Abstract

This paper proposes an accurate modeling technique of concatenated long-period fiber gratings (LPFGs). The proposed technique is then applied to the synthesis of LPFGs for the erbium gain equalization using both the simulated annealing and the steepest descent minimization technique. A piecewise-uniform LPFG is theoretically synthesized according to the inverted gain spectrum of a commercially available erbium-doped fiber amplifier (EDFA) over the range of 1525-1570 nm. Sensitivity analysis of the designed structure is presented by Monte Carlo simulation with regard to the manufactured amplitude mask. To verify a synthesizing technique using the proposed modeling, the piecewise-uniform LPFGs for gain flattening of EDFA are fabricated and their spectra are also presented experimentally.

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Appl. Opt. (1)

J. Lightwave Technol. (2)

M. Harumoto, M. Shigehara and H. Suganuma, "Gain-flattening filter using long-period fiber gratings", J. Lightwave Technol., vol. 20, pp. 1027-1033, June 2002.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan and J. E. Sipe, "Long-period fiber gratings as band-rejection filters", J. Lightwave Technol., vol. 14, pp. 58-64, Jan. 1996.

Other (27)

T. Erdogan, "Fiber grating spectra", J. Lightwave Technol. , vol. 15, pp. 1277-1294, Aug. 1997.

B. Lee, Y. Liu, S. Lee, S. Choi and J. Jang, "Displacements of the resonant peaks of a long-period fiber grating induced by a change of ambient refractive index", Opt. Lett. , vol. 22, no. 23, pp. 1769-1771, 1997.

M. Yamada and K. Sakuda, "Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach", Appl. Opt., vol. 26, no. 16, pp. 3474-3478, 1987.

J. Bae, J. Chun and S. B. Lee, "Multiport lattice filter model for long-period fiber gratings", Jpn. J. Appl. Phys. Part I, vol. 39, no. 12A, pp. 6576-6577, 2000.

J. Bae, J. Chun and S. B. Lee, "Equalization of the nonflat erbium gain spectrum using the multiport lattice filter model", in Proc. Optical Fiber Communication (OFC 2000), vol. WE7, 2000, pp. 80-83.

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C, New York: Cambridge Univ. Press, 1992.

I. O. Bohachevsky, M. E. Johnson and M. L. Stein, "Generalized simulated annealing for function optimization", Technometrics, vol. 28, no. 3, pp. 209 -217, 1986.

J. Bae, S. B. Lee, H. D. Ku, S. H. Kim and J. Chun, "Fabrication of piecewise-uniform lpfg designed using multiport lattice filter model", in Proc. Optical Fiber Communication (OFC 2003), vol. 2, 2003, pp. 570-571.

H. Kogelnik, "Theory of optical waveguides," in Guided-Wave Optoelectronics, T. Tamir, Ed. Berlin: Springer-Verlag, 1990.

T. Erdogan, "Cladding-mode resonances in short-and long-period fiber grating filters", J. Opt. Soc. Amer. A, vol. 14, no. 8, pp. 1760-1773, 1997.

R. Kashyap, Fiber Bragg Gratings, New York: Academic, 1999.

A. Othonos and K. Kalli, Fiber Bragg Gratings-Fundamentals and Applications in Telecommunications and Sensing, Boston, MA: Artech House, 1999.

A. Corana, M. Marchesi, C. Martini and S. Ridella, "Minimizing multimodal functions of continuous variables with the simulated annealing algorithm", ACM Trans. on Math. Soft., vol. 13, no. 3, pp. 262-280, 1987.

J. Bae, J. Chun and S. B. Lee, "Two methods for synthesizing the long period fiber gratings with the inverted erbium gain spectrum", Jpn. J. Appl. Phys. , vol. 38, no. 7B, pp. L819-L822, 1999.

J. K. Bae, S. H. Kim, J. H. Kim, J. Bae, S. B. Lee and J. M. Jeong, "Spectral shape tunable band-rejection filter using a long-period fiber grating with divided coil heaters", IEEE Photon. Technol. Lett., vol. 15, pp. 407-409, Mar. 2003.

T. Kailath, "Signal processing applications of some moment problems", in Proc. Sym. Appl. Math., vol. 37, 1987, pp. 71-109.

A. Bruckstein, B. Levy and T. Kailath, "Differential methods in inverse scattering", SIAM J. Appl. Math, vol. 45, no. 2, pp. 312-335, 1985.

A. Bruckstein and T. Kailath, "Inverse scattering for discrete transmission-line models", SIAM Rev., vol. 29, no. 3, pp. 359-389, 1987.

R. Feced, M. N. Zervas and M. A. Muriel, "An efficient inverse scattering algorithm for the design of nonuniform fiber bragg gratings", IEEE J. Quantum Electron. , vol. 35, no. 8, pp. 1105-1115, 1999.

J. Skaar, L. Wang and T. Erdogan, "On the synthesis of fiber bragg gratings by layer peeling", J. Quantum Electron., vol. 37, no. 2, pp. 165-173, 2001.

L. Wang and T. Erdogan, "Layer peeling algorithm for reconstruction of long-period fiber gratings", Electron. Lett., vol. 37, no. 3, pp. 154-156, 2001.

G. Song and S. Shin, "Design of corrugated waveguide filters by the gel'fand-levitan-marchenko inverse-scattering method", J. Opt. Soc. Amer. A, vol. 2, no. 11, pp. 1905-1915, 1985.

G. Song and S. Shin, "Inverse scattering problem for the coupled-wave equations when the reflection coefficient is a rational function", Proc. IEEE, vol. 71, pp. 266-268, 1983.

E. Peral, J. Capmany and J. Marti, "Iterative solution to the Gel'fand-Levitan-Marchenko coupled equations and application to synthesis of fiber gratings", J. Quantum Electron., vol. 32, no. 12, pp. 2078-2084, 1996.

A. Yariv, Optical Electronics in Modern communications, New York: Oxford Univ. Press, 1996.

A. M. Vengsarkar, J. R. Pedrazzani, J. B. Judkins and P. J. Lemaire, "Long-period fiber-grating-based gain equalizers", Opt. Lett., vol. 21, no. 5, pp. 336-338, 1996.

Y. Liu, J. A. R. Williams, L. Zhang and I. Bennion, "Phase shifted and cascaded long-period fiber gratings", Opt. Commun., vol. 164, pp. 27-31, 1999.

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