Abstract

We apply a multi-objective evolutionary algorithm to a grating problem where only very specific features of the transmission spectrum are specified during the optimisation process. The design problem analysed here relates to the passive extraction of 10 GHz clock signals from a 10 Gbps OTDM RZ encoded data stream. Four spectral features of interest such as bandwidth and passband quality are explicitly defined. Using a real-encoded evolutionary algorithm along with an elitist multi-objective selection method, we arrive at a group of solutions which each satisfy the objectives to various degrees in the presence of manufacturing and other design constraints.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. G.-H. Song and S.-Y. Shin, �??Design of corrugated waveguide filters by the Gel�??fand-Levitan-Marchenko inverse-scattering method,�?? J. Opt. Soc. Am. A 2, 1905�??1915 (1985).
    [CrossRef]
  2. 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. 35, 1105�??1115 (1999).
    [CrossRef]
  3. L. Poladian, �??Simple Grating Synthesis Algorithm,�?? Opt. Lett. 25, 787�??789 (2000).
    [CrossRef]
  4. J. Skaar and K. M. Risvik, �??A Genetic Algorithm for the Inverse Problem in Synthesis of Fiber Gratings,�?? J. Lightwave Technol. 16, 1928�??1932 (1998).
    [CrossRef]
  5. G. Cormier, R. Boudreau, and S. Theriault, �??Real-Coded Genetic Algorithm for Bragg Grating Parameter Synthesis,�?? J. Opt. Soc. Am. B 18, 1771�??1776 (2001).
    [CrossRef]
  6. G.-W. Chern and L. A. Wang, �??Design of Binary Long-Period Fiber Grating Filters by the Inverse-Scattering Method with Genetic Algorithm Optimization,�?? J. Opt. Soc. Am. A 19, 772�??780 (2002).
    [CrossRef]
  7. C. L. Lee and Y. Lai, �??Evolutionary Programming Synthesis of Optimal Long-Period Fiber Grating Filters for EDFA Gain Flattening,�?? IEEE Photonics Technol. Lett. 14, 1557�??1559 (2002).
    [CrossRef]
  8. C. L. Lee and Y. C. Lai, �??Optimal Narrowband Dispersion Less Fiber Bragg Grating Filters with Short Grating Length and Smooth Dispersion Profile,�?? Opt. Commun. 235, 99�??106 (2004).
    [CrossRef]
  9. C. L. Lee and Y. C. Lai, �??Long-Period Fiber Grating Filter Synthesis Using Evolutionary Programming,�?? Fiber Int. Opt. 23, 249�??261 (2004).
    [CrossRef]
  10. D. Wiesman, R. Germann, G.-L. Bona, C. David, D. Erni, and H. Jackel, �??Add-Drop Filter Based on Apodized Surface-Corrugated Gratings,�?? J. Opt. Soc. Am. B 20, 417�??423 (2003).
    [CrossRef]
  11. S. F. Shu, Y. Lai, and C. L. Pan, �??Learning Evolution Design of Multiband-Transmission Fiber Grating Filters,�?? Opt. Eng. 42, 2856�??2860 (2003).
    [CrossRef]
  12. F. Casagrande, P. Crespi, A. M. Grassi, A. Lulli, R. P. Kenny, and M. P. Whelan, �??From The Reflected Spectrum to the Properties of a Fiber Bragg Grating: A Genetic Algorithm Approach with Application to Distributed Strain Sensing,�?? Appl. Opt. 41, 5238�??5244 (2002).
    [CrossRef] [PubMed]
  13. A. Gill, K. Peters, and M. Studer, �??Genetic Algorithm for the Reconstruction of Bragg Grating Sensor Strain Profiles,�?? Meas. Sci. Technol. 15, 1877�??1884 (2004).
