Abstract

We present a new hybrid optimization method for the synthesis of fiber Bragg gratings (FBGs) with complex characteristics. The hybrid optimization method is a two-tier search that employs a global optimization algorithm [i.e., the tabu search (TS) algorithm] and a local optimization method (i.e., the quasi-Netwon method). First the TS global optimization algorithm is used to find a “promising” FBG structure that has a spectral response as close as possible to the targeted spectral response. Then the quasi-Newton local optimization method is applied to further optimize the FBG structure obtained from the TS algorithm to arrive at a targeted spectral response. A dynamic mechanism for weighting of different requirements of the spectral response is employed to enhance the optimization efficiency. To demonstrate the effectiveness of the method, the synthesis of three linear-phase optical filters based on FBGs with different grating lengths is described.

© 2004 Optical Society of America

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  1. R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
    [CrossRef]
  2. L. Poladian, “Simple grating synthesis algorithm,” Opt. Lett. 25, 787–789 (2000).
    [CrossRef]
  3. J. Skaar, L. Wang, T. Erdogan, “On the synthesis of fiber Bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
    [CrossRef]
  4. M. Ibsen, P. Petropoulos, “Dispersion-free fibre Bragg gratings,” Optical Fiber Communications Conference, Vol. 1 of 2001 Trends in Optics and Photonics Series, Postconference Digest (Optical Society of America, Washington, D.C., 2001), pp. MC1/1–MC1/3.
  5. 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]
  6. J. Bae, J. Chun, “Design of fiber Bragg gratings using the simulated annealing technique for an ideal WDM filter Bank,” MILCOM 2000: 21st Century Military Communications Conference Proceedings (IEEE Press, Piscataway, N.J., 2000), Vol. 2, pp. 892–896.
  7. F. Glover, M. Laguna, Tabu Search (Kluwer Academic, Dordrecht, The Netherlands, 1998).
  8. F. Glover, J. P. Kelly, M. Laguna, “Genetic algorithms and tabu search: hybrids for optimization,” Comput. Operations Res. 22, 111–134 (1995).
    [CrossRef]
  9. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]
  10. D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24, 647–656 (1970).
    [CrossRef]
  11. G. Nykolak, G. Lenz, B. J. Eggleton, T. A. Strasser, “Impact of fiber grating dispersion on WDM system performance,” Optical Fiber Communications Conference(OFC ’98) Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 4–5.
  12. M. J. N. Lima, A. L. J. Teixeira, J. R. F. Rocha, “Optimization of apodized fibre grating filters for WDM systems,” IEEE Lasers and Electro-Optics Society 1999 12th Annual Meeting (LEOS ’99) (IEEE Press, Piscataway, N.J., 1999), Vol. 2, pp. 876–877.
    [CrossRef]
  13. A. Asseh, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol. 15, 1419–1423 (1997).
    [CrossRef]
  14. I. Petermann, B. Sahlgren, S. Helmfrid, A. T. Friberg, P. Y. Fonjallaz, “Fabrication of advanced fiber Bragg gratings by use of sequential writing with a continuous-wave ultraviolet laser source,” Appl. Opt. 41, 1051–1056 (2002).
    [CrossRef] [PubMed]

2002

2001

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

2000

1999

R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

1998

1997

A. Asseh, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol. 15, 1419–1423 (1997).
[CrossRef]

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

1995

F. Glover, J. P. Kelly, M. Laguna, “Genetic algorithms and tabu search: hybrids for optimization,” Comput. Operations Res. 22, 111–134 (1995).
[CrossRef]

1970

D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24, 647–656 (1970).
[CrossRef]

Asseh, A.

A. Asseh, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol. 15, 1419–1423 (1997).
[CrossRef]

Bae, J.

J. Bae, J. Chun, “Design of fiber Bragg gratings using the simulated annealing technique for an ideal WDM filter Bank,” MILCOM 2000: 21st Century Military Communications Conference Proceedings (IEEE Press, Piscataway, N.J., 2000), Vol. 2, pp. 892–896.

Chun, J.

J. Bae, J. Chun, “Design of fiber Bragg gratings using the simulated annealing technique for an ideal WDM filter Bank,” MILCOM 2000: 21st Century Military Communications Conference Proceedings (IEEE Press, Piscataway, N.J., 2000), Vol. 2, pp. 892–896.

Eggleton, B. J.

G. Nykolak, G. Lenz, B. J. Eggleton, T. A. Strasser, “Impact of fiber grating dispersion on WDM system performance,” Optical Fiber Communications Conference(OFC ’98) Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 4–5.

Erdogan, T.

J. Skaar, L. Wang, 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 spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Feced, R.

