Abstract

In this paper, we introduce a simulation-driven optimization approach for achieving the optimal design of electromagnetic wave (EMW) filters consisting of one-dimensional (1D) multilayer photonic crystal (PC) structures. The PC layers’ thicknesses and/or material types are considered as designable parameters. The optimal design problem is formulated as a minimax optimization problem that is entirely solved by making use of readily available software tools. The proposed approach allows for the consideration of problems of higher dimension than usually treated before. In addition, it can proceed starting from bad initial design points. The validity, flexibility, and efficiency of the proposed approach is demonstrated by applying it to obtain the optimal design of two practical examples. The first is (SiC/Ag/SiO2)N wide bandpass optical filter operating in the visible range. Contrarily, the second example is (Ag/SiO2)N EMW low pass spectral filter, working in the infrared range, which is used for enhancing the efficiency of thermophotovoltaic systems. The approach shows a good ability to converge to the optimal solution, for different design specifications, regardless of the starting design point. This ensures that the approach is robust and general enough to be applied for obtaining the optimal design of all 1D photonic crystals promising applications.

© 2015 Optical Society of America

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References

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    [Crossref]
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  25. C. Charalambous and A. Conn, “An efficient method to solve the minimax problem directly,” SIAM Journal on Numerical Analysis 15, 162–187 (1978).
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  26. J. W. Bandler, W. Kellermann, and K. Madsen, “A superlinearly convergent minimax algorithm for microwave circuit design,” IEEE Trans. Microwave Theory Tech. 33, 1519–1530 (1985).
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    [Crossref]
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    [Crossref]
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2013 (1)

H. A. Badaoui and M. Abri, “One-dimensional photonic crystal selective filters design using simulated annealing optimization technique,” Prog. Electromagn. Res. B 53, 107–125 (2013).

2012 (5)

J. He, P. Liu, Y. He, and Z. Hong, “Narrow bandpass tunable terahertz filter based on photonic crystal cavity,” Appl. Opt. 51, 776–779 (2012).
[Crossref]

G. Nehmetallah, R. Aylo, P. Powers, A. Sarangan, J. Gao, H. Li, A. Achari, and P. Banerjee, “Co-sputtered sic+Ag nanomixtures as visible wavelength negative index metamaterials,” Opt. Express 20, 7095–7100 (2012).
[Crossref]

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

S. I. Mostafa, N. H. Rafat, and S. A. El-Naggar, “One-dimensional metallic-dielectric (Ag/SiO2) photonic crystals filter for thermophotovoltaic applications,” Renewable Energy 45, 245–250 (2012).
[Crossref]

A.-K. S. Hassan and A. Abdel-Naby, “A new hybrid method for optimal circuit design using semi-definite programming,” Engineering Optimization 44, 725–740 (2012).
[Crossref]

2011 (4)

Y. Xuan, X. Chen, and Y. Han, “Design and analysis of solar thermophotovoltaic systems,” Renewable Energy 36, 374–387 (2011).
[Crossref]

N. H. Rafat, 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. Opt. 13, 085101 (2011).
[Crossref]

Y. Ohtera, D. Kurniatan, and H. Yamada, “Design and fabrication of multichannel Si/SiO2 autocloned photonic crystal edge filters,” Appl. Opt. 50, C50–C54 (2011).
[Crossref]

A. Baldycheva, V. A. Tolmachev, T. S. Perova, Y. A. Zharova, E. V. Astrova, and K. Berwick, “Silicon photonic crystal filter with ultrawide passband characteristics,” Opt. Lett. 36, 1854–1856 (2011).
[Crossref]

2010 (2)

J. Xu, “Optimization of construction of multiple one-dimensional photonic crystals to extend bandgap by genetic algorithm,” J. Lightwave Technol. 28, 1114–1120 (2010).

J. Baedi, H. Arabshahi, M. G. Armaki, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

2009 (3)

X.-F. Xu and J.-Y. Ding, “A wide band-pass filter of broad angle incidence based on one-dimensional metallo-dielectric ternary photonic crystal,” Opt. Quantum Electron. 41, 1027–1032 (2009).
[Crossref]

M. H. Asghar, M. Shoaib, F. Placido, and S. Naseem, “Modeling and preparation of practical optical filters,” Curr. Appl. Phys. 9, 1046–1053 (2009).
[Crossref]

S. Chen, Y. Wang, D. Yao, and Z. Song, “Absorption enhancement in 1D Ag/SiO2 metallic-dielectric photonic crystals,” Opt. Appl. 39, 473–479 (2009).

