Liliana I. Perez

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.

Zernike expansion coefficients: rescaling and decentring for different pupils and evaluation of corneal aberrations

An analytical method to convert the set of Zernike coefficients that fits the wavefront aberration for a pupil into another corresponding to a contracted and horizontally translated pupil is proposed. The underlying selection rules are provided and the resulting conversion formulae for a seventh-order expansion are given. These formulae are applied to calculate corneal aberrations referred to a given pupil centre in terms of those referred to the keratometric vertex supplied by the SN CT1000 topographer. Four typical cases are considered: a sphere and three eyes—normal, keratoconic and post-LASIK. When the pupil centre is fixed and the pupil diameter decreases from 6 mm to the photopic natural one, leaving aside piston, tilt and defocus, the difference between the root mean square wavefront error computed with the formulae and the topographer is less than 0.04 µm. When the pupil diameter is kept equal to the natural one and the pupil centre is displaced, coefficients vary according to the eye. For a 0.3 mm pupil shift, the variation of coma is at most 0.35 µm and that of spherical aberration 0.01 µm.

Wavefront aberrations: analytical method to convert Zernike coefficients from a pupil to a scaled arbitrarily decentered one

The wavefront aberration of any image forming system and, in particular, of a human eye, is often expanded in Zernike modes each mode being weighed by a coefficient that depends both on the image forming components of the system and on the contour, size and centering of the pupil. In the present article, expanding up to 7th order the wavefront aberration, an analytical method to compute a new set of Zernike coefficients corresponding to a pupil in terms of an original set evaluated via ray tracing for a dilated and transversally arbitrarily displaced pupil is developed. A transformation matrix of dimension 36×36 is attained multiplying the scaling‐horizontal traslation matrix previously derived by appropriate rotation matrices. Multiplying the original coefficients by this transformation matrix, analytical formulas for each new coefficient are attained and supplied and, for the information concerning the wavefront aberration to be available, these formulas must be employed in cases in which the new pupil ...

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.

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.

Active isotropic slabs: conditions for amplified reflection

We analyse in detail the necessary conditions to obtain amplified reflection (AR) in isotropic interfaces when a plane wave propagates from a transparent medium towards an active one. First, we demonstrate analytically that AR is not possible if a single interface is involved. Then, we study the conditions for AR in a very simple configuration: normal incidence on an active slab immersed in transparent media. Finally, we develop an analysis in the complex plane in order to establish a geometrical method that not only describes the behaviour of active slabs but also helps to simplify the calculus.

Evanescent waves associated with internal reflection in uniaxial crystals

A study of the polarization of evanescent waves associated to internal total and inhibited reflection is done for ordinary and extraordinary incident wave on a uniaxial crystal-isotropic medium interface. It is shown that the field describe ellipses that are contained in planes that depend on the kind of evanescent wave. Furthermore the characteristics of the ellipses depend on the direction of incidence and/or on the direction of the optical axis. This behavior differs from that of isotropic interfaces.

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.