    [CrossRef]
  14. H.-C. Cheng and Y.-L. Lo, �??Arbitrary Strain Distribution Measurement Using a Genetic Algorithm Approach and Two Fiber Bragg Grating Intensity Spectra,�?? Opt. Comm. 239, 323�??332 (2004).
    [CrossRef]
  15. 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. Comm. 2004, 79�??83 (241).
  16. P. Dong, J. Azana, and A. G. Kirk, �??Synthesis of Fiber Bragg Grating Parameters from Reflectivity by Means of a Simulated Annealing Algorithm,�?? Opt. Comm. 228, 303�??308 (2003).
    [CrossRef]
  17. C. Caucheteur, F. Lhomme, K. Chah, M. Blondel, and P. Megret, �??Fiber Bragg Grating Sensor Demodulation Technique by Synthesis of Grating Parameters from its Reflection Spectrum,�?? Opt. Comm. 240, 329�??336 (2004).
    [CrossRef]
  18. S. Baskar, A. Alphones, N. Q. Ngo, P. N. Suganthan, and P. Shun, �??Design of Optimal Length Low-Dispersion FBG Filter Using Covariance Matrix Adapted Evolution,�?? Opt. Express To Appear (2005).
  19. D. Correia, V. F. Rodriguez-Esquerre, and H. E. Hernandez-Figueroa, �??Genetic-Algorithm and Finite-Element Approach to the Synthesis of Dispersion-Flattened Fiber,�?? Microwave Opt. Techn. Lett. 31, 245�??248 (2001).
    [CrossRef]
  20. S. Manos and L. Poladian, �??Optical fibre design using Evolutionary Strategies,�?? Eng. Comp. 21, 564�??576 (2004).
    [CrossRef]
  21. Y. Y. Haimes, L. S. Lasdon, and D. A. Wismer, �??On a bicriterion formulation of the problems of intergrated system identification and system optimization,�?? IEEE Trans. Sys. Man and Cyb. 1, 296�??297 (1971).
    [CrossRef]
  22. J. D. Schaffer, �??Multiple objective optimization with vector evaluated genetic algorithms,�?? in Proc. of the First Int. Conf. on Genetic Algorithms, pp. 93�??100 (1985).
  23. D. E. Goldberg, Genetic Algorithms for Search, Optimization and Machine Learning (Addison-Wesley, 1989).
  24. E. Zitzler, M. Laumanns, and L. Thiele, �??SPEA2: Improving the Strength Pareto Evolutionary Algorithm,�?? Tech. Rep. 103, Gloriastrasse 35, CH-8092 Zurich, Switzerland (2001). URL <a href="http://citeseer.ist.psu.edu/">http://citeseer.ist.psu.edu/</a>
  25. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, �??A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,�?? IEEE Transactions on Evolutionary Computation 6, 182�??197 (2002).
    [CrossRef]
  26. M. Attygalle, B. Ashton, A. Nirmalathas, L. Poladian, and W. Padden, �??Novel technique for all-optical clock extraction using fibre bragg gratings,�?? in OptoElectronics and Communications Conference, Shanghai, China, pp. 13�??16 (2003).
  27. M. Yamada and K. Sakuda, �??Analysis of almost-periodic distributed feedback slab waveguide via a fundamental matrix approach,�?? Applied Optics 26, 3474�??3478 (1987).
    [CrossRef] [PubMed]
  28. K. Deb and R. B. Agrawal, �??Simulated binary crossover for continuous search space,�?? Complex Systems 9, 115�??148 (1995).
  29. J. B. Tenenbaum, V. de Silva, and J. C. Langford, �??A Global Geometric Framework for Nonlinear Dimensionality Reduction,�?? Science 290, 2319�??2323 (2000).
    [CrossRef] [PubMed]

