Abstract

The depth-resolved luminescence of whispering gallery modes (WGMs) was studied in TiO2:Eu3+ microsphere using cathode luminescence. As the penetration depth of the electron beam into the microsphere was increased through the control of the accelerating voltage, periodic structures appeared superimposed over the intrinsic transition lines of Eu3+, which were attributable to the cavity enhancement effect of the spontaneous emission by WGM resonance. The calculated radial intensity distribution of the WGM and the penetration depth explained the observed dependence of the WGM structure’s visibility on the accelerating voltage.

© 2008 Optical Society of America

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References

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S. F. Preble, Q. Xu, and Mi. Lipson, Nat. Photonics 5, 241 (2007).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

2006

M. Tomita, K. Totsuka, H. Ikari, K. Ohara, H. Mimura, H. Watanabe, H. Kume, and T. Matsumoto, Appl. Phys. Lett. 89, 061126 (2006).
[CrossRef]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

K. Totsuka and M. Tomita, J. Opt. Soc. Am. B 23, 2194 (2006).
[CrossRef]

2005

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

2004

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

2003

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

2001

H. C. Ong, A. S. K. Li, and G. T. Du, Appl. Phys. Lett. 78, 2667 (2001).
[CrossRef]

1995

1993

A. B. Hardy, W. E. Rhine, and H. K. Bowen, J. Am. Ceram. Soc. 76, 97 (1993).
[CrossRef]

1984

1960

C. S. Feldman, Phys. Rev. 117, 455 (1960).
[CrossRef]

Appl. Phys. Lett.

H. C. Ong, A. S. K. Li, and G. T. Du, Appl. Phys. Lett. 78, 2667 (2001).
[CrossRef]

M. Tomita, K. Totsuka, H. Ikari, K. Ohara, H. Mimura, H. Watanabe, H. Kume, and T. Matsumoto, Appl. Phys. Lett. 89, 061126 (2006).
[CrossRef]

J. Am. Ceram. Soc.

A. B. Hardy, W. E. Rhine, and H. K. Bowen, J. Am. Ceram. Soc. 76, 97 (1993).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nat. Photonics

S. F. Preble, Q. Xu, and Mi. Lipson, Nat. Photonics 5, 241 (2007).
[CrossRef]

Nature

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

Opt. Lett.

Phys. Rev.

C. S. Feldman, Phys. Rev. 117, 455 (1960).
[CrossRef]

Phys. Rev. Lett.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. 93, 233903 (2004).
[CrossRef] [PubMed]

M. F. Yanik and S. Fan, Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

A. Schliesser, P. Del'Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, Phys. Rev. Lett. 97, 243905 (2006).
[CrossRef]

K. Totsuka, N. Kobayashi, and M. Tomita, Phys. Rev. Lett. 98, 213904 (2007).
[CrossRef] [PubMed]

Other

H. Ikari, K. Okanishi, M. Tomita, and T. Ishidate, Opt. Mater. "Flourescence MDR features of Eu3+ doped sol-gel TiO2 hydrate microspheres" (to be published).

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific Publishing, 1996).
[CrossRef]

R. K. Chang, Optical Effects Associated with Small Particles (World Scientific Publishing, 1988).

W. M. Yen, S. Shionoya, and H. Yamamoto, Phosphor Handbook (CRC Press, 2006).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the experimental setup. EB, electron beam; SM, spherical mirror; CCD, charge-coupled device camera. (b) Scanning electron microscope photograph of the fabricated microsphere.

Fig. 2
Fig. 2

Cathode luminescence spectra of d = 12.2 μ m Ti O 2 : Eu 3 + . The vertical lines indicate the free spectral range of Δ ν = 5.0 THz .

Fig. 3
Fig. 3

Solid circles indicate the normalized visibility of the WGM structure in the cathode luminescence as a function of the accelerating voltage. The solid curve denotes the penetration depth as a function of the accelerating voltage. The inset shows the definition of the visibility: 1 2 C ( A + B ) .

Fig. 4
Fig. 4

Thick dashed, solid, and dotted curves show the normalized radial intensity distribution of WGM, TE 144 , 1 , TE 137 , 2 , and TE 131 , 3 , respectively, calculated using the Mie theorem. The thin curves represent the normalized electron beam intensity from the sphere surface calculated using the Feldman formalism.

Equations (1)

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E ( z ) = E 0 ( 1 z R ) 1 2 , R = 250 A 0 ρ ( E 0 Z 1 2 ) n , n = 1.2 1 0.29 log 10 Z ,

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