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The paper presents a simple and effective method to calculate polarization and diffraction of the Gaussian beam in nonlinear and weakly dissipative plasma. The presented approach is a combination of quasi-isotropic approximation of geometric optics with complex geometrical optics. Quasi-isotropic approximation describes the evolution of polarization vector reducing the Maxwell equations to coupled ordinary differential equations of the first order for the transverse components of the electromagnetic field. Complex geometrical optics describes the Gaussian beam diffraction and self-focusing and deals with ordinary differential equations for Gaussian beam width, wave front curvature, and amplitude evolution. As a result, the quasi-isotropic approximation + complex geometrical optics combination reduces the problem of diffraction and polarization evolution of an electromagnetic beam to the solution of the ordinary differential equations, which enable to prepare fast and effective numerical algorithms. Using combined complex geometrical optics/quasi-isotropic approximation for weakly anisotropic plasma, we assume that nonlinearity of anisotropy tensor is small and we restrict ourselves to considering only isotropic nonlinearity. The quasi-isotropic approximation effectively describes the evolution of microwave and IR electromagnetic beams in polarimetric and interferometric measurements in thermonuclear reactors and the complex geometrical optics method can be applied for modeling of electron cyclotron absorption and current drive in tokamaks.

Gaussian Beam Diffraction and Self-Focusing in Weakly Anisotropic and Dissipative Nonlinear Plasma