Abstract

We show that manipulation by a spatial profile of the refractive index of a circularly symmetric dielectric cavity results in a novel way of fine tuning frequency separations as well as spatial localizations of high-Q whispering-gallery modes excited in the cavity. The method permits dispersion compensation in the modes (spectrum equalization), diminishes the quality-factor limitation by surface roughness and contamination, and allows critical coupling to ultra-high-Q modes without maintaining an air gap with evanescent couplers.

© 2003 Optical Society of America

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  1. V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
    [CrossRef]
  2. L. Collot, V. Lefevre-Seguin, M. Brune, J.-M. Raimond, S. Haroshe, “Very high-Q whispering-gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
    [CrossRef]
  3. M. L. Gorodetsky, A. A. Savchenkov, V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996).
    [CrossRef] [PubMed]
  4. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
    [CrossRef]
  5. H. M. Tzeng, K. F. Wall, M. B. Long, R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984).
    [CrossRef] [PubMed]
  6. J. C. Knight, H. S. T. Driver, R. J. Hutcheon, G. N. Robertson, “Core-resonance capillary-fiber whispering-gallery-mode laser,” Opt. Lett. 17, 1280–1282 (1992).
    [CrossRef] [PubMed]
  7. A. F. J. Levi, S. L. McCall, S. J. Pearton, R. A. Logan, “Room-temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1668 (1993).
    [CrossRef]
  8. V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
    [CrossRef] [PubMed]
  9. F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
    [CrossRef]
  10. F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).
  11. M. Pelton, Y. Yamamoto, “Ultralow threshold laser using a single quantum dot and a microsphere cavity,” Phys. Rev. A 59, 2418–2421 (1999).
    [CrossRef]
  12. A. N. Oraevsky, M. O. Scully, T. V. Sarkisyan, D. K. Bandy, “Using whispering gallery modes in semiconductor microdevices,” Laser Phys. 9, 990–1003 (1999).
  13. M. Cai, O. Painter, K. J. Vahala, P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25, 1430–1432 (2000).
    [CrossRef]
  14. F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
    [CrossRef]
  15. Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).
  16. D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
    [CrossRef]
  17. G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
    [CrossRef]
  18. V. S. Ilchenko, X. S. Yao, L. Maleki, “Microsphere integration in active and passive photonics devices,” in Laser Resonators III, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE3930, 154–162 (2000).
    [CrossRef]
  19. V. S. Ilchenko, L. Maleki, “Novel whispering-gallery resonators for lasers, modulators, and sensors,” in Laser Resonators IV, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE4270, 120–130 (2001).
    [CrossRef]
  20. W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, V. Lefevre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” New J. Phys. 3, 141–144 (2001).
    [CrossRef]
  21. S. Blair, Y. Chen, “Resonant-enhanced evanescent-wave fluorescence biosensing with cylindrical optical cavities,” Appl. Opt. 40, 570–582 (2001).
    [CrossRef]
  22. R. W. Boyd, J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742–5747 (2001).
    [CrossRef]
  23. A. Eschmann, C. W. Gardiner, “Stability and switching in whispering gallery mode microdisk lasers,” Phys. Rev. A 49, 2907–2913 (1994).
    [CrossRef] [PubMed]
  24. F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, T. J. A. Pompa, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
    [CrossRef]
  25. J. Popp, M. H. Fields, R. K. Chang, “Q switching by saturable absorption in microdroplets: elastic scattering and laser emission,” Opt. Lett. 22, 1296–1298 (1997).
    [CrossRef]
  26. J. E. Heebner, R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
    [CrossRef]
  27. V. V. Klimov, M. Ducloy, V. S. Letokhov, “Strong interaction between a two-level atom and the whispering-gallery modes of a dielectric microsphere: quantum-mechanical consideration,” Phys. Rev. A 59, 2996–3014 (1999).
    [CrossRef]
  28. V. S. Ilchenko, M. L. Gorodetsky, X. S. Yao, L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt. Lett. 26, 256–258 (2001).
    [CrossRef]
  29. D. Q. Chowdhury, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in radially inhomogeneous spheres,” J. Opt. Soc. Am. A 8, 1702–1705 (1991).
    [CrossRef]
  30. The equation for TM modes looks similar; however, we do not consider it here for the sake of clarity.
  31. C. C. Lam, P. T. Leung, K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
    [CrossRef]
  32. L. G. Guimaraes, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
    [CrossRef]
  33. M. L. Gorodetsky, A. D. Pryamikov, V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000).
    [CrossRef]

