Nonparaxial equation for linear and nonlinear optical propagation.

Nonparaxial equation for linear and nonlinear optical propagation: errata.

Vectorial nonparaxial propagation equation in the presence of a tensorial refractive-index perturbation

The standard scalar paraxial parabolic (Fock–Leontovich) propagation equation is generalized to include allorder nonparaxial corrections in the significant case of a tensorial refractive-index perturbation on a homogeneous isotropic background. In the resultant equation, each higher-order nonparaxial term (associated with diffraction in homogeneous space and scaling as the ratio between beam wa...

Nonparaxial spatial solitons and propagation-invariant pattern solutions in optical Kerr media.

We investigate nonlinear propagation in the presence of the optical Kerr effect by relying on a rigorous generalization of the standard parabolic equation that includes nonparaxial and vectorial terms. We show that, in the (1 + 1)-D case, both soliton and propagation-invariant pattern solutions exist (while the standard hyperbolic-secant function is not a solution).

Nonparaxial dark solitons in optical Kerr media.

We show that the nonlinear equation that describes nonparaxial Kerr propagation, together with the already reported bright-soliton solutions, admits of (1 + 1)D dark-soliton solutions. Unlike their paraxial counterparts, dark solitons can be excited only if their asymptotic normalized intensity u2infinity is below 3/7; their width becomes constant when u2infinity approaches this value.

Generation of linear and nonlinear nonparaxial accelerating beams.

We study linear and nonlinear self-accelerating beams propagating along circular trajectories beyond the paraxial approximation. Such nonparaxial accelerating beams are exact solutions of the Helmholtz equation, preserving their shapes during propagation even under nonlinearity. We generate experimentally and observe directly these large-angle bending beams in colloidal suspensions of polystyre...