Self-focusing of laser beams in inhomogeneous dielectrics

Abstract

This paper presents a theoretical investigation of the propagation and focusing of an electromagnetic wave in an inhomogeneous dielectric whose dielectric constant is given bywhere Z-axis is the direction of propagation of the beam. The quantity ~(r, z) may either be due to non-linear effects or due to inhomogeneity in the actual fabrication of the guide.Numerical calculations show that for a cylindrically symmetrical Gaussian beam, even a small axial inhomogeneity has appreciable effect on self-focusing; if the real part of d~o(z)/dz is larger than zero the focusing effect increases with z, and vice-versa.157

Transient Self-focusing of Electromagnetic Waves in a Weakly Ionized Decaying Plasma

“…Such study in the case of a stationary plasma has been made by Sodha et al [14] by using W .K.B . approximation.…”

“…The equation governing the beam-width parameter (f) can be obtained from equation (13) using equation (14) in the paraxial ray approximations and is given by…”

Electromagnetic Wave Propagation through a Gas Lens

“…If we neglect terms involving r4 and higher-order terms in equation (6), the solution of the wave equation can be written as [12] and aA 2 aA 2 as a 2S 1 as az + ar ar + ( ar t + r ar ) Ao2 = 0 .…”

“…is determined by the intensity distribution at z=0, the entrance aperture of the guide. If we substitute for S in equation (11 a), then in the geometrical optics approximation (k 0 -aoo), the dimensionless beam width parameter will be found to satisfy the following differential equation [12] dz~…”

Effects of self-focusing on the selfdistortion of amplitude modulated microwaves in non-parabolic semiconductors

“…There could also be some reactive mechanisms which may promote the distortion of the modulated signal. In recent papers of Akhmanov et al [3], Sodha et al [4,5,8], Tewari et al [7] and Dawes and Margburger [6], a detailed discussion of the effect of reactive non-linearities on electromagnetic wave propagation may be found. A very important effect of these non-linearities is the selffocusing of waves.…”