Abstract

We discuss different geometrical structures of optical switches based on two-dimensional photonic crystals with hexagonal geometry of the unit cell and a magneto-optical resonator. Transition between the states on and off in these switches is achieved by an external DC magnetic field. The input and output waveguides can be front–front, side–side, or front–side coupled to the resonator and these different types of coupling can lead to different mechanisms of switching. Analysis of symmetry and scattering matrices of the switches is based on magnetic group theory. Two examples of switches with 60° and 120° bends and their characteristics are also presented.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. Z. Wu, M. Levy, V. J. Fratello, and A. M. Merzlikin, “Gyrotropic photonic crystal waveguide switches,” Appl. Phys. Lett. 96, 051125 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. V. Dmitriev, “Permeability tensor versus permittivity one in theory of nonreciprocal optical components,” Photon. Nanostr. Fundam. Appl. 11, 203–209 (2013).
    [CrossRef]
  14. A. A. Barybin and V. A. Dmitriev, Modern Electrodynamics and Coupled-Mode Theory: Application to Guided-Wave Optics (Rinton, 2002).
  15. Q. Wang, Z. Ouyang, K. Tao, M. Lin, and S. Ruan, “T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal,” Phys. Lett. A 376, 646–649 (2012).
    [CrossRef]
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    [CrossRef]
  17. F. Fan, S.-J. Chang, C. Niu, Y. Hou, and X.-H. Wang, “Magnetically tunable silicon-ferrite photonic crystals for terahertz circulator,” Opt. Commun. 285, 3763–3769 (2012).
    [CrossRef]
  18. S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE J. Quantum Electron. 39, 1081–1085 (2003).
    [CrossRef]
  19. M. C. Sekhar, M. R. Singh, S. Basu, and S. Pinnepalli, “Giant Faraday rotation in BixCe3−xFe5O12 epitaxial garnet films,” Opt. Express 20, 9624–9639 (2012).
    [CrossRef]
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    [CrossRef]
  21. S. Methfessel and D. C. Mattis, “Magnetic semiconductors,” in Handbuch der Physik, S. Fliigge and H. P. J. Wijn, eds. (Springer, 1968).
  22. A. K. Zvezdin and V. A. Kotov, Modern Magneto-Optics and Magneto-Optical Materials (IOP, 1997).
  23. http://ab-initio.mit.edu .
  24. www.comsol.com .

2013 (3)

2012 (4)

Q. Wang, Z. Ouyang, K. Tao, M. Lin, and S. Ruan, “T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal,” Phys. Lett. A 376, 646–649 (2012).
[CrossRef]

F. Fan, S.-J. Chang, C. Niu, Y. Hou, and X.-H. Wang, “Magnetically tunable silicon-ferrite photonic crystals for terahertz circulator,” Opt. Commun. 285, 3763–3769 (2012).
[CrossRef]

M. C. Sekhar, M. R. Singh, S. Basu, and S. Pinnepalli, “Giant Faraday rotation in BixCe3−xFe5O12 epitaxial garnet films,” Opt. Express 20, 9624–9639 (2012).
[CrossRef]

V. Dmitriev, M. Kawakatsu, and F. J. M. de Souza, “Compact three-port optical 2D photonic crystal-based circulator of W-format,” Opt. Lett. 37, 3192–3194 (2012).
[CrossRef]

2010 (2)

2009 (1)

D. M. Beggs, T. P. White, L. Cairns, L. O’Faolain, and T. F. Krauss, “Ultrashort photonic crystal optical switch actuated by a microheater,” IEEE Photon. Technol. Lett. 21, 24–26 (2009).
[CrossRef]

2005 (3)

V. Dmitriev, “Symmetry properties of 2D magnetic photonic crystals with square lattice,” Eur. Phys. J. Appl. Phys. 32, 159–165 (2005).
[CrossRef]

Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B 81, 369–375 (2005).
[CrossRef]

Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystal,” Opt. Lett. 30, 1989–1991 (2005).
[CrossRef]

2004 (1)

2003 (2)

M. Yanik and S. Fan, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[CrossRef]

S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE J. Quantum Electron. 39, 1081–1085 (2003).
[CrossRef]

2002 (1)

1975 (1)

E. L. Nagaev, “Ferromagnetic and antiferromagnetic semiconductors,” Sov. Phys. Usp. 18, 863–892 (1975).
[CrossRef]

Barybin, A. A.

