Abstract

Coupling between whispering-gallery modes is studied using imaging spectroscopy in pairs of size-selected (size deviation of <0.03%) spheres in a touching position. In a special geometrical configuration, peculiar shapes resembling kites are observed in the spectral images of bispheres by coupling of multiple pairs of azimuthal modes. The maximal WGM coupling is observed in the equatorial plane of spheres determined by the substrate. The WGM coupling constant is quantified for spheres from 2.9 to 6μm for such modes.

© 2009 Optical Society of America

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2008

J. Ng and C. T. Chan, Appl. Phys. Lett. 92, 251109 (2008).
[CrossRef]

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A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

N. Le Thomas, U. Woggon, W. Langbein, and M. V. Artemyev, J. Opt. Soc. Am. B 23, 2361 (2006).
[CrossRef]

2005

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

2004

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

2000

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

1999

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, Opt. Lett. 24, 711 (1999).
[CrossRef]

Artemyev, M. V.

Ashili, S. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Astratov, V. N.

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Bardley, A. L.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Boland, J. J.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Cai, W.

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

Chan, C. T.

J. Ng and C. T. Chan, Appl. Phys. Lett. 92, 251109 (2008).
[CrossRef]

Connolly, T. M.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Donegan, J. F.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Franchak, J. P.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

Gaponik, N.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Gerlach, M.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Hara, Y.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

Jimba, Y.

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Kanaev, A. V.

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

Kuwata-Gonokami, M.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Langbein, W.

Lee, R. K.

Miyazaki, H.

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Mukaiyama, T.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Ng, J.

J. Ng and C. T. Chan, Appl. Phys. Lett. 92, 251109 (2008).
[CrossRef]

Rakovich, Y. P.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Rogach, A.

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Scherer, A.

Takeda, K.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Thomas, N. Le

Woggon, U.

Xu, Y.

Yariv, A.

Appl. Phys. Lett.

V. N. Astratov, J. P. Franchak, and S. P. Ashili, Appl. Phys. Lett. 85, 5508 (2004).
[CrossRef]

A. V. Kanaev, V. N. Astratov, and W. Cai, Appl. Phys. Lett. 88, 111111 (2006).
[CrossRef]

J. Ng and C. T. Chan, Appl. Phys. Lett. 92, 251109 (2008).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

Y. P. Rakovich, J. F. Donegan, M. Gerlach, A. L. Bardley, T. M. Connolly, J. J. Boland, N. Gaponik, and A. Rogach, Phys. Rev. A 70, 051801 (2004).
[CrossRef]

Phys. Rev. B

H. Miyazaki and Y. Jimba, Phys. Rev. B 62, 7976 (2000).
[CrossRef]

Phys. Rev. Lett.

T. Mukaiyama, K. Takeda, H. Miyazaki, Y. Jimba, and M. Kuwata-Gonokami, Phys. Rev. Lett. 82, 4623 (1999).
[CrossRef]

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, Phys. Rev. Lett. 94, 203905 (2005).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) FL emission spectrum with WGM peaks along with the spectral image of a 5 μ m microsphere. (b) Schematic of WGMs ( | m | = l ) in the equatorial planes of two separated microspheres. (c) First Korean letter formed by spheres manipulated by a tapered fiber. (d),(e) Bispheres assembled parallel and perpendicular to the edge of the substrate, respectively.

Fig. 2
Fig. 2

FL spectral images (right) obtained from the same pair of size-matched 5 μ m cavities assembled on a substrate in different configurations shown on the left. (a) Separated spheres ( d = 5 μ m ) with collection of FL emission through the substrate. (b) Touching spheres with collection of light perpendicular to the axis of the bisphere. The slit is aligned with the equatorial plane. (c) Touching spheres with collection of light along the axis of the bisphere. The slit is oriented perpendicular to the equatorial plane.

Fig. 3
Fig. 3

Mechanism of formation of kites illustrated for the TE 36 2 peak. Intensity distributions are shown for (a) fundamental and (b) lower-order ( | m | < l ) azimuthal WGMs. The locations of their intensity maxima on the slit are indicated by dotted line A for (c) fundamental and by dotted lines B and C for (e) lower-order azimuthal modes. (d) Comparison of the splitting observed in kites along the lines A, B, and C.

Fig. 4
Fig. 4

Coupling coefficient κ as a function of the angular ( l ) mode numbers measured for TE l n and TM l n WGMs in size-matched bispheres with sizes from 2.9 to 6 μ m in a contact position.

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