Abstract

In this paper, we propose a method for designing Photonic Crystal (PhC) devices that consist of dielectric rods with varying size. In the proposed design method, PhC devices are modeled with the Transformation Optics (TO) approach, and then they are optimized using the gradient method. By applying the TO technique, the original device model is transformed into an equivalent model that consists of uniform and fixed-sized rods, with parameterized permittivity and permeability distributions. Therefore, mesh refinement around small rods can be avoided, and PhC devices can be simulated more efficiently. In addition, gradient of the optimization object function is calculated with the Adjoint-Variable Method (AVM), which is very efficient for optimizing devices subject to multiple design variables. The proposed method opens up a new avenue to design and optimize a variety of photonic devices for optical computing and information processing.

© 2014 Optical Society of America

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2013 (3)

O. Ozgun, M. Kuzuoglu, “Software metamaterials: Transformation media based multiscale techniques for computational electromagnetics”, J. Comput. Phys. 236, 203–219 (2013).
[CrossRef]

Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[CrossRef] [PubMed]

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design.” Opt. Express 21(18), 21693–21701 (2013).
[CrossRef] [PubMed]

2012 (4)

M. Minkov, V. Savona, “Effect of hole-shape irregularities on photonic crystal waveguides,” Opt. Lett. 37(15), 3108–3110 (2012).
[CrossRef] [PubMed]

Y. M. Liu, X. Zhang, “Recent advances in transformation optics,” Nanoscale 4(17), 5277–5292 (2012).
[CrossRef] [PubMed]

L. H. Gabrielli, D. Liu, S. G. Johnson, M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3:1217(2012).
[PubMed]

Q. Wu, J. P. Turpin, D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light: Science & Applications 1, e38; (2012).
[CrossRef]

2011 (1)

V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B 83, 085301 (2011).
[CrossRef]

2009 (1)

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

2006 (2)

K. Dossou, L. C. Botten, C. M. Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

G. Veronis, R. W. Dutton, S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29(19), 2288–2290 (2004).
[CrossRef] [PubMed]

2003 (1)

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[CrossRef]

2002 (1)

N. K. Georgieva, S. Glavic, M. H. Bakr, J. W. Bandler, “Feasible Adjoint Sensitivity Technique for EM Design Optimization,” IEEE Tans. Microwave Theory Tech. 50(12), 2751–2758 (2002).
[CrossRef]

2001 (3)

S. G. Johnson, J. D. Joanopoulos, “Block-iterative frequency-domain methods for Maxwell’s equation in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, “Guiding mechanisms in dielectric-core photonic-crystal optical waveguides,” Phys. Rev. B 64, 033308 (2001).
[CrossRef]

A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightw. Technol., 19(6), 861–865 (2001).
[CrossRef]

1996 (1)

A. J. Ward, J. B. Pendry, “Refraction and geometry in Maxwell’s equation,” J. Mod. Opt. 43(4), 773–793 (1996).
[CrossRef]

Adibi, A.

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, “Guiding mechanisms in dielectric-core photonic-crystal optical waveguides,” Phys. Rev. B 64, 033308 (2001).
[CrossRef]

Asatryan, A. A.

K. Dossou, L. C. Botten, C. M. Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
[CrossRef]

Assefa, S.

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[CrossRef]

Baehr-Jones, T.

Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[CrossRef] [PubMed]

Bakr, M. H.

N. K. Georgieva, S. Glavic, M. H. Bakr, J. W. Bandler, “Feasible Adjoint Sensitivity Technique for EM Design Optimization,” IEEE Tans. Microwave Theory Tech. 50(12), 2751–2758 (2002).
[CrossRef]

Bandler, J. W.

N. K. Georgieva, S. Glavic, M. H. Bakr, J. W. Bandler, “Feasible Adjoint Sensitivity Technique for EM Design Optimization,” IEEE Tans. Microwave Theory Tech. 50(12), 2751–2758 (2002).
[CrossRef]

Bhargava, S.