A. A. Barybin and V. A. Dmitriev, Modern Electrodynamics and Coupled-Mode Theory: Application to Guided-Wave Optics (Rinton, 2002).

Basu, S.

Beggs, D. M.

D. M. Beggs, T. P. White, L. Cairns, L. O’Faolain, and T. F. Krauss, “Ultrashort photonic crystal optical switch actuated by a microheater,” IEEE Photon. Technol. Lett. 21, 24–26 (2009).
[CrossRef]

Borel, P. I.

Cairns, L.

D. M. Beggs, T. P. White, L. Cairns, L. O’Faolain, and T. F. Krauss, “Ultrashort photonic crystal optical switch actuated by a microheater,” IEEE Photon. Technol. Lett. 21, 24–26 (2009).
[CrossRef]

Chang, S.-J.

F. Fan, S.-J. Chang, C. Niu, Y. Hou, and X.-H. Wang, “Magnetically tunable silicon-ferrite photonic crystals for terahertz circulator,” Opt. Commun. 285, 3763–3769 (2012).
[CrossRef]

Dagens, B.

de Souza, F. J. M.

Dmitriev, V.

Dmitriev, V. A.

A. A. Barybin and V. A. Dmitriev, Modern Electrodynamics and Coupled-Mode Theory: Application to Guided-Wave Optics (Rinton, 2002).

Fan, F.

F. Fan, S.-J. Chang, C. Niu, Y. Hou, and X.-H. Wang, “Magnetically tunable silicon-ferrite photonic crystals for terahertz circulator,” Opt. Commun. 285, 3763–3769 (2012).
[CrossRef]

Fan, S.

Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B 81, 369–375 (2005).
[CrossRef]

Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystal,” Opt. Lett. 30, 1989–1991 (2005).
[CrossRef]

M. Yanik and S. Fan, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[CrossRef]

Frandsen, L. H.

Fratello, V. J.

Z. Wu, M. Levy, V. J. Fratello, and A. M. Merzlikin, “Gyrotropic photonic crystal waveguide switches,” Appl. Phys. Lett. 96, 051125 (2010).
[CrossRef]

Gralak, B.

Harpoth, A.

Hou, Y.

F. Fan, S.-J. Chang, C. Niu, Y. Hou, and X.-H. Wang, “Magnetically tunable silicon-ferrite photonic crystals for terahertz circulator,” Opt. Commun. 285, 3763–3769 (2012).
[CrossRef]

Joannopoulos, J. D.

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

Johnson, S. G.

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

Kawakatsu, M.

Kim, S.-H.

S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE J. Quantum Electron. 39, 1081–1085 (2003).
[CrossRef]

Kotov, V. A.

A. K. Zvezdin and V. A. Kotov, Modern Magneto-Optics and Magneto-Optical Materials (IOP, 1997).

Krauss, T. F.

D. M. Beggs, T. P. White, L. Cairns, L. O’Faolain, and T. F. Krauss, “Ultrashort photonic crystal optical switch actuated by a microheater,” IEEE Photon. Technol. Lett. 21, 24–26 (2009).
[CrossRef]

Kristensen, M.

Lee, Y.-H.

S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE J. Quantum Electron. 39, 1081–1085 (2003).
[CrossRef]

Levy, M.

Z. Wu, M. Levy, V. J. Fratello, and A. M. Merzlikin, “Gyrotropic photonic crystal waveguide switches,” Appl. Phys. Lett. 96, 051125 (2010).
[CrossRef]

Lin, M.

Q. Wang, Z. Ouyang, K. Tao, M. Lin, and S. Ruan, “T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal,” Phys. Lett. A 376, 646–649 (2012).
[CrossRef]

Magdenko, L.

Mattis, D. C.

S. Methfessel and D. C. Mattis, “Magnetic semiconductors,” in Handbuch der Physik, S. Fliigge and H. P. J. Wijn, eds. (Springer, 1968).

Meade, R. D.

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

Merzlikin, A. M.

Z. Wu, M. Levy, V. J. Fratello, and A. M. Merzlikin, “Gyrotropic photonic crystal waveguide switches,” Appl. Phys. Lett. 96, 051125 (2010).
[CrossRef]

Methfessel, S.

