Abstract

Coupled microcircular resonators tangentially coupled to a bus waveguide, which is between the resonators, are numerically investigated by the finite-difference time-domain technique. For symmetrically coupled microcircular resonators with refractive index of 3.2, radius of 2μm, and width of the bus waveguide of 0.4 μm, a mode Q factor of the order of 105 is obtained for a mode at the frequency of 243THz. An output coupling efficiency of as high as 0.99 is calculated for a mode with a Q factor ranging from 103 to 104. The mode Q factor is 2 orders larger than that of the modes confined in a single circular resonator tangentially coupled to the same bus waveguide. Furthermore, the high Q traveling modes in the coupled microcircular resonators are suitable for optical single processing.

© 2010 Optical Society of America

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  1. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
    [CrossRef]
  2. J. U. Nöckel, A. D. Stone, G. Chen, H. L. Grossman, and R. K. Chang, Opt. Lett. 21, 1609 (1996).
    [CrossRef]
  3. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
    [CrossRef] [PubMed]
  4. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
    [CrossRef]
  5. S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
    [CrossRef]
  6. M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, Appl. Phys. Lett. 88, 031108 (2006).
    [CrossRef]
  7. S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, IEEE Photonics Technol. Lett. 15, 1330 (2003).
    [CrossRef]
  8. J. Van Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. Van Thourhout, S. Verstuyft, L. Di Cioccio, J. M. Fedeli, C. Lagahe, and R. Baets, Opt. Express 15, 6744 (2007).
    [CrossRef] [PubMed]
  9. J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. Y. D. Yang, S. J. Wang, and Y. Z. Huang, Opt. Express 17, 23010 (2009).
    [CrossRef]
  15. A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time Domain Method, 3rd ed. (Artech House, 2005).
  16. W. H. Guo, W. J. Li, and Y. Z. Huang, IEEE Microw. Wireless Compon. Lett. 11, 223 (2001).
    [CrossRef]
  17. Q. Chen, Y.-D. Yang, and Y.-Z. Huang, Opt. Lett. 32, 1851(2007).
    [CrossRef] [PubMed]
  18. Y. D. Yang, Y. Z. Huang, and Q. Chen, Phys. Rev. A 75, 013817 (2007).
    [CrossRef]

2009 (1)

2008 (1)

2007 (4)

2006 (3)

J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, Appl. Phys. Lett. 88, 031108 (2006).
[CrossRef]

2004 (1)

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
[CrossRef]

2003 (3)

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, IEEE Photonics Technol. Lett. 15, 1330 (2003).
[CrossRef]

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, IEEE J. Quantum Electron. 39, 1563 (2003).
[CrossRef]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

2001 (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, IEEE Microw. Wireless Compon. Lett. 11, 223 (2001).
[CrossRef]

1998 (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

1996 (1)

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Baets, R.

Capasso, F.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

Chang, R. K.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

J. U. Nöckel, A. D. Stone, G. Chen, H. L. Grossman, and R. K. Chang, Opt. Lett. 21, 1609 (1996).
[CrossRef]

Che, K. J.

Chen, G.

Chen, Q.

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photonics Technol. Lett. 19, 963 (2007).
[CrossRef]

Q. Chen, Y.-D. Yang, and Y.-Z. Huang, Opt. Lett. 32, 1851(2007).
[CrossRef] [PubMed]

Y. D. Yang, Y. Z. Huang, and Q. Chen, Phys. Rev. A 75, 013817 (2007).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Cho, A. Y.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

Choi, S. J.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, IEEE Photonics Technol. Lett. 15, 1330 (2003).
[CrossRef]

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, IEEE Photonics Technol. Lett. 15, 1330 (2003).
[CrossRef]

Dapkus, P. D.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, IEEE Photonics Technol. Lett. 15, 1330 (2003).
[CrossRef]

Di Cioccio, L.

Djordjev, K.

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, IEEE Photonics Technol. Lett. 15, 1330 (2003).
[CrossRef]

Du, Y.

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, Opt. Lett. 33, 2170 (2008).
[CrossRef] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photonics Technol. Lett. 19, 963 (2007).
[CrossRef]

Faist, J.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

Fan, Z. C.

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, Opt. Lett. 33, 2170 (2008).
[CrossRef] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photonics Technol. Lett. 19, 963 (2007).
[CrossRef]

Fedeli, J. M.

Gmachl, C.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

Grossman, H. L.

Guo, W. H.

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, IEEE J. Quantum Electron. 39, 1563 (2003).
[CrossRef]

W. H. Guo, W. J. Li, and Y. Z. Huang, IEEE Microw. Wireless Compon. Lett. 11, 223 (2001).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time Domain Method, 3rd ed. (Artech House, 2005).

Hentschel, M.

J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
[CrossRef]

Hierle, R.

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, Appl. Phys. Lett. 88, 031108 (2006).
[CrossRef]

Hu, Y. H.

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photonics Technol. Lett. 19, 963 (2007).
[CrossRef]

Huang, Y. Z.