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design.” Opt. Express 21(18), 21693–21701 (2013).
[CrossRef] [PubMed]

Bienstman, P.

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[CrossRef]

Botten, L. C.

K. Dossou, L. C. Botten, C. M. Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
[CrossRef]

Brimont, A.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

Brnovic, J.

K. Dossou, L. C. Botten, C. M. Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
[CrossRef]

Chen, S.

K. Dossou, L. C. Botten, C. M. Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
[CrossRef]

Cuesta, F.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

Dossou, K.

K. Dossou, L. C. Botten, C. M. Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
[CrossRef]

Dutton, R. W.

G. Veronis, R. W. Dutton, S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29(19), 2288–2290 (2004).
[CrossRef] [PubMed]

Fan, S.

G. Veronis, R. W. Dutton, S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29(19), 2288–2290 (2004).
[CrossRef] [PubMed]

Gabrielli, L. H.

L. H. Gabrielli, D. Liu, S. G. Johnson, M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3:1217(2012).
[PubMed]

Galán, J. V.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

Galland, C.

Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[CrossRef] [PubMed]

Georgieva, N. K.

N. K. Georgieva, S. Glavic, M. H. Bakr, J. W. Bandler, “Feasible Adjoint Sensitivity Technique for EM Design Optimization,” IEEE Tans. Microwave Theory Tech. 50(12), 2751–2758 (2002).
[CrossRef]

Glavic, S.

N. K. Georgieva, S. Glavic, M. H. Bakr, J. W. Bandler, “Feasible Adjoint Sensitivity Technique for EM Design Optimization,” IEEE Tans. Microwave Theory Tech. 50(12), 2751–2758 (2002).
[CrossRef]

Griol, A.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

Guryev, I. V.

I. A. Sukhoivanov, I. V. Guryev, Photonic Crystals: Physics and Practical Modeling (Springer-Verlag, Berlin, 2009).

Håkansson, A.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

Hochberg, M.

Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[CrossRef] [PubMed]

Jensen, J. S.

Joannopoulos, J. D.

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[CrossRef]

A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightw. Technol., 19(6), 861–865 (2001).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2 (Princeton University, 2008).

Joanopoulos, J. D.

Johnson, S. G.

L. H. Gabrielli, D. Liu, S. G. Johnson, M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3:1217(2012).
[PubMed]

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[CrossRef]

S. G. Johnson, J. D. Joanopoulos, “Block-iterative frequency-domain methods for Maxwell’s equation in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2 (Princeton University, 2008).

Kolodziejski, L. A.

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[CrossRef]

Kuzuoglu, M.

O. Ozgun, M. Kuzuoglu, “Software metamaterials: Transformation media based multiscale techniques for computational electromagnetics”, J. Comput. Phys. 236, 203–219 (2013).
[CrossRef]

Lalau-Keraly, C. M.

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design.” Opt. Express 21(18), 21693–21701 (2013).
[CrossRef] [PubMed]

Lee, R. K.

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, “Guiding mechanisms in dielectric-core photonic-crystal optical waveguides,” Phys. Rev. B 64, 033308 (2001).
[CrossRef]

Lim, A. E. J.

Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[CrossRef] [PubMed]

Lipson, M.

L. H. Gabrielli, D. Liu, S. G. Johnson, M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3:1217(2012).
[PubMed]

Liu, D.

L. H. Gabrielli, D. Liu, S. G. Johnson, M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3:1217(2012).
[PubMed]

Liu, Y. M.

Y. M. Liu, X. Zhang, “Recent advances in transformation optics,” Nanoscale 4(17), 5277–5292 (2012).
[CrossRef] [PubMed]

Lo, G. Q.

Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[CrossRef] [PubMed]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides(Academic Press, 1974).

Marti, J.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

McPhedran, R. C.