S. Methfessel and D. C. Mattis, “Magnetic semiconductors,” in Handbuch der Physik, S. Fliigge and H. P. J. Wijn, eds. (Springer, 1968).

Nagaev, E. L.

E. L. Nagaev, “Ferromagnetic and antiferromagnetic semiconductors,” Sov. Phys. Usp. 18, 863–892 (1975).
[CrossRef]

Niu, C.

F. Fan, S.-J. Chang, C. Niu, Y. Hou, and X.-H. Wang, “Magnetically tunable silicon-ferrite photonic crystals for terahertz circulator,” Opt. Commun. 285, 3763–3769 (2012).
[CrossRef]

O’Faolain, L.

D. M. Beggs, T. P. White, L. Cairns, L. O’Faolain, and T. F. Krauss, “Ultrashort photonic crystal optical switch actuated by a microheater,” IEEE Photon. Technol. Lett. 21, 24–26 (2009).
[CrossRef]

Ouyang, Z.

Q. Wang, Z. Ouyang, K. Tao, M. Lin, and S. Ruan, “T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal,” Phys. Lett. A 376, 646–649 (2012).
[CrossRef]

Pinnepalli, S.

Portela, G.

Prather, D. W.

Romero-Vivas, J.

Ruan, S.

Q. Wang, Z. Ouyang, K. Tao, M. Lin, and S. Ruan, “T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal,” Phys. Lett. A 376, 646–649 (2012).
[CrossRef]

Sekhar, M. C.

Sharkawy, A.

Shi, S.

Singh, M. R.

Smigaj, W.

Tao, K.

Q. Wang, Z. Ouyang, K. Tao, M. Lin, and S. Ruan, “T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal,” Phys. Lett. A 376, 646–649 (2012).
[CrossRef]

Vanwolleghem, M.

Wang, Q.

Q. Wang, Z. Ouyang, K. Tao, M. Lin, and S. Ruan, “T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal,” Phys. Lett. A 376, 646–649 (2012).
[CrossRef]

Wang, X.-H.

F. Fan, S.-J. Chang, C. Niu, Y. Hou, and X.-H. Wang, “Magnetically tunable silicon-ferrite photonic crystals for terahertz circulator,” Opt. Commun. 285, 3763–3769 (2012).
[CrossRef]

Wang, Z.

Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B 81, 369–375 (2005).
[CrossRef]

Z. Wang and S. Fan, “Optical circulators in two-dimensional magneto-optical photonic crystal,” Opt. Lett. 30, 1989–1991 (2005).
[CrossRef]

White, T. P.

D. M. Beggs, T. P. White, L. Cairns, L. O’Faolain, and T. F. Krauss, “Ultrashort photonic crystal optical switch actuated by a microheater,” IEEE Photon. Technol. Lett. 21, 24–26 (2009).
[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, 2008).

Wu, Z.

Z. Wu, M. Levy, V. J. Fratello, and A. M. Merzlikin, “Gyrotropic photonic crystal waveguide switches,” Appl. Phys. Lett. 96, 051125 (2010).
[CrossRef]

Yanik, M.

M. Yanik and S. Fan, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[CrossRef]

Zimmer, D.

Zvezdin, A. K.

A. K. Zvezdin and V. A. Kotov, Modern Magneto-Optics and Magneto-Optical Materials (IOP, 1997).

Appl. Phys. B (1)

Z. Wang and S. Fan, “Magneto-optical defects in two-dimensional photonic crystals,” Appl. Phys. B 81, 369–375 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

Z. Wu, M. Levy, V. J. Fratello, and A. M. Merzlikin, “Gyrotropic photonic crystal waveguide switches,” Appl. Phys. Lett. 96, 051125 (2010).
[CrossRef]

M. Yanik and S. Fan, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

V. Dmitriev, “Symmetry properties of 2D magnetic photonic crystals with square lattice,” Eur. Phys. J. Appl. Phys. 32, 159–165 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

S.-H. Kim and Y.-H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE J. Quantum Electron. 39, 1081–1085 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

D. M. Beggs, T. P. White, L. Cairns, L. O’Faolain, and T. F. Krauss, “Ultrashort photonic crystal optical switch actuated by a microheater,” IEEE Photon. Technol. Lett. 21, 24–26 (2009).
[CrossRef]