Y. D. Yang, S. J. Wang, and Y. Z. Huang, Opt. Express 17, 23010 (2009).
[CrossRef]

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, Y. Du, and Z. C. Fan, Opt. Lett. 33, 2170 (2008).
[CrossRef] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photonics Technol. Lett. 19, 963 (2007).
[CrossRef]

Y. D. Yang, Y. Z. Huang, and Q. Chen, Phys. Rev. A 75, 013817 (2007).
[CrossRef]

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, IEEE J. Quantum Electron. 39, 1563 (2003).
[CrossRef]

W. H. Guo, W. J. Li, and Y. Z. Huang, IEEE Microw. Wireless Compon. Lett. 11, 223 (2001).
[CrossRef]

Huang, Y.-Z.

Johnson, N. M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Kim, G. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
[CrossRef]

Kim, S. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
[CrossRef]

Kim, S. K.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
[CrossRef]

Kneissl, M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Lagahe, C.

Lauret, J. S.

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, Appl. Phys. Lett. 88, 031108 (2006).
[CrossRef]

Lebental, M.

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, Appl. Phys. Lett. 88, 031108 (2006).
[CrossRef]

Lee, Y. H.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
[CrossRef]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Li, W. J.

W. H. Guo, W. J. Li, and Y. Z. Huang, IEEE Microw. Wireless Compon. Lett. 11, 223 (2001).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Lu, Q. Y.

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, IEEE J. Quantum Electron. 39, 1563 (2003).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Narimanov, E. E.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

Nöckel, J. U.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

J. U. Nöckel, A. D. Stone, G. Chen, H. L. Grossman, and R. K. Chang, Opt. Lett. 21, 1609 (1996).
[CrossRef]

Park, H. G.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
[CrossRef]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Regreny, P.

Rojo-Romeo, P.

Seassal, C.

Shin, D. J.

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
[CrossRef]

Sivco, D. L.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Stone, A. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

J. U. Nöckel, A. D. Stone, G. Chen, H. L. Grossman, and R. K. Chang, Opt. Lett. 21, 1609 (1996).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time Domain Method, 3rd ed. (Artech House, 2005).

Tureci, H. E.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Van Campenhout, J.

Van Thourhout, D.

Verstuyft, S.

Wang, S. J.

Wiersig, J.

J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
[CrossRef]

Yang, Y. D.

Yang, Y.-D.

Yu, L. J.

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, IEEE J. Quantum Electron. 39, 1563 (2003).
[CrossRef]

Zyss, J.

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, Appl. Phys. Lett. 88, 031108 (2006).
[CrossRef]

Appl. Phys. Lett. (4)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

S. K. Kim, S. H. Kim, G. H. Kim, H. G. Park, D. J. Shin, and Y. H. Lee, Appl. Phys. Lett. 84, 861 (2004).
[CrossRef]

M. Lebental, J. S. Lauret, R. Hierle, and J. Zyss, Appl. Phys. Lett. 88, 031108 (2006).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, IEEE J. Quantum Electron. 39, 1563 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Z. Huang, Q. Chen, W. H. Guo, Q. Y. Lu, and L. J. Yu, IEEE J. Sel. Top. Quantum Electron. 12, 59 (2006).
[CrossRef]

IEEE Microw. Wireless Compon. Lett. (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, IEEE Microw. Wireless Compon. Lett. 11, 223 (2001).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, IEEE Photonics Technol. Lett. 19, 963 (2007).
[CrossRef]

S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, IEEE Photonics Technol. Lett. 15, 1330 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (2)

J. Wiersig and M. Hentschel, Phys. Rev. A 73, 031802 (2006).
[CrossRef]

Y. D. Yang, Y. Z. Huang, and Q. Chen, Phys. Rev. A 75, 013817 (2007).
[CrossRef]

Science (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef] [PubMed]

Other (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time Domain Method, 3rd ed. (Artech House, 2005).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of coupled circular resonators tangentially coupled with a bus waveguide. Single circular resonator tangentially coupled with a bus waveguide is the same diagram, but without the dashed-line resonator.

Fig. 2
Fig. 2

Field intensity spectra are plotted as the dashed and the solid curves for the single circular resonator and coupled circular resonators tangentially coupled with the bus waveguide, respectively. The radius of the circular resonator is 2 μm , and the width of the bus waveguide is 0.4 μm .

Fig. 3
Fig. 3

Electric field distributions of the modes near a frequency of 243 THz in the coupled circular resonators with the bus waveguide for (a) TM 20 , 3 , (b) TM 17 , 4 , and (c) the antisymmetrical coupled mode between TM 20 , 3 and TM 17 , 4 . The resonators and the bus waveguide are plotted by solid lines.

Fig. 4
Fig. 4

Mode Q factors and output coupling efficiency are plotted as the functions of the width of the bus waveguide for the TM 24 , 2 mode in the coupled circular resonators.

Fig. 5
Fig. 5

Electric field distribution of the TM 24 , 2 mode in the coupled circular resonators with a 0.4-μm-wide bus waveguide.

Tables (1)

Tables Icon

Table 1 Mode Frequencies, Q Factors, and Output Coupling Efficiencies for the Symmetric Modes versus the Width of the Bus Waveguide d

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