2001 (5)

Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, V. Lefevre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” New J. Phys. 3, 141–144 (2001).
[CrossRef]

S. Blair, Y. Chen, “Resonant-enhanced evanescent-wave fluorescence biosensing with cylindrical optical cavities,” Appl. Opt. 40, 570–582 (2001).
[CrossRef]

V. S. Ilchenko, M. L. Gorodetsky, X. S. Yao, L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt. Lett. 26, 256–258 (2001).
[CrossRef]

R. W. Boyd, J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742–5747 (2001).
[CrossRef]

2000 (4)

M. Cai, O. Painter, K. J. Vahala, P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25, 1430–1432 (2000).
[CrossRef]

M. L. Gorodetsky, A. D. Pryamikov, V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000).
[CrossRef]

F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
[CrossRef]

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

1999 (4)

V. V. Klimov, M. Ducloy, V. S. Letokhov, “Strong interaction between a two-level atom and the whispering-gallery modes of a dielectric microsphere: quantum-mechanical consideration,” Phys. Rev. A 59, 2996–3014 (1999).
[CrossRef]

M. Pelton, Y. Yamamoto, “Ultralow threshold laser using a single quantum dot and a microsphere cavity,” Phys. Rev. A 59, 2418–2421 (1999).
[CrossRef]

A. N. Oraevsky, M. O. Scully, T. V. Sarkisyan, D. K. Bandy, “Using whispering gallery modes in semiconductor microdevices,” Laser Phys. 9, 990–1003 (1999).

J. E. Heebner, R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24, 847–849 (1999).
[CrossRef]

1998 (4)

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

1997 (2)

J. Popp, M. H. Fields, R. K. Chang, “Q switching by saturable absorption in microdroplets: elastic scattering and laser emission,” Opt. Lett. 22, 1296–1298 (1997).
[CrossRef]

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, T. J. A. Pompa, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

1996 (2)

M. L. Gorodetsky, A. A. Savchenkov, V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996).
[CrossRef] [PubMed]

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

1994 (1)

A. Eschmann, C. W. Gardiner, “Stability and switching in whispering gallery mode microdisk lasers,” Phys. Rev. A 49, 2907–2913 (1994).
[CrossRef] [PubMed]

1993 (2)

L. Collot, V. Lefevre-Seguin, M. Brune, J.-M. Raimond, S. Haroshe, “Very high-Q whispering-gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

A. F. J. Levi, S. L. McCall, S. J. Pearton, R. A. Logan, “Room-temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1668 (1993).
[CrossRef]

1992 (3)

1991 (1)

1989 (1)

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

1984 (1)

An, K. Y.

Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).

Annino, G.

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

Bandy, D. K.

A. N. Oraevsky, M. O. Scully, T. V. Sarkisyan, D. K. Bandy, “Using whispering gallery modes in semiconductor microdevices,” Laser Phys. 9, 990–1003 (1999).

Barber, P. W.

Blair, S.

Blom, F. C.

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, T. J. A. Pompa, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Boyd, R. W.

Braginsky, V. B.

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Brune, M.

L. Collot, V. Lefevre-Seguin, M. Brune, J.-M. Raimond, S. Haroshe, “Very high-Q whispering-gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Cai, M.

Cassettari, M.

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

Chang, J. S.

Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).

Chang, R. K.

Chen, Y.

Choi, Y. S.

Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).

Chowdhury, D. Q.

Collot, L.

L. Collot, V. Lefevre-Seguin, M. Brune, J.-M. Raimond, S. Haroshe, “Very high-Q whispering-gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Domokos, P.

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

Driessen, A.

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, T. J. A. Pompa, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Driver, H. S. T.

Dubreuil, N.

F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
[CrossRef]

Ducloy, M.

V. V. Klimov, M. Ducloy, V. S. Letokhov, “Strong interaction between a two-level atom and the whispering-gallery modes of a dielectric microsphere: quantum-mechanical consideration,” Phys. Rev. A 59, 2996–3014 (1999).
[CrossRef]

Dupriez, P.

F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
[CrossRef]

Eschmann, A.

A. Eschmann, C. W. Gardiner, “Stability and switching in whispering gallery mode microdisk lasers,” Phys. Rev. A 49, 2907–2913 (1994).
[CrossRef] [PubMed]

Feron, P.

F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
[CrossRef]

Fields, M. H.

Fittipaldi, M.

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

Furusawa, A.

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Gardiner, C. W.

A. Eschmann, C. W. Gardiner, “Stability and switching in whispering gallery mode microdisk lasers,” Phys. Rev. A 49, 2907–2913 (1994).
[CrossRef] [PubMed]

Georgiades, N. P.

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Gorodetsky, M. L.

Guimaraes, L. G.

L. G. Guimaraes, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Hare, J.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, V. Lefevre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” New J. Phys. 3, 141–144 (2001).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Haroche, S.

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Haroshe, S.

L. Collot, V. Lefevre-Seguin, M. Brune, J.-M. Raimond, S. Haroshe, “Very high-Q whispering-gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Heebner, J. E.

Hill, S. C.

Hoekstra, H. J. W. M.

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, T. J. A. Pompa, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Hutcheon, R. J.

Ilchenko, V. S.

V. S. Ilchenko, M. L. Gorodetsky, X. S. Yao, L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt. Lett. 26, 256–258 (2001).
[CrossRef]

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, V. Lefevre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” New J. Phys. 3, 141–144 (2001).
[CrossRef]

M. L. Gorodetsky, A. D. Pryamikov, V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000).
[CrossRef]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
[CrossRef]

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

M. L. Gorodetsky, A. A. Savchenkov, V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996).
[CrossRef] [PubMed]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

V. S. Ilchenko, X. S. Yao, L. Maleki, “Microsphere integration in active and passive photonics devices,” in Laser Resonators III, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE3930, 154–162 (2000).
[CrossRef]

V. S. Ilchenko, L. Maleki, “Novel whispering-gallery resonators for lasers, modulators, and sensors,” in Laser Resonators IV, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE4270, 120–130 (2001).
[CrossRef]

Kimble, H. J.

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
[CrossRef]

Klimov, V. V.

V. V. Klimov, M. Ducloy, V. S. Letokhov, “Strong interaction between a two-level atom and the whispering-gallery modes of a dielectric microsphere: quantum-mechanical consideration,” Phys. Rev. A 59, 2996–3014 (1999).
[CrossRef]

Knight, J. C.

Lam, C. C.

Lee, J. H.

Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).

Lee, S. B.

Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).

Lefevre, V.

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

Lefevre-Seguin, V.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, V. Lefevre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” New J. Phys. 3, 141–144 (2001).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

L. Collot, V. Lefevre-Seguin, M. Brune, J.-M. Raimond, S. Haroshe, “Very high-Q whispering-gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Lenci, L.

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

Letokhov, V. S.

V. V. Klimov, M. Ducloy, V. S. Letokhov, “Strong interaction between a two-level atom and the whispering-gallery modes of a dielectric microsphere: quantum-mechanical consideration,” Phys. Rev. A 59, 2996–3014 (1999).
[CrossRef]

Leung, P. T.

