the change of vortices positions. Basically it is sufficient to determine the relative change in the positions of three optical vortices (vortex triplet). If there are 200 vortices in the measurement field then we can choose about 1 million vortex triplets. The important advantage of this measurement is that two rotation angles through two perpendicular axes can be determined into one step. Also the mechanical vibrations are automatically subtracted and the system is simple. Our first results show5 that using about 1000 triplets we can measure the small angle with an error of 1.2arcsec (on the base of standard deviation). Performing the analysis we observed however that the real sensitivity of the OVI is higher than resolution resulting from the basic analysis methods. We observe the change of the histogram of the calculated angle if the tilt by the angle of 0.05arcsec is introduced. In the paper we analyze this effect. If the rotation angle is small then optical vortices change their positions by the small part of the distance between the measurement points. Due to detector quantization some of vortices can be still localized as lying in the same measurement point while the others are localized as shifted. This effect causes the histogram shift. The method of recomputing such histogram shift into the value of rotation angle is presented. In result we can achieve 6-10 times better resolution of the OVI.

Testing a new method for small- angle rotation measurements

We present one of the applications of the Optical Vortex Interferometer (OVI). OVI is based on the regular net of optical vortices which are generated by the interference of three plane waves. Disturbing one of the interfering waves causes a change in the position of the vortex points in the vortex net. The measurement is based on tracking the vortex position change. This method can be used to determine small-angle rotation. OVI distinguishes two axis of rotation and the corresponding two rotation angles can be measured with sub-second resolution. The linear vibrations of the measured element are automatically subtracted. The single measurement provides hundreds of measurements points, so the statistical methods for data analysis and corrections can be effectively applied. In the paper we present the experimental testing of the method. To get the precise rotation of one of the interfering waves the optical wedge is put into one of the interferometers arm. The analysis shows that the amplitude`s decrease does not influence the measurement accuracy. From the vortex net shifting the rotation angle of one of the interfering waves is calculated and this rotation is also used to calculate the refracting angle of the applied optical wedge.