## Design of corrugated optical waveguide filters through a direct numerical solution of the coupled Gel’fand–Levitan–Marchenko integral equations

JOSA A, Vol. 19, Issue 5, pp. 1005-1012 (2002)

http://dx.doi.org/10.1364/JOSAA.19.001005

Acrobat PDF (177 KB)

### Abstract

Regarding the design problem of corrugated planar optical waveguide filters, a new numerical method is presented consisting of a direct numerical solution of the coupled Gel’fand–Levitan–Marchenko integral equations. This method, which uses leapfrogging in space and time, is exact in principle and avoids some difficulties encountered in previously derived analytical methods of solution. Straightforward numerical calculations permit the design of several classes of filters such as Butterworth, Chebyshev, Cauer (elliptic) and others, as presented in the paper. The accuracy of our proposed method of design is checked in several ways, mainly through the numerical solution of the corresponding direct-scattering problem (Riccati differential equation).

© 2002 Optical Society of America

**OCIS Codes**

(130.0130) Integrated optics : Integrated optics

(290.3200) Scattering : Inverse scattering

**Citation**

Christos Papachristos and Panayiotis Frangos, "Design of corrugated optical waveguide filters through a direct numerical solution of the coupled Gel’fand–Levitan–Marchenko integral equations," J. Opt. Soc. Am. A **19**, 1005-1012 (2002)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-5-1005

Sort: Year | Journal | Reset

### References

- M. Matsuhara, K. O. Hill and A. Watanabe, “Optical waveguide filters: synthesis,” J. Opt. Soc. Am. 64, 804–809 (1975).
- H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1976).
- P. C. Cross and H. Kogelnik, “Sidelobe suppression in corrugated waveguide filters,” Opt. Lett. 1, 43–45 (1977).
- H. Kogelnik, “Theory of dielectric waveguides,” in Integrated Optics, 2nd ed., T. Tamir, ed. (Springer, New York, 1979), pp. 66–79.
- G. H. Song and 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).
- G. H. Song and S. Y. Shin, “Design of corrugated waveguide filters by the Gel’fand–Levitan–Marchenko inverse-scattering method,” J. Opt. Soc. Am. A 2, 1905–1915 (1985).
- G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980).
- P. Frangos and D. L. Jaggard, “A numerical solution to the Zakharov–Shabat inverse scattering problem,” IEEE Trans. Antennas Propag. 39, 74–79 (1991).
- I. M. Gel’fand and B. M. Levitan, “On the determination of a differential equation by its spectral function,” Am. Math. Soc. Trans. 1, 253–304 (1955).
- V. A. Marchenko, “Reconstruction of the potential energy from the phase of scattered waves,” Dokl. Akad. Nauk SSSR 104, 635–698 (1955).
- M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, “The inverse scattering transform–Fourier analysis for nonlinear problems,” Stud. Appl. Math. 53, 249–315 (1974).
- I. Kay, “The inverse scattering problem when the reflection coefficient is a rational function,” Commun. Pure Appl. Math. 13, 371–393 (1960).
- H. N. Kritikos, D. L. Jaggard, and D. B. Ge, “Numeric reconstruction of smooth dielectric profiles,” Proc. IEEE 70, 295–297 (1982).
- D. L. Jaggard and K. E. Olson, “Numerical reconstruction for dispersionless refractive profiles,” J. Opt. Soc. Am. A 2, 1931–1936 (1985).
- D. L. Jaggard and P. V. Frangos, “The electromagnetic inverse scattering problem for layered dispersionless dielectrics,” IEEE Trans. Antennas Propag. 35, 934–936 (1987).
- P. V. Frangos, “One-dimensional inverse scattering: exact methods and applications,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1986).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1995).
- M. E. Van Valkenburg, Analog Filter Design (Saunders College Publishing, Harcourt Brace Jovanovich College Publishers, New York, 1982).

## 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.