Levi, A. F. J.

A. F. J. Levi, S. L. McCall, S. J. Pearton, R. A. Logan, “Room-temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1668 (1993).
[CrossRef]

Lissillour, F.

F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
[CrossRef]

Logan, R. A.

A. F. J. Levi, S. L. McCall, S. J. Pearton, R. A. Logan, “Room-temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1668 (1993).
[CrossRef]

Long, M. B.

Long, R.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, V. Lefevre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” New J. Phys. 3, 141–144 (2001).
[CrossRef]

Longo, I.

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

Mabuchi, H.

Maleki, L.

V. S. Ilchenko, M. L. Gorodetsky, X. S. Yao, L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt. Lett. 26, 256–258 (2001).
[CrossRef]

V. S. Ilchenko, X. S. Yao, L. Maleki, “Microsphere integration in active and passive photonics devices,” in Laser Resonators III, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE3930, 154–162 (2000).
[CrossRef]

V. S. Ilchenko, L. Maleki, “Novel whispering-gallery resonators for lasers, modulators, and sensors,” in Laser Resonators IV, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE4270, 120–130 (2001).
[CrossRef]

Martinelli, M.

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

Massa, C. A.

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

McCall, S. L.

A. F. J. Levi, S. L. McCall, S. J. Pearton, R. A. Logan, “Room-temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1668 (1993).
[CrossRef]

Moon, H. J.

Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).

Nussenzveig, H. M.

L. G. Guimaraes, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Oraevsky, A. N.

A. N. Oraevsky, M. O. Scully, T. V. Sarkisyan, D. K. Bandy, “Using whispering gallery modes in semiconductor microdevices,” Laser Phys. 9, 990–1003 (1999).

Painter, O.

Pardi, L. A.

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

Pearton, S. J.

A. F. J. Levi, S. L. McCall, S. J. Pearton, R. A. Logan, “Room-temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1668 (1993).
[CrossRef]

Pelton, M.

M. Pelton, Y. Yamamoto, “Ultralow threshold laser using a single quantum dot and a microsphere cavity,” Phys. Rev. A 59, 2418–2421 (1999).
[CrossRef]

Pompa, T. J. A.

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, T. J. A. Pompa, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Popp, J.

Poulain, M.

F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
[CrossRef]

Pryamikov, A. D.

Raimond, J. M.

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Raimond, J.-M.

L. Collot, V. Lefevre-Seguin, M. Brune, J.-M. Raimond, S. Haroshe, “Very high-Q whispering-gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Robertson, G. N.

Roch, J. F.

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

Sandoghdar, V.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Sarkisyan, T. V.

A. N. Oraevsky, M. O. Scully, T. V. Sarkisyan, D. K. Bandy, “Using whispering gallery modes in semiconductor microdevices,” Laser Phys. 9, 990–1003 (1999).

Savchenkov, A. A.

Scully, M. O.

A. N. Oraevsky, M. O. Scully, T. V. Sarkisyan, D. K. Bandy, “Using whispering gallery modes in semiconductor microdevices,” Laser Phys. 9, 990–1003 (1999).

Sercel, P. C.

Stephan, G. M.

F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
[CrossRef]

Streed, E. W.

Treussart, F.

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

Tzeng, H. M.

Vahala, K. J.

van Dijk, D. R.

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, T. J. A. Pompa, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Vernooy, D. W.

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247–249 (1998).
[CrossRef]

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

von Klitzing, W.

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, V. Lefevre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” New J. Phys. 3, 141–144 (2001).
[CrossRef]

Wall, K. F.

Yamamoto, Y.

M. Pelton, Y. Yamamoto, “Ultralow threshold laser using a single quantum dot and a microsphere cavity,” Phys. Rev. A 59, 2418–2421 (1999).
[CrossRef]

Yao, X. S.