Appl. Opt. (1)

Applied Optics (1)

M. Yamada and K. Sakuda, �??Analysis of almost-periodic distributed feedback slab waveguide via a fundamental matrix approach,�?? Applied Optics 26, 3474�??3478 (1987).
[CrossRef] [PubMed]

Complex Systems (1)

K. Deb and R. B. Agrawal, �??Simulated binary crossover for continuous search space,�?? Complex Systems 9, 115�??148 (1995).

Eng. Comp. (1)

S. Manos and L. Poladian, �??Optical fibre design using Evolutionary Strategies,�?? Eng. Comp. 21, 564�??576 (2004).
[CrossRef]

Fiber Int. Opt. (1)

C. L. Lee and Y. C. Lai, �??Long-Period Fiber Grating Filter Synthesis Using Evolutionary Programming,�?? Fiber Int. Opt. 23, 249�??261 (2004).
[CrossRef]

Genetic Algorithms 1985 (1)

J. D. Schaffer, �??Multiple objective optimization with vector evaluated genetic algorithms,�?? in Proc. of the First Int. Conf. on Genetic Algorithms, pp. 93�??100 (1985).

IEEE J. Quantum Electron. (1)

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. 35, 1105�??1115 (1999).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

C. L. Lee and Y. Lai, �??Evolutionary Programming Synthesis of Optimal Long-Period Fiber Grating Filters for EDFA Gain Flattening,�?? IEEE Photonics Technol. Lett. 14, 1557�??1559 (2002).
[CrossRef]

IEEE Trans. Sys. Man and Cyb. (1)

Y. Y. Haimes, L. S. Lasdon, and D. A. Wismer, �??On a bicriterion formulation of the problems of intergrated system identification and system optimization,�?? IEEE Trans. Sys. Man and Cyb. 1, 296�??297 (1971).
[CrossRef]

IEEE Transactions on Evolutionary Comput (1)

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, �??A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II,�?? IEEE Transactions on Evolutionary Computation 6, 182�??197 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

Meas. Sci. Technol. (1)

A. Gill, K. Peters, and M. Studer, �??Genetic Algorithm for the Reconstruction of Bragg Grating Sensor Strain Profiles,�?? Meas. Sci. Technol. 15, 1877�??1884 (2004).
[CrossRef]

Microwave Opt. Techn. Lett. (1)

D. Correia, V. F. Rodriguez-Esquerre, and H. E. Hernandez-Figueroa, �??Genetic-Algorithm and Finite-Element Approach to the Synthesis of Dispersion-Flattened Fiber,�?? Microwave Opt. Techn. Lett. 31, 245�??248 (2001).
[CrossRef]

Opt. Comm. (4)

H.-C. Cheng and Y.-L. Lo, �??Arbitrary Strain Distribution Measurement Using a Genetic Algorithm Approach and Two Fiber Bragg Grating Intensity Spectra,�?? Opt. Comm. 239, 323�??332 (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. Comm. 2004, 79�??83 (241).

P. Dong, J. Azana, and A. G. Kirk, �??Synthesis of Fiber Bragg Grating Parameters from Reflectivity by Means of a Simulated Annealing Algorithm,�?? Opt. Comm. 228, 303�??308 (2003).
[CrossRef]

C. Caucheteur, F. Lhomme, K. Chah, M. Blondel, and P. Megret, �??Fiber Bragg Grating Sensor Demodulation Technique by Synthesis of Grating Parameters from its Reflection Spectrum,�?? Opt. Comm. 240, 329�??336 (2004).
[CrossRef]

Opt. Commun. (1)

C. L. Lee and Y. C. Lai, �??Optimal Narrowband Dispersion Less Fiber Bragg Grating Filters with Short Grating Length and Smooth Dispersion Profile,�?? Opt. Commun. 235, 99�??106 (2004).
[CrossRef]

Opt. Eng. (1)

S. F. Shu, Y. Lai, and C. L. Pan, �??Learning Evolution Design of Multiband-Transmission Fiber Grating Filters,�?? Opt. Eng. 42, 2856�??2860 (2003).
[CrossRef]

Opt. Lett. (1)

OptoElectronics and Communications 2003 (1)

M. Attygalle, B. Ashton, A. Nirmalathas, L. Poladian, and W. Padden, �??Novel technique for all-optical clock extraction using fibre bragg gratings,�?? in OptoElectronics and Communications Conference, Shanghai, China, pp. 13�??16 (2003).

