Abstract

Whispering gallery modes in a microsphere coated with three layers of high, low, and high refractive indices (RIs) are considered. Coastal modes and inland modes, centered on the outer and inner high-RI layers, exist as different radial modes. At right values of RI and thickness of the three layers, an inland mode and a coastal mode couple to produce a radial distribution of the photonic field that resembles bonding and antibonding orbitals. The coupling occurs across a layer of the middle low-RI layer, much thicker than the wavelength of light. The coupling is analyzed in a quantum-mechanical analog of a one-dimensional particle in a double-well potential.

© 2007 Optical Society of America

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References

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2006 (3)

B. Möller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113 (2006).
[CrossRef]

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

I. Teraoka and S. Arnold, J. Opt. Soc. Am. B 23, 1434 (2006).
[CrossRef]

2004 (1)

2002 (2)

D. D. Smith and K. A. Fuller, J. Opt. Soc. Am. B 19, 2449 (2002).
[CrossRef]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 80, 4057 (2002).
[CrossRef]

1999 (1)

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

1998 (1)

1992 (1)

Arnold, S.

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

I. Teraoka and S. Arnold, J. Opt. Soc. Am. B 23, 1434 (2006).
[CrossRef]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 80, 4057 (2002).
[CrossRef]

S. Arnold, J. Comunale, W. B. Whitte, J. M. Ramsey, and K. A. Fuller, J. Opt. Soc. Am. B 9, 819 (1992).
[CrossRef]

Artemyev, M. V.

B. Möller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113 (2006).
[CrossRef]

Braun, D.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 80, 4057 (2002).
[CrossRef]

Comunale, J.

Culic-Viskota, J.

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

Fuller, K. A.

Gaathon, O.

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

Ilchenko, V. S.

Jimba, Y.

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

Khoshsima, M.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 80, 4057 (2002).
[CrossRef]

Kimble, H. J.

Kuwata-Gonokami, M.

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

Libchaber, A.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 80, 4057 (2002).
[CrossRef]

Mabuchi, H.

Maleki, L.

Matsko, A. B.

Mihnev, M.

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

Miyazaki, H.

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

Möller, B.

B. Möller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113 (2006).
[CrossRef]

Mukaiyama, T.

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

Ramsey, J. M.

Savchenkov, A. A.

Smith, D. D.

Streed, E. W.

Takeda, K.

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

Teraoka, I.

I. Teraoka and S. Arnold, J. Opt. Soc. Am. B 23, 1434 (2006).
[CrossRef]

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 80, 4057 (2002).
[CrossRef]

Vernooy, D. W.

Vollmer, F.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 80, 4057 (2002).
[CrossRef]

Whitte, W. B.

Woggon, U.

B. Möller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 80, 4057 (2002).
[CrossRef]

O. Gaathon, J. Culic-Viskota, M. Mihnev, I. Teraoka, and S. Arnold, Appl. Phys. Lett. 89, 223901 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

B. Möller, U. Woggon, and M. V. Artemyev, J. Opt. A, Pure Appl. Opt. 8, S113 (2006).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

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

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Figures (4)

Fig. 1
Fig. 1

Triple-layer-coated microsphere with equatorial and meridional cross sections. Radial functions of the coupled modes are also shown.

Fig. 2
Fig. 2

Resonance wave vector k of TE modes ( l = 695 ) , plotted as a function of thickness t A of the outer high-RI layer in a microsphere of total radius a = 100 μ m having the RI profile shown in Fig. 1 ( n 1 = 1.452 , n 2 = 1.32 , n A = n C = 1.7 , n B = 1.4 , t B = 2.4 μ m , t C = 0.4 μ m ). IN i and CO j indicate the i th inland mode and the j th coastal mode, respectively.

Fig. 3
Fig. 3

Diagram of resonance k versus outer high-RI layer thickness t A , zoomed for a region where the first two radial modes couple. The parameters used were the same as those in Fig. 2. Radial functions S l are also shown for WGM (indicated by arrows).

Fig. 4
Fig. 4

Minimum resonance splitting Δ k min reached by changing t A , plotted as a function of the thickness t B of the middle layer. The values of n A = n C are indicated adjacent to the curves. The common parameters are: n B = 1.4 , t C = 0.4 μ m . Inset, square of the slope in ln Δ k min at t B = 0.4 μ m , plotted as a function of n A 2 . The line is the optimal linear fit.

Equations (1)

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X l m ( θ ) = i m [ P l m ( cos θ ) sin θ ] e ̂ θ ( θ ) P l m ( cos θ ) e ̂ φ ,

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