Reflection and refraction of narrow Gaussian beams with general astigmatism at tilted optical surfaces: a derivation oriented toward lens design

Year: 2007

Authors: Greco V., Giusfredi G.

Autors Affiliation: Istituto Nazionale di Ottica Applicata (INOA) – CNR

Abstract: The formulas for the reflection and refraction of a narrow Gaussian beam with general astigmatism at a tilted optical surface are derived by ray tracing techniques. The propagation direction of the reflected and refracted beams is computed by tracing the central ray of the incident beam, and the characteristic parameters of the respective wave fronts are worked out by applying the formulas developed for the generalized ray tracing. Moreover, the Gaussian form of the reflected and refracted amplitude distribution along the transverse coordinates is determined by requiring the matching of the incident, reflected and refracted light spots on the optical surface. No limiting assumptions are made regarding the form of the optical interface or the orientation of the incident astigmatic wave front. At the end, to illustrate a simple application of these formulas the reflection of a Gaussian beam at a conicoid is considered and a simple property of the conicoidal mirrors is reported .

Journal/Review: APPLIED OPTICS (2004)

Volume: 46 (4)      Pages from: 513  to: 521

KeyWords: Gaussian beam; general astigmatism; Coddinton equations
DOI: 10.1364/AO.46.000513

Citations: 7
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