Abstract

Combining the traditional nonlinear least squares (NLLS) method with a discrete layer peeling (DLP) algorithm, we propose a new method (for the first time to our knowledge) to synthesize triangular-spectrum fiber Bragg gratings (TS-FBGs) with chirp-free structures. In this method, the DLP algorithm is used to generate an appropriate initial value, and the NLLS method is successfully used to optimize the design parameters from the initial value in the previous step. Numerical results show that our method can design both single- and multiple-channel TS-FBGs with their maximum index modulations being effectively suppressed to a feasible level. These novel TS-FBGs thus designed can act as wavelength readout devices and provide potential applications to wavelength interrogation in optical sensor systems.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]

2008

X. Liu, “Tunable ultranarrow dual-channel filter based on sampled FBGs,” J. Lightwave Technol. 26, 1885-1890 (2008).
[CrossRef]

X. M. Liu, A. Lin, G. Sun, D. Moon, D. Hwang, and Y. Chung, “Identical-dual-bandpass sampled fiber Bragg grating and its application to ultranarrow filters,” Appl. Opt. 47, 5637-5643 (2008).
[CrossRef] [PubMed]

T. Allsop, R. Neal, S. Rehman, D. J. Webb, D. Mapps, and I. Bennion, “Characterization of infrared surface plasmon resonances generated from a fiber-optical sensor utilizing tilted Bragg gratings,” J. Opt. Soc. Am. B 25, 481-490 (2008).
[CrossRef]

P. Tsai, F. G. Sun, G. Z. Xiao, Z. Y. Zhang, S. Rahimi, and D. Y. Ban, “A new fiber-Bragg-grating sensor interrogation system deploying free-spectral-range-matching scheme with high precision and fast detection rate,” IEEE Photon. Technol. Lett. 20, 300-302 (2008).
[CrossRef]

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett. 20, 933-935 (2008).
[CrossRef]

2007

2006

K. Zhou, L. Zhang, X. Chen, and I. Bennion, “Optic sensors of high refractive-index responsivity and low thermal cross sensitivity that use fiber Bragg gratings of >80° tilted structures,” Opt. Lett. 31, 1193-1195 (2006).
[CrossRef] [PubMed]

C. Lee, R. Lee, and Y. Kao, “Design of multichannel DWDM fiber Bragg grating filters by Lagrange multiplier constrained optimization,” Opt. Express 14, 11002-11011 (2006).
[CrossRef] [PubMed]

H. Li, M. Li, K. Ogusu, Y. Sheng, and J. Rothenberg, “Optimization of a continuous phase-only sampling for high channel-count fiber Bragg gratings,” Opt. Express 14, 3152-3160 (2006).
[CrossRef] [PubMed]

A. Rosenthal and M. Horowitz, “Analysis and design of nonlinear fiber Bragg gratings and their application for optical compression of reflected pulses,” Opt. Lett. 31, 1334-1336 (2006).
[CrossRef] [PubMed]

Q. Wang, G. Farrell, T. Freir, G. Rajan, and P. F. Wang, “Low-cost wavelength measurement based on a macrobending single-mode fiber,” Opt. Lett. 31, 1785-1787 (2006).
[CrossRef] [PubMed]

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

J. C. C. Carvalho, M. J. Sousa, C. S. S. Junior, J. C. W. A. Costa, C. R. L. Frances, and M. E. V. Segatto, “A new acceleration technique for the design of fibre gratings,” Opt. Express 14, 10715-10725 (2006).
[CrossRef] [PubMed]

2005

2004

2003

2002

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

2001

J. Skaar, W. L. Gang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

H. Chi, X. Tao, D. Yang, and K. Chen, “Simultaneous measurement of axial strain, temperature, and transverse load by a superstructure fiber grating,” Opt. Lett. 26, 1949-1951 (2001).
[CrossRef]

1999

1998

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

1997

T. Erdogan, “Fiber grating spectrum,” J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263-1276 (1997).
[CrossRef]

Aksnes, K.

Allsop, T.

Alphones, A.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, “Particle swarm optimization for the design of low-dispersion fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Ban, D. Y.

P. Tsai, F. G. Sun, G. Z. Xiao, Z. Y. Zhang, S. Rahimi, and D. Y. Ban, “A new fiber-Bragg-grating sensor interrogation system deploying free-spectral-range-matching scheme with high precision and fast detection rate,” IEEE Photon. Technol. Lett. 20, 300-302 (2008).
[CrossRef]

Baskar, S.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, “Particle swarm optimization for the design of low-dispersion fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Bennion, I.

Bernier, M.

Borrelli, N. F.

Burani, N.

Cai, H. W.

R. Ubang, Y. W. Zhou, H. W. Cai, R. H. Qu, and Z. J. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Carvalho, J. C. C.

Chen, K.

Chen, X.

Chi, H.

Chung, Y.

Cole, M. J.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Cooper, D. J. F.

Costa, J. C. W. A.

Durkin, M. K.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Erdogan, T.

