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

Applied Optics, Vol. 46, Issue 4, pp. 513-521 (2007)

http://dx.doi.org/10.1364/AO.46.000513

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### 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 wavefronts are worked out by applying the formulas developed for the generalized ray tracing. Moreover, the Gaussian form of the reflected and refracted amplitude distributions 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 wavefront. In 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.

© 2007 Optical Society of America

**OCIS Codes**

(080.1010) Geometric optics : Aberrations (global)

(080.2740) Geometric optics : Geometric optical design

(140.3300) Lasers and laser optics : Laser beam shaping

(220.1010) Optical design and fabrication : Aberrations (global)

(220.2740) Optical design and fabrication : Geometric optical design

(230.4040) Optical devices : Mirrors

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: May 23, 2006

Revised Manuscript: September 28, 2006

Manuscript Accepted: October 1, 2006

**Citation**

Vincenzo Greco and Giovanni Giusfredi, "Reflection and refraction of narrow Gaussian beams with general astigmatism at tilted optical surfaces: a derivation oriented toward lens design," Appl. Opt. **46**, 513-521 (2007)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-4-513

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