2007 (1)

2005 (2)

Z. Jakšić, M. Maksimović, and M. Sarajlić, “Silver–silica transparent metal structures as bandpass filters for the ultraviolet range,” J. Opt. A 7, 51–55 (2005).
[Crossref]

H. Kurt and D. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).
[Crossref]

2004 (1)

2003 (1)

A.-K. S. Hassan, “Normed distances and their applications in optimal circuit design,” Optim. Eng. 4, 197–213 (2003).

1994 (1)

J. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209–229 (1994).
[Crossref]

1985 (1)

J. W. Bandler, W. Kellermann, and K. Madsen, “A superlinearly convergent minimax algorithm for microwave circuit design,” IEEE Trans. Microwave Theory Tech. 33, 1519–1530 (1985).

1981 (1)

J. Hald and K. Madsen, “Combined LP and quasi-Newton methods for minimax optimization,” Mathematical Programming 20, 49–62 (1981).
[Crossref]

1978 (1)

C. Charalambous and A. Conn, “An efficient method to solve the minimax problem directly,” SIAM Journal on Numerical Analysis 15, 162–187 (1978).
[Crossref]

1967 (1)

A. D. Waren, L. S. Lasdon, and D. F. Suchman, “Optimization in engineering design,” Proc. IEEE 55, 1885–1897 (1967).
[Crossref]

Abdel-Naby, A.

A.-K. S. Hassan and A. Abdel-Naby, “A new hybrid method for optimal circuit design using semi-definite programming,” Engineering Optimization 44, 725–740 (2012).
[Crossref]

Abri, M.

H. A. Badaoui and M. Abri, “One-dimensional photonic crystal selective filters design using simulated annealing optimization technique,” Prog. Electromagn. Res. B 53, 107–125 (2013).

Achari, A.

Aliyazicioglu, Z.

J. Jen, M. Qian, Z. Aliyazicioglu, and H. Hwang, “Performance studies of antenna pattern design using the minimax algorithm,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Signal and Telecommunications (World Scientific and Engineering Academy and Society, 2011), pp. 50–55.

Arabshahi, H.

J. Baedi, H. Arabshahi, M. G. Armaki, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Armaki, M. G.

J. Baedi, H. Arabshahi, M. G. Armaki, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Asghar, M. H.

M. H. Asghar, M. Shoaib, F. Placido, and S. Naseem, “Modeling and preparation of practical optical filters,” Curr. Appl. Phys. 9, 1046–1053 (2009).
[Crossref]

Astrova, E. V.

Aylo, R.

Badaoui, H. A.

H. A. Badaoui and M. Abri, “One-dimensional photonic crystal selective filters design using simulated annealing optimization technique,” Prog. Electromagn. Res. B 53, 107–125 (2013).

Baedi, J.

J. Baedi, H. Arabshahi, M. G. Armaki, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Bakr, M. H.

Baldycheva, A.

Bandler, J. W.

J. W. Bandler, W. Kellermann, and K. Madsen, “A superlinearly convergent minimax algorithm for microwave circuit design,” IEEE Trans. Microwave Theory Tech. 33, 1519–1530 (1985).

Banerjee, P.

Berwick, K.

Celanovic, I.

Chan, C.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

Charalambous, C.

C. Charalambous and A. Conn, “An efficient method to solve the minimax problem directly,” SIAM Journal on Numerical Analysis 15, 162–187 (1978).
[Crossref]

Chemmangat, K.

K. Chemmangat, F. Ferranti, T. Dhaene, and L. Knockaert, “Optimization of high-speed electromagnetic systems with accurate parametric macromodels generated using sequential sampling of the design space,” in International Conference on Electromagnetics in Advanced Applications (IEEE, 2012), pp. 128–131.

Chen, S.

S. Chen, Y. Wang, D. Yao, and Z. Song, “Absorption enhancement in 1D Ag/SiO2 metallic-dielectric photonic crystals,” Opt. Appl. 39, 473–479 (2009).

Chen, X.

Y. Xuan, X. Chen, and Y. Han, “Design and analysis of solar thermophotovoltaic systems,” Renewable Energy 36, 374–387 (2011).
[Crossref]

Chubb, D.

D. Chubb, Fundamentals of Thermophotovoltaic Energy Conversion (Elsevier, 2007).

Citrin, D.

H. Kurt and D. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).
[Crossref]

Conn, A.

