Abstract

In this paper we propose a novel acceleration technique for the design of fibre gratings based on Genetic Algorithm (GA). It is shown that with an appropriate reformulation of the wavelength sampling scheme it is possible to design high quality optical filters with low computational effort. Our results will show that the proposed technique can reduce significantly the GA’s processing time.

© 2006 Optical Society of America

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References

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  1. T. Erdogan. "Fiber grating spectra," IEEE J. Lightwave Technol. 15, 1277-1294 (1997).
    [CrossRef]
  2. R. Kashyap. "Fibre Bragg Gratings". Academic Press, San Diego, (1999).
  3. I. Del Villar, I. R. Matas, and F. J. Arregui. "Optimization of sensitivity in long period fiber gratings with overlay deposition," Opt. Express 13, 56-69 (2004).
    [CrossRef]
  4. L. Poladian. "Simple grating synthesis algorithm," Opt. Lett. 25, 787-789 (2000).
    [CrossRef]
  5. J. Skaar and K. M. Risvik. "A genetic algorithm for the inverse problem in synthesis of fiber gratings," IEEE J. Lightwave Technol. 16, 1928-1932 (1998).
    [CrossRef]
  6. P. Dong, J. Azana, and A. G. Kirk. "Synthesis of fiber bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
    [CrossRef]
  7. N. Q. Ngo, R. T. Zheng, S. C. Tjin, and S. Y. Li. "Tabu search synthesis of cascaded fiber bragg gratings for linear phase filters," Opt. Commun. 241, 7983 (2004).
    [CrossRef]
  8. S. Manos and L. Poladian. "Multi-objective and constrained design of fibre bragg gratings using evolutionary algorithms," Opt. Express 13, 7350-7364 (2005).
    [CrossRef] [PubMed]
  9. S. Baskar, R. T. Zheng andA. Alphones, N.Q. N. Q. Ngo, and P. N. Suganthan. "Particle swarm optimization for the design of the low-dispersion fiber bragg gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
    [CrossRef]
  10. M. Yamada and K. Sakuda. "Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach," Appl. Opt.  26, 3473-3478 (1987).
    [CrossRef]
  11. D. E. Goldberg. "Genetic Algorithms in Search, Optimization, and Machine Learning". Addison-Wesley Publishing Company (1989).
  12. J. A. Dowbrolwisk, F. C. Ho, A. Belkind, and V. Koss. "Merit functions for more effective thin film calculations," Appl. Opt. 28, 2824-2831 (1989).
    [CrossRef]
  13. 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]

2006 (1)

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]

2005 (2)

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

S. Manos and L. Poladian. "Multi-objective and constrained design of fibre bragg gratings using evolutionary algorithms," Opt. Express 13, 7350-7364 (2005).
[CrossRef] [PubMed]

2004 (2)

I. Del Villar, I. R. Matas, and F. J. Arregui. "Optimization of sensitivity in long period fiber gratings with overlay deposition," Opt. Express 13, 56-69 (2004).
[CrossRef]

N. Q. Ngo, R. T. Zheng, S. C. Tjin, and S. Y. Li. "Tabu search synthesis of cascaded fiber bragg gratings for linear phase filters," Opt. Commun. 241, 7983 (2004).
[CrossRef]

2003 (1)

P. Dong, J. Azana, and A. G. Kirk. "Synthesis of fiber bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[CrossRef]

2000 (1)

1998 (1)

J. Skaar and K. M. Risvik. "A genetic algorithm for the inverse problem in synthesis of fiber gratings," IEEE J. Lightwave Technol. 16, 1928-1932 (1998).
[CrossRef]

1997 (1)

T. Erdogan. "Fiber grating spectra," IEEE J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

1989 (1)

1987 (1)

M. Yamada and K. Sakuda. "Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach," Appl. Opt.  26, 3473-3478 (1987).
[CrossRef]

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]

Arregui, F. J.

Azana, J.

P. Dong, J. Azana, and A. G. Kirk. "Synthesis of fiber bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[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 andA. Alphones, N.Q. N. Q. Ngo, and P. N. Suganthan. "Particle swarm optimization for the design of the low-dispersion fiber bragg gratings," IEEE Photon. Technol. Lett. 17, 615-617 (2005).
[CrossRef]

Belkind, A.

Del Villar, I.

Dong, P.

P. Dong, J. Azana, and A. G. Kirk. "Synthesis of fiber bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[CrossRef]

Dowbrolwisk, J. A.

Erdogan, T.

T. Erdogan. "Fiber grating spectra," IEEE J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

Ho, F. C.

Kirk, A. G.

P. Dong, J. Azana, and A. G. Kirk. "Synthesis of fiber bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[CrossRef]

Koss, V.

Li, S. Y.

N. Q. Ngo, R. T. Zheng, S. C. Tjin, and S. Y. Li. "Tabu search synthesis of cascaded fiber bragg gratings for linear phase filters," Opt. Commun. 241, 7983 (2004).
[CrossRef]

Manos, S.

