Abstract

We investigate the process of light matter interaction in a spherical Mie nanolaser. We derive a rigorous theory based on a three dimensional vector set of Maxwell-Bloch equations and solve the resulting equations through a parallel Finite-Difference Time-Domain Maxwell-Bloch (FDTD-MB) code. Our results predicts a rich physical scenario, ranging from nontrivial vectorial energy matter interplay in the pre-lasing regime to mode competitions and dynamical frequency pulling phenomena. Application of these effects could favor the realization of largely-tunable, nonlinearly controlled nanolaser devices.

© 2008 Optical Society of America

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  1. G. Mie, "Beitrge zur Optik trber Medien, speziell kolloidaler Metallsungen," Ann. Phys. 330, 377-445 (1908).
    [CrossRef]
  2. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  3. M. Xu and R. R. Alfano, "Random Walk of Polarized Light in Turbid Media," Phys. Rev. Lett. 95, 213901-(4) (2005).
    [CrossRef] [PubMed]
  4. Y. Yamamoto, F. Tassone, and H. Cao, Semiconductor Cavity Quantum Electrodynamics (Springer, Berlin, 2000).
  5. H. Yukawa, S. Arnold, and K. Miyano, "Microcavity effect of dyes adsorbed on a levitated droplet," Phys. Rev. A 60, 2491-2496 (1999).
    [CrossRef]
  6. P. W. Barber and K. Chang, Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988).
  7. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  8. P. J. Wyatt, "Scattering of Electromagnetic Plane Waves from Inhomogeneous Spherically Symmetric Objects," Phys. Rev. 127, 1837-1843 (1962).
    [CrossRef]
  9. A. Ashkin and J. M. Dziedzic, "Observation of Resonances in the Radiation Pressure on Dielectric Spheres," Phys. Rev. Lett. 38, 1351-1354 (1977).
    [CrossRef]
  10. L. Yang and K. J. Vahala, "Gain functionalization of silica microresonators," Opt. Lett. 28, 592-(3) (2003).
    [CrossRef] [PubMed]
  11. Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46, 66-73 (1993).
    [CrossRef]
  12. U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
    [CrossRef]
  13. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-(3) (2002).
    [CrossRef] [PubMed]
  14. V. Sandoghdar, F. Treussart, J. Hare, V. Lefvre-Seguin, and J. -M. Raimond, "Very low threshold whisperinggallery- mode microsphere laser," Phys. Rev. A 54, R1777-(4) (1996).
    [CrossRef] [PubMed]
  15. E. T. Jaynes and F. W. Cummings, "Comparison of Quantum and Semiclassical Radiation Theory with Application to the Beam Maser," Proc. IEEE. 51, 89-109 (1963).
    [CrossRef]
  16. G. W. Gardiner and P. Zoller, Quantum noise (Springer, Berlin, 2000).
  17. W. E. Lamb, "Theory of an Optical Maser," Phys. Rev. 134, A1429-A1450 (1964).
    [CrossRef]
  18. A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).
  19. G. Slavcheva, J. Arnold, and R. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Top. Quantum Electron. 10, 1052-1062 (2004).
    [CrossRef]
  20. G. Slavcheva, J. M. Arnold, I. Wallace, and R. W. Ziolkowski, "Coupled Maxwell-pseudospin equations for investigation of self-induced transparency effects in a degenerate three-level quantum system in two dimensions: Finite-difference time-domain study," Phys. Rev. A 66, 063418-(21) (2002).
    [CrossRef]
  21. B. Bid???egaray-Fesquet, F. Castella, and P. Degond, "From Bloch model to the rate equations," Disc. Cont. Dyn. Sys. 11, 1-26 (2004).
    [CrossRef]
  22. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Press, New York, 1995).
  23. S. L. McCall and E. L. Hahn, "Self-Induced Transparency," Phys. Rev. 183, 457-485 (1969).
    [CrossRef]
  24. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1997).
  25. K. Li, M. I. Stockman, and D. J. Bergman, "Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens," Phys. Rev. Lett. 91, 227402-(4) (2003).
    [CrossRef] [PubMed]
  26. C. Conti, L. Angelani, and G. Ruocco, "Light diffusion and localization in three-dimensional nonlinear disordered media," Phys. Rev. A 75, 033812-(5) (2007).
    [CrossRef]
  27. L. Rojas-Ochas, J. Mendez-Alcaraz, P. S. J.J. Saenz, and F. Scheffold, "Photonic Properties of Strongly Correlated Colloidal Liquids," Phys.Rev.Lett. 93, 073903-(4) (2004).
    [CrossRef]
  28. F. T. Hioe and J. H. Eberly, "N-Level Coherence Vector and Higher Conservation Laws in Quantum Optics and Quantum Mechanics," Phys. Rev. Lett. 47, 838-(4) (1981).
    [CrossRef]
  29. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2005).
  30. Y. Y. Lee and C. T. Chen-Tsay, "The fifteenfold way of the SU(4) symmetry scheme of strongly interacting particles," Chinese Journal of Physics 3, 45-68 (1965).

