Abstract

We present an optical coupling system, which consists of waveguide, cavity and waveguide resonator, to investigate coupled-resonator-induced transparency effect. The transmission properties are analyzed theoretically by using coupled-mode theory in time domain. We also numerically demonstrate the effect by simulating the propagation of electromagnetic waves in photonic crystals by finite-difference time-domain method.

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  1. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
    [CrossRef]
  2. H. Ren, C. Jiang, W. Hu, M. Gao, Y. Qu, and J. Wang, “Channel drop filter in two-dimensional triangular lattice photonic crystals,” J. Opt. Soc. Am. A 24(10), 7–11 (2007).
    [CrossRef]
  3. H. Ren, C. Jiang, W. Hu, M. Gao, and J. Wang, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14(6), 2446–2458 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2446 .
    [CrossRef] [PubMed]
  4. S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18(2), 162–165 (2001).
    [CrossRef]
  5. J. Zhou, Q. Chang, D. Mu, J. Yang, W. Han, and L. Wang, “Theoretical investigation of waveguide power splitters with parallel output ports in two-dimensional square-lattice photonic crystals,” J. Opt. Soc. Am. B 26(12), 2469 (2009).
    [CrossRef]
  6. S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998).
    [CrossRef]
  7. S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046603 (2006).
    [CrossRef] [PubMed]
  8. S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, “Coupled-resonator-induced reflection in photonic-crystal waveguide structures,” Opt. Express 16(15), 11647–11659 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-11647 .
    [CrossRef] [PubMed]
  9. R. W. Boyd and D. J. Gauthier, “Photonics: transparency on an optical chip,” Nature 441(7094), 701–702 (2006).
    [CrossRef] [PubMed]
  10. A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
    [CrossRef]
  11. X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102(17), 173902 (2009).
    [CrossRef] [PubMed]
  12. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
    [CrossRef] [PubMed]
  13. B. Maes, P. Bienstman, and R. Baets, “Switching in coupled nonlinear photonic-crystal resonators,” J. Opt. Soc. Am. B 22(8), 1778–1784 (2005).
    [CrossRef]
  14. Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
    [CrossRef] [PubMed]
  15. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  16. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
    [CrossRef]
  17. A. Taflove, and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech House, 2000).

2009

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102(17), 173902 (2009).
[CrossRef] [PubMed]

J. Zhou, Q. Chang, D. Mu, J. Yang, W. Han, and L. Wang, “Theoretical investigation of waveguide power splitters with parallel output ports in two-dimensional square-lattice photonic crystals,” J. Opt. Soc. Am. B 26(12), 2469 (2009).
[CrossRef]

2008

2007

H. Ren, C. Jiang, W. Hu, M. Gao, Y. Qu, and J. Wang, “Channel drop filter in two-dimensional triangular lattice photonic crystals,” J. Opt. Soc. Am. A 24(10), 7–11 (2007).
[CrossRef]

2006

R. W. Boyd and D. J. Gauthier, “Photonics: transparency on an optical chip,” Nature 441(7094), 701–702 (2006).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
[CrossRef] [PubMed]

S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046603 (2006).
[CrossRef] [PubMed]

H. Ren, C. Jiang, W. Hu, M. Gao, and J. Wang, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Opt. Express 14(6), 2446–2458 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2446 .
[CrossRef] [PubMed]

2005

B. Maes, P. Bienstman, and R. Baets, “Switching in coupled nonlinear photonic-crystal resonators,” J. Opt. Soc. Am. B 22(8), 1778–1784 (2005).
[CrossRef]

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

2001

2000

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

1998

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[CrossRef]

S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998).
[CrossRef]

1997

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[CrossRef]

Baets, R.

Bienstman, P.

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, “Photonics: transparency on an optical chip,” Nature 441(7094), 701–702 (2006).
[CrossRef] [PubMed]

Busch, K.

S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046603 (2006).
[CrossRef] [PubMed]

Chang, Q.

Fan, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
[CrossRef] [PubMed]

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18(2), 162–165 (2001).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[CrossRef]

S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[CrossRef]

Farca, G.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Gao, M.

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “Photonics: transparency on an optical chip,” Nature 441(7094), 701–702 (2006).
[CrossRef] [PubMed]

Han, W.

Haus, H. A.

Hu, W.

Jiang, C.

Joannopoulos, J. D.

S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” J. Opt. Soc. Am. B 18(2), 162–165 (2001).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[CrossRef]

S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[CrossRef]

Johnson, S. G.

Kivshar, Y. S.

S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, “Coupled-resonator-induced reflection in photonic-crystal waveguide structures,” Opt. Express 16(15), 11647–11659 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-11647 .
[CrossRef] [PubMed]

S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046603 (2006).
[CrossRef] [PubMed]

Kwong, D. L.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102(17), 173902 (2009).
[CrossRef] [PubMed]

Lee, R. K.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Li, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Lipson, M.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
[CrossRef] [PubMed]

Maes, B.