Matas, I. 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]

N. Q. Ngo, R. T. Zheng, S. C. Tjin, and S. Y. Li. "Tabu search synthesis of cascaded fiber bragg gratings for linear phase filters," Opt. Commun. 241, 7983 (2004).
[CrossRef]

Poladian, L.

Risvik, K. M.

J. Skaar and K. M. Risvik. "A genetic algorithm for the inverse problem in synthesis of fiber gratings," IEEE J. Lightwave Technol. 16, 1928-1932 (1998).
[CrossRef]

Sakuda, K.

M. Yamada and K. Sakuda. "Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach," Appl. Opt.  26, 3473-3478 (1987).
[CrossRef]

Skaar, J.

J. Skaar and K. M. Risvik. "A genetic algorithm for the inverse problem in synthesis of fiber gratings," IEEE J. Lightwave Technol. 16, 1928-1932 (1998).
[CrossRef]

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]

Tjin, S. C.

N. Q. Ngo, R. T. Zheng, S. C. Tjin, and S. Y. Li. "Tabu search synthesis of cascaded fiber bragg gratings for linear phase filters," Opt. Commun. 241, 7983 (2004).
[CrossRef]

Yamada, M.

M. Yamada and K. Sakuda. "Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach," Appl. Opt.  26, 3473-3478 (1987).
[CrossRef]

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]

N. Q. Ngo, R. T. Zheng, S. C. Tjin, and S. Y. Li. "Tabu search synthesis of cascaded fiber bragg gratings for linear phase filters," Opt. Commun. 241, 7983 (2004).
[CrossRef]

Appl. Opt (1)

M. Yamada and K. Sakuda. "Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach," Appl. Opt.  26, 3473-3478 (1987).
[CrossRef]

Appl. Opt. (1)

IEEE J. Lightwave Technol. (2)

J. Skaar and K. M. Risvik. "A genetic algorithm for the inverse problem in synthesis of fiber gratings," IEEE J. Lightwave Technol. 16, 1928-1932 (1998).
[CrossRef]

T. Erdogan. "Fiber grating spectra," IEEE J. Lightwave Technol. 15, 1277-1294 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

Opt. Commun. (3)

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]

P. Dong, J. Azana, and A. G. Kirk. "Synthesis of fiber bragg grating parameters from reflectivity by means of a simulated annealing algorithm," Opt. Commun. 228, 303-308 (2003).
[CrossRef]

N. Q. Ngo, R. T. Zheng, S. C. Tjin, and S. Y. Li. "Tabu search synthesis of cascaded fiber bragg gratings for linear phase filters," Opt. Commun. 241, 7983 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Other (2)

R. Kashyap. "Fibre Bragg Gratings". Academic Press, San Diego, (1999).

D. E. Goldberg. "Genetic Algorithms in Search, Optimization, and Machine Learning". Addison-Wesley Publishing Company (1989).

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Figures (9)

Fig. 1.
Fig. 1.

The transfer matrix method applied to obtain the spectral characteristics of a fibre grating.

Fig. 2.
Fig. 2.

The encoded chromosome: a float-point vector of amplitude modulations and section periods.

Fig. 3.
Fig. 3.

Fitness for standard sampling (SS) and for reduced stochatic sampling (RSS) as a function of the processing time.

Fig. 4.
Fig. 4.

Speedup fator as a function of the ratio SRSS /SSS when NP = 50. The stars represent the results obtained with the RSS technique.

Fig. 5.
Fig. 5.

Reflectivity curves obtained via standard sampling (SS) and reduced stochastic sampling (RSS). The dotted line represents the SS technique.(a) Reflectivity and (b) phase response.

Fig. 6.
Fig. 6.

Profile of the perturbation to the effective refractive index. (a) SS and (b) RSS techniques.

Fig. 7.
Fig. 7.

Target and computed reflectivities using both SS and RSS techniques of a TFBG.

Fig. 8.
Fig. 8.

Fitness for standard sampling (SS) and for reduced stochatic sampling (RSS) as a function of the processing time.

Fig. 9.
Fig. 9.

(a) amplitude modulation and (b) section period profiles of the best individual using the RSS technique.

Equations (8)

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n ( z ) = n eff + Δ n i cos ( 2 πz Λ i ) .
[ R i S i ] = F i [ R i 1 S i 1 ] .
F i = [ cosh ( γ i Δ z i ) j σ ̂ i γ i sinh ( γ i Δ z i ) j κ i γ i sinh ( γ i Δ z i ) j κ i γ i sinh ( γ i Δ z i ) cosh ( γ i Δ z i ) + j σ ̂ i γ i sinh ( γ i Δ z i ) ]
[ R M S M ] = F [ R 0 S 0 ] ; F = F M · F M 1 · · F i · · F 1 .
Fitness = [ 1 S j = 1 S ( Γ ( λ j ) Γ t arg et ( λ i ) δ Γ j ) 2 ] 1 .
λ j = λ min + ( j 1 ) Δλ
λ j = λ min + ( j 1 ) Δλ ξ Δλ
f = S SS N P S SS + S RSS N P .

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