Abstract

The effect of coating thickness on photon tunneling behavior was investigated by measuring lasing spectra from a dielectric inner-coated cylindrical capillary filled with a dye-doped liquid. The lasing spectra showed a blueshift as the coating thickness decreased due to an enhanced photon tunneling probability of whispering gallery modes (WGMs). Cavity quality factors Q were quantitatively estimated from the center wavelengths and compared to those deduced by the WKB approximation model as well as a simplified multiple scattering formalism. The validity and limitation of two models were discussed at various coating thicknesses.

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    [CrossRef]
  2. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
    [CrossRef]
  3. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925-929 (2003).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2007 (2)

2004 (2)

J. E. Heebner, N. N. Lepeshkin, A. Schweinsber, G. W. Wicks, R. W. Boyd, R. Grover, and P.-T. Ho, “Enhanced linear and nonlinear optical phase response of AlGaAs microring resonators,” Opt. Lett. 29, 769-771 (2004).
[CrossRef] [PubMed]

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84, 4547-4549 (2004).
[CrossRef]

2003 (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

2001 (1)

M. V. Artemyev, U. Woggon, and R. Wannemacher, “Photons confined in hollow microspheres,” Appl. Phys. Lett. 78, 1032-1034 (2001).
[CrossRef]

2000 (1)

H. J. Moon, Y. T. Chough, and K. An, “Microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85, 3161-3164 (2000).
[CrossRef] [PubMed]

1995 (1)

1993 (1)

T. Kaiser and G. Schweiger, “Stable algorithm for the computation of Mie coefficients for scattered and transmitted fields of a coated sphere,” Comput. Phys. 7, 682-686 (1993).
[CrossRef]

1992 (2)

J. H. Lowry, J. S. Mendlowitz, and N. S. Subramanian, “Optical characteristics of Teflon AFR fluoroplastic materials,” Opt. Eng. 31, 1982-1985 (1992).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

1988 (1)

An, K.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84, 4547-4549 (2004).
[CrossRef]

H. J. Moon, Y. T. Chough, and K. An, “Microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85, 3161-3164 (2000).
[CrossRef] [PubMed]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Arnold, S.

Artemyev, M. V.

M. V. Artemyev, U. Woggon, and R. Wannemacher, “Photons confined in hollow microspheres,” Appl. Phys. Lett. 78, 1032-1034 (2001).
[CrossRef]

Barber, P. W.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990), Chapt. 2.
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999), p. 70.

Boyd, R. W.

Chang, R. K.

Chen, G.

Chough, Y. T.

H. J. Moon, Y. T. Chough, and K. An, “Microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85, 3161-3164 (2000).
[CrossRef] [PubMed]

Gillespie, J. B.

Grover, R.

Heebner, J. E.

Hightower, R. L.

Hill, S. C.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990), Chapt. 2.
[CrossRef]

Ho, P.-T.

Kaiser, T.

T. Kaiser and G. Schweiger, “Stable algorithm for the computation of Mie coefficients for scattered and transmitted fields of a coated sphere,” Comput. Phys. 7, 682-686 (1993).
[CrossRef]

Kang, D. Y.

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Lee, J. H.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84, 4547-4549 (2004).
[CrossRef]

Lee, S. B.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84, 4547-4549 (2004).
[CrossRef]

Lepeshkin, N. N.

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Lowry, J. H.

J. H. Lowry, J. S. Mendlowitz, and N. S. Subramanian, “Optical characteristics of Teflon AFR fluoroplastic materials,” Opt. Eng. 31, 1982-1985 (1992).
[CrossRef]

Mazumder, M. M.

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Mendlowitz, J. S.

J. H. Lowry, J. S. Mendlowitz, and N. S. Subramanian, “Optical characteristics of Teflon AFR fluoroplastic materials,” Opt. Eng. 31, 1982-1985 (1992).
[CrossRef]

Moon, H. J.

H. J. Moon and D. Y. Kang, “Strongly enhanced mode selection in a thin dielectric-coated layered microcavity laser,” Opt. Lett. 32, 1554-1556 (2007).
[CrossRef] [PubMed]

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84, 4547-4549 (2004).
[CrossRef]

H. J. Moon, Y. T. Chough, and K. An, “Microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85, 3161-3164 (2000).
[CrossRef] [PubMed]

Nöckel, J. U.

J. U. Nöckel, Resonance in Nonintegrable Open System, Ph.D. Dissertation, Yale Univ. (1997), Chapt. 8.

Park, G. W.

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84, 4547-4549 (2004).
[CrossRef]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Richardson, C. B.

Schweiger, G.

T. Kaiser and G. Schweiger, “Stable algorithm for the computation of Mie coefficients for scattered and transmitted fields of a coated sphere,” Comput. Phys. 7, 682-686 (1993).
[CrossRef]

Schweinsber, A.

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Subramanian, N. S.

J. H. Lowry, J. S. Mendlowitz, and N. S. Subramanian, “Optical characteristics of Teflon AFR fluoroplastic materials,” Opt. Eng. 31, 1982-1985 (1992).
[CrossRef]

Teraoka, I.

Vahala, K. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Wannemacher, R.

M. V. Artemyev, U. Woggon, and R. Wannemacher, “Photons confined in hollow microspheres,” Appl. Phys. Lett. 78, 1032-1034 (2001).
[CrossRef]

Wicks, G. W.

