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The role of the Gouy phase anomaly in the unification of the geometric and physical models for the propagation of focussed fields |
O. Baladron-Zorita, F. Wyrowski
Institut für Angewandte Physik, Friedrich-Schiller-Universität Jena
olga.baladron.zorita@uni-jena.de |
It is commonly assumed that, outside the focal zone, geometrical optics provides a good model to describe the propagation of a spherical wave. It is seldom, however, that any proof, numbers or guidelines are added to this assertion. In this work the authors analyse this assumption in depth and give experimental results and theoretical explanations. Experimentally, the simulations consider a convergent spherical wave, which is propagated towards and through its focus employing a rigorous diffraction integral, to obtain a reference for each z position. Against each of these references we compare the same source field, propagated to the same position, but this time using a propagation operator obtained from a geometric electromagnetic model. That this geometric model works with fields is vital to enable the comparison of both results and the gauging of the error. This quantitative study also yields the remarkable conclusion that propagating the field geometrically from one side of the focus to the other provides the correct result save for a constant phase term which can be explained as a Gouy-like effect. Finally, we show how to extend the geometric model to include the Gouy anomaly. |
Keywords:
Theoretical Foundations, Diffraction Theory, Optical Systems |
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