C. Charalambous and A. Conn, “An efficient method to solve the minimax problem directly,” SIAM Journal on Numerical Analysis 15, 162–187 (1978).
[Crossref]

Danner, A. J.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

Deng, J.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

Dhaene, T.

K. Chemmangat, F. Ferranti, T. Dhaene, and L. Knockaert, “Optimization of high-speed electromagnetic systems with accurate parametric macromodels generated using sequential sampling of the design space,” in International Conference on Electromagnetics in Advanced Applications (IEEE, 2012), pp. 128–131.

Ding, J.-Y.

X.-F. Xu and J.-Y. Ding, “A wide band-pass filter of broad angle incidence based on one-dimensional metallo-dielectric ternary photonic crystal,” Opt. Quantum Electron. 41, 1027–1032 (2009).
[Crossref]

El-Naggar, S. A.

S. I. Mostafa, N. H. Rafat, and S. A. El-Naggar, “One-dimensional metallic-dielectric (Ag/SiO2) photonic crystals filter for thermophotovoltaic applications,” Renewable Energy 45, 245–250 (2012).
[Crossref]

N. H. Rafat, 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. Opt. 13, 085101 (2011).
[Crossref]

El-Sharabasy, A. Y.

A.-K. Hassan, A. S. Mohamed, and A. Y. El-Sharabasy, “Statistical microwave circuit optimization via a non-derivative trust region approach and space mapping surrogates,” in Microwave Symposium Digest (MTT), IEEE MTT-S International (IEEE, 2011), pp. 1–4.

Ferranti, F.

K. Chemmangat, F. Ferranti, T. Dhaene, and L. Knockaert, “Optimization of high-speed electromagnetic systems with accurate parametric macromodels generated using sequential sampling of the design space,” in International Conference on Electromagnetics in Advanced Applications (IEEE, 2012), pp. 128–131.

Gao, J.

Hald, J.

J. Hald and K. Madsen, “Combined LP and quasi-Newton methods for minimax optimization,” Mathematical Programming 20, 49–62 (1981).
[Crossref]

Han, Y.

Y. Xuan, X. Chen, and Y. Han, “Design and analysis of solar thermophotovoltaic systems,” Renewable Energy 36, 374–387 (2011).
[Crossref]

Hassan, A.-K.

A.-K. Hassan, A. S. Mohamed, and A. Y. El-Sharabasy, “Statistical microwave circuit optimization via a non-derivative trust region approach and space mapping surrogates,” in Microwave Symposium Digest (MTT), IEEE MTT-S International (IEEE, 2011), pp. 1–4.

Hassan, A.-K. S.

A.-K. S. Hassan and A. Abdel-Naby, “A new hybrid method for optimal circuit design using semi-definite programming,” Engineering Optimization 44, 725–740 (2012).
[Crossref]

A.-K. S. Hassan, “Normed distances and their applications in optimal circuit design,” Optim. Eng. 4, 197–213 (2003).

He, J.

He, Y.

Hong, Z.

Hosseini, E.

J. Baedi, H. Arabshahi, M. G. Armaki, and E. Hosseini, “Optical design of multilayer filter by using PSO algorithm,” Res. J. Appl. Sci. Eng. Technol. 2, 56–59 (2010).

Hwang, H.

J. Jen, M. Qian, Z. Aliyazicioglu, and H. Hwang, “Performance studies of antenna pattern design using the minimax algorithm,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Signal and Telecommunications (World Scientific and Engineering Academy and Society, 2011), pp. 50–55.

Ilak, M.

Jakšic, Z.

Z. Jakšić, M. Maksimović, and M. Sarajlić, “Silver–silica transparent metal structures as bandpass filters for the ultraviolet range,” J. Opt. A 7, 51–55 (2005).
[Crossref]

Jen, J.

J. Jen, M. Qian, Z. Aliyazicioglu, and H. Hwang, “Performance studies of antenna pattern design using the minimax algorithm,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Signal and Telecommunications (World Scientific and Engineering Academy and Society, 2011), pp. 50–55.

Jia, W.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

Joannopoulos, J. D.

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

Johnson, S. G.

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

Kassakian, J.

Kellermann, W.

J. W. Bandler, W. Kellermann, and K. Madsen, “A superlinearly convergent minimax algorithm for microwave circuit design,” IEEE Trans. Microwave Theory Tech. 33, 1519–1530 (1985).

Knockaert, L.