V. S. Ilchenko, M. L. Gorodetsky, X. S. Yao, L. Maleki, “Microtorus: a high-finesse microcavity with whispering-gallery modes,” Opt. Lett. 26, 256–258 (2001).
[CrossRef]

V. S. Ilchenko, X. S. Yao, L. Maleki, “Microsphere integration in active and passive photonics devices,” in Laser Resonators III, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE3930, 154–162 (2000).
[CrossRef]

Young, K.

Appl. Magn. Res. (1)

G. Annino, M. Cassettari, M. Fittipaldi, L. Lenci, I. Longo, M. Martinelli, C. A. Massa, L. A. Pardi, “Whispering gallery mode dielectric resonators in EMR spectroscopy above 150 GHz: problems and perspectives,” Appl. Magn. Res. 19, 495–506 (2000).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, T. J. A. Pompa, “Experimental study of integrated-optics microcavity resonators: toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997).
[CrossRef]

Electron. Lett. (2)

F. Lissillour, P. Feron, N. Dubreuil, P. Dupriez, M. Poulain, G. M. Stephan, “Erbium-doped microspherical lasers at 1.56 µm,” Electron. Lett. 36, 1382–1384 (2000).
[CrossRef]

A. F. J. Levi, S. L. McCall, S. J. Pearton, R. A. Logan, “Room-temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1668 (1993).
[CrossRef]

Eur. Phys. J. D (1)

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium,” Eur. Phys. J. D 1, 235–238 (1998).

Europhys. Lett. (1)

L. Collot, V. Lefevre-Seguin, M. Brune, J.-M. Raimond, S. Haroshe, “Very high-Q whispering-gallery mode resonances observed in fused silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

J. Korean Phys. Soc. (1)

Y. S. Choi, H. J. Moon, K. Y. An, S. B. Lee, J. H. Lee, J. S. Chang, “Ultrahigh-Q microsphere dye laser based on evanescent-wave coupling,” J. Korean Phys. Soc. 39, 928–931 (2001).

J. Lumin. (1)

F. Treussart, V. S. Ilchenko, J. F. Roch, P. Domokos, J. Hare, V. Lefevre, J. M. Raimond, S. Haroche, “Whispering gallery mode microlaser at liquid helium temperature,” J. Lumin. 76, 670–673 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

Laser Phys. (1)

A. N. Oraevsky, M. O. Scully, T. V. Sarkisyan, D. K. Bandy, “Using whispering gallery modes in semiconductor microdevices,” Laser Phys. 9, 990–1003 (1999).

New J. Phys. (1)

W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, V. Lefevre-Seguin, “Tunable whispering gallery modes for spectroscopy and CQED experiments,” New J. Phys. 3, 141–144 (2001).
[CrossRef]

Opt. Commun. (1)

L. G. Guimaraes, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Opt. Lett. (8)

Phys. Lett. A (1)

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[CrossRef]

Phys. Rev. A (5)

V. Sandoghdar, F. Treussart, J. Hare, V. Lefevre-Seguin, J. M. Raimond, S. Haroche, “Very low threshold whispering-gallery-mode microsphere laser,” Phys. Rev. A 54, R1777–R1780 (1996).
[CrossRef] [PubMed]

M. Pelton, Y. Yamamoto, “Ultralow threshold laser using a single quantum dot and a microsphere cavity,” Phys. Rev. A 59, 2418–2421 (1999).
[CrossRef]

A. Eschmann, C. W. Gardiner, “Stability and switching in whispering gallery mode microdisk lasers,” Phys. Rev. A 49, 2907–2913 (1994).
[CrossRef] [PubMed]

V. V. Klimov, M. Ducloy, V. S. Letokhov, “Strong interaction between a two-level atom and the whispering-gallery modes of a dielectric microsphere: quantum-mechanical consideration,” Phys. Rev. A 59, 2996–3014 (1999).
[CrossRef]

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Other (3)

V. S. Ilchenko, X. S. Yao, L. Maleki, “Microsphere integration in active and passive photonics devices,” in Laser Resonators III, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE3930, 154–162 (2000).
[CrossRef]

V. S. Ilchenko, L. Maleki, “Novel whispering-gallery resonators for lasers, modulators, and sensors,” in Laser Resonators IV, A. Kudryashov, A. H. Paxton, eds., Proc. SPIE4270, 120–130 (2001).
[CrossRef]

The equation for TM modes looks similar; however, we do not consider it here for the sake of clarity.

