Abstract

In this Letter, we report on a perpendicular coupler (PC) for whispering-gallery resonators; it is a near field waveguide optimized for high coupling efficiency. The PC provides highly efficient tunneling coupling between the waveguide and microresonator without the need of a phase matching condition, and saves space for integration components. Compared to the Lorentz-shape in the transmission spectrum of the parallel coupler, the reflection spectrum of the PC shows an asymmetric Fano-shape near resonance. Furthermore, we demonstrate that the collection efficiency can be enhanced by near field scatterers, with a maximal efficiency of about 75%. Our simulations show that the PC is not sensitive to most parameters (including the refractive index of the waveguide), which makes the PC optimal for the application of whispering-gallery modes.

© 2012 Optical Society of America

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G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, Laser Photon. Rev. 5, 737 (2011).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

Y.-Z. Yan, C.-L. Zou, S.-B. Yan, F.-W. Sun, Z. Ji, J. Liu, Y.-G. Zhang, L. Wang, C.-Y. Xue, W.-D. Zhang, Z.-F. Han, and J.-J. Xiong, Opt. Express 19, 5753 (2011).
[CrossRef]

2010

F. Ou, X. Li, B. Liu, Y. Huang, and S.-T. Ho, Opt. Lett. 35, 1722 (2010).
[CrossRef]

E. H. Kho, E. P. Li, I. Ahmed, Y. Huang, and S.-T. Ho, IEEE J. Quantum Electron. 46, 128 (2010).
[CrossRef]

C.-H. Dong, Y. Yang, Y.-L. Shen, C.-L. Zou, F.-W. Sun, H. Ming, G.-C. Guo, and Z.-F. Han, Opt. Commun. 283, 5117 (2010).
[CrossRef]

2009

2008

2003

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

2000

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

1994

M. L. Gorodetsky and V. S. Ilchenko, Opt. Commun. 113, 133 (1994).
[CrossRef]

Ahmed, I.

E. H. Kho, E. P. Li, I. Ahmed, Y. Huang, and S.-T. Ho, IEEE J. Quantum Electron. 46, 128 (2010).
[CrossRef]

Arnold, S.

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef]

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

Dominguez-Juarez, J. L.

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, Laser Photon. Rev. 5, 737 (2011).
[CrossRef]

Dong, C.-H.

Gorodetsky, M. L.

M. L. Gorodetsky and V. S. Ilchenko, Opt. Commun. 113, 133 (1994).
[CrossRef]

Guo, G.-C.

Han, Z.-F.

Ho, S.-T.

E. H. Kho, E. P. Li, I. Ahmed, Y. Huang, and S.-T. Ho, IEEE J. Quantum Electron. 46, 128 (2010).
[CrossRef]

F. Ou, X. Li, B. Liu, Y. Huang, and S.-T. Ho, Opt. Lett. 35, 1722 (2010).
[CrossRef]

Holzwarth, R.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

Huang, Y.

E. H. Kho, E. P. Li, I. Ahmed, Y. Huang, and S.-T. Ho, IEEE J. Quantum Electron. 46, 128 (2010).
[CrossRef]

F. Ou, X. Li, B. Liu, Y. Huang, and S.-T. Ho, Opt. Lett. 35, 1722 (2010).
[CrossRef]

Huang, Y. -Z.

Ilchenko, V. S.

M. L. Gorodetsky and V. S. Ilchenko, Opt. Commun. 113, 133 (1994).
[CrossRef]

Ji, Z.

Kho, E. H.

E. H. Kho, E. P. Li, I. Ahmed, Y. Huang, and S.-T. Ho, IEEE J. Quantum Electron. 46, 128 (2010).
[CrossRef]

Kimble, H. J.

H. J. Kimble, Nature 453, 1023 (2008).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

Kozyreff, G.

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, Laser Photon. Rev. 5, 737 (2011).
[CrossRef]

Li, E. P.

E. H. Kho, E. P. Li, I. Ahmed, Y. Huang, and S.-T. Ho, IEEE J. Quantum Electron. 46, 128 (2010).
[CrossRef]

Li, X.

Liu, B.

Liu, J.

Martorell, J.

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, Laser Photon. Rev. 5, 737 (2011).
[CrossRef]

Ming, H.

