Effective stretching strategies for paraxial lightwave propagation simulations

Stretching computation strategies, including the hyperbolic exponential fittings along the lens interface, stretching transformations in z- and r-directions are discussed in this paper. The resulted adapted finite difference schemes are not only simple in structure, but also highly effective and efficient in the solution of paraxial Helmholtz equations for light beam propagation simulations and high performance lens designs. Cylindrically symmetric lens domains are assumed. Simulation results are given to illustrate the aforementioned numerical strategies with laboratory applications. Detailed algorithmic structures are given for immediate programming implementations and for similar lightwave propagation computation issues.