K. Chemmangat, F. Ferranti, T. Dhaene, and L. Knockaert, “Optimization of high-speed electromagnetic systems with accurate parametric macromodels generated using sequential sampling of the design space,” in International Conference on Electromagnetics in Advanced Applications (IEEE, 2012), pp. 128–131.

Koziel, S.

S. Koziel and L. Leifsson, Surrogate-Based Modeling and Optimization (Springer, 2013).

Kurniatan, D.

Kurt, H.

H. Kurt and D. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).
[Crossref]

Lasdon, L. S.

A. D. Waren, L. S. Lasdon, and D. F. Suchman, “Optimization in engineering design,” Proc. IEEE 55, 1885–1897 (1967).
[Crossref]

Leifsson, L.

S. Koziel and L. Leifsson, Surrogate-Based Modeling and Optimization (Springer, 2013).

Li, H.

Li, X.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

M. A. Swillam, M. H. Bakr, and X. Li, “The design of multilayer optical coatings using convex optimization,” J. Lightwave Technol. 25, 1078–1085 (2007).

Liu, P.

Madsen, K.

J. W. Bandler, W. Kellermann, and K. Madsen, “A superlinearly convergent minimax algorithm for microwave circuit design,” IEEE Trans. Microwave Theory Tech. 33, 1519–1530 (1985).

J. Hald and K. Madsen, “Combined LP and quasi-Newton methods for minimax optimization,” Mathematical Programming 20, 49–62 (1981).
[Crossref]

Maksimovic, M.

Z. Jakšić, M. Maksimović, and M. Sarajlić, “Silver–silica transparent metal structures as bandpass filters for the ultraviolet range,” J. Opt. A 7, 51–55 (2005).
[Crossref]

Meade, R. D.

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

Mohamed, A. S.

A.-K. Hassan, A. S. Mohamed, and A. Y. El-Sharabasy, “Statistical microwave circuit optimization via a non-derivative trust region approach and space mapping surrogates,” in Microwave Symposium Digest (MTT), IEEE MTT-S International (IEEE, 2011), pp. 1–4.

Mostafa, S. I.

S. I. Mostafa, N. H. Rafat, and S. A. El-Naggar, “One-dimensional metallic-dielectric (Ag/SiO2) photonic crystals filter for thermophotovoltaic applications,” Renewable Energy 45, 245–250 (2012).
[Crossref]

N. H. Rafat, 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. Opt. 13, 085101 (2011).
[Crossref]

Naseem, S.

M. H. Asghar, M. Shoaib, F. Placido, and S. Naseem, “Modeling and preparation of practical optical filters,” Curr. Appl. Phys. 9, 1046–1053 (2009).
[Crossref]

Nehmetallah, G.

O’Sullivan, F.

Ohtera, Y.

Pendry, J.

J. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209–229 (1994).
[Crossref]

Perova, T. S.

Perreault, D.

Placido, F.

M. H. Asghar, M. Shoaib, F. Placido, and S. Naseem, “Modeling and preparation of practical optical filters,” Curr. Appl. Phys. 9, 1046–1053 (2009).
[Crossref]

Powers, P.

Prather, D. W.

D. W. Prather, Photonic Crystals, Theory, Applications and Fabrication, Vol. 68 (Wiley, 2009).

Qian, M.

J. Jen, M. Qian, Z. Aliyazicioglu, and H. Hwang, “Performance studies of antenna pattern design using the minimax algorithm,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Signal and Telecommunications (World Scientific and Engineering Academy and Society, 2011), pp. 50–55.

Rafat, N. H.

S. I. Mostafa, N. H. Rafat, and S. A. El-Naggar, “One-dimensional metallic-dielectric (Ag/SiO2) photonic crystals filter for thermophotovoltaic applications,” Renewable Energy 45, 245–250 (2012).
[Crossref]

N. H. Rafat, 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. Opt. 13, 085101 (2011).
[Crossref]

Reid, B. P.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

Sarajlic, M.

Z. Jakšić, M. Maksimović, and M. Sarajlić, “Silver–silica transparent metal structures as bandpass filters for the ultraviolet range,” J. Opt. A 7, 51–55 (2005).
[Crossref]

Sarangan, A.

Shoaib, M.

M. H. Asghar, M. Shoaib, F. Placido, and S. Naseem, “Modeling and preparation of practical optical filters,” Curr. Appl. Phys. 9, 1046–1053 (2009).
[Crossref]

Song, Z.