Woggon, U.

M. V. Artemyev, U. Woggon, and R. Wannemacher, “Photons confined in hollow microspheres,” Appl. Phys. Lett. 78, 1032-1034 (2001).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999), p. 70.

Appl. Opt. (1)

Appl. Phys. Lett. (3)

H. J. Moon, G. W. Park, S. B. Lee, K. An, and J. H. Lee, “Waveguide mode lasing via evanescent-wave-coupled gain from a thin cylindrical shell resonator,” Appl. Phys. Lett. 84, 4547-4549 (2004).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

M. V. Artemyev, U. Woggon, and R. Wannemacher, “Photons confined in hollow microspheres,” Appl. Phys. Lett. 78, 1032-1034 (2001).
[CrossRef]

Comput. Phys. (1)

T. Kaiser and G. Schweiger, “Stable algorithm for the computation of Mie coefficients for scattered and transmitted fields of a coated sphere,” Comput. Phys. 7, 682-686 (1993).
[CrossRef]

Nature (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Opt. Eng. (1)

J. H. Lowry, J. S. Mendlowitz, and N. S. Subramanian, “Optical characteristics of Teflon AFR fluoroplastic materials,” Opt. Eng. 31, 1982-1985 (1992).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

H. J. Moon, Y. T. Chough, and K. An, “Microcavity laser based on the evanescent-wave-coupled gain,” Phys. Rev. Lett. 85, 3161-3164 (2000).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of Optics (Cambridge Univ. Press, 1999), p. 70.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990), Chapt. 2.
[CrossRef]

J. U. Nöckel, Resonance in Nonintegrable Open System, Ph.D. Dissertation, Yale Univ. (1997), Chapt. 8.

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Figures (8)

Fig. 1
Fig. 1

Quasi-bound states in an effective potential well V eff ( ρ ) of a circular microcavity (radius a, refractive index m 1 ) with a mode number n. δ n , l is the penetration depth defined as the width of the classically forbidden region.

Fig. 2
Fig. 2

Considered thin dielectric-coated circular microcavity.

Fig. 3
Fig. 3

Quasi-bound states in a potential well of a coated cylindrical cavity in the case of m 3 > m 1 > m 2 .

Fig. 4
Fig. 4

Typical cross-sectional SEM images of AF1600 inner-coated capillaries. (a) d 0.6 μ m , (b) d 1.3 μ m .

Fig. 5
Fig. 5

Typical lasing spectra at various thickness d of AF 1600. (a) d 2.0 μ m , (b) d 1.3 ( 0.1 ) μ m , (c) d 0.9 ( 0.1 ) μ m , (d) d 0.5 0.6 μ m , (e) d 0.3 0.4 μ m .

Fig. 6
Fig. 6

Plot of γ ( λ ) at various values of Q. (a) Q = 1 × 10 5 , (b) Q = 4.5 × 10 4 , (c) Q = 3 × 10 3 . The minimum of γ ( λ ) or center wavelength of lasing, its location denoted by an arrow, is fitted as about 583 nm , 576 nm , and 563 nm , respectively.

Fig. 7
Fig. 7

Schematic of multiple scattering (refraction/reflection) by a flat thin film.

Fig. 8
Fig. 8

Calculated quality factor Q mult by multiple scattering formalism with respect to θ 1 . (a) d 2.0 μ m , (b) d 1.2 1.4 μ m , (c) d 0.8 1.0 μ m , (d) d 0.5 0.6 μ m , (e) d 0.4 μ m . The position of θ 1 = 80.5 ° is denoted by a vertical line.

Tables (1)

Tables Icon

Table 1 Summarized Quality Factors ( Q mea , Q WKB , Q mult ) at Various d

Equations (8)

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V eff ( ρ ) = [ k n , l 2 ( 1 m 2 ( ρ ) ) + n 2 ρ 2 ] ,
γ ( λ ) = 2 π m 1 [ λ Q n t ] + σ a ( λ ) σ e ( λ ) + σ a ( λ ) ,
T exp ( 2 barrier d ρ V eff ( ρ ) E ) = exp ( 2 barrier d ρ n 2 ρ 2 ( m 2 k n , l ) 2 ) = exp ( 2 n [ 1 ( m 2 k n , l ρ n ) 2 ln | ( n ρ ) ( 1 + 1 ( m 2 k n , l ρ n ) 2 ) | ] a δ n , l or d ) ,
Q WKB ω W P 2 m 1 k a cos θ 1 T = 2 m r x cos θ 1 T .
r 12 = m 1 cos θ 1 j m 1 2 sin 2 θ 1 m 2 2 m 1 cos θ 1 + j m 1 2 sin 2 θ 1 m 2 2 ,
r 23 = j m 1 2 sin 2 θ 1 m 2 2 m 3 2 m 1 2 sin 2 θ 1 j m 1 2 sin 2 θ 1 m 2 2 + m 3 2 m 1 2 sin 2 θ 1 .
R = e 2 b + e 2 b + 2 cos ( φ 12 φ 23 ) e 2 b + e 2 b + 2 cos ( φ 12 + φ 23 ) ,
Q mult 2 π m 1 a λ R t 1 4 1 R t 1 2 .

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