R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Fonjallaz, P. Y.

Friberg, A. T.

Glover, F.

F. Glover, J. P. Kelly, M. Laguna, “Genetic algorithms and tabu search: hybrids for optimization,” Comput. Operations Res. 22, 111–134 (1995).
[CrossRef]

F. Glover, M. Laguna, Tabu Search (Kluwer Academic, Dordrecht, The Netherlands, 1998).

Helmfrid, S.

Ibsen, M.

M. Ibsen, P. Petropoulos, “Dispersion-free fibre Bragg gratings,” Optical Fiber Communications Conference, Vol. 1 of 2001 Trends in Optics and Photonics Series, Postconference Digest (Optical Society of America, Washington, D.C., 2001), pp. MC1/1–MC1/3.

Kelly, J. P.

F. Glover, J. P. Kelly, M. Laguna, “Genetic algorithms and tabu search: hybrids for optimization,” Comput. Operations Res. 22, 111–134 (1995).
[CrossRef]

Laguna, M.

F. Glover, J. P. Kelly, M. Laguna, “Genetic algorithms and tabu search: hybrids for optimization,” Comput. Operations Res. 22, 111–134 (1995).
[CrossRef]

F. Glover, M. Laguna, Tabu Search (Kluwer Academic, Dordrecht, The Netherlands, 1998).

Lenz, G.

G. Nykolak, G. Lenz, B. J. Eggleton, T. A. Strasser, “Impact of fiber grating dispersion on WDM system performance,” Optical Fiber Communications Conference(OFC ’98) Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 4–5.

Lima, M. J. N.

M. J. N. Lima, A. L. J. Teixeira, J. R. F. Rocha, “Optimization of apodized fibre grating filters for WDM systems,” IEEE Lasers and Electro-Optics Society 1999 12th Annual Meeting (LEOS ’99) (IEEE Press, Piscataway, N.J., 1999), Vol. 2, pp. 876–877.
[CrossRef]

Muriel, M. A.

R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Nykolak, G.

G. Nykolak, G. Lenz, B. J. Eggleton, T. A. Strasser, “Impact of fiber grating dispersion on WDM system performance,” Optical Fiber Communications Conference(OFC ’98) Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 4–5.

Petermann, I.

Petropoulos, P.

M. Ibsen, P. Petropoulos, “Dispersion-free fibre Bragg gratings,” Optical Fiber Communications Conference, Vol. 1 of 2001 Trends in Optics and Photonics Series, Postconference Digest (Optical Society of America, Washington, D.C., 2001), pp. MC1/1–MC1/3.

Poladian, L.

Risvik, K. M.

Rocha, J. R. F.

M. J. N. Lima, A. L. J. Teixeira, J. R. F. Rocha, “Optimization of apodized fibre grating filters for WDM systems,” IEEE Lasers and Electro-Optics Society 1999 12th Annual Meeting (LEOS ’99) (IEEE Press, Piscataway, N.J., 1999), Vol. 2, pp. 876–877.
[CrossRef]

Sahlgren, B.

Shanno, D. F.

D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24, 647–656 (1970).
[CrossRef]

Skaar, J.

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

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]

Strasser, T. A.

G. Nykolak, G. Lenz, B. J. Eggleton, T. A. Strasser, “Impact of fiber grating dispersion on WDM system performance,” Optical Fiber Communications Conference(OFC ’98) Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 4–5.

Teixeira, A. L. J.

M. J. N. Lima, A. L. J. Teixeira, J. R. F. Rocha, “Optimization of apodized fibre grating filters for WDM systems,” IEEE Lasers and Electro-Optics Society 1999 12th Annual Meeting (LEOS ’99) (IEEE Press, Piscataway, N.J., 1999), Vol. 2, pp. 876–877.
[CrossRef]

Wang, L.

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

Zervas, M. N.

R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

Appl. Opt.

Comput. Operations Res.

F. Glover, J. P. Kelly, M. Laguna, “Genetic algorithms and tabu search: hybrids for optimization,” Comput. Operations Res. 22, 111–134 (1995).
[CrossRef]

IEEE J. Quantum Electron.

R. Feced, M. N. Zervas, M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron. 35, 1105–1115 (1999).
[CrossRef]

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

J. Lightwave Technol.

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

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. Asseh, “A writing technique for long fiber Bragg gratings with complex reflectivity profiles,” J. Lightwave Technol. 15, 1419–1423 (1997).
[CrossRef]

Math. Comput.

D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24, 647–656 (1970).
[CrossRef]

Opt. Lett.