Opt. Commun. (1)

F. Fan, S.-J. Chang, C. Niu, Y. Hou, and X.-H. Wang, “Magnetically tunable silicon-ferrite photonic crystals for terahertz circulator,” Opt. Commun. 285, 3763–3769 (2012).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Photon. Nanostr. Fundam. Appl. (1)

V. Dmitriev, “Permeability tensor versus permittivity one in theory of nonreciprocal optical components,” Photon. Nanostr. Fundam. Appl. 11, 203–209 (2013).
[CrossRef]

Phys. Lett. A (1)

Q. Wang, Z. Ouyang, K. Tao, M. Lin, and S. Ruan, “T-shaped optical circulator based on coupled magneto-optical rods and a side-coupled cavity in a square-lattice photonic crystal,” Phys. Lett. A 376, 646–649 (2012).
[CrossRef]

Sov. Phys. Usp. (1)

E. L. Nagaev, “Ferromagnetic and antiferromagnetic semiconductors,” Sov. Phys. Usp. 18, 863–892 (1975).
[CrossRef]

Other (6)

S. Methfessel and D. C. Mattis, “Magnetic semiconductors,” in Handbuch der Physik, S. Fliigge and H. P. J. Wijn, eds. (Springer, 1968).

A. K. Zvezdin and V. A. Kotov, Modern Magneto-Optics and Magneto-Optical Materials (IOP, 1997).

http://ab-initio.mit.edu .

www.comsol.com .

A. A. Barybin and V. A. Dmitriev, Modern Electrodynamics and Coupled-Mode Theory: Application to Guided-Wave Optics (Rinton, 2002).

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

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Figures (14)

Fig. 1.
Fig. 1.

Examples of front–front coupling of waveguides and resonator and symmetry elements of switches in magnetized and nonmagnetized states: (a) 120° bend, (b) 60° bend, and (c) without bending.

Fig. 2.
Fig. 2.

Examples of side–side coupling of waveguides and resonator and symmetry elements of switches in magnetized and nonmagnetized states: (a), (d), (f) 60° bend, (b) 120° bend, (c) 180° bend, and (e) without bending.

Fig. 3.
Fig. 3.

Examples of combined front–side coupling of waveguides and resonator: (a), (c), (f) 60° bend, (e) 120° bend, (d) 180° bend, and (b) without bending.

Fig. 4.
Fig. 4.

Examples of standing eigenmodes in nonmagnetized resonator with symmetry C6v.

Fig. 5.
Fig. 5.

Rotating eigenvectors for (a) nonmagnetized and (b) magnetized resonator.

Fig. 6.
Fig. 6.

First and second TE frequency bands for nonmagnetized PhC.

Fig. 7.
Fig. 7.

Resonant frequency of dipole mode versus radius r0 of resonator central hole.

Fig. 8.
Fig. 8.

Frequency splitting of dipole modes excited in an MO resonator, r0=0.8625a.

Fig. 9.
Fig. 9.

Substitution of the circular central hole by an elliptical one, 60° bend.

Fig. 10.
Fig. 10.

Frequency response of switch, 60° bend.

Fig. 11.
Fig. 11.

Hz distribution at central frequency of switch, 60° bend: (a) state on and (b) state off.

Fig. 12.
Fig. 12.

Substitution of the circular central hole by an elliptical one, 120° bend.

Fig. 13.
Fig. 13.

Frequency response of switch, 120° bend.

Fig. 14.
Fig. 14.

Hz distribution at central frequency of switch, 120° bend. (a) state on and (b) state off.

Equations (8)

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

Vi=(ab).
V+=(1i),V=(1i).
[R]σ1=(1001),[R]σ2=[R]C2=(0110).
[S]C2v=(S11S12S12S11),[S]C2v(C2)=(S11S12S12S11),
[S]Cs=(S11S12S12S11),[S]Cs(C1)=(S11S12S21S11).
[S]C2=(S11S12S12S11),[S]C2=(S11S12S21S11).
[S]Cs=(S11S12S12S22),[S]Cs(C1)=(S11S12S12S22).
[ϵ]=ϵ0(ϵrig0igϵr000ϵr),

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