In this study, we consider three main collisions in dusty plasmas and investigate the effects of dust grains on the propagation of electromagnetic (EM) waves through uniform, unmagnetized and weakly ionized dusty plasma. The Drude model is improved to describe the dielectric property of dusty plasmas, which accounts for collisions including electron-molecule, electronion, and electron-dust particles. Based on the improved Drude model, the propagation characteristics of microwaves in dusty plasmas have been numerically calculated and studied. The results show that the propagation characteristics of microwaves through dusty plasmas are different from those through normal plasmas. The effects of dust density and size are mainly studied. Numerical results indicate that the momentum transfer between electrons and dust grains makes more energy loss. The dust density and dust size have a similar influence on EM wave propagation, resulting in less transmission and more absorption.

The multiple coherent identical Gaussian beams with symmetry distribution are abbreviated as multi-Gaussian beam, of which the propagation characters in collisionless plasma are studied with the WKB method and higher order paraxial theory. The initial beam profile presents the flat top like or hollow like distribution when the eccentric displacement is large enough. Based on the derived nonlinear propagation equations, the initial condition analyses are performed, and the impact of eccentric displacement on the free propagation effect and ponderomotive nonlinearity is thoroughly discussed. The propagation characters of dimensionless beam width parameter, spot intensity, and spatial distribution of plasma electron density are presented. Results show that the initial spot intensity is expanding outwards along the propagation and the ring structure of electron evacuation in plasmas is generated.