Abstract

A pump–probe two-photon-excited fluorescence technique deciphers in space and time the propagation of ballistic wave packets sustained by whispering-gallery modes (WGMs) in a spiral-shaped microcavity. Diffraction on the spiral discontinuity does not prevent the WGMs from closing. The resultant average Q of the resonator is 3×104 ±50%. Experimental results are compared with numerical simulations, providing evidence of a new contribution to output coupling: Part of the WGM evanescent wave is reflected at the spiral notch and leads to a propagating wave at an angle that matches the previously observed laser emission direction in 4-dicyanomethylene-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran-doped poly(methyl methacrylate) and InGaN spiral lasers.

© 2005 Optical Society of America

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2004 (4)

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

H. G. L. Schwefel, N. B. Rex, H. R. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, J. Opt. Soc. Am. B 21, 923 (2004).
[CrossRef]

H. Gersen, D. J. W. Klunder, J. P. Korterik, A. Driessen, N. F. van Hulst, and L. Kuipers, Opt. Lett. 29, 1291 (2004).
[CrossRef] [PubMed]

2003 (3)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

D. V. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

T. Ben-Messaoud, D. Wright, E. Toussaere, S. Dou, and J. Zyss, Synth. Met. 138, 347 (2003).
[CrossRef]

2001 (2)

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

A. W. Poon, F. Courvoisier, and R. K. Chang, Opt. Lett. 26, 632 (2001).
[CrossRef]

1993 (1)

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

1983 (1)

Armani, D. V.

D. V. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Beard, M. C.

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

Ben-Messaoud, T.

Brune, M.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Cao, H.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Chang, R. K.

H. G. L. Schwefel, N. B. Rex, H. R. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, J. Opt. Soc. Am. B 21, 923 (2004).
[CrossRef]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

A. W. Poon, F. Courvoisier, and R. K. Chang, Opt. Lett. 26, 632 (2001).
[CrossRef]

Chang, R. P. H.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Chen, X. H.

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Collot, L.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Courvoisier, F.

Dou, S.

T. Ben-Messaoud, D. Wright, E. Toussaere, S. Dou, and J. Zyss, Synth. Met. 138, 347 (2003).
[CrossRef]

Drake, J. M.

Driessen, A.

Fang, W.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Gersen, H.

Guo, W. H.

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

Haroche, S.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Ho, S. T.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Holler, S.

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

Huang, Y.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Huang, Y. Z.

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

Johnson, N. M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Kippenberg, T. J.

D. V. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Klunder, D. J. W.

Kneissl, M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Korterik, J. P.

Kuipers, L.

Lefevre-Seguin, V.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Lesiecki, M. L.

Liu, X.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Lu, Q. Y.

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

Luo, Y.

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

Pan, Y.-L.

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

Poon, A. W.

Raimond, J. M.

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

Rex, N. B.

Sansregret, J.

Schmuttenmaer, C. A.

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

Schwefel, H. G. L.

Spillane, S. M.

D. V. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Stone, A. D.

H. G. L. Schwefel, N. B. Rex, H. R. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, J. Opt. Soc. Am. B 21, 923 (2004).
[CrossRef]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Thomas, W. R. L.

Toussaere, E.

T. Ben-Messaoud, D. Wright, E. Toussaere, S. Dou, and J. Zyss, Synth. Met. 138, 347 (2003).
[CrossRef]

Tureci, H. E.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Tureci, H. R.

Turner, G. M.

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

Vahala, K. J.

D. V. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

van Hulst, N. F.

Wang, J.

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

Wolf, J.-P.

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

Wright, D.

T. Ben-Messaoud, D. Wright, E. Toussaere, S. Dou, and J. Zyss, Synth. Met. 138, 347 (2003).
[CrossRef]

Wu, X. H.

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Yu, L. J.

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

Zyss, J.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, Appl. Phys. Lett. 84, 2488 (2004).
[CrossRef]

Europhys. Lett. (1)

L. Collot, V. Lefevre-Seguin, M. Brune, J. M. Raimond, and S. Haroche, Europhys. Lett. 23, 327 (1993).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

Q. Y. Lu, X. H. Chen, W. H. Guo, L. J. Yu, Y. Z. Huang, J. Wang, and Y. Luo, IEEE Photonics Technol. Lett. 16, 359 (2004).
[CrossRef]

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

Nature (1)

D. V. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature 421, 925 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (1)

J.-P. Wolf, Y.-L. Pan, G. M. Turner, M. C. Beard, C. A. Schmuttenmaer, S. Holler, and R. K. Chang, Phys. Rev. A 64, 023808 (2001).
[CrossRef]

Synth. Met. (1)

T. Ben-Messaoud, D. Wright, E. Toussaere, S. Dou, and J. Zyss, Synth. Met. 138, 347 (2003).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of femtosecond pump–probe 2PEF to follow the wave packet traveling in the WGM of a spiral MC.

Fig. 2
Fig. 2

Sequence of 2PEF images during the first round trip of the pump pulse as a function of time delay with the probe. False color scale.

Fig. 3
Fig. 3

Left column, sequence of 2PEF images with a higher time resolution and new intensity scale to show the pulse propagating while it interacts with the notch. Despite its scattering, the pulse is recoupled in the WGMs for the second round trip. Right column, comparison with a 2D finite difference time domain in a spiral. The pulse behavior on the notch is the same as was observed experimentally. In the calculation a smaller radius ( r 0 = 37 μ m ) was used because of computation capacity constraints; this explains the recoupling in higher-order modes (closer to the MC center) than in the experiment with larger MCs.

Fig. 4
Fig. 4

2D finite difference time domain simulations, showing the reflection of the WGM evanescent part of the pulse on the notch side ( n = 2.6 , as for InGaN). The resultant propagating wave merges at 40° from the normal of the notch, as was observed in an InGaN spiral microlaser.[7] In the high-intensity region, fringes result from the interference between the totally reflected part of the pulse and the releasing part, which is unaffected by the discontinuity.

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