Paraxial Assumption Research Articles

General formalism for Bragg acousto-optic interaction beyond the paraxial approximation

Most of the conventional studies of acousto-optics (AO) are under the paraxial approximation; that is, the propagation directions of the scattered light are almost along the optic axis of the AO system, or, equivalently, the envelope of the light wave varies slowly with respect to the direction of propagation. This assumption should not, however, be carried too far in the cases in which the incident or the Bragg angles are large enough that the scattered light waves do not propagate closely along the optic axis of the AO system. We study the Bragg AO effect beyond the paraxial assumption for small- and large-Bragg-angle incidence. Starting from the wave equations, which are derived from Maxwell's equations, a set of coupled equations that depict the AO interaction are derived in the Bragg regime without the paraxial assumption; i.e., the second derivative terms of the scattered-light amplitudes with respect to the propagation direction are nonnegligible. Analytic solutions that describe the evolution of the scattered light that is due to the acousto-optic effect beyond the paraxial approximation can then be found from the coupled equations. Simulation results are provided to check the validity of our solutions.

Far-field radiation of planar Gaussian sources and comparison with solutions based on the parabolic approximation

Previous research on the Gaussian beam was restricted in scope because of the paraxial assumption. Based on a rigorous solution of the Helmholtz equation, the radiation properties of a Gaussian source are reexamined. The results are different from what previous paraxial theory predicted. It is shown that the commonly used concept of the Gaussian beam and the separability of the field distribution along the two transverse axes may be misleading in certain conditions. Furthermore the theoretical upper limit on the beam divergence angle is shown to be 65.5 degrees .

Method for Generating the Anterior Surface of an Aberration-Free Contact Lens for an Arbitrary Posterior Surface

Advances in accuracy of the measurement of corneal topography have made it possible to design contact lenses whose posterior surface is based on the corneal contour. Our goal is to design a contact lens of focal length, f, given an arbitrarily shaped posterior surface without assuming rotational symmetry. The shape of the anterior surface is calculated using the principle of least time, thereby going beyond paraxial assumptions and the thin lens approximation. There is no requirement that the reference ray be normal to either the anterior or posterior surface of the lens.

Seismic modelling over 3-D homogeneous layered structures-summation of Gaussian beams

SUMMARY The summation of Gaussian beams in homogeneous layered media has been implemented for 3-D seismic forward modelling in this paper. The Gaussian beam method, which considers a bundle of rays in the vicinity of a central ray with a bell-shaped amplitude, is known as an extended ray method for handling caustics and diffractions. However, owing to the restriction of the paraxial assumption and the lack of a universal beam phase, this method has not been accurately applied to 3-D problems. These difficulties are overcome in this paper by providing (i) the optimal determination of the beam orientation and the beam shape by minimizing their beam widths; (ii) the ranges of validity, such as the beam conditions and the paraxial condition; and (iii) the diffractions of Gaussian beams from edges and tips. Comparisons with other solutions for caustics and diffractions demonstrate the accuracy of this extended method even in singular regions.

Compression, self-bending, and collapse of Gaussian beams in photorefractive crystals

By means of an exact solution, we demonstrate that a Gaussian beam can undergo spatial compression when it traverses a photorefractive medium. This is possible provided that the external bias field exceeds the critical value necessary to establish photorefractive spatial solitons. In this regime and under paraxial assumptions our analysis indicates that a Gaussian beam tends to exhibit self-focusing collapse. Beam self-deflection effects that arise from the pi/2-phase-shifted component of the photorefractive grating are also considered in our study.

Adiabatic beam dynamics in a modified betatron

Electron beams in modified betatrons were previously analyzed by using a paraxial treatment. This treatment is valid only for a beam where particles have an axial velocity much larger than their perpendicular velocity. However, in accelerators such as the UCI Modified Betatron, the beam does not satisfy the paraxial assumption. Another treatment based on the guiding center equations is presented. In this treatment the paraxial assumption is not necessary. Corrections to the conventional ‘‘betatron condition’’ are found and compared with recent experiments. Additionally, this treatment can describe nonparaxial quasiconfined particles. The effect of these quasiconfined particles is examined, and it is shown that they provide fields that are necessary to stabilize the beam.