Abstract

This paper presents a formulation for the application of the transfer matrix method to Bragg grating strain sensors. A modified T-matrix representation is detailed for the sensor problem based on an effective period derived from the coupling coefficients. This modified T-matrix formulation is shown to converge to the coupled-mode equations solution for a large number of grating segments, even in the presence of significant strain gradients. Several numerical examples are presented to demonstrate the importance of inclusion of the strain gradient in the calculation. In addition, the current formulation is validated by application to previously published experimental data.

© 2004 IEEE

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Appl. Opt. (2)

Other (18)

T. Erdogan, "Fiber grating spectra", J. Lightwave Technol. , vol. 15, pp. 1227-1294, Aug. 1997.

M. Studer, K. Peters and J. Botsis, "Method for determination of crack bridging parameters using long optical fiber Bragg grating sensors", Compos. Part B-Eng., vol. 34, pp. 347-359, 2003.

Y. Okabe, R. Tsuji and N. Takeda, "Application of chirped fiber Bragg gratings sensors for identification of crack locations in composites", Compos. Part A-Appl. S., vol. 35, pp. 59-65, 2004.

T. Mizutani, Y. Okabe and N. Takeda, "Quantitative evaluation of transverse cracks in carbon fiber reinforced plastic quasiisotropic laminates with embedded small-diameter fiber Bragg grating sensors", Smart Materials Structures, vol. 12, pp. 898-903, 2003.

Y. Okabe, T. Mizutani, S. Yashiro and N. Takeda, "Detection of microscopic damages in composite laminates with embedded small-diameter fiber Bragg grating sensors", Composites Science Technology, vol. 62, pp. 951-958, 2002.

K. Peters, P. Pattis and J. Botsis, "Novel technique to measure axial strain distribution along fiber during pullout test", J. Mater. Sci. Lett., vol. 21, pp. 887-891, 2002.

S. Takeda, Y. Okabe and N. Takeda, "Delamination detection in CFRP laminates with embedded small-diameter fiber Bragg grating sensors", Compos. Part A-Appl. S., vol. 33, pp. 971-980, 2002.

Y. Okabe, N. Tanaka and N. Takeda, "Effect of fiber coating on crack detection in carbon fiber reinforced plastic composites using fiber Bragg grating sensors", Smart Mater. Struct., vol. 11, pp. 892-898, 2002.

P. Torres and L. C. G. Valente, "Spectral response of locally pressed fiber Bragg grating", Opt. Commun., vol. 208, pp. 285 -291, 2002.

A. Yariv, "Coupled-mode theory for guided-wave optics", IEEE J. Quantum Electron., vol. QE-9, pp. 919-933, Sept. 1973 .

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

R. Kashyap, Fiber Bragg Gratings, San Diego, CA: Academic, 1999, ch. 4.

K. Peters, M. Studer, J. Botsis, A. Iocco, H. Limberger and R. Salathé, "Embedded optical fiber Bragg grating sensor in a nonuniform strain field: Measurements and simulations", Exp. Mech., vol. 41, pp. 19-28, 2001.

S. Huang, M. M. Ohn, M. LeBlanc and R. M. Measures, "Continuous arbitrary strain profile measurements with fiber Bragg gratings", Smart Mater. Struct., vol. 7, pp. 248-256, 1998.

G. Cormier, R. Boudreau and S. Thériault, "Real-coded genetic algorithm for Bragg grating parameter synthesis", J. Opt. Soc. Amer. B, Opt. Phys., vol. 18, pp. 1771-1776, 2001.

A. Gill, K. Peters and M. Studer, "Genetic algorithm for the reconstruction of Bragg grating sensor distribution profiles", Measurement Science Technology., vol. 15, pp. 1877-1884, 2004.

H. Kogelnik, "Filter response of nonuniform almost-periodic structures", AT&T Bell Lab. Tech. J., vol. 55, pp. 109 -126, 1976.

C. Chang and S. T. Vohra, "Spectral broadening due to nonuniform strain fields in fiber Bragg grating based transducers", Electron. Lett., vol. 34, pp. 1778-1779, 1998.

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