Nonparaxial Beam Propagation Method Research Articles

Helmholtz non-paraxial beam propagation method: An assessment

We present a performance evaluation of a non-paraxial beam propagation method suitable for the study of Helmholtz solitons. The analysis aims to determine the accuracy limits of the numerical scheme in terms of the maximum propagation angle addressable. Our investigation is based on the spectral representation of the exact soliton solutions and the study of their evolution at extreme propagation angles, together with the analysis of the propagation invariants. Based on these results, a simple heuristic criterion for the boundaries of the validity domain of the algorithm is provided.

Efficient parallel implementation of the nonparaxial beam propagation method

An efficient parallel implementation of a nonparaxial beam propagation method for the numerical study of the nonlinear Helmholtz equation is presented. Our solution focuses on minimizing communication and computational demands of the method which are dependent on a nonparaxiality parameter. Performance tests carried out on different types of parallel systems behave according theoretical predictions and show that our proposal exhibits a better behavior than those solutions based on the use of conventional parallel fast Fourier transform implementations. The application of our design is illustrated in a particularly demanding scenario: the study of dark solitons at interfaces separating two defocusing Kerr media, where it is shown to play a key role.

An Efficient Scalar, Non-Paraxial Beam Propagation Method

A fast non-paraxial beam propagation method (BPM) is developed. Our method is based on expanding the field and the refractive index distributions in azimuthal harmonics, thus replacing a 3-D wave equation with a small number of 2-D wave equations. The method is shown to be substantially faster than standard 3-D finite-difference methods with comparable accuracy and works well with wide-angle waves.

Three-dimensional finite difference split-step nonparaxial beam propagation method: new method for splitting of operators

We present a new method for splitting of operators in the three-dimensional finite difference split-step nonparaxial beam propagation method. The method increases the accuracy and the efficiency in terms of speed and memory requirements for three-dimensional wide-angle beam propagation. It also makes the application of the perfectly matched layer (PML) boundary condition very simple.

Complex Padé approximants for bidirectional and nonparaxial beam propagation method

The nonparaxial and bidirectional beam propagation method suitable for modelling near-field and high numerical aperture (NA) optical storage systems is suggested for 2D geometry and TE polarization of incident light beam. The complex Pade approximants are introduced for correct approximation of evanescent field in the near-field optics. Pole–zero shifting and branch-cut rotation methods of building complex Pade approximants are studied and compared.

Modelling efficient NL–PML boundary conditions for the nonparaxial beam propagation method

The nonlinear perfectly matched layer (NL-PML) boundary conditions were successfully applied to the nonparaxial beam propagation method. It is demonstrated that the NL-PML is extremely effective in absorbing the outgoing spatial solitons that impinge the boundary of computation domain for a wide angular spectrum of wave propagation. Using of sufficiently smooth conductivity profiles and termination of NL-PMLmedia by controlled transparent boundary conditions offer further significant improvement in the accuracy of the numerical solutions of the nonparaxial beam propagation method at the grazing angles.

Propagation of nonparaxial beams with a modified Arnoldi method

We have developed a modified Arnoldi method that includes a complex square-root approximation, which excels at modeling the propagation of highly diverging beams in various media. Simulations of one transverse dimensional beam with an ultranarrow width and of cylindrical Gaussian beams with various divergence angles reveal the strength of this nonparaxial-beam propagation method.

Finite element method resolution of non-linear Helmholtz equation

A non-paraxial beam propagation method for non-linear media is presented. It directly implements the non-linear Helmholtz equation without introducing the slowing varying envelope approximation. The finite element method has been used to describe the field and the medium characteristics on the transverse cross-section as well as along the longitudinal direction. The finite element capabilities as, for example, the non-uniform mesh distribution, the use of adaptive mesh techniques and the high sparsity of the system matrices, allow one to obtain a fast, versatile and accurate tool for beam propagation analysis. Examples of spatial soliton evolution describe phenomena not predicted in the frame of the slowing varying envelope approximation.