Manolatou, C.

Mingaleev, S. F.

S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, “Coupled-resonator-induced reflection in photonic-crystal waveguide structures,” Opt. Express 16(15), 11647–11659 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-11647 .
[CrossRef] [PubMed]

S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046603 (2006).
[CrossRef] [PubMed]

Miroshnichenko, A. E.

S. F. Mingaleev, A. E. Miroshnichenko, and Y. S. Kivshar, “Coupled-resonator-induced reflection in photonic-crystal waveguide structures,” Opt. Express 16(15), 11647–11659 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-15-11647 .
[CrossRef] [PubMed]

S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046603 (2006).
[CrossRef] [PubMed]

Mu, D.

Naweed, A.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Povinelli, M. L.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
[CrossRef] [PubMed]

Qu, Y.

H. Ren, C. Jiang, W. Hu, M. Gao, Y. Qu, and J. Wang, “Channel drop filter in two-dimensional triangular lattice photonic crystals,” J. Opt. Soc. Am. A 24(10), 7–11 (2007).
[CrossRef]

Ren, H.

Rosenberger, A. T.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Sandhu, S.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
[CrossRef] [PubMed]

Shakya, J.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
[CrossRef] [PubMed]

Shopova, S. I.

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[CrossRef]

S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett. 23(23), 1855–1857 (1998).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[CrossRef]

Wang, J.

Wang, L.

Wong, C. W.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102(17), 173902 (2009).
[CrossRef] [PubMed]

Xu, Q.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
[CrossRef] [PubMed]

Xu, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Yang, J.

Yang, X.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102(17), 173902 (2009).
[CrossRef] [PubMed]

Yariv, A.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Yu, M.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102(17), 173902 (2009).
[CrossRef] [PubMed]

Zhou, J.

J. Opt. Soc. Am. A

H. Ren, C. Jiang, W. Hu, M. Gao, Y. Qu, and J. Wang, “Channel drop filter in two-dimensional triangular lattice photonic crystals,” J. Opt. Soc. Am. A 24(10), 7–11 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Nature

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Photonics: transparency on an optical chip,” Nature 441(7094), 701–702 (2006).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. A

A. Naweed, G. Farca, S. I. Shopova, and A. T. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71(4), 043804 (2005).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

S. F. Mingaleev, A. E. Miroshnichenko, Y. S. Kivshar, and K. Busch, “All-optical switching, bistability, and slow-light transmission in photonic crystal waveguide-resonator structures,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046603 (2006).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Phys. Rev. Lett.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. 102(17), 173902 (2009).
[CrossRef] [PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96(12), 123901 (2006).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Phys. Rev. Lett. 80(5), 960–963 (1998).
[CrossRef]

Other

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

A. Taflove, and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method (Artech House, 2000).

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Figures (5)

Fig. 1
Fig. 1

Optical system consisting of a cavity side coupled to bus waveguide and resonant waveguide.

Fig. 2
Fig. 2

Theoretical transmission spectra though the optical system as shown in Fig. 1. The spectra are calculated from Eq. (6) with the phase shift φ ω l / c . We plot the frequency in the unit of 2 π c / l . The resonant frequency of the cavity is ω 0 = 0.50 ( 2 π c / l ) . The decay rates are taken to be 1 / τ 1 = 1 / τ 2 (dash line) and 500 / τ 1 = 1 / τ 2 (solid line) with 1 / τ 2 = 0.002 ( 2 π c / l ) .

Fig. 3
Fig. 3

(a) Photonic crystal structure. The bus waveguide is formed by removing a single row of rods. The resonant waveguide, created by removing a row of five rods, is 4 a away from the center of the bus waveguide. A point defect is placed between the center of the two waveguides. (b) Transmission spectra calculated by the finite-difference time-domain method at the resonant frequency of the cavity ω 0 = 0.3642 ( 2 π / a ) .

Fig. 4
Fig. 4

(a) Photonic crystal structure. (b) and (c) Transmission spectra of the structure at different resonant frequencies of the cavity. The solid lines are the transmission spectra through the structure as shown in (a). The dashed line is the transmission spectra for the same structure without the resonant waveguide. The resonant frequencies of the cavity are taken to be: (b) ω 0 = 0.3722 ( 2 π c / a ) , (c) ω 0 = 0.3702 ( 2 π c / a ) .

Fig. 5
Fig. 5

Steady-state electric field distribution in the structure shown as shown in Fig. 4(a) at frequencies: (a) ω = 0 .3725 ( 2 π c / a ) , (b) ω = 0 .3718 ( 2 π c / a ) . The resonant frequency of the cavity is ω 0 = 0.3722 ( 2 π c / a ) .

Equations (1)

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S 11 = S + 12 e j θ 1 2 τ 1 a ,

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