M. T. Garea

Phase shift formulas in uniaxial media: an application to waveplates

The calculation of phase shift and optical path difference in birefringent media is related to a wide range of applications and devices. We obtain an explicit formula for the phase shift introduced by an anisotropic uniaxial plane-parallel plate with arbitrary orientation of the optical axis when the incident wave has an arbitrary direction. This allows us to calculate the phase shift introduced by waveplates when considering oblique incidence as well as optical axis misalignments. The expressions were obtained by using Maxwells equations and boundary conditions without any approximation. They can be applied both to single plane wave and space-limited beams.

Wide angle conoscopic interference patterns in uniaxial crystals

The fringe pattern obtained when a divergent (or convergent) beam goes through a sample of birefringent crystal between two crossed polarizers contains information that is inherent to the crystalline sample under study. The formation of fringe patterns is analyzed from distinct approaches and with different degrees of approximation considering cones of light of large numerical aperture. We obtain analytic explicit formulas of the phase shift on the screen and compare them with the exact numerical solution. The results obtained are valid for arbitrary orientation of the optical axis and are not restricted either to low birefringence or to small angles of incidence. Moreover, they enable the extraction of the main features related to the characterization of uniaxial crystal slabs, such as the optical axis tilt angle and the principal refractive indices.

Characterization of uniaxial crystals through the study of fringe patterns

The fringe pattern obtained when a divergent (or convergent) beam goes through a sample of birefringent crystal between two polarizers contains information which is inherent of the crystalline sample under study. On the other hand, by considering the design details of the experience and the parameters that are characteristic of the uniaxial plate, it is possible to theoretically obtain the luminous intensity corresponding to each point on a screen or CCD. Thus, this theoretical model allows us to obtain, from images experimentally obtained and theoretical expressions, the parameters that are characteristic of the plates. The results obtained proved the concordance between theory and experience while endorsing this technique for the characterization of birrefringent crystals and devices based on this type of materials.

Phase shift in dielectric reflection.

The phase shifts in external dielectric reflection were analyzed as a function of the incident angle. The contrast of the interference fringes formed between the incident and the reflected beams was considered. For the parallel mode the phase shift disappears between 45 degrees and the Brewster angle. Experimental results are shown which demonstrate the contrast inversion in this region.

Reflection and refraction in active dielectric materials

In this work we study and analyze in detail the characteristics of the modulus and phase of the reflection and transmission coefficients in interfaces between isotropic media, when the incident electromagnetic wave is propagating from a transparent medium towards an active one. We also demonstrate analytically that Amplified Reflection is impossible if semi-infinite media are involved. Due to these coefficients, the oscillatory or monotonic character of the phase difference between p and s modes is shown as a function of the angle of incidence for different active media. A qualitative and quantitative comparison between our own results and those obtained by many authors on absorbing media is made. We consider that this work can clarify some aspects that can contribute in the use of ellipsometric techniques for the determination of optical properties of active media.

Image formation through birefringent uniaxial wedges

We develop the formulae for the position and first-order astigmatism of the ordinary and extraordinary images formed through an uniaxial birefringent wedge when the incident beam is not collimated. The variation of this position as a function of the characteristic parameters of the system under consideration is analysed.

Ultrasonic Lamb waves detection using an unstabilized optical interferometer with uncalibrated phase shifts

We present an experimental and post-processing scheme that allows ultrasound surface wave detection by means of an unstabilized homodyne interferometric technique. We register interference signals for a set of uncalibrated phase shifts and, from them, we are able to retrieve the normal surface displacement of a thin aluminium plate. The results obtained with this technique are then compared to robust and more traditional phase recovery methods such as the Carré algorithm and the 11-step windowed discrete Fourier transform algorithm. For both algorithms, we found a correlation superior to 99.9%, when compared to the results of the proposed technique. This non-destructive testing scheme represents a simpler and less-expensive alternative to other existing laser ultrasonic techniques.

Birefringent phase demodulator: application to wave plate characterization

The scope of this work is to present a phase demodulator that enables the recovery of temporal phase information contained in the phase difference between two signals with different polarizations. This demodulator is a polarization interferometer that may consist only of a uniaxial crystal slab and a polarizer sheet. The phase shift between two orthogonal components of the electric field is translated into space by means of birefringent crystals, which act as demodulators or phase analyzers with great robustness. The experimental scheme utilized is based on a simple conoscopic interference setup. Each portion of the space in which the interference pattern is projected contains not only the unknown temporal phase we want to recover, but also a phase shift due to the uniaxial crystal itself. The underlying idea is developing simultaneous phase shifting with uniaxial crystals. Thus, different phase recovery techniques can be applied in order to maximize their ability to track high-speed signals. Depending on the characteristics of the fringe pattern, it will permit phase recovery via different classical procedures. In order to prove the demodulator under different experimental and signal processing schemes, we employed it for wave plate characterization. The results obtained not only allow some wave plate features such as axes determination and retardance to be characterized, but also prove the working principle and capabilities of the demodulator.

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.

Implementation and comparison of dynamic and static light scattering techniques for polidisperse particle sizing using a CCD camera

Laser techniques for particle sizing are used in industrial as well as in scientific applications due to the direct connection between the measured quantities in light dispersion processes and particle properties. We have successfully implemented two light scattering techniques, adapted to function with a CCD camera as detector: the dynamic technique, studies the temporal correlation of the scattered light in a fixed direction (known as DLS for Dynamic Light Scattering); the static technique, retrieves the mean intensity distribution as a function of the scattering direction. We present experimental results on monodisperse and polidisperse solutions of latex spheres diffusing in water and compare the performance of these techniques. The statistical averaging over the CCD pixels allows significant reduction of measurement times.