Abstract

We propose to approximate a spherically symmetric Bragg resonator in an onionlike geometry. We develop a transfer-matrix theory for calculation of the quality factors and analyze the effect of the onion stem on cavity Q factors. We find that it is possible to achieve significant inhibition of spontaneous emission in an onion resonator with omnidirectional cladding layers.

© 2003 Optical Society of America

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References

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  1. E. M. Purcell, Phys. Rev. 69, 681 (1946).
    [CrossRef]
  2. J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
    [CrossRef]
  3. J. R. Buck and H. J. Kimble, Phys. Rev. A 67, 033806 (2003).
    [CrossRef]
  4. D. Brady, G. Papen, and J. E. Sipe, J. Opt. Soc. Am. B 10, 644 (1993).
    [CrossRef]
  5. M. A. Kaliteevski, S. Brand, R. A. Abram, and V. V. Nikolaev, J. Mod. Opt. 48, 1503 (2001).
    [CrossRef]
  6. J. G. Fleming, S.-Y. Lin, and R. Handley, in Proceedings of the Solid-State Sensor, Actuator, and Microsystems Workshop (Transducer Research Foundation, Cleveland, Ohio, 2002), p. 173.
  7. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
    [CrossRef]
  8. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  9. S. John and T. Quang, Phys. Rev. Lett. 74, 3419 (1995).
    [CrossRef] [PubMed]

2003 (1)

J. R. Buck and H. J. Kimble, Phys. Rev. A 67, 033806 (2003).
[CrossRef]

2002 (1)

J. G. Fleming, S.-Y. Lin, and R. Handley, in Proceedings of the Solid-State Sensor, Actuator, and Microsystems Workshop (Transducer Research Foundation, Cleveland, Ohio, 2002), p. 173.

2001 (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, and V. V. Nikolaev, J. Mod. Opt. 48, 1503 (2001).
[CrossRef]

1999 (1)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

1998 (2)

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[CrossRef]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
[CrossRef]

1995 (1)

S. John and T. Quang, Phys. Rev. Lett. 74, 3419 (1995).
[CrossRef] [PubMed]

1993 (1)

D. Brady, G. Papen, and J. E. Sipe, J. Opt. Soc. Am. B 10, 644 (1993).
[CrossRef]

1946 (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Abram, R. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, and V. V. Nikolaev, J. Mod. Opt. 48, 1503 (2001).
[CrossRef]

Brady, D.

D. Brady, G. Papen, and J. E. Sipe, J. Opt. Soc. Am. B 10, 644 (1993).
[CrossRef]

Brand, S.

M. A. Kaliteevski, S. Brand, R. A. Abram, and V. V. Nikolaev, J. Mod. Opt. 48, 1503 (2001).
[CrossRef]

Buck, J. R.

J. R. Buck and H. J. Kimble, Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Costard, E.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
[CrossRef]

Fan, S.

Fink, Y.

Fleming, J. G.

J. G. Fleming, S.-Y. Lin, and R. Handley, in Proceedings of the Solid-State Sensor, Actuator, and Microsystems Workshop (Transducer Research Foundation, Cleveland, Ohio, 2002), p. 173.

Gayral, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
[CrossRef]

Gérard, J. M.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
[CrossRef]

Handley, R.

J. G. Fleming, S.-Y. Lin, and R. Handley, in Proceedings of the Solid-State Sensor, Actuator, and Microsystems Workshop (Transducer Research Foundation, Cleveland, Ohio, 2002), p. 173.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

Joannopoulos, J. D.

John, S.

S. John and T. Quang, Phys. Rev. Lett. 74, 3419 (1995).
[CrossRef] [PubMed]

Kaliteevski, M. A.

M. A. Kaliteevski, S. Brand, R. A. Abram, and V. V. Nikolaev, J. Mod. Opt. 48, 1503 (2001).
[CrossRef]

Kimble, H. J.

J. R. Buck and H. J. Kimble, Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Legrand, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
[CrossRef]

Lin, S.-Y.

J. G. Fleming, S.-Y. Lin, and R. Handley, in Proceedings of the Solid-State Sensor, Actuator, and Microsystems Workshop (Transducer Research Foundation, Cleveland, Ohio, 2002), p. 173.

Nikolaev, V. V.

M. A. Kaliteevski, S. Brand, R. A. Abram, and V. V. Nikolaev, J. Mod. Opt. 48, 1503 (2001).
[CrossRef]

Papen, G.

D. Brady, G. Papen, and J. E. Sipe, J. Opt. Soc. Am. B 10, 644 (1993).
[CrossRef]

Purcell, E. M.

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Quang, T.

S. John and T. Quang, Phys. Rev. Lett. 74, 3419 (1995).
[CrossRef] [PubMed]

Sermage, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
[CrossRef]

Sipe, J. E.

D. Brady, G. Papen, and J. E. Sipe, J. Opt. Soc. Am. B 10, 644 (1993).
[CrossRef]

Thierry-Mieg, V.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
[CrossRef]

Winn, J. N.

J. Mod. Opt. (1)

M. A. Kaliteevski, S. Brand, R. A. Abram, and V. V. Nikolaev, J. Mod. Opt. 48, 1503 (2001).
[CrossRef]

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

D. Brady, G. Papen, and J. E. Sipe, J. Opt. Soc. Am. B 10, 644 (1993).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Phys. Rev. A (1)

J. R. Buck and H. J. Kimble, Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Phys. Rev. Lett. (2)

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, Phys. Rev. Lett. 81, 1110 (1998).
[CrossRef]

S. John and T. Quang, Phys. Rev. Lett. 74, 3419 (1995).
[CrossRef] [PubMed]

Other (2)

J. G. Fleming, S.-Y. Lin, and R. Handley, in Proceedings of the Solid-State Sensor, Actuator, and Microsystems Workshop (Transducer Research Foundation, Cleveland, Ohio, 2002), p. 173.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

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Figures (3)

Fig. 1
Fig. 1

Schematics of a Bragg onion resonator.

Fig. 2
Fig. 2

(a), (b) Wavelength and Q factor of the onion resonator modes. (c) Quality factor of the TM20 modes as a function of the Bragg cladding pair number. The filled circles represent the analytical results, whereas the solid line represents the numerical fit of QDNclad.

Fig. 3
Fig. 3

Radial dependence of the TE50 and TE70 field.

Equations (5)

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

E=Znl m=-llikn×flknrXlm+glknrXlm,
MlZn,kn,rnAnBn=MlZn+1,kn+1,rnAn+1Bn+1,
MZn,kn,rn=unhl1knrnunhl2knrnvnrhl1knrrrnvnrhl2knrrrn,
AoutBout=T11T12T21T22AcoBco.
Qstem=l+12ll!22l+1!l1θ02l.

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