C.-H. Dong, Y. Yang, Y.-L. Shen, C.-L. Zou, F.-W. Sun, H. Ming, G.-C. Guo, and Z.-F. Han, Opt. Commun. 283, 5117 (2010).
[CrossRef]

Ou, F.

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

Park, Y.-S.

Y.-S. Park and H. Wang, Nat. Phys. 5, 489 (2009).
[CrossRef]

Shen, Y.-L.

C.-H. Dong, Y. Yang, Y.-L. Shen, C.-L. Zou, F.-W. Sun, H. Ming, G.-C. Guo, and Z.-F. Han, Opt. Commun. 283, 5117 (2010).
[CrossRef]

Sun, F.-W.

Y.-Z. Yan, C.-L. Zou, S.-B. Yan, F.-W. Sun, Z. Ji, J. Liu, Y.-G. Zhang, L. Wang, C.-Y. Xue, W.-D. Zhang, Z.-F. Han, and J.-J. Xiong, Opt. Express 19, 5753 (2011).
[CrossRef]

C.-H. Dong, Y. Yang, Y.-L. Shen, C.-L. Zou, F.-W. Sun, H. Ming, G.-C. Guo, and Z.-F. Han, Opt. Commun. 283, 5117 (2010).
[CrossRef]

Vahala, K. J.

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

Vollmer, F.

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef]

Wang, H.

Y.-S. Park and H. Wang, Nat. Phys. 5, 489 (2009).
[CrossRef]

Wang, L.

Wang, S. -J.

Wu, X.-W.

Xiao, Y.-F.

Xiong, J.-J.

Xue, C.-Y.

Yan, S.-B.

Yan, Y.-Z.

Yang, L.

Yang, Y.

C.-H. Dong, Y. Yang, Y.-L. Shen, C.-L. Zou, F.-W. Sun, H. Ming, G.-C. Guo, and Z.-F. Han, Opt. Commun. 283, 5117 (2010).
[CrossRef]

Yang, Y. -D.

Yong, Y.

Zhang, W.-D.

Zhang, Y.-G.

Zou, C.-L.

IEEE J. Quantum Electron.

E. H. Kho, E. P. Li, I. Ahmed, Y. Huang, and S.-T. Ho, IEEE J. Quantum Electron. 46, 128 (2010).
[CrossRef]

J. Opt. Soc. Am. B

Laser Photon. Rev.

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, Laser Photon. Rev. 5, 737 (2011).
[CrossRef]

Nat. Methods

F. Vollmer and S. Arnold, Nat. Methods 5, 591 (2008).
[CrossRef]

Nat. Phys.

Y.-S. Park and H. Wang, Nat. Phys. 5, 489 (2009).
[CrossRef]

Nature

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef]

H. J. Kimble, Nature 453, 1023 (2008).
[CrossRef]

Opt. Commun.

C.-H. Dong, Y. Yang, Y.-L. Shen, C.-L. Zou, F.-W. Sun, H. Ming, G.-C. Guo, and Z.-F. Han, Opt. Commun. 283, 5117 (2010).
[CrossRef]

M. L. Gorodetsky and V. S. Ilchenko, Opt. Commun. 113, 133 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef]

Science

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematics of the parallel coupler (a) and the waveguide PC (b).

Fig. 2.
Fig. 2.

False color patterns of an even (a) and an odd (b) mode with logarithm scale. The Q-factor and η depend on the gap between the waveguide and resonator (c), (d) with width=200nm, and the width of the waveguide (e), (f) with gap=250nm.

Fig. 3.
Fig. 3.

(a) Schematics of the Fano coupling process. (b) False color pattern of an excited WGM. (c) Spectrum of reflection light with different gap width.

Fig. 4.
Fig. 4.

The Q-factor (a) and the collection efficiency (b) against the distance between the scatterers and the cavity. (c) The collection efficiency of the resonator with three scatterers varying with the refractive index of the waveguide. Insert: false color pattern of the coupling mode with three scatterers. The parameters are gap=250nm, width=300nm in (a), (b), and (c), and distance=700nm in (c).

Equations (4)

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

κtotal=κi+κr+κw,
Er=reiϕEin2κwEcav,
ddtEcav=[i(ωω0)κtotal]Ecav+2κwEin,
Er/Ein=reiϕ+2κwi(ωω0)κtotal.

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