## Wavefront and caustics of a plane wave refracted by an arbitrary surface

JOSA A, Vol. 25, Issue 9, pp. 2370-2382 (2008)

http://dx.doi.org/10.1364/JOSAA.25.002370

Enhanced HTML Acrobat PDF (709 KB)

### Abstract

A simple expression is given for the k-function associated with the general solution of Stavroudis to the eikonal equation for refraction or reflection of a plane wave from an arbitrary surface. Using this result, we specialize the solution to derive analytic expressions for the wavefront and caustic surfaces after refraction of a plane wave from any rotationally symmetric surface. The method is applied to evaluating and comparing the wavefront and caustic surfaces formed both by a planospherical lens and a planoaspheric lens used for laser beam shaping, which provides understanding of how the irradiance is redistributed over a beam as the wavefront folds back on itself within the focal region.

© 2008 Optical Society of America

**OCIS Codes**

(080.0080) Geometric optics : Geometric optics

(080.2720) Geometric optics : Mathematical methods (general)

(080.2740) Geometric optics : Geometric optical design

**History**

Original Manuscript: April 28, 2008

Revised Manuscript: July 3, 2008

Manuscript Accepted: July 27, 2008

Published: August 25, 2008

**Citation**

David L. Shealy and John A. Hoffnagle, "Wavefront and caustics of a plane wave refracted by an arbitrary surface," J. Opt. Soc. Am. A **25**, 2370-2382 (2008)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-9-2370

Sort: Year | Journal | Reset

### References

- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
- M. Kline and I. Kay, Electromagnetic Theory and Geometrical Optics (Pure and Applied Mathematics, Interscience Publishers, Wiley, 1965).
- S. Solimeno, B. Crosignani, and P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, 1986).
- O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics (Wiley-VCH Verlag, 2006). [CrossRef]
- D. L. Shealy, “Geometrical optics: some applications of the law of intensity,” Proc. SPIE 6289, 62890F-1-16 (2006).
- O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, 1972).
- O. N. Stavroudis and R. C. Fronczek, “Caustic surfaces and the structure of the geometrical image,” J. Opt. Soc. Am. 66, 795-800 (1976). [CrossRef]
- O. N. Stavroudis, R. C. Fronczek, and R.-S. Chang, “Geometry of the half-symmetric image,” J. Opt. Soc. Am. 68, 739-742 (1978). [CrossRef]
- O. N. Stavroudis, “The k function in geometrical optics and its relationship to the archetypal wave front and the caustic surface,” J. Opt. Soc. Am. A 12, 1010-1016 (1995). [CrossRef]
- J. A. Hoffnagle and D. L. Shealy, “Caustic surfaces of a keplerian two-lens beam shaper,” Proc. SPIE 6663, 666304-1-9 (2007).
- D. L. Shealy and J. A. Hoffnagle, “Wavefront and caustic surfaces of refractive laser beam shaper,” Proc. SPIE 6668, 666805-1-11 (2007).
- D. G. Burkhard and D. L. Shealy, “Simplified formula for the illuminance in an optical system,” Appl. Opt. 20, 897-909 (1981). [CrossRef] [PubMed]
- E. Kreyszig, Introduction to Differential Geometry and Riemannian Geometry, Mathematical Exposition No. 16 (University of Toronto Press, 1968), p. 87.
- G. W. Forbes and M. A. Alonso, “The holy grail of ray-based optical modelling,” Proc. SPIE 4832, 186-197 (2002). [CrossRef]
- H. Guo and X. Deng, “Differential geometrical methods in the study of optical transmission (scalar theory). I Static transmission case,” J. Opt. Soc. Am. A 12, 600-606 (1995). [CrossRef]
- L. Luneburg, Mathematical Theory of Optics (University of California Press, 1964).
- H. Römer, Theoretical Optics, An Introduction (Wiley-VCH Verlag, 2005).
- J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” US Patent 3,476,463, November 4, 1969.
- P. W. Rhodes and D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545-3553 (1980). [CrossRef] [PubMed]
- D. L. Shealy and J. A. Hoffnagle, “Aspheric optics for laser beam shaping,” in Encyclopedia of Optical Engineering, R.Driggers, ed. (Taylor and Francis, 2006). DOI: 10.1081/E-E0E-120029768, ISBN: 0-8247-0940-3 (paper), 0-8247-0939-X (electronic).
- J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39, 5488-5499 (2000). [CrossRef]
- J. Hoffnagle and C. Jefferson, “Refractive optical system that converts a laser beam to a collimated flat-top beam,” US Patent 6,295,168, September 25, 2001.
- J. Hoffnagle and C. Jefferson, “Beam shaping with a plano-aspheric lens pair,” Opt. Eng. (Bellingham) 42, 3090-3099 (2003). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.