Progress In Electromagnetics Research M
ISSN: 1937-8726
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 49 > pp. 153-165


By A.-K. S. O. Hassan, A. S. A. Mohamed, M. M. Taha, and N. H. Rafat

Full Article PDF (504 KB)

A statistical design centering approach is introduced, to achieve the optimal design center point of one-dimensional photonic crystal-based filters which are parts of several optoelectronic systems. Up to our knowledge, it is the first time that a design centering approach is applied to such a design problem. The proposed approach seeks nominal designable parameter values that maximize the probability of satisfying the design specifications (yield function). Thus, the achieved optimal design center point is much more robust to unavoidable designable parameter variations, occurring during fabrication process, for example. The yield maximization problem is formulated as an unconstrained optimization problem solved by derivative-free based-algorithm (NEWUOA) coupled with a variance reduction yield estimator to reduce large number of required system simulations. The flexibility and efficiency of the proposed design centering approach are demonstrated by two practical examples: band pass optical filter and spectral control filter. A comparison with Minimax optimization technique is also given.

A.-K. S. O. Hassan, A. S. A. Mohamed, M. M. Taha, and N. H. Rafat, "Statistical Design Centering Optimization of 1D Photonic Crystal Filters," Progress In Electromagnetics Research M, Vol. 49, 153-165, 2016.

1. John, S. and K. Busch, "Photonic bandgap formation and tunability in certain self-organizing systems," J. Lightwave Technology, Vol. 17, No. 11, 1931-1943, 1999.

2. Lee, C., R. Radhakrishnan, C.-C. Chen, J. Li, J. Thillaigovindan, and N. Balasubramanian, "Design and modeling of a nanomechanical sensor using silicon photonic crystals," J. Lightwave Technology, Vol. 26, No. 7, 839-846, 2008.

3. Prather, D. W., Photonic Crystals, Theory, Applications and Fabrication, John Wiley & Sons, 2009.

4. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, Princeton University Press, 2011.

5. Celanovic, I., F. O. Sullivan, M. Ilak, J. Kassakian, and D. Perreault, "Design and optimization of one dimensional photonic crystals for thermophotovoltaic applications," Optics Letters, Vol. 29, No. 8, 863-865, 2004.

6. Del Villar, I., I. R. Matias, and F. J. Arregui, "Fiber-optic multiple-wavelength filter based on one-dimensional photonic bandgap structures with defects," J. Lightwave Technology, Vol. 22, No. 6, 1615-1621, 2004.

7. Kurt, H. and D. S. Citrin, "Photonic crystals for biochemical sensing in the terahertz region," Applied Physics Letters, Vol. 87, No. 4, 041108-041108, 2005.

8. Chubb, D., Fundamentals of Thermophotovoltaic Energy Conversion, Elsevier, 2007.

9. Swillam, M. A., M. H. Bakr, and X. Li, "The design of multilayer optical coatings using convex optimization," J. Lightwave Technology, Vol. 25, No. 4, 1078-1085, 2007.

10. Baedi, J., H. Arabshahi, M. G. Armaki, and E. Hosseini, "Optical design of multilayer filter by using pso algorithm," Research Journal of Applied Sciences, Engineering and Technology, Vol. 2, No. 1, 56-59, 2010.

11. Xu, J., "Optimization of construction of multiple one dimensional photonic crystals to extend bandgap by genetic algorithm," J. Lightwave Technology, Vol. 28, No. 7, 1114-1120, 2010.

12. Rafat, N. H., S. A. El-Naggar, and S. I. Mostafa, "Modeling of a wide band pass optical filter based on 1d ternary dielectric-metallic-dielectric photonic crystals," J. Optics, Vol. 13, No. 8, 085101, 2011.

13. Jia, W., J. Deng, B. P. L. Reid, X. Wang, C. Chan, H. Wu, X. Li, R. A. Taylor, and A. J. Danner, "Design and fabrication of optical filters with very large stopband (500 nm) and small passband (1 nm) in silicon-on insulator," Photonics and Nanostructures-Fundamentals and Applications, Vol. 10, No. 4, 447-451, 2012.

14. Mostafa, S. I., N. H. Rafat, and S. A. El-Naggar, "One-dimensional metallic-dielectric (Ag/Sio2) photonic crystals filter for thermophotovoltaic applications," Renewable Energy, Vol. 45, 245-250, 2012.

15. Badaoui, H. A. and M. Abri, "One-dimensional photonic crystal selective filters design using simulated annealing optimization technique," Progress In Electromagnetics Research B, Vol. 53, 107-129, 2013.

16. Hassan, A. S. O., A. S. A. Mohamed, M. M. T. Maghrabi, and N. H. Rafat, "Optimal design of one-dimensional photonic crystal filters using minimax optimization approach," Applied Optics, Vol. 54, No. 6, 1399-1409, 2015.

17. Asghar, M. H., M. Shoaib, F. Placido, and S. Naseem, "Wide bandpass optical filters with TiO2 and Ta2O5," Cent. Eur. J. Phys., Vol. 6, No. 4, 853-863, 2008.

18. Hassan, A. S. O. and A. S. A. Mohamed, "Surrogate-based circuit design centering," Surrogate-Based Modeling and Optimization, 27-49, Springer, 2013.

19. Zaabab, A. H., Q.-J. Zhang, and M. Nakhla, "A neural network modelling approach to circuit optimization and statistical design," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 6, 1349-1358, 1995.

20. Keramat, M. and R. Kielbasa, "A study of stratified sampling in variance reduction techniques for parametric yield estimation," IEEE Trans Circuits and Systems II: Analog and Digital Signal Processing, Vol. 45, No. 5, 575-583, 1998.

21. Hassan, A. S. O., H. L. Abdel-Malek, and A. A. Rabie, "Non-derivative design centering algorithm using trust region optimization and variance reduction," Eng. Opt., Vol. 38, No. 1, 37-51, 2006.

22. Hassan, A. S. O., A. S. A. Mohamed, and A. Y. El-Sharabasy, "EM-based yield optimization exploiting trust region optimization and space mapping technology," Int. J. RF and Microwave Computer-Aided Engineering, Vol. 25, No. 6, 474-484, 2015.

23. Powell, M. J. D., The Newuoa Software for Unconstrained Optimization Without Derivatives. Large-scale Nonlinear Optimization, 255-297, Springer, 2006.

24. Powell, M. J. D., "A view of algorithms for optimization without derivatives," Mathematics Today-Bulletin of the Institute of Mathematics and its Applications, Vol. 43, No. 5, 170-174, 2007.

25. McKay, M. D., R. J. Beckman, and W. J. Conover, "Comparison of three methods for selecting values of input variables in the analysis of output from a computer code," Technometrics, Vol. 21, No. 2, 239-245, 1979.

26. Metropolis, N. and S. Ulam, "The monte carlo method," J. the American Statistical Association, Vol. 44, No. 247, 335-341, 1949.

27. Hocevar, D. E., M. R. Lightner, and T. N. Trick, "A study of variance reduction techniques for estimating circuit yields," IEEE Trans Computer-Aided Design of Integrated Circuits and Systems, Vol. 2, No. 3, 180-192, 1983.

28. Pendry, J., "Photonic band structures," J. Modern Optics, Vol. 41, No. 2, 209-229, 1994.

29. Ni, X., Z. Liu, and A. V. Kildishev, PhotonicsDB: Optical Constants, 2010, http://nanohub.org/resources/PhotonicsDB/usage.

© Copyright 2010 EMW Publishing. All Rights Reserved