Propagation of 3-D Beams Using a Finite-Difference Algorithm: Practical Considerations

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.