OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 65, Iss. 2 — Feb. 1, 1975
  • pp: 169–173

Ray and energy propagation in graded-index media

A. K. Ghatak and K. Thyagarajan  »View Author Affiliations

JOSA, Vol. 65, Issue 2, pp. 169-173 (1975)

View Full Text Article

Acrobat PDF (440 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We have studied the validity of the eikonal equation for an inhomogeneous medium. The propagation of an electromagnetic wave in a medium that is characterized by a parabolic dielectric constant variation in the transverse direction, has been studied in detail. The general path of a ray has been calculated and the irradiance distribution near the focal point has been analytically obtained.

A. K. Ghatak and K. Thyagarajan, "Ray and energy propagation in graded-index media," J. Opt. Soc. Am. 65, 169-173 (1975)

Sort:  Author  |  Journal  |  Reset


  1. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970).
  2. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).
  3. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N. J., 1973).
  4. M. Kline and I. Kay, Electromagnetic Theory and Geometrical Optics (Interscience, New York, 1965).
  5. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1968).
  6. E. Wolf (private communication).
  7. J. B. Keller and W. Streifer, J. Opt. Soc. Am. 61, 40 (1971).
  8. K. Koizumi, Y. Ikeda, I. Kitano, M. Furukawa, and T. Sumimoto, Appl. Opt. 13, 255 (1974).
  9. It may be added that this failure is not due to the particular form of ∊(γ) chosen, which is unbounded as γ→∞. Even for the case in which ∊(x)=∊e + ∊2a2/cosh2x/a, which is bounded, the term (1/k20ψ0)∇2ψ0 is finite and equal to ∊2a2 tanh2x/a.
  10. A. Erdelyi, Higher Transcendental Functions (McGraw-Hill, New York. 1953).
  11. G. P. Agrawal, A. K. Ghatak, and C. L. Mehta, Opt. Comm. 12, 333 (1974).
  12. A two-dimensional analysis is given here for simplicity.
  13. M. S. Sodha, A. K. Ghatak, and D. P. S. Malik, J. Phys. D 4, 1887 (1971).
  14. This implies that the neglect of terms O(1/k0) in βmn and ∂2A/∂z2 in Ref. 13, is equivalent to paraxial approximation.

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