OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 2, Iss. 11 — Nov. 1, 1985
  • pp: 1905–1915

Design of corrugated waveguide filters by the Gel’fand–Levitan–Marchenko inverse-scattering method

Ghie-Hugh Song and Sang-Yung Shin  »View Author Affiliations


JOSA A, Vol. 2, Issue 11, pp. 1905-1915 (1985)
http://dx.doi.org/10.1364/JOSAA.2.001905


View Full Text Article

Enhanced HTML    Acrobat PDF (1192 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A rigorous design rule of corrugated waveguide filters is developed by employing the Gel’fand–Levitan–Marchenko inverse-scattering method for the two-component coupled-wave equations of the Zakharov–Shabat type. In the course of developing the design method, the coupled Gel’fand–Levitan–Marchenko integral equations for the Zakharov–Shabat system having no discrete spectrum are shown to be reducible to a set of linear simultaneous equations amenable to simple numerical calculations when the reflection coefficient is a rational function.

© 1985 Optical Society of America

History
Original Manuscript: December 10, 1984
Manuscript Accepted: July 23, 1985
Published: November 1, 1985

Citation
Ghie-Hugh Song and Sang-Yung Shin, "Design of corrugated waveguide filters by the Gel’fand–Levitan–Marchenko inverse-scattering method," J. Opt. Soc. Am. A 2, 1905-1915 (1985)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-2-11-1905


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. Chadan, P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer, New York, 1977). [CrossRef]
  2. M. J. Ablowitz, “Lectures on the inverse scattering transform,” Stud. Appl. Math. 58, 17–94 (1978).
  3. G. L. Lamb, Elements of SolitonTheory (Wiley, New York, 1980).
  4. H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, 2nd ed., T. Tamir, ed. (Springer, New York, 1979).
  5. M. Matsuhara, K. O. Hill, A. Watanabe, “Optical waveguide filters; synthesis,” J. Opt. Soc. Am. 65, 804–809 (1975). [CrossRef]
  6. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976). [CrossRef]
  7. P. C. Cross, H. Kogelnik, “Sidelobe suppression in corrugated waveguide filters,” Opt. Lett.1, 43–45 (1977).
  8. L. Weinberg, Network Analysis and Synthesis (McGraw-Hill, New York, 1962), p. 495.
  9. I. Kay, “The inverse scattering problem when the reflection coefficient is a rational function,” Commun. Pure Appl. Math. XIII, 371–393 (1960). [CrossRef]
  10. H. H. Szu, C. E. Caroll, C. C. Yang, S. Ahn, “A new functional equation in the plasma inverse problem and its analytic properties,” J. Math. Phys. 7, 1236–1247 (1976). [CrossRef]
  11. H. Mathews, Surface Wave Filters (Wiley, New York, 1977), pp. 381–442.
  12. C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, “Broad-band grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 31, 276–278 (1977). [CrossRef]
  13. B.-G. Kim, S.-Y. Shin, “An asymptotic approximation of linear-chirped grating filter response,” Opt. Commun. 44, 371–376 (1983). [CrossRef]
  14. For the −q* case, the physical interpretations are well described in H. A. Haus, “Physical interpretation of inverse scattering formalism applied to self-induced transparency,” Rev. Mod. Phys. 51, 331–339 (1979). [CrossRef]
  15. We shall call the (z, τ) plane the time domain, since that τ provides the time base to the timelike evolution of waves according to Eqs. (13).
  16. R. P. Boas, Entire Functions (Academic, New York, 1954).
  17. K. R. Pechenik, J. M. Cohen, “Inverse scattering—exact solution of the Gel’fand–Levitan equation,” J. Math. Phys. 22, 1513–1516 (1981). [CrossRef]
  18. H. E. Moses, “An example of the effect of the rescaling of the reflection coefficient on the scattering potential for the one-dimensional Schrödinger equation,” Stud. Appl. Math. 60, 177–181 (1979).
  19. P. Deift, E. Trubowitz, “Inverse scattering on the line,” Commun. Pure Appl. Math. XXXII, 121–151 (1979). [CrossRef]
  20. G.-H. Song, S.-Y. Shin, “Inverse scattering problem for the coupled-wave equations when the reflection coefficient is a rational function,” Proc. IEEE 71, 266–268 (1983). [CrossRef]

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