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Figures (5)

Fig. 1
Fig. 1

Normalized second-order dispersion 2kq,ν/(kq,ν2) versus a normalized gradient of the index of refraction of the material ϵR/ϵ0 for ν0600. Unity dispersion corresponds to |2k1,ν/(k1,ν2)|ϵ=0 at ν=ν0.

Fig. 2
Fig. 2

Dependence of wave-vector eigenvalues kq,ν on a normalized gradient of the index of refraction ϵR/ϵ0 for ν600. Modes with different q become closer as the gradient increases. The modes pushed far away from the cavity boundary are nearly equidistant. Inset: amplitude profile for the fields for large index gradients. The mode wave functions are nearly symmetric.

Fig. 3
Fig. 3

Effective optical potential U for a transparent dielectric resonator with radius R. Solid curve, ϵ(r)=const. (R>r); short-dashed curve, ϵ(r)=ϵ0(3-2r/R) (critical gradient); long dashed curve, ϵ(r)=ϵ0(5-4r/R).

Fig. 4
Fig. 4

Radial dependencies of the susceptibility of a cavity material as well as of the amplitude profiles of the field (q=1) inside the cavity for various ϵ. Top, real scale for the field distributions in the case of ν0=600. The fields are localized close to the cavity surface. Bottom, amplitude profiles in detail. Curve (1) of the bottom plot corresponds to ϵR/ϵ0=0, curve (2) to ϵR/ϵ0=1, curve (3) to ϵR/ϵ0=2, and curve (4) to ϵR/ϵ0=2.4. It is easy to observe the pushing of the mode out of the cavity boundary (r=R) and into the cavity.

Fig. 5
Fig. 5

Quality factor Q˜ of a cavity with a gradient of the refractive index normalized by the quality factor Q of a cavity of the same radius without the gradient versus a normalized gradient of the refractive index. The plot is created for a cavity with radius R=4 mm, susceptibility ϵ0=2.1, and mode wavelength λ=1.55 µm.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

×(×E)+ϵ(r)c2 2Et2=0,
×(×e)-k2ϵ(r)e=0,
e=ν,m 1r ΨYν,m+1ϵ(r) ×(ΦYν,m),
2Ψr2+k2ϵ(r)-ν(ν+1)r2Ψ=0,
kν,q1Rϵ0 ν+αqν21/3-ϵ0ϵ0-11/2+3αq220 2ν1/3+O(ν-2/3),
2Ψr2+k2ϵ0-ν(ν+1)R2-r 2ν(ν+1)R3Ψ=0,
N=maxq2kν,qν2-1 kν,q2Q.
N11.2 ν8/3Q.
ϵ(r)=ϵ0+ϵ(R-r).
2Ψr2+k2ϵ0-ν(ν+1)R2-r2ν(ν+1)R3-k2ϵΨ=0.
Ψq(r)=Ψq,0Ai2ν(ν+1)R3-kq2ϵ1/3 rαq-αq,
kq2ϵ0-ν(ν+1)R2=αq2ν(ν+1)R3-kq2ϵ2/3.
kν,q1Rϵ0 ν+αqν21/31-R2 ϵϵ02/3.
N21.2 ν8/3Q 1-R2 ϵϵ0-2/3.
Qlexp4πdϵ0-1λ,
QlQ˜lQssQ˜ssψ2(r=R)0RΨ2(r)dr R(ϵ0-1)2ϵ0,

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