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Applied Optics

Applied Optics


  • Vol. 38, Iss. 3 — Jan. 20, 1999
  • pp: 554–562

Grazing reflection of Gaussian beams

Lee W. Casperson  »View Author Affiliations

Applied Optics, Vol. 38, Issue 3, pp. 554-562 (1999)

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The reflectivities of most surfaces are higher for grazing or near-90-deg angles of incidence than for more perpendicular or near-zero-deg angles. Grazing-incidence configurations are especially important in the development of lasers and optical systems that operate in the far-ultraviolet and soft-x-ray regions of the spectrum, where transparent or highly reflecting media are almost unknown. Analytical solutions of the paraxial wave equation are obtained for the grazing reflection and complex interference effects that take place when a Gaussian beam interacts at shallow angles with a reflecting surface.

© 1999 Optical Society of America

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(240.0240) Optics at surfaces : Optics at surfaces
(260.0260) Physical optics : Physical optics
(350.5500) Other areas of optics : Propagation

Original Manuscript: July 6, 1998
Published: January 20, 1999

Lee W. Casperson, "Grazing reflection of Gaussian beams," Appl. Opt. 38, 554-562 (1999)

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  1. G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Sys. Tech. J. 40, 489–508 (1961). [CrossRef]
  2. H. Kogelnik, “Imaging of optical modes—resonators with internal lenses,” Bell Sys. Tech. J. 44, 455–494 (1965). [CrossRef]
  3. H. Kogelnik, “On the propagation of Gaussian beams of light through lenslike media including those with a loss or gain variation,” Appl. Opt. 4, 1562–1569 (1965). [CrossRef]
  4. L. W. Casperson, S. D. Lunnam, “Gaussian modes in high loss laser resonators,” Appl. Opt. 14, 1193–1199 (1975), and references therein.
  5. L. W. Casperson, “Beam modes in complex lenslike media and resonators,” J. Opt. Soc. Am. 66, 1373–1379 (1976). [CrossRef]
  6. A. A. Tovar, L. W. Casperson, “Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems,” J. Opt. Soc. Am. 12, 1522–1533 (1995). [CrossRef]
  7. W. S. Bacsa, A. Kulik, “Interference scanning optical probe microscopy,” Appl. Phys. Lett. 70, 3507–3509 (1997). [CrossRef]
  8. See, for example, J. A. R. Samson, Techniques of Vacuum Ultraviolet Spectroscopy (Wiley, New York, 1967), Section 2.8 and references therein.
  9. See, for example, A. N. Zaidel, E. Y. Shreider, Vacuum Ultraviolet Spectroscopy (Ann Arbor-Humphrey Science Publishers, Inc., Ann Arbor, Mich., 1970), pp. 119–126.
  10. H. Krammer, “Light waves guided by a single curved metallic strip,” Appl. Opt. 17, 316–319 (1978). [CrossRef] [PubMed]
  11. L. W. Casperson, T. S. Garfield, “Guided beams in concave metallic waveguides,” IEEE J. Quantum Electron. QE-15, 491–496 (1979), and references therein. [CrossRef]
  12. M. E. Marhic, L. I. Kwan, M. Epstein, “Whispering-gallery CO2 laser,” IEEE J. Quantum Electron. QE-15, 487–490 (1979). [CrossRef]
  13. J. G. Grossman, L. W. Casperson, O. M. Stafsudd, “Radio-frequency-excited carbon dioxide metal waveguide laser,” Appl. Opt. 22, 1298–1305 (1983). [CrossRef] [PubMed]
  14. F. S. Al-Mashaabi, L. W. Casperson, “Direct current-excited cw CO2 metal waveguide laser,” Appl. Opt. 28, 1897–1903 (1989). [CrossRef] [PubMed]
  15. J. M. Eggleston, “Angularly stable ring resonators for high power FELs,” in Proceedings of the International Conference on Lasers 1983, R. Powell, ed. (STS, McLean, Va., 1985), p. 305.
  16. E. Sklar, “The tilt sensitivity of a grazing incidence confocal unstable resonator with applications to free-electron lasers,” IEEE J. Quantum Electron. QE-23, 229–233 (1987). [CrossRef]
  17. K. C. Sun, “Grazing incidence ring resonator for visible wavelength free electron laser,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 409–422 (1990). [CrossRef]
  18. D. H. Dowell, M. L. Laucks, A. R. Lowrey, J. L. Adamski, D. J. Pistoresi, D. R. Shoffstall, M. P. Bentz, R. H. Burns, J. Guha, K. C. Sun, W. Tomita, A. H. Lumpkin, S. C. Bender, D. Byrd, R. L. Tokar, “Tests of a grazing-incidence ring resonator free-electron laser,” IEEE J. Quantum Electron. 27, 2613–2625 (1991). [CrossRef]
  19. D. H. Dowell, M. L. Laucks, A. R. Lowrey, J. L. Adamski, D. J. Pistoresi, D. R. Shoffstall, A. H. Lumpkin, S. Bender, D. Byrd, R. L. Tokar, K. Sun, M. Bentz, R. Burns, J. Guha, W. Tomita, “Final results of the Boeing and Los Alamos grazing incidence ring-resonator free electron laser experiment,” Nucl. Instrum. Methods A 318, 74–80 (1992). [CrossRef]
  20. D. R. Gabardi, D. L. Shealy, “Optical analysis of grazing incidence ring resonators for free-electron lasers,” Opt. Eng. 29, 641–648 (1990). [CrossRef]
  21. M. C. Wang, Y. Yuan, Z. Wang, “The grazing incidence ring resonator for a free-electron laser,” Nucl. Instrum. Methods A 318, 874–876 (1992). [CrossRef]
  22. J. P. Braud, “Laser cavities and polarization optics for soft X-rays and the extreme ultraviolet,” Appl. Phys. B 50, 205–212 (1990). [CrossRef]
  23. J. F. Young, J. J. Macklin, S. E. Harris, “Grazing-incidence ellipsoidal reflector for longitudinally pumping short-wavelength lasers,” Opt. Lett. 12, 90–92 (1987). [CrossRef] [PubMed]
  24. L. W. Casperson, “Gaussian light beams in inhomogeneous media,” Appl. Opt. 12, 2434–2441 (1973). [CrossRef] [PubMed]
  25. A. A. Tovar, L. W. Casperson, “Generalized beam matrices: Gaussian beam propagation in misaligned complex optical systems,” J. Opt. Soc. Am. A 12, 1522–1533 (1995), Eq. (24).

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