Search

© Taylor & Francis, Ltd., We study monomode slab and cylindrical waveguides, in which the dielectric permittivity l has both a graded spatial variation and finite discontinuities at the boundaries. New integral equations for the H-type propagation mode in the slab and for the one in the cylinder are obtained, which display separate contributions due to both the graded variations and the discontinuities, and in which the boundary value problem arising from the latter is solved. Based on the specific long wavelength singularities of the free-space Green's functions in one and two dimensions, exact dispersion relations are presented for the slab and cylinder propagation modes, respectively. We give approximate explicit solutions of those dispersion relations, which are correct up to and including second order (in some parameter measuring the deviation of l from unity), and present applications for parabolic permittivity profiles in both geometries. The discontinuities of l at the boundary give rise to contributions of second and higher orders in the dispersion relations, but never at first order. Electromagnetic scattering by the cylinder in general and, in particular, its long wavelength behaviour, are studied briefly., Depto. de Óptica, Fac. de Ciencias Físicas, TRUE, pub

© Taylor & Francis, Ltd., In this work we present a general formulation of the corrections to the Raman-Nath approximation for the diffracted field by a volume hologram, based on integral equations. An approximate analytic expression is given for the first correction. Numerical evaluations of this correction are also presented., Depto. de Óptica, Fac. de Ciencias Físicas, TRUE, pub

© Taylor & Francis Ltd., We consider a general class of inhomogeneous dielectric slabs, where the dielectric permittivity (l) is assumed to depend on the frequency (y) at each position, through the Kramers-Krönig dispersion relation. The physical basis for this assumption is discussed and the following general consequences of it are established. First, using integral relations for propagation modes, we prove the absence of the latter for physically unwanted values of y and of the propagation constant. Secondly, we treat the transmission and reflection of electromagnetic waves by the slab through rigorous eikonal methods, and prove that improvement of convergence does occur at high y. Thirdly, we derive analytic representations for the phases of the transmission and reflection amplitudes in terms of their moduli and their complex zeros in the y -plane, at normal incidence. Finally, we present a formal construction of l at high y, in terms of the reflection amplitude at normal incidence, thus giving a partial mathematical solution for the inverse scattering problem. Most of the previous results break down if l is y -independent. We also study the dispersion relation for the propagation mode, when the slab is a monomode optical waveguide., Depto. de Óptica, Fac. de Ciencias Físicas, TRUE, pub

© Taylor & Francis, Ltd., The scattering of electromagnetic waves by dielectric cylinders and, in particular, by optical fibres is studied through integral equations. The convergence of the iterations of the integral equations is established under certain conditions. The latter are satisfied for long wavelengths, and for optical fibres and wavelengths, when the dielectric permeability variation is rather small. An approximate eikonal solution is applied to optical fibres, and its reliability is discussed. A systematic procedure for estimating corrections to the eikonal approximation is proposed., Depto. de Óptica, Fac. de Ciencias Físicas, TRUE, pub