Control of the radiation parameters in a longitudinally inhomogeneous nonlinear medium with a quadratic refractive-index profile

The paraxial approximation is used in an investigation of nonlinear propagation of an axial Gaussian light beam in a longitudinally inhomogeneous medium with a quadratic refractive-index profile. Explicit expressions are obtained for the width and radius of curvature of the beam wavefront. It is shown that variation of the beam power and of the law governing the longitudinal variation of the gradient parameter can be used to control the width and radius of curvature of a beam in a finite longitudinally homogeneous section of a nonlinear medium. Explicit expressions are obtained for the coefficients describing excitation of Gaussian–Hermitian modes in a finite region of a linear medium with a quadratic refractive-index profile. The results obtained can be useful in the design of variable-sensitivity power sensors and of various matching devices.