## Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers

JOSA A, Vol. 17, Issue 9, pp. 1573-1582 (2000)

http://dx.doi.org/10.1364/JOSAA.17.001573

Enhanced HTML Acrobat PDF (243 KB)

### Abstract

An efficient method for the design of optical devices based on codirectional grating-assisted mode coupling is presented. A low-complexity algorithm is developed to calculate the coupling function of a grating that accurately matches an arbitrarily given target spectral response. The method relies on the synthesis of the grating impulse response by means of an exact differential layer-peeling algorithm.

© 2000 Optical Society of America

**OCIS Codes**

(050.2770) Diffraction and gratings : Gratings

(060.2340) Fiber optics and optical communications : Fiber optics components

(290.3200) Scattering : Inverse scattering

**History**

Original Manuscript: August 4, 1999

Revised Manuscript: April 25, 2000

Manuscript Accepted: April 25, 2000

Published: September 1, 2000

**Citation**

Ricardo Feced and Michalis N. Zervas, "Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers," J. Opt. Soc. Am. A **17**, 1573-1582 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-9-1573

Sort: Year | Journal | Reset

### References

- A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973). [CrossRef]
- D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. Part II: grating assisted couplers,” J. Lightwave Technol. 5, 268–273 (1987). [CrossRef]
- W. P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11, 963–983 (1994). [CrossRef]
- G. Meltz, W. W. Morey, W. H. Glen, “Formation of Bragg gratings in optical fibres by a transverse holographic method,” Opt. Lett. 14, 823–825 (1989). [CrossRef] [PubMed]
- A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, C. R. Davidson, “Long-period fiber-grating-based gain equalisers,” Opt. Lett. 21, 336–338 (1996). [CrossRef] [PubMed]
- P. St. J. Russell, D. P. Hand, “Rocking filter formation in photosensitive high birefringence optical fibres,” Electron. Lett. 26, 1846–1848 (1990). [CrossRef]
- J. N. Blake, B. Y. Kim, H. E. Engan, H. J. Shaw, “Analysis of intermodal coupling in a two-mode fiber with periodic microbends,” Opt. Lett. 12, 281–283 (1987). [CrossRef] [PubMed]
- K. I. Hopcraft, P. R. Smith, An Introduction to Electromagnetic Inverse Scattering (Kluwer Academic, Dordrecht, The Netherlands, 1992).
- J. A. Dobrowolski, D. Lowe, “Optical thin film synthesis program based on the use of Fourier transforms,” Appl. Opt. 17, 3039–3050 (1978). [CrossRef] [PubMed]
- B. G. Bovard, “Fourier transform technique applied to quarterwave optical coatings,” Appl. Opt. 27, 3062–3063 (1988). [CrossRef] [PubMed]
- K. A. Winick, J. E. Roman, “Design of corrugated waveguide filters by Fourier-transform techniques,” IEEE J. Quantum Electron. 26, 1918–1929 (1990). [CrossRef]
- I. M. Gel’fand, B. M. Levitan, “On a determination of a differential equation from its spectral function,” Am. Math. Soc. Trans. 1, 253–304 (1955).
- I. Kay, “The inverse scattering problem when the reflection coefficient is a rational function,” Commun. Pure Appl. Math. 13, 371–393 (1960). [CrossRef]
- G. H. Song, 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). [CrossRef]
- J. E. Roman, K. A. Winick, “Waveguide grating filters for dispersion compensation and pulse compression,” IEEE J. Quantum Electron. 29, 975–982 (1993). [CrossRef]
- E. Peral, J. Capmany, J. Marti, “Iterative solution to the Gel’fand–Levitan–Marchenko coupled equations and application to synthesis of fiber gratings,” IEEE J. Quantum Electron. 32, 2078–2084 (1996). [CrossRef]
- B. E. Little, C. Wu, W. P. Huang, “Synthesis of codirectional couplers with ultralow sidelobes and minimum bandwidth,” Opt. Lett. 20, 1259–1261 (1995). [CrossRef] [PubMed]
- J. Skaar, K. M. Risvik, “A genetic algorithm for the inverse problem in synthesis of fiber gratings,” J. Lightwave Technol. 16, 1928–1932 (1998). [CrossRef]
- A. M. Bruckstein, B. C. Levy, T. Kailath, “Differential methods in inverse scattering,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 45, 312–335 (1995). [CrossRef]
- A. M. Bruckstein, T. Kailath, “Inverse scattering for discrete transmission-line models,” SIAM Rev. 29, 359–389 (1987). [CrossRef]
- R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fibre Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999). [CrossRef]
- H. Kogelnik, C. V. Shank, “Coupled-wave theory of distributed feedback lasers,” J. Appl. Phys. 43, 2327–2335 (1972). [CrossRef]
- J. G. Proakis, D. G. Manolakis, Introduction to Digital Signal Processing (Macmillan, New York, 1988).
- E. M. Dowling, D. L. MacFarlane, “Lightwave lattice filters for optically multiplexed communication systems,” J. Lightwave Technol. 12, 471–486 (1994). [CrossRef]
- G. L. Lamb, Elements of Soliton Theory (Wiley, New York, 1980), pp. 107–112.
- G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), pp. 104–146.
- A. B. Carlson, Communication Systems (McGraw-Hill, Singapore, 1986), pp. 103–105.
- L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995), pp. 92–108 and 384–388.

## 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.