K. Dossou, L. C. Botten, C. M. Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2 (Princeton University, 2008).

Mekis, A.

A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightw. Technol., 19(6), 861–865 (2001).
[CrossRef]

Miller, O. D.

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design.” Opt. Express 21(18), 21693–21701 (2013).
[CrossRef] [PubMed]

Minkov, M.

M. Minkov, V. Savona, “Effect of hole-shape irregularities on photonic crystal waveguides,” Opt. Lett. 37(15), 3108–3110 (2012).
[CrossRef] [PubMed]

Ozgun, O.

O. Ozgun, M. Kuzuoglu, “Software metamaterials: Transformation media based multiscale techniques for computational electromagnetics”, J. Comput. Phys. 236, 203–219 (2013).
[CrossRef]

Pendry, J. B.

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

A. J. Ward, J. B. Pendry, “Refraction and geometry in Maxwell’s equation,” J. Mod. Opt. 43(4), 773–793 (1996).
[CrossRef]

Petrich, G. S.

P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” J. Opt. Soc. Am. B 20, 1817–1821 (2003).
[CrossRef]

Sanchis, P.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

Savona, V.

M. Minkov, V. Savona, “Effect of hole-shape irregularities on photonic crystal waveguides,” Opt. Lett. 37(15), 3108–3110 (2012).
[CrossRef] [PubMed]

V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B 83, 085301 (2011).
[CrossRef]

Scherer, A.

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, “Guiding mechanisms in dielectric-core photonic-crystal optical waveguides,” Phys. Rev. B 64, 033308 (2001).
[CrossRef]

Schurig, D.

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Sigmund, O.

Smith, D. R.

J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Sterke, C. M.

K. Dossou, L. C. Botten, C. M. Sterke, R. C. McPhedran, A. A. Asatryan, S. Chen, J. Brnovic, “Efficient couplers for photonic crystal waveguides,” Opt. Commun. 265, 207–219 (2006).
[CrossRef]

Sukhoivanov, I. A.

I. A. Sukhoivanov, I. V. Guryev, Photonic Crystals: Physics and Practical Modeling (Springer-Verlag, Berlin, 2009).

Turpin, J. P.

Q. Wu, J. P. Turpin, D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light: Science & Applications 1, e38; (2012).
[CrossRef]

Veronis, G.

G. Veronis, R. W. Dutton, S. Fan, “Method for sensitivity analysis of photonic crystal devices,” Opt. Lett. 29(19), 2288–2290 (2004).
[CrossRef] [PubMed]

Villalba, P.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009).
[CrossRef] [PubMed]

Ward, A. J.

A. J. Ward, J. B. Pendry, “Refraction and geometry in Maxwell’s equation,” J. Mod. Opt. 43(4), 773–793 (1996).
[CrossRef]

Werner, D. H.

Q. Wu, J. P. Turpin, D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light: Science & Applications 1, e38; (2012).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2 (Princeton University, 2008).

Wu, Q.

Q. Wu, J. P. Turpin, D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light: Science & Applications 1, e38; (2012).
[CrossRef]

Xu, Y.

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, “Guiding mechanisms in dielectric-core photonic-crystal optical waveguides,” Phys. Rev. B 64, 033308 (2001).
[CrossRef]

Yablonovitch, E.

C. M. Lalau-Keraly, S. Bhargava, O. D. Miller, E. Yablonovitch, “Adjoint shape optimization applied to electromagnetic design.” Opt. Express 21(18), 21693–21701 (2013).
[CrossRef] [PubMed]

Yang, S.

Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
[CrossRef] [PubMed]

Yariv, A.

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Y. Zhang, S. Yang, A. E. J. Lim, G. Q. Lo, C. Galland, T. Baehr-Jones, M. Hochberg, “A compact and low loss Y-junction for submicron silicon waveguide,” Opt. Express 21(1), 1310–1316 (2013).
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