OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 31, Iss. 25 — Sep. 1, 1992
  • pp: 5201–5210

Beam propagation in gradient refractive-index media

G. N. Lawrence and S.-H. Hwang  »View Author Affiliations


Applied Optics, Vol. 31, Issue 25, pp. 5201-5210 (1992)
http://dx.doi.org/10.1364/AO.31.005201


View Full Text Article

Enhanced HTML    Acrobat PDF (1161 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A generalized beam propagation method is described that uses the ABCD matrices to treat optical systems that have modest amounts of aberrations including gradient refractive-index elements. We can make calculations from any point in the near or far field to any other point by using appropriate numerical algorithms. The variation of the reduced length is discussed as a limitation to accuracy. The diffraction properties of a complex stigmatic system may be represented by those of an equivalent elementary system. This facilitates calculations using the standard diffraction operations for homogeneous media. The modified propagation technique replaces the large number of diffraction steps commonly used for the split-step solution of inhomogeneous media with one step for stigmatic media and in general no more than a few steps for aberrated media. Maxwell’s fisheye lens is discussed in detail to show application of the method.

© 1992 Optical Society of America

History
Original Manuscript: September 30, 1991
Published: September 1, 1992

Citation
G. N. Lawrence and S.-H. Hwang, "Beam propagation in gradient refractive-index media," Appl. Opt. 31, 5201-5210 (1992)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-31-25-5201


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 77–96.
  2. E. A. Sziklas, A. E. Siegman, “Mode calculations in unstable resonator with flowing saturable gain. Fast Fourier transform method,” Appl. Opt. 14, 1874–1889 (1975). [CrossRef] [PubMed]
  3. R. H. Hardin, F. D. Tappert, “Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations,” SIAM Rev. 15, 423–433 (1973).
  4. A. Korpel, H. H. Lin, D. J. Mehrl, “Convenient operator formalism for Fourier optics and inhomogeneous and nonlinear wave propagation,” J. Opt. Soc. Am. A 6, 630–635 (1989). [CrossRef]
  5. J. J. Gribble, J. M. Arnold, “Beam-propagation method ray equations,” Opt. Lett. 13, 611–613 (1988). [CrossRef] [PubMed]
  6. W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964).
  7. L. Casperson, “Synthesis of Gaussian beam optical systems,” Appl. Opt. 20, 2243–2249 (1981). [CrossRef] [PubMed]
  8. A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 20.
  9. H. T. Yura, S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987). [CrossRef]
  10. A. E. Siegman, “A canonical formulation for analyzing multielement unstable resonators,” IEEE J. Quantum Electron. QE-12, 35–40 (1976). [CrossRef]
  11. E. W. Marchand, Gradient Index Optics (Academic, New York, 1978).
  12. W. T. Welford, Aberrations of Optical Systems (Hilger, Boston, 1986).
  13. S.-H. Hwang, G. Lawrence, “Physical optics analysis of gradient index optics,” in Current Developments in Optical Engineering and Commercial Optics, R. E. Fischer, H. M. Pollicove, W. J. Smith, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1168, 360–368 (1989).
  14. glad Users Manual, a physical optics propagation program (Applied Optics Research, Tucson, Ariz.).
  15. Optical Design, MIL-HDBK-141 (U.S. Government Printing Office, Washington, D.C., 1962).
  16. P. Baues, “Huygens’ principle in inhomogeneous, isotropic media and a general integral equation applicable to optical resonators,” Opto-electronics 1, 751–758 (1971).
  17. S. Eckhardt, “Beam propagation and shift-variant optics,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1990).
  18. S. Eckhardt, “Non-shift-invariant diffraction effects in simple optical systems,” to be submitted to Opt. Lett.
  19. H. Kraus, “Huygens–Fresnel–Kirchhoff wave-front diffraction formulation: spherical waves,” J. Opt. Soc. Am. A 6, 1196–1205 (1989). [CrossRef]
  20. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), Chap 4, p. 81.

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.

CrossCheck Deposited