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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 11 — Nov. 1, 2000
  • pp: 1828–1834

Observation of emission from chaotic lasing modes in deformed microspheres: displacement by the stable-orbit modes

Seongsik Chang, Richard K. Chang, A. Douglas Stone, and Jens U. Nöckel  »View Author Affiliations

JOSA B, Vol. 17, Issue 11, pp. 1828-1834 (2000)

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By combining detailed imaging measurements at different tilt angles with simulations of ray emission from prolate-deformed lasing microdroplets, we conclude that the dominant contribution to the laser emission of such three-dimensional dielectric microcavities must come from modes associated with the chaotic region of the ray phase space. As a particularly striking signature, maximum emission from such chaotic lasing modes is not from tangent rays emerging from the highest curvature part of the rim. The laser emission is observed and calculated to be nontangent and displaced from the highest curvature regions owing to the presence of stable orbits. In this paper we present the first experimental evidence for this phenomenon of dynamical eclipsing.

© 2000 Optical Society of America

OCIS Codes
(140.1540) Lasers and laser optics : Chaos
(140.3410) Lasers and laser optics : Laser resonators
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators
(260.2110) Physical optics : Electromagnetic optics
(290.4020) Scattering : Mie theory

Seongsik Chang, Richard K. Chang, A. Douglas Stone, and Jens U. Nöckel, "Observation of emission from chaotic lasing modes in deformed microspheres: displacement by the stable-orbit modes," J. Opt. Soc. Am. B 17, 1828-1834 (2000)

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  1. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York, 1990).
  2. J. U. Nöckel, A. D. Stone, and R. K. Chang, “Q spoiling and directionality in deformed ring cavities,” Opt. Lett. 19, 1693–1695 (1994). [CrossRef]
  3. A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, and R. K. Chang, “Ray chaos and Q-spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2685 (1995). [CrossRef] [PubMed]
  4. J. U. Nöckel, A. D. Stone, G. Chen, H. Grossman, and R. K. Chang, “Directional emission from asymmetric resonant cavities,” Opt. Lett. 21, 1609–1611 (1996). [CrossRef]
  5. J. U. Nöckel and A. D. Stone, “Chaotic light: a theory of asymmetric cavity resonators,” in Optical Processes in Microcavities, R. K. Chang and A. J. Campillo, eds. (World Scientific, Singapore, 1996), Chap. 11.
  6. J. U. Nöckel and A. D. Stone, “Ray and wave chaos in asymmetric resonant cavities,” Nature (London) 385, 45–47 (1997). [CrossRef]
  7. B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993). [CrossRef]
  8. Because the system of interest has a low refractive index, the polarization dependence of decay rates will be neglected in this work, allowing us to reduce Maxwell’s equation to the scalar wave equation.
  9. P. LeBoeuf and M. Saraceno, “Eigenfunctions of nonintegrable systems in generalized phase spaces,” J. Phys. A Math. Nucl. Gen. 23, 1745–1764 (1990). [CrossRef]
  10. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998). [CrossRef] [PubMed]
  11. H. Waalkens, J. Wiersig, and H. Dullin, “The elliptic quantum billiard,” Ann. Phys. (N.Y.) 260, 50 (1997). [CrossRef]
  12. L. E. Reichl, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, New York, 1992).
  13. R. N. Berglund and B. Y. H. Liu, “Generation of monodis-perse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973). [CrossRef]
  14. H. Lamb, Hydrodynamics (Dover, New York, 1945), pp. 473–475.
  15. S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486 (1986). [CrossRef] [PubMed]
  16. The effect of gravity on the droplet trajectory is negligible owing to the relatively high speed of the droplets. The initial speed of the droplets emerging from the orifice of the droplet generator is 10 m/s, and the droplets used in the experiment are located ~1 cm below the orifice. For example, when the droplet generator shoots droplets horizontally, deviation between the true droplet trajectory and the one without gravity is only 0.028°.
  17. J. C. Swindal, D. H. Leach, R. K. Chang, and K. Young, “Precession of morphology-dependent resonances in nonspherical droplets,” Opt. Lett. 18, 191–193 (1993). [CrossRef]
  18. S. Chang, N. B. Rex, and R. K. Chang, “Chemical lasing in pendant droplets: lasing-spectra, emission-pattern, and cavity-lifetime measurements,” J. Opt. Soc. Am. B 16, 1224–1235 (1999). [CrossRef]
  19. Because the ray simulations do not include tunneling, they cannot account for the bright rims in the experimental images at θD=90°.

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