Improved beam propagation method equations
1998; Optica Publishing Group; Volume: 37; Issue: 1 Linguagem: Inglês
10.1364/ao.37.000009
ISSN0003-6935
Autores Tópico(s)Optical Coatings and Gratings
ResumoImproved beam propagation method (BPM) equations are derived for the general case of arbitrary refractive-index spatial distributions. It is shown that in the paraxial approximation the discrete equations admit an analytical solution for the propagation of a paraxial spherical wave, which converges to the analytical solution of the paraxial Helmholtz equation. The generalized Kirchhoff-Fresnel diffraction integral between the object and the image planes can be derived, with its coefficients expressed in terms of the standard ABCD matrix. This result allows the substitution, in the case of an unaberrated system, of the many numerical steps with a single analytical step. We compared the predictions of the standard and improved BPM equations by considering the cases of a Maxwell fish-eye and of a Luneburg lens.
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