J. Skaar, W. L. Gang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

T. Erdogan, “Fiber grating spectrum,” J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

Fang, Z. J.

R. Ubang, Y. W. Zhou, H. W. Cai, R. H. Qu, and Z. J. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Farrell, G.

Frances, C. R. L.

Freir, T.

Gaeta, A. L.

Gang, W. L.

J. Skaar, W. L. Gang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

Gillet, J. N.

Gong, Y. K.

Hill, K. O.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263-1276 (1997).
[CrossRef]

Homoelle, D.

Horowitz, M.

Hwang, D.

Ibsen, M.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Junior, C. S. S.

Kao, Y.

Kristensen, M.

Lagsgaard, J.

Laming, R. I.

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fiber Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10, 842-844 (1998).
[CrossRef]

Lee, C.

Lee, R.

Li, H.

H. Li, M. Li, K. Ogusu, Y. Sheng, and J. Rothenberg, “Optimization of a continuous phase-only sampling for high channel-count fiber Bragg gratings,” Opt. Express 14, 3152-3160 (2006).
[CrossRef] [PubMed]

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

Li, M.

Li, Y.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

Lin, A.

Liu, D.

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett. 20, 933-935 (2008).
[CrossRef]

Liu, H.

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett. 20, 933-935 (2008).
[CrossRef]

Liu, X.

Liu, X. M.

Lu, K. Q.

Madsen, K.

K. Madsen, H. B. Nielsen, and O. Tingleff, Method for Non-linear Least Squares Problems, 2nd ed. (Informatics and Mathematical Modelling, Technical University of Denmark, 2004).

Malathi, P.

Mapps, D.

Meltz, G.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263-1276 (1997).
[CrossRef]

Moon, D.

Neal, R.

Ngo, N. Q.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, “Particle swarm optimization for the design of low-dispersion fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Nielsen, H. B.

K. Madsen, H. B. Nielsen, and O. Tingleff, Method for Non-linear Least Squares Problems, 2nd ed. (Informatics and Mathematical Modelling, Technical University of Denmark, 2004).

Ogusu, K.

Ouyang, Y.

Paul, G.

Plougmann, N.

Popelek, J.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

Porsezian, K.

Qu, R. H.

R. Ubang, Y. W. Zhou, H. W. Cai, R. H. Qu, and Z. J. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Rahimi, S.

P. Tsai, F. G. Sun, G. Z. Xiao, Z. Y. Zhang, S. Rahimi, and D. Y. Ban, “A new fiber-Bragg-grating sensor interrogation system deploying free-spectral-range-matching scheme with high precision and fast detection rate,” IEEE Photon. Technol. Lett. 20, 300-302 (2008).
[CrossRef]

Rajan, G.

Rehman, S.

Rosenthal, A.

Rothenberg, J.

Rothenberg, J. E.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

Segatto, M. E. V.

Senthilnathan, K.

Sheng, Y.

Shum, P.

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett. 20, 933-935 (2008).
[CrossRef]

Skaar, J.

K. Aksnes and J. Skaar, “Design of short fiber Bragg gratings by use of optimization,” Appl. Opt. 43, 2226-2230 (2004).
[CrossRef] [PubMed]

J. Skaar, W. L. Gang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

J. Skaar, “Synthesis and characterization of fiber Bragg gratings,” Ph.D. dissertation (Norwegian University of Science and Technology, 2000).

Smith, C.

Smith, P. W. E.

Sousa, M. J.

Suganthan, P. N.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, “Particle swarm optimization for the design of low-dispersion fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Sun, F. G.

P. Tsai, F. G. Sun, G. Z. Xiao, Z. Y. Zhang, S. Rahimi, and D. Y. Ban, “A new fiber-Bragg-grating sensor interrogation system deploying free-spectral-range-matching scheme with high precision and fast detection rate,” IEEE Photon. Technol. Lett. 20, 300-302 (2008).
[CrossRef]

Sun, G.

Sun, Q.

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett. 20, 933-935 (2008).
[CrossRef]

Tao, X.

Tingleff, O.

K. Madsen, H. B. Nielsen, and O. Tingleff, Method for Non-linear Least Squares Problems, 2nd ed. (Informatics and Mathematical Modelling, Technical University of Denmark, 2004).

Tremblay, G.

Tsai, P.

P. Tsai, F. G. Sun, G. Z. Xiao, Z. Y. Zhang, S. Rahimi, and D. Y. Ban, “A new fiber-Bragg-grating sensor interrogation system deploying free-spectral-range-matching scheme with high precision and fast detection rate,” IEEE Photon. Technol. Lett. 20, 300-302 (2008).
[CrossRef]

Ubang, R.

R. Ubang, Y. W. Zhou, H. W. Cai, R. H. Qu, and Z. J. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Wang, J.

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett. 20, 933-935 (2008).
[CrossRef]

Wang, L. R.

Wang, P. F.

Wang, Q.

Wang, T.

Wang, Y.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

Webb, D. J.

