In this paper we are concerned with the propagation of a light beam through an inhomogeneous, isotropic medium with a possibly nonlinear index of refraction. The customary paraxial approximations of neglecting grad $\mathrm{div}\mathcal{E}$ and seeking a plane-polarized solution are shown to be incompatible with the exact Maxwell equations. By starting from Maxwell's equations, and scaling transverse and longitudinal distances by the beam waist ${w}_{0}$ and diffraction length $l$, respectively, an expansion procedure in powers of $\frac{{w}_{0}}{l}$ is developed. The exact equations obeyed by the zeroth-order fields are not Maxwell's equations but the customary paraxial approximation to Maxwell's equations. Equations for the first-, second-, and third-order fields are developed. The first-order field is found to be a longitudinal field. It is solved for explicitly in terms of the zeroth-order field which is transverse. Thus a precise knowledge of the meaning and accuracy of paraxial wave optics is obtained.
This paper deals with time-domain finite-difference (TDFD) techniques for solutions of Maxwell's equations. Two types of algorithms are treated: scattered-field algorithms in wh...
Bistability of the transverse configuration of the optical field is found for a helium–neon laser oscillating in the TEM01* hybrid optical-resonator mode. Optically induced swit...
We examine a simple relativistic theory of two scalar fields, first discussed by Goldstone, in which as a result of spontaneous breakdown of $U(1)$ symmetry one of the scalar bo...
A direct approach to calculate the phonon dispersion using an ab initio force constant method is introduced. The phonon dispersion and structural instability of cubic ${\mathrm{...
Part 1 Liquid crystals - main types and properties: introduction - what is a liquid crystal? the building blocks nematics and cholesterics smectics columnar phases more on long-...
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