Other

G. Nykolak, G. Lenz, B. J. Eggleton, T. A. Strasser, “Impact of fiber grating dispersion on WDM system performance,” Optical Fiber Communications Conference(OFC ’98) Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 4–5.

M. J. N. Lima, A. L. J. Teixeira, J. R. F. Rocha, “Optimization of apodized fibre grating filters for WDM systems,” IEEE Lasers and Electro-Optics Society 1999 12th Annual Meeting (LEOS ’99) (IEEE Press, Piscataway, N.J., 1999), Vol. 2, pp. 876–877.
[CrossRef]

M. Ibsen, P. Petropoulos, “Dispersion-free fibre Bragg gratings,” Optical Fiber Communications Conference, Vol. 1 of 2001 Trends in Optics and Photonics Series, Postconference Digest (Optical Society of America, Washington, D.C., 2001), pp. MC1/1–MC1/3.

J. Bae, J. Chun, “Design of fiber Bragg gratings using the simulated annealing technique for an ideal WDM filter Bank,” MILCOM 2000: 21st Century Military Communications Conference Proceedings (IEEE Press, Piscataway, N.J., 2000), Vol. 2, pp. 892–896.

F. Glover, M. Laguna, Tabu Search (Kluwer Academic, Dordrecht, The Netherlands, 1998).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the proposed hybrid optimization method.

Fig. 2
Fig. 2

Model of the cascaded AFBGs optimized by the first step of the hybrid optimization method.

Fig. 3
Fig. 3

Flowchart of the tabu search optimization algorithm used to optimize the cascaded AFBGs to obtain the “promising” FBG.

Fig. 4
Fig. 4

(a) Index-modulation profiles of a 17.1-mm-long optimized linear phase filter. Dashed curve, profile obtained from the first step (with the TS algorithm) of the hybrid optimization algorithm. Solid curve, profile obtained from the second step (with the quasi-Newton method) of the hybrid optimization algorithm. (b) Corresponding reflective spectra calculated from the index-modulation profiles shown in (a). Dashed curve, reflective spectrum obtained from the first step (with the TS algorithm) of the hybrid optimization algorithm. Solid curve, reflective spectrum obtained from the second step (with the quasi-Newton method) of the hybrid optimization algorithm. (c) Corresponding group delay responses calculated from the index-modulation profiles shown in (a). Dashed curve, group delay response first step (with the TS algorithm) of the hybrid optimization algorithm. Solid curve, group delay response obtained from the second step (with the quasi-Newton method) of the hybrid optimization algorithm. Dotted curve, group delay response obtained from a single apodized FBG with a length of 17.1 mm. (d) Enlargement of part of (c).

Fig. 5
Fig. 5

(a) Index-modulation profile of a 25.8-mm-long optimized linear phase filter obtained from the hybrid optimization algorithm. (b) Corresponding reflective spectrum calculated from the index modulation profile shown in (a). (c) Corresponding group delay responses calculated from the index modulation profiles shown in (a). Solid curve, group delay response obtained from the hybrid optimization algorithm. Dotted curve, group delay response obtained from a single apodized FBG with a length of 25.8 mm.

Fig. 6
Fig. 6

(a) Index-modulation profile of a 31.1-mm-long optimized linear phase filter obtained with the hybrid optimization algorithm. (b) Corresponding reflective spectrum calculated from the index-modulation profile shown in (a). (c) Corresponding group delay responses calculated from the index-modulation profiles shown in (a). Solid curve, group delay response obtained with the hybrid optimization algorithm. Dotted curve, group delay response obtained from a single apodized FBG with a length of 31.1 mm.

Tables (1)

Tables Icon

Table 1 Comparison of the Performance of Three Linear-Phase Optical Filters with Different Lengths as Designed with the Hybrid Optimization Algorithm

Equations (11)

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δn(z)=Δnf(z)cos2πzΛ+ϕ(z),
Ef(0)Eb(0)=T1T2TNEf(N)Eb(N),
ρ=Eb(0)Ef(0).
τρ=-λ22πcdθρdλ,
dρ=dτρdλ=-λ22πcd2θρdλ2+2λdθρdλ.
Var={Δn1,,ΔnN, δl1,,δlN},
error(Var)=iwindowWiR[|Ri(Var)-Ritar|]1/2+bkpassband|Dk(Var)-Dktarget|,
neighbori={Var(1),,lbi+(ubi0-lbi)β,,Var(2N)},
error(δn)=iwindowWiR[|Ri(δn)-Ritarget|]1/2+bkpassband|Dk(δn)-Dktarget|,
Rtargetλ=1,λpassband0,λstopband.
WiR=λ0|λ0-i|,istopband,ipassband,

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