An effective z-stretching method for paraxial light beam propagation simulations

Abstract

A z-stretching finite difference method is developed for simulating the paraxial light beam propagation through a lens in a cylindrically symmetric domain. By introducing a domain transformation in the z-direction, we solve the corresponding complex difference equations containing an interface singularity over a computational space for great simplicity and efficiency. A specially designed matrix analysis is constructed to the study the numerical stability. Computational experiments are carried out for demonstrating our results.

An exponential transformation based splitting method for fast computations of highly oscillatory solutions

“…Again, a reduced viewing domain of −4 ≤ x, y ≤ 4 is used. Oscillations are not visible in the functions due to the lower wave number used[9,16,5]. Simulation results again match satisfactorily standard laboratorial experiments with clipped focused-Gaussian beams[9,16].…”

“…The above compact form of quintic diagonal systems can be solved conveniently without using any matrix decompositions or band system solvers [5,15,7]. To summarize, for solving (2.16), (2.17) together with homogeneous Neumann boundary conditions, we only need to solve the following systems in order:…”

“…F-5400-04-06-SC01-00) from the Air Force Research Laboratory and General Dynamics Information Technology. and ℓ is a finite boundary location needed by computations [4][5][6][7]. Eq.…”

“…Different coordinate transforms have been investigated for overcoming such a numerical inefficiency [10,3]. Although integral or spectrum methods possess certain advantages in similar circumstances, the same challenges remain in balancing the algorithmic simplicity, accuracy and efficiency [1,8,5,11,12].…”

“…The idea is to take advantage of the well-known optical disturbance function, that is, u(x, y, z) = φ(x, y, z) exp{iκψ (x, y, z)}, (1.2) where φ, ψ are nonoscillatory real functions and φ ̸ = 0 [9,5]. Surfaces φ = c are often called wavefronts of the disturbance.…”