Science (1)

J. B. Tenenbaum, V. de Silva, and J. C. Langford, �??A Global Geometric Framework for Nonlinear Dimensionality Reduction,�?? Science 290, 2319�??2323 (2000).
[CrossRef] [PubMed]

Other (3)

D. E. Goldberg, Genetic Algorithms for Search, Optimization and Machine Learning (Addison-Wesley, 1989).

E. Zitzler, M. Laumanns, and L. Thiele, �??SPEA2: Improving the Strength Pareto Evolutionary Algorithm,�?? Tech. Rep. 103, Gloriastrasse 35, CH-8092 Zurich, Switzerland (2001). URL <a href="http://citeseer.ist.psu.edu/">http://citeseer.ist.psu.edu/</a>

S. Baskar, A. Alphones, N. Q. Ngo, P. N. Suganthan, and P. Shun, �??Design of Optimal Length Low-Dispersion FBG Filter Using Covariance Matrix Adapted Evolution,�?? Opt. Express To Appear (2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

Overview of the FBG design parameters and there contribution to various features of the profile.

Fig. 2.
Fig. 2.

Outline of the various spectral traits extracted using a peak-finding algorithm and used to evaluate the objectives of a design.

Fig. 3.
Fig. 3.

Scatterplots of FBG solutions in design parameter space. Light grey dots indicate the initial population, and black dots indicate the final non-dominated set after 1000 generations.

Fig. 4.
Fig. 4.

Visualisation of the four dimensional non-dominated set in three dimensions after dimensionality reduction. The axis of the FBG spectra and profiles have been removed for clarity but are in the range λ → [1549.5,1550.5] nm, T → [-90,0] dB for the spectra and z → [-1,1] cm, q 0 → [0,10]cm-1 for the FBG profiles. The red lines represent the phase profile in the range ϕ → [0, π] . The two clusters labeled A and B were extracted using a hierarchical clustering algorithm. The designs labeled I, II, III, IV correspond to the corner designs shown in greater detail in Fig. 5.

Fig. 5.
Fig. 5.

Transmission spectra and FBG q and phase ϕ profiles of the four designs corresponding to the corner designs on the non-dominated set (Fig. 4). Designs I and IV are most optimal with respect to bandwidth, but design I simultaneously exhibits the worst (widest) peak separation. Design II is the best with respect to peak separation, but worst in terms of the transmission. Design III simultaneously exhibits optimal peak full-width half-maximum and transmission objectives, but average bandwidth and peak separation objectives.

Fig. 6.
Fig. 6.

Instead of looking at non-linear reduction from 4 dimensions to 3 dimensions as in Fig. 4, we can further reduce the non-dominated set to 2 dimensions. Values of the design variables L,z 0,α,n can then be shown as height above the x-y plane, giving us an indication of how the design variables change as you move around the designs which form the non-dominated set. The plots for q 0, ϕ are not shown since they are relatively constant across the population with average values of q 0ϕ = 9.997cm-1 and ϕ ¯ =π.

Fig. 7.
Fig. 7.

Plots for the transmission, bandwidth, peak separation and peak FWHM objective values across the 2-dimensional representation of the non-dominated set. The tradeoff and harmony between spectral characteristics is obvious here, for example, minimal FWHM results in non-optimal BW (conflicting relationship) but on the other hand results in optimal transmission (harmonious relationship).

Tables (3)

Tables Icon

Table 1. Outline of the parameter bounds

Tables Icon

Table 2. Minimum and maximum values of the FBG design parameters in the non-dominated set.

Tables Icon

Table 3. Minimum and maximum values of the FBG spectral characteristics and objectives in the non-dominated set.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

F = λ i w i R ( λ i ) R ̄ ( λ i ) p
f i ( a ) f i ( b ) , i = 1 , , M and ∃i ( 1 , , M ) , f i ( a ) < f i ( b )
q ( z ) = q 0 cos α ( π 2 2 z L n ) e ( z )
+ iu z δ + δu z δ + q ( z ) e + ( z ) v z δ = 0
+ iv z δ + δv z δ + q ( z ) e - ( z ) u z δ = 0
δ = 2 π n ̄ ( 1 λ 1 λ B )
T κ = [ cosh ( qh ) sinh ( qh ) e + sinh ( qh ) e cosh ( qh ) ]
T δ = [ e + iδh 0 0 e iδh ]
[ u ( L 2 ) v ( L 2 ) ] = T κ T δ T κ T δ [ u ( L 2 ) v ( L 2 ) ]
T dB ( λ ) = 20 log 10 1 u ( L 2 )

Metrics