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A new $z$-stretching finite difference method is established for simulatingthe paraxial light beam propagation through a lens in a cylindrically symmetricdomain. By introducing proper domain transformations, we solve correspondingdifference approximations on a uniform grid in the computational space forgreat efficiency. A specialized matrix analysis method is constructed to studythe numerical stability. Interesting computational results are presented.

An Effective $z$-Stretching Adaptive Finite Difference Method for Paraxial Light Beam Propagation Simulations