OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 8 — Aug. 1, 2000
  • pp: 1482–1484

Finite mode analysis through harmonic waveguides

Tatiana Alieva and Kurt Bernardo Wolf  »View Author Affiliations

JOSA A, Vol. 17, Issue 8, pp. 1482-1484 (2000)

View Full Text Article

Acrobat PDF (112 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The mode analysis of signals in a multimodal shallow harmonic waveguide whose eigenfrequencies are equally spaced and finite can be performed by an optoelectronic device, of which the optical part uses the guide to sample the wave field at a number of sensors along its axis and the electronic part computes their fast Fourier transform. We illustrate this process with the Kravchuk transform.

© 2000 Optical Society of America

OCIS Codes
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(200.1130) Optics in computing : Algebraic optical processing
(230.7390) Optical devices : Waveguides, planar

Tatiana Alieva and Kurt Bernardo Wolf, "Finite mode analysis through harmonic waveguides," J. Opt. Soc. Am. A 17, 1482-1484 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. J. D. Secada, “Numerical evaluation of the Hankel transform,” Comput. Phys. Commun. 116, 278–294 (1999).
  2. T. Alieva and M. J. Bastiaans, “Mode analysis through the fractional transforms in optics,” Opt. Lett. 24, 1206–1208 (1999).
  3. B. Santhanam and J. H. McClellan, “The discrete rotational Fourier transform,” IEEE Trans. Signal Process. 44, 994–998 (1996).
  4. S.-Ch. Pei, M.-H. Yeh, and Ch.-Ch. Tseng, “Discrete fractional Fourier transform based on orthogonal projections,” IEEE Trans. Signal Process. 47, 1335–1348 (1999).
  5. H. M. Ozaktas, M. Alper Kutay, and D. Mendlovic, “Intro-duction to the fractional Fourier transform and its applications,” Adv. Imaging Electron Phys. 106, 239–291 (1999); M. Alper Kutay, H. Özataş, H. M. Ozaktas, and O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999); Ç. Candan, M. A. Kutay, and H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. (to be published).
  6. L. Barker, Ç. Candan, T. Hakioğlu, M. Alper Kutay, and H. M. Ozaktas, “The discrete harmonic oscillator, Harper’s equation, and the discrete fractional Fourier transform,” J. Phys. A 33, 2209–2222 (2000).
  7. N. M. Atakishiyev and K. B. Wolf, “Fractional Fourier–Kravchuk transform,” J. Opt. Soc. Am. A 14, 1467–1477 (1997).
  8. T. Alieva and A. Barbé, “Self-fractional Fourier functions and selection of modes,” J. Phys. A 30, L211–L215 (1997).
  9. M. Arik, N. M. Atakishlyev, and K. B. Wolf, “Quantum algebraic structures compatible with the harmonic oscillator Newton equation,” J. Phys. A 32, L371–L376 (1999).
  10. N. M. Atakishiyev and S. K. Suslov, “Difference analogs of the harmonic oscillator,” Teor. Mat. Fiz. 85, 1055–1062 (1991).
  11. A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable (Springer-Verlag, Berlin, 1991).
  12. N. M. Atakishiyev, L. E. Vicent, and K. B. Wolf, “Continuous vs. discrete fractional Fourier transforms,” J. Comput. Appl. Math. 107, 73–95 (1999).
  13. N. M. Atakishiyev and K. B. Wolf, “Approximation on a finite set of points through Kravchuk functions,” Rev. Mex. Fis. 40, 366–377 (1994).
  14. T. Hakioğlu and K. B. Wolf, “The canonical Kravchuk basis for discrete quantum mechanics,” J. Phys. A 33, 3313–3324 (2000).
  15. L. C. Biedenharn and J. D. Louck, “Angular momentum in quantum physics,” Encyclopedia of Mathematics and its Applications (Addison-Wesley, Reading, Mass., 1981), Vol. 8.
  16. P. Feinsilver and R. Schott, “Operator calculus approach to orthogonal polynomial expansions,” J. Comput. Appl. Math. 66, 185–199 (1996).

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