Propagation of 3D beams using a finite-difference algorithm: practical considerations

Abstract

We discuss practical aspects of the use of the finite-difference, alternating-direction implicit (ADI), numerical solution of the paraxial wave equation, for the free-space propagation of light beams. Results of calculations solving the finite-difference equations are compared with fresnel-integral solutions. Calculations are for round beams, but the field is represented in cartesian coordinates. Modes for empty unstable resonators are also obtained using the finite-difference algorithm and are compared with fresnel-integral solutions.

Unstable ring resonator with bidirectional propagation through the gain medium: analysis

“…The fields were propagated using the alternating-direction implicit finite-difference propagation algorithm that is discussed in Ref. 7. The grid resolution was 600 by 600 pounts in a transverse plane.…”