S. Chen, Y. Wang, D. Yao, and Z. Song, “Absorption enhancement in 1D Ag/SiO2 metallic-dielectric photonic crystals,” Opt. Appl. 39, 473–479 (2009).

Suchman, D. F.

A. D. Waren, L. S. Lasdon, and D. F. Suchman, “Optimization in engineering design,” Proc. IEEE 55, 1885–1897 (1967).
[Crossref]

Swillam, M. A.

Taylor, R. A.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

Tolmachev, V. A.

Wang, X.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

Wang, Y.

S. Chen, Y. Wang, D. Yao, and Z. Song, “Absorption enhancement in 1D Ag/SiO2 metallic-dielectric photonic crystals,” Opt. Appl. 39, 473–479 (2009).

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A. D. Waren, L. S. Lasdon, and D. F. Suchman, “Optimization in engineering design,” Proc. IEEE 55, 1885–1897 (1967).
[Crossref]

Winn, J. N.

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

Wu, H.

W. Jia, J. Deng, B. P. 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,” Photon. Nanostruct. Fundamentals Appl. 10, 447–451 (2012).

Xu, J.

Xu, X.-F.

X.-F. Xu and J.-Y. Ding, “A wide band-pass filter of broad angle incidence based on one-dimensional metallo-dielectric ternary photonic crystal,” Opt. Quantum Electron. 41, 1027–1032 (2009).
[Crossref]

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Y. Xuan, X. Chen, and Y. Han, “Design and analysis of solar thermophotovoltaic systems,” Renewable Energy 36, 374–387 (2011).
[Crossref]

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Yao, D.

S. Chen, Y. Wang, D. Yao, and Z. Song, “Absorption enhancement in 1D Ag/SiO2 metallic-dielectric photonic crystals,” Opt. Appl. 39, 473–479 (2009).

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Appl. Opt. (2)

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H. Kurt and D. Citrin, “Photonic crystals for biochemical sensing in the terahertz region,” Appl. Phys. Lett. 87, 041108 (2005).
[Crossref]

Curr. Appl. Phys. (1)

M. H. Asghar, M. Shoaib, F. Placido, and S. Naseem, “Modeling and preparation of practical optical filters,” Curr. Appl. Phys. 9, 1046–1053 (2009).
[Crossref]

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[Crossref]

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N. H. Rafat, 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. Opt. 13, 085101 (2011).
[Crossref]

J. Opt. A (1)

Z. Jakšić, M. Maksimović, and M. Sarajlić, “Silver–silica transparent metal structures as bandpass filters for the ultraviolet range,” J. Opt. A 7, 51–55 (2005).
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S. Chen, Y. Wang, D. Yao, and Z. Song, “Absorption enhancement in 1D Ag/SiO2 metallic-dielectric photonic crystals,” Opt. Appl. 39, 473–479 (2009).

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

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[Crossref]

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H. A. Badaoui and M. Abri, “One-dimensional photonic crystal selective filters design using simulated annealing optimization technique,” Prog. Electromagn. Res. B 53, 107–125 (2013).

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Y. Xuan, X. Chen, and Y. Han, “Design and analysis of solar thermophotovoltaic systems,” Renewable Energy 36, 374–387 (2011).
[Crossref]

