Gaussian Beams In Media Research Articles

Self-trapped pulsed beams with finite power in Kerr media excited by time-diffracting, space-time beams.

We study the nonlinear propagation of space-time pulsed beams, also known as time-diffracting beams, a recently introduced class of diffraction-free spatiotemporal wave packets whose temporal-transversal structure is that of diffraction in time. We report on the spontaneous formation of propagation-invariant, spatiotemporally compressed pulsed beams carrying finite power from exciting time-diffracting Gaussian beams in media with cubic Kerr nonlinearity at powers below the critical power for collapse, and also with other collapse-arresting nonlinearities above the critical power. Their attraction property makes the experimental observation of the self-trapped pulsed beams in cubic Kerr media feasible. The structure in the temporal and transversal dimensions of the self-trapped wave packets is shown to be the same as the structure in the axial and transversal dimensions of the self-focusing and (arrested) collapse of monochromatic Gaussian beams.

Gaussian beams in media with transverse gain inhomogeneity

Gaussian beams of higher orders in a medium with a quadratic variation of gain and refractive index with distance from the optic axis are analytically obtained. Gaussian waveguide beams of higher orders are found that remain unchanged with propagation, and their additional losses (gain) are determined for a nonuniform medium. A propagation problem for an arbitrary beam in an active medium nonuniform in cross-section is solved due to the functional completeness of the obtained system of functions. The eigenfunctions and eigenfrequencies of a cavity with plane mirrors and parabolic inhomogeneity of the active medium are found.

Density-matrix formalism for partially coherent optical fields propagating in slightly inhomogeneous media

The integral of motion method and the density matrix formalism are used to describe the propagation of partially coherent radiation in slightly inhomogeneous media. Expressions for the parameters of partially coherent gaussian beams in media with general square-law refractive-index distributions are obtained using operator algebra. New equations for the correlation function are formulated and beam invariants are obtained.

Beam propagation in periodic quadratic-index waveguides

Several techniques are described for studying the propagation of off-axis polynomial Gaussian beams in media having straight axes and periodic z variations of the quadratic refraction and loss coefficients. For some periodic variations, exact analytical solutions of the paraxial equations are possible, and for sufficiently slow variations, WKB solutions can always be obtained. All results are expressed in conventional beam matrix form.

Propagation of laser beams through inhomogeneous media

The propagation of gaussian beams in media with an arbitrary gain and/or dispersion profile is discussed using a variational method. Simple analytic formulae are derived and applied to the spin-flip laser which has a gaussian gain profile. The results are a significant improvement on the quadratic-gain approximation.