Abstract

We report a simple and robust mechanism that can result in highly directional emission from long-lived resonances in microcavities. By placing a nanoparticle (NP) into the evanescent wave region of microcavities, highly directional outputs with divergence angle 1.9°10° can be obtained in single or double directions. The perturbation of NP on evanescent waves preserves the high-quality (Q) factors, and the collimation of microcavities generates the highly directional outputs. Our numerical simulations show that this mechanism is very robust to the size of NP and the refractive index/separation distance/size of microcavities.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2010 (3)

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

Q. H. Song and H. Cao, Phys. Rev. Lett. 105, 053902 (2010).
[CrossRef] [PubMed]

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[CrossRef]

2009 (2)

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Phys. Rev. A 80, 063813 (2009).
[CrossRef]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, Phys. Rev. A 80, 041807 (2009).
[CrossRef]

2008 (3)

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Europhys. Lett. 82, 34002 (2008).
[CrossRef]

J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901 (2008).
[CrossRef] [PubMed]

L. Shang, L. Y. Liu, and L. Xu, Appl. Phys. Lett. 92, 071111 (2008).
[CrossRef]

2007 (1)

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[CrossRef]

2006 (1)

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

2005 (1)

2004 (2)

T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
[CrossRef]

Z. G. Chen, A. Taflove, and V. Beckman, Opt. Express 12, 1214 (2004).
[CrossRef] [PubMed]

2003 (1)

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

2002 (1)

1997 (1)

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

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]

Backman, V.

Beckman, V.

Benson, O.

Bogomolny, E.

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[CrossRef]

Cao, H.

Q. H. Song and H. Cao, Phys. Rev. Lett. 105, 053902 (2010).
[CrossRef] [PubMed]

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, Phys. Rev. A 80, 041807 (2009).
[CrossRef]

Chen, D. R.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[CrossRef]

Chen, Z. G.

Dettmann, C. P.

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Phys. Rev. A 80, 063813 (2009).
[CrossRef]

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Europhys. Lett. 82, 34002 (2008).
[CrossRef]

Fang, W.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, Phys. Rev. A 80, 041807 (2009).
[CrossRef]

Fukushima, T.

T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
[CrossRef]

Ge, L.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

Götzinger, S.

Harayama, T.

T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
[CrossRef]

He, L. N.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[CrossRef]

Hentschel, M.

J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901 (2008).
[CrossRef] [PubMed]

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

Ho, S. T.

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, Phys. Rev. A 80, 041807 (2009).
[CrossRef]

Lauret, J. S.

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[CrossRef]

Lebental, M.

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[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, L.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[CrossRef]

Li, X.

Liu, B. Y.

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, Phys. Rev. A 80, 041807 (2009).
[CrossRef]

Liu, L. Y.

L. Shang, L. Y. Liu, and L. Xu, Appl. Phys. Lett. 92, 071111 (2008).
[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]

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]

Morozov, G. V.

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Phys. Rev. A 80, 063813 (2009).
[CrossRef]

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Europhys. Lett. 82, 34002 (2008).
[CrossRef]

Nöckel, J. U.

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Ozdemir, S. K.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[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]

Sandoghdar, V.

Schmit, C.

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[CrossRef]

Shang, L.

L. Shang, L. Y. Liu, and L. Xu, Appl. Phys. Lett. 92, 071111 (2008).
[CrossRef]

Shim, J.-B.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

Sieber, M.

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Phys. Rev. A 80, 063813 (2009).
[CrossRef]

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Europhys. Lett. 82, 34002 (2008).
[CrossRef]

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]

Solomon, G. S.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, Phys. Rev. A 80, 041807 (2009).
[CrossRef]

Song, Q. H.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

Q. H. Song and H. Cao, Phys. Rev. Lett. 105, 053902 (2010).
[CrossRef] [PubMed]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, Phys. Rev. A 80, 041807 (2009).
[CrossRef]

Stone, A. D.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Taflove, A.

Vahala, K. J.

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

Waalkens, H.

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Phys. Rev. A 80, 063813 (2009).
[CrossRef]

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Europhys. Lett. 82, 34002 (2008).
[CrossRef]

Wierisig, J.

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

Wiersig, J.

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901 (2008).
[CrossRef] [PubMed]

Xiao, Y. F.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[CrossRef]

Xu, L.

L. Shang, L. Y. Liu, and L. Xu, Appl. Phys. Lett. 92, 071111 (2008).
[CrossRef]

Yang, L.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[CrossRef]

Zhu, J. G.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[CrossRef]

Zyss, J.

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

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

L. Shang, L. Y. Liu, and L. Xu, Appl. Phys. Lett. 92, 071111 (2008).
[CrossRef]

Europhys. Lett. (1)

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Europhys. Lett. 82, 34002 (2008).
[CrossRef]

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

T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
[CrossRef]

Nat. Photon. (1)

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, Nat. Photon. 4, 46 (2010).
[CrossRef]

Nature (2)

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

J. U. Nöckel and A. D. Stone, Nature 385, 45 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (4)

M. Lebental, J. S. Lauret, J. Zyss, C. Schmit, and E. Bogomolny, Phys. Rev. A 75, 033806 (2007).
[CrossRef]

Q. H. Song, W. Fang, B. Y. Liu, S. T. Ho, G. S. Solomon, and H. Cao, Phys. Rev. A 80, 041807 (2009).
[CrossRef]

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

C. P. Dettmann, G. V. Morozov, M. Sieber, and H. Waalkens, Phys. Rev. A 80, 063813 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

Q. H. Song, L. Ge, A. D. Stone, H. Cao, J.-B. Shim, J. Wiersig, W. Fang, and G. S. Solomon, Phys. Rev. Lett. 105, 103902 (2010).
[CrossRef] [PubMed]

J. Wiersig and M. Hentschel, Phys. Rev. Lett. 100, 033901 (2008).
[CrossRef] [PubMed]

Q. H. Song and H. Cao, Phys. Rev. Lett. 105, 053902 (2010).
[CrossRef] [PubMed]

Other (1)

The highest Q factor in two-dimensional simulation with the cavity shape in Ref. 21 at kR∼22 is below 200.

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Figures (3)

Fig. 1
Fig. 1

(a) Plane wave is focused into a nanojet by a microcavity with R = 5 μm . (b) Eigenvalues in microcavity with a nanoparticle. The radius of NP is 250 nm away from the cavity edge with R 2 = 250 nm . (c) Far-field angular distribution of total emission with Re ( k R ) 25.198 (d) FFPs log ( | E z | ) of symmetric (left) and antisymmetric modes (right). z direction is vertical to the plane. The scale bar in left panel is 10 μm , which is valid for all of the other field patterns.

Fig. 2
Fig. 2

(a) Schematic picture of two cavities with a NP. (b) FFP from the same resonant mode in Fig. 1. (c), (d) Field patterns log | E z | of symmetric and antisymmetric modes. Highly directional beams can be observed even 40 μm away from cavities.

Fig. 3
Fig. 3

(a), (b) Dependence of divergent angles on refractive index (n) and cavity size (R). Other parameters are same as in Figs. 1, 2. (c), (d) Dependence of divergence angle on separation distance between cavities (d) with R 2 = 125 nm and the size of NP ( R 2 ) with d = 550 nm . Other param eters in (c), (d) are set as: n = 1.757 , R = 5 μm , R 3 = 5.01 μm .

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