Abstract

Van de Hulst’s localization principle relates the principal mode number to the external beam position that maximizes energy coupling to a spherical cavity mode. Our experiments in lasing microdroplets verify localization but only for low-Q modes, when the cavity may be considered to be a nearly perfect homogeneous sphere. The principle fails in the perturbation-dominated high-Q limit. Surprisingly, near-surface resonances are still efficiently excited in these cases but require impact parameters slightly smaller than the sphere radius. Numerical modeling suggests that this new input channel depends on surface scattering.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
  2. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stairs, R. C. Tiberio, and S. T. Ho, Opt. Lett. 22, 1244 (1997).
    [CrossRef] [PubMed]
  3. B. E. Little, S. T. Chu, and H. A. Haus, Opt. Lett. 23, 894 (1998).
    [CrossRef]
  4. H.-B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994).
    [CrossRef] [PubMed]
  5. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, Opt. Lett. 23, 247 (1998).
    [CrossRef]
  6. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 208.
  7. J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 65, 2900 (1989); J. P. Barton and D. R. Alexander, Proc. SPIE 1497, 64 (1991).
    [CrossRef]
  8. J. A. Lock, Appl. Opt. 34, 559 (1995).
    [CrossRef] [PubMed]
  9. E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, Appl. Opt. 9, 1166 (1992).
    [CrossRef]
  10. A. W. Snyder and J. D. Love, IEEE Trans. Microwave Theory Tech. 23, 134 (1975).
    [CrossRef]
  11. J. D. Eversole, H.-B. Lin, and A. J. Campillo, J. Opt. Soc. Am. B 12, 287 (1995).
    [CrossRef]
  12. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 499 (1984); H.-B. Lin, A. L. Huston, B. L. Justus, and A. J. Campillo, Opt. Lett. 11, 614 (1986).
    [CrossRef] [PubMed]
  13. A. L. Huston, H.-B. Lin, J. D. Eversole, and A. J. Campillo, J. Opt. Soc. Am. B 13, 521 (1996).
    [CrossRef]
  14. J. P. Barton and D. R. Alexander, J. Appl. Phys. 69, 7973 (1991).
    [CrossRef]
  15. J.-Z. Zhang, D. H. Leach, and R. K. Chang, Opt. Lett. 13, 270 (1988).
    [CrossRef] [PubMed]

1998 (2)

1997 (1)

1996 (1)

1995 (2)

1994 (1)

H.-B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994).
[CrossRef] [PubMed]

1992 (1)

E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, Appl. Opt. 9, 1166 (1992).
[CrossRef]

1991 (1)

J. P. Barton and D. R. Alexander, J. Appl. Phys. 69, 7973 (1991).
[CrossRef]

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 65, 2900 (1989); J. P. Barton and D. R. Alexander, Proc. SPIE 1497, 64 (1991).
[CrossRef]

1988 (1)

1984 (1)

1975 (1)

A. W. Snyder and J. D. Love, IEEE Trans. Microwave Theory Tech. 23, 134 (1975).
[CrossRef]

Alexander, D. R.

J. P. Barton and D. R. Alexander, J. Appl. Phys. 69, 7973 (1991).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 65, 2900 (1989); J. P. Barton and D. R. Alexander, Proc. SPIE 1497, 64 (1991).
[CrossRef]

Barber, P. W.

E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, Appl. Opt. 9, 1166 (1992).
[CrossRef]

Barton, J. P.

J. P. Barton and D. R. Alexander, J. Appl. Phys. 69, 7973 (1991).
[CrossRef]

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 65, 2900 (1989); J. P. Barton and D. R. Alexander, Proc. SPIE 1497, 64 (1991).
[CrossRef]

Campillo, A. J.

Chang, R. K.

Chowdhury, D. Q.

E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, Appl. Opt. 9, 1166 (1992).
[CrossRef]

Chu, S. T.

Eversole, J. D.

Hagness, S. C.

Haus, H. A.

Hill, S. C.

E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, Appl. Opt. 9, 1166 (1992).
[CrossRef]

Ho, S. T.

Huston, A. L.

Ilchenko, V. S.

Khaled, E. E. M.

E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, Appl. Opt. 9, 1166 (1992).
[CrossRef]

Kimble, H. J.

Leach, D. H.

Lin, H.-B.

Little, B. E.

Lock, J. A.

Long, M. B.

Love, J. D.

A. W. Snyder and J. D. Love, IEEE Trans. Microwave Theory Tech. 23, 134 (1975).
[CrossRef]

Mabuchi, H.

Rafizadeh, D.

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 65, 2900 (1989); J. P. Barton and D. R. Alexander, Proc. SPIE 1497, 64 (1991).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, IEEE Trans. Microwave Theory Tech. 23, 134 (1975).
[CrossRef]

Stairs, K. A.

Streed, E. W.

Taflove, A.

Tiberio, R. C.

Tzeng, H.-M.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 208.

Vernooy, D. W.

Wall, K. F.

Zhang, J. P.

Zhang, J.-Z.

Appl. Opt. (2)

J. A. Lock, Appl. Opt. 34, 559 (1995).
[CrossRef] [PubMed]

E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, Appl. Opt. 9, 1166 (1992).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. W. Snyder and J. D. Love, IEEE Trans. Microwave Theory Tech. 23, 134 (1975).
[CrossRef]

J. Appl. Phys. (2)

J. P. Barton, D. R. Alexander, and S. A. Schaub, J. Appl. Phys. 65, 2900 (1989); J. P. Barton and D. R. Alexander, Proc. SPIE 1497, 64 (1991).
[CrossRef]

J. P. Barton and D. R. Alexander, J. Appl. Phys. 69, 7973 (1991).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

H.-B. Lin and A. J. Campillo, Phys. Rev. Lett. 73, 2440 (1994).
[CrossRef] [PubMed]

Other (2)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), p. 208.

R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Total fluorescence versus the vibrating-orifice frequency used to generate the monodisperse droplet stream. The orifice frequency is inversely proportional to radius a of the generated droplets. At specific droplet sizes, significant increases in the total fluorescence are observed, which correspond to input resonances (i.e., where the excitation laser and a given resonance mode have equal wavelength). Modes whose numbers are given with (without) boxes are TM (TE) modes. The upper (lower) number corresponds to the mode order (principal mode number).

Fig. 2
Fig. 2

Experimentally observed lasing intensity versus beam position in 6.795µm-radius water droplets for a third-order mode TE913,x=83.065,m=1.332 with a Q of 1.16×104. Solid curves, average fit to data from five radial scans. Dashed vertical lines, positions of the droplet water–air interfaces (i.e., a). Optimum excitation occurs at a spatial position outside the droplet rim, consistent with the localization principle. Arrows, optimal positions predicted by the approximate b=n+1/2λ/2π formula. Inset, the beam geometry used.

Fig. 3
Fig. 3

Same as in Fig. 2, except for 6.64µm-radius droplets and for a second-order mode TE942,x=81.256,m=1.332 with Q0=1.2×106.

Fig. 4
Fig. 4

Same as in Fig. 3, except for 6.43µm-radius droplets and for a first-order mode TE971,x=78.558,m=1.332 with Q0=1.4×109. Optimum excitation occurs at an impact parameter smaller than the droplet radius. The localization principle apparently fails because surface perturbations in the water droplets limit mode Q to a value of QS5×107Q0.

Fig. 5
Fig. 5

Numerical simulation for the TE971 resonance condition, assuming a sphere containing a small perturbation of the form r/a=1+εcos20 θ. As ε increases, the optimal excitation position moves closer to and finally slightly within the droplet, consistent with the data of Fig. 4.

Metrics