S. I. Mostafa, N. H. Rafat, and S. A. El-Naggar, “One-dimensional metallic-dielectric (Ag/SiO2) photonic crystals filter for thermophotovoltaic applications,” Renewable Energy 45, 245–250 (2012).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. Basic structure of a 1D PC filter.
Fig. 2.
Fig. 2. Flow diagram for the proposed optimization algorithm.
Fig. 3.
Fig. 3. (a) Transmittance and (b) absorbance of ( SiC / Ag / SiO 2 ) 5 , before and after optimization, starting from an initial point: d 1 = 20 nm , d 2 = 10 nm , and d 3 = 70 nm . The case of PSCT is considered.
Fig. 4.
Fig. 4. (a) Transmittance and (b) absorbance of ( SiC / Ag / SiO 2 ) 5 before and after the optimization. Solution A is assigned to the initial design point. The case of PLSVT is considered.
Fig. 5.
Fig. 5. (a) Transmittance and (b) absorbance of ( SiC / Ag / SiO 2 ) 5 before and after optimizing. Starting from initial point: d 1 = 3 nm , d 2 = 3 nm and d 3 = 3 nm . The case of PLSVT is considered.
Fig. 6.
Fig. 6. (a) Transmittance and (b) absorbance of ( SiC / Ag / SiO 2 ) 5 , before and after optimizing starting from initial point: d 1 = 70 nm , d 2 = 10 nm , and d 3 = 70 nm . The case of PLSVT is considered.
Fig. 7.
Fig. 7. (a) Transmittance and (b) absorbance of ( SiC / Ag / SiO 2 ) 5 before and after optimizing. Solution B is assigned to the initial design point. The case of PLSVT is considered, and the ripples constraint is taken into consideration.
Fig. 8.
Fig. 8. (a) Transmittance and (b) absorbance of the SiO 2 ( Ag / SiO 2 ) 3 spectral filter, before and after optimizing for the highest passband transmittance. The initial point is assumed as the QWTD for SiO 2 -layers, while the Ag layers are fixed to 10 nm. The obtained optimal solution is referred to as solution 1.
Fig. 9.
Fig. 9. (a) Transmittance and (b) absorbance of the SiO 2 ( Ag / SiO 2 ) 3 spectral filter, before and after optimizing for the least stopband transmittance. The initial point is assumed as the QWTD for SiO 2 layers, while the Ag layers are fixed to 10 nm. The obtained optimal solution is referred to as solution 2.
Fig. 10.
Fig. 10. (a) Transmittance and (b) absorbance of the D ( Ag / D ) 3 spectral filter, before and after optimizing for the least possible stopband transmittance, where D refers to a dielectric layer. Solution 2 is considered as an initial point. Both the refractive index of the dielectric layers and the thickness of layers are optimized.

Tables (4)

Tables Icon

Table 1. Figures of Merit of the ( SiC / Ag / SiO 2 ) 5 Filter a

Tables Icon

Table 2. Design Data of the Filter ( SiC / Ag / SiO 2 ) 5 a

Tables Icon

Table 3. Design Data of the D ( Ag / D ) 3 Spectral Filter, where D Refers to a Dielectric Layer a

Tables Icon

Table 4. Figures of Merit of the D ( Ag / D ) 3 Spectral Filter, where D Refers to a Dielectric Layer a

Equations (25)

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

× × E ( r ) = ω 2 c 2 ε r ( r ) E ( r ) ,
2 E z ( x ) x 2 + ω 2 c 2 ε r ( x ) E z ( x ) = 0 .
E j ( x ) = a j e i n j k ( x x j ) + b j e i n j k ( x x j ) ,
M j , j + 1 = [ 1 2 ( 1 + γ j ) e i n j k d j 1 2 ( 1 γ j ) e i n j k d j 1 2 ( 1 γ j ) e i n j k d j 1 2 ( 1 + γ j ) e i n j k d j ] ,
[ a j + 1 b j + 1 ] = M j , j + 1 [ a j b j ] .
[ t 0 ] = M T [ r 0 r ] .
t = ( M 11 M 12 M 21 M 22 ) r 0 and r = M 21 M 22 r 0 ,
T = n s n 0 | t | 2 and R = | r | 2 .
T I ( λ ) = { 100 % , for λ Λ p 0 % , for λ Λ s ,
U ( λ ) { τ Γ 2 < T < τ + Γ 2 , for λ Λ p T < β , for λ Λ s ,
U i { τ Γ 2 < T ( λ i ) < τ + Γ 2 , i I 1 T ( λ i ) < β , i I 2 ,
ξ l j < x j < ξ u j , j J ,
e i ( x ) < 0 , for all i I 1 I 2 ,
e i ( x ) { τ Γ 2 T ( x , λ i ) , i I 1 T ( x , λ i ) τ Γ 2 , i I 1 T ( x , λ i ) β , i I 2 .
R f = { x R n : e i ( x ) < 0 , for all i I 1 I 2 } .
min x { max i { e i ( x ) } }
ξ l j < x j < ξ u j ,
min imize z
{ z > e i ( x ) , i I ξ l j < x j < ξ u j , j J z < 0 ,
minimize z
{ f i ( z , x ) > 0 , i I x j ξ l j > 0 , j J x j + ξ u j > 0 , j J z > 0 ,
BF = Δ λ 50 / Δ λ 10 ,
P abg = 0 λ g I ( λ , T e m ) T ( λ ) d λ ,
P bbg = λ g I ( λ , T e m ) R ( λ ) d λ ,
I ( λ , T e m ) = 2 π h c 2 λ 5 ( e h c / λ K T e m 1 ) ,

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