OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 10 — Oct. 1, 1999
  • pp: 2555–2566

Theory of continuous-wave excitation of the sodium beacon

Peter W. Milonni, Heidi Fearn, John M. Telle, and Robert Q. Fugate  »View Author Affiliations

JOSA A, Vol. 16, Issue 10, pp. 2555-2566 (1999)

View Full Text Article

Enhanced HTML    Acrobat PDF (232 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We extend our previous analysis of the sodium beacon [J. Opt. Soc. Am. A 15, 217 (1998)] to the case of continuous-wave excitation. Various effects that could be ignored in the case of pulsed excitation, such as the geomagnetic field, the recoil of the sodium atoms upon absorption and emission, and collisions of the sodium atoms with other mesospheric species, are included. Spin-relaxation collisions are among the most important of these effects for the cases considered. Analytical approximations to numerical results are presented, and using a semi-empirical estimate for Na-O2 spin relaxation, we compute photon returns in good agreement with recently reported measurements at the Steward Observatory.

© 1999 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(020.2070) Atomic and molecular physics : Effects of collisions
(280.3640) Remote sensing and sensors : Lidar
(350.1260) Other areas of optics : Astronomical optics

Original Manuscript: December 7, 1998
Revised Manuscript: April 23, 1999
Manuscript Accepted: April 23, 1999
Published: October 1, 1999

Peter W. Milonni, Heidi Fearn, John M. Telle, and Robert Q. Fugate, "Theory of continuous-wave excitation of the sodium beacon," J. Opt. Soc. Am. A 16, 2555-2566 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. See, for instance, the following reviews and references therein: M. C. Roggemann, B. M. Welsh, R. Q. Fugate, “Improving the resolution of ground-based telescopes,” Rev. Mod. Phys. 69, 437–505 (1997);J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31, 13–62 (1993);N. Hubin, L. Noethe, “Active optics, adaptive optics, and laser guide stars,” Science 262, 1390–1394 (1993). [CrossRef] [PubMed]
  2. M. Lloyd-Hart, J. R. P. Angel, B. Jacobsen, D. Wittman, R. Dekany, D. McCarthy, E. Kibblewhite, W. Wild, B. Carter, J. Beletic, “Adaptive optics experiments using sodium laser guide stars,” Astrophys. J. 439, 455–473 (1995);C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, M. C. Liu, B. Macintosh, K. P. Neeb, J. Patience, K. E. Waltjen, “Image improvement from a sodium-layer guide star adaptive optics system,” Science 277, 1649–1652 (1997);M. Lloyd-Hart, J. R. P. Angel, T. D. Groesbeck, T. Martinez, B. P. Jacobsen, B. A. McLeod, D. W. McCarthy, E. J. Hooper, E. K. Hege, D. G. Sandler, “First astronomical images sharpened with adaptive optics using a sodium laser guide star,” Astrophys. J. 493, 950–954 (1998). [CrossRef]
  3. P. W. Milonni, R. Q. Fugate, J. M. Telle, “Analysis of measured photon returns from sodium beacons,” J. Opt. Soc. Am. A 15, 217–233 (1998). [CrossRef]
  4. J. Ge, B. P. Jacobsen, J. R. P. Angel, P. C. McGuire, T. Roberts, B. A. McLeod, M. Lloyd-Hart, “Simultaneous measurements of sodium column density and laser guide star brightness,” in SPIE Proceedings on Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 242–254 (1998). [CrossRef]
  5. W. Hanle, “Über magnetische Beeinflussung der Polarisation der Resonanzfluoreszenz,” Z. Phys. 30, 93–105 (1924);A. Kastler, “Quelques suggestions concernant la production optique et la détection optique d’une inégalité de population des niveaux de quantification spatiale des atomes. Application à l’expérience de Stern et Gerlach et à la résonance magnétique,” J. Phys. Radium 11, 255–265 (1950);A. Kastler, “La détection optique de la résonance électronique paramagnétique par la mesure de la polarisation rotatoire paramagnétique d’une radiation visible,” Compt. Rendu 232, 953–957 (1951). [CrossRef]
  6. W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44, 169–249 (1972). [CrossRef]
  7. J. J. McClelland, M. H. Kelley, “Detailed look at aspects of optical pumping in sodium,” Phys. Rev. A 31, 3704–3710 (1985). [CrossRef] [PubMed]
  8. L. C. Bradley, “Pulse-train excitation of sodium for use as a synthetic beacon,” J. Opt. Soc. Am. B 9, 1931–1944 (1992). [CrossRef]
  9. J. R. Morris, “Efficient excitation of a mesospheric sodium laser guide star by intermediate-duration pulses,” J. Opt. Soc. Am. A 11, 832–845 (1994). [CrossRef]
  10. B. Jacobsen, T. Martinez, J. R. P. Angel, M. Lloyd-Hart, S. Benda, D. Middleton, H. W. Friedman, “Field evaluation of two new continuous-wave dye laser systems optimized for sodium beacon excitation,” in SPIE Proceedings on Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 342–351 (1994). [CrossRef]
  11. An unpublished report detailing the calculation of the dipole matrix elements and radiative transition rates used in this work is available upon request.
  12. E. Arimondo, M. Inguscio, P. Violino, “Experimental determination of the hyperfine structure in alkali atoms,” Rev. Mod. Phys. 49, 31–75 (1977). [CrossRef]
  13. See, for instance, K. Gottfried, Quantum Mechanics (Benjamin, Reading, Mass., 1977), p. 269.
  14. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1996).
  15. S. Berman, M. Jacob, “Systematics of angular and polarization distributions in three-body decays,” Phys. Rev. 139, B1023 (1965). [CrossRef]
  16. See E. J. Chernosky, P. F. Fougere, R. O. Hutchinson, “The geomagnetic field,” in Handbook of Geophysics and Space Environments, S. L. Valley, ed. (McGraw-Hill, New York, 1965), Chap. 11.
  17. See, for instance, J. A. Abate, “Preparation of atomic sodium as a two-level atom,” Opt. Commun. 10, 269–272 (1974). [CrossRef]
  18. Equation (9) follows from the expression R=σI/hν, where σ=3λ2AS(ν)/8π is the stimulated emission/absorption cross section and S(ν)=(4 ln 2/π)1/2/δνD is the Doppler lineshape function at line center.
  19. A. T. Ramsey, L. W. Anderson, “Spin relaxation in an optically pumped sodium vapor,” Nuovo Cimento 32, 1151–1157 (1964). [CrossRef]
  20. N. W. Ressler, R. H. Sands, T. E. Stark, “Measurement of the spin-exchange cross sections for Cs133,Rb87,Rb85,K39, and Na23,” Phys. Rev. 184, 102–118 (1969);A. Moretti, F. Strumia, “Hyperfine optical pumping of sodium vapor,” Phys. Rev. A 3, 349–354 (1971). [CrossRef]
  21. The suggestion to use the Na-Na spin-relaxation cross section as a rough estimate for the unknown Na-O2 cross section is due to W. Happer, Department of Physics, Princeton University, Princeton, New Jersey 08544 (personal communication, June1997).
  22. J. Ge, Lawrence Livermore National Laboratory, 7000 East Ave., Livermore, Calif. 94550 (personal communication, April1998).

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