Wielandy, S.

Wilcox, R. B.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

Xia, L.

Q. Sun, D. Liu, L. Xia, J. Wang, H. Liu, and P. Shum, “Experimental demonstration of multipoint temperature warning sensor using a multichannel matched fiber Bragg grating,” IEEE Photon. Technol. Lett. 20, 933-935 (2008).
[CrossRef]

Xiao, G. Z.

P. Tsai, F. G. Sun, G. Z. Xiao, Z. Y. Zhang, S. Rahimi, and D. Y. Ban, “A new fiber-Bragg-grating sensor interrogation system deploying free-spectral-range-matching scheme with high precision and fast detection rate,” IEEE Photon. Technol. Lett. 20, 300-302 (2008).
[CrossRef]

Yang, D.

Zhang, L.

Zhang, T. Y.

Zhang, Z. Y.

P. Tsai, F. G. Sun, G. Z. Xiao, Z. Y. Zhang, S. Rahimi, and D. Y. Ban, “A new fiber-Bragg-grating sensor interrogation system deploying free-spectral-range-matching scheme with high precision and fast detection rate,” IEEE Photon. Technol. Lett. 20, 300-302 (2008).
[CrossRef]

Zhao, W.

Zheng, R. T.

S. Baskar, P. N. Suganthan, N. Q. Ngo, A. Alphones, and R. T. Zheng, “Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm,” Opt. Commun. 260, 716-722 (2006).
[CrossRef]

S. Baskar, R. T. Zheng, A. Alphones, N. Q. Ngo, and P. N. Suganthan, “Particle swarm optimization for the design of low-dispersion fiber Bragg gratings,” IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Zhou, K.

Zhou, Y. W.

R. Ubang, Y. W. Zhou, H. W. Cai, R. H. Qu, and Z. J. Fang, “A fiber Bragg grating with triangular spectrum as wavelength readout in sensor systems,” Opt. Commun. 229, 197-201 (2004).
[CrossRef]

Zweiback, J.

J. E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox, and J. Zweiback, “Dammann fiber Bragg gratings and phase-only sampling for high channel counts,” IEEE Photon. Technol. Lett. 14, 1309-1311 (2002).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

J. Skaar, W. L. Gang, and T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165-173 (2001).
[CrossRef]

IEEE Photon. Technol. Lett.

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Figures (5)

Fig. 1
Fig. 1

Flowchart of the proposed method.

Fig. 2
Fig. 2

Single-channel TS-FBGs with a bandwidth of 1 nm . (a) Reconstructed index modulation under the boundary of q [ Inf , Inf ] and q [ 0 , Inf ] . (b) Corresponding reflectivity of (a). (c) Evolution of the cost function χ in optimal iterations. Here, Inf and Inf represent positive infinite and negative infinite, respectively.

Fig. 3
Fig. 3

Single-channel TS-FBGs with a bandwidth of 2.5 nm . (a) Reconstructed index modulation with the same lower bound and a different upper bound. (b) Corresponding reflectivity of (a).

Fig. 4
Fig. 4

Designed triple-channel TS-FBGs. (a) Reconstructed index modulation under boundaries of q [ Inf , Inf ] and q [ 0 , 1800 ] , respectively. (b) Corresponding reflectivity of (a).

Fig. 5
Fig. 5

Influence of perturbation on the designed TS-FBGs. (a) Perturbation on the index modulation of single-channel TS-FBGs. (b) Corresponding reflectivity of the index modulation in (a). (c) Perturbation on the index modulation of triple-channel TS-FBGs. (d) Corresponding reflectivity of the index modulation in (c).

Tables (1)

Tables Icon

Table 1 Comparisons of Three Methods

Equations (13)

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δ n eff ( z ) = δ n ¯ eff ( z ) { 1 + v cos [ 2 π Λ z + Φ ( z ) ] } ,
F i B = [ cosh ( γ B Δ z ) i δ γ B sinh ( γ B Δ z ) i q γ B sinh ( γ B Δ z ) i q γ B sinh ( γ B Δ z ) cosh ( γ B Δ z ) + i δ γ B sinh ( γ B Δ z ) ] ,
χ = k = 1 M [ R d ( q k ) R t ( q k ) σ ] 2 = k = 1 M f ( q k ) 2 ,
q [ q l , q u ] ,
q = π δ n ¯ eff ( z ) λ B ,
q j + 1 = q j + Δ q .
( J T J ) × Δ q = J T ,
T = T ρ × T Δ ,
ρ = tanh ( q Δ ) q * q .
ρ j = F 1 [ r j ( σ ) ] t = 0 ,
r j + 1 ( δ ) = exp ( i 2 δ Δ ) r j ( δ ) ρ j 1 ρ j * r j ( δ ) .
Λ eff ( z ) = Λ ( 1 + Λ 2 π d θ d z η Δ n dc ( z ) n eff ) 1 ,
Δ n ( z ) = δ n ¯ eff ( z ) × [ 1 + e ( z ) ] ,

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