2004 (2)

G. Slavcheva, J. Arnold, and R. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Top. Quantum Electron. 10, 1052-1062 (2004).
[CrossRef]

B. Bid???egaray-Fesquet, F. Castella, and P. Degond, "From Bloch model to the rate equations," Disc. Cont. Dyn. Sys. 11, 1-26 (2004).
[CrossRef]

1999 (1)

H. Yukawa, S. Arnold, and K. Miyano, "Microcavity effect of dyes adsorbed on a levitated droplet," Phys. Rev. A 60, 2491-2496 (1999).
[CrossRef]

1993 (1)

Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46, 66-73 (1993).
[CrossRef]

1977 (1)

A. Ashkin and J. M. Dziedzic, "Observation of Resonances in the Radiation Pressure on Dielectric Spheres," Phys. Rev. Lett. 38, 1351-1354 (1977).
[CrossRef]

1969 (1)

S. L. McCall and E. L. Hahn, "Self-Induced Transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

1965 (1)

Y. Y. Lee and C. T. Chen-Tsay, "The fifteenfold way of the SU(4) symmetry scheme of strongly interacting particles," Chinese Journal of Physics 3, 45-68 (1965).

1964 (1)

W. E. Lamb, "Theory of an Optical Maser," Phys. Rev. 134, A1429-A1450 (1964).
[CrossRef]

1963 (1)

E. T. Jaynes and F. W. Cummings, "Comparison of Quantum and Semiclassical Radiation Theory with Application to the Beam Maser," Proc. IEEE. 51, 89-109 (1963).
[CrossRef]

1962 (1)

P. J. Wyatt, "Scattering of Electromagnetic Plane Waves from Inhomogeneous Spherically Symmetric Objects," Phys. Rev. 127, 1837-1843 (1962).
[CrossRef]

1908 (1)

G. Mie, "Beitrge zur Optik trber Medien, speziell kolloidaler Metallsungen," Ann. Phys. 330, 377-445 (1908).
[CrossRef]

Abraham, M.

U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
[CrossRef]

Alfano, R. R.

M. Xu and R. R. Alfano, "Random Walk of Polarized Light in Turbid Media," Phys. Rev. Lett. 95, 213901-(4) (2005).
[CrossRef] [PubMed]

Angelani, L.

C. Conti, L. Angelani, and G. Ruocco, "Light diffusion and localization in three-dimensional nonlinear disordered media," Phys. Rev. A 75, 033812-(5) (2007).
[CrossRef]

Arnold, J.

G. Slavcheva, J. Arnold, and R. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Top. Quantum Electron. 10, 1052-1062 (2004).
[CrossRef]

Arnold, S.

H. Yukawa, S. Arnold, and K. Miyano, "Microcavity effect of dyes adsorbed on a levitated droplet," Phys. Rev. A 60, 2491-2496 (1999).
[CrossRef]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, "Observation of Resonances in the Radiation Pressure on Dielectric Spheres," Phys. Rev. Lett. 38, 1351-1354 (1977).
[CrossRef]

Bergman, D. J.

K. Li, M. I. Stockman, and D. J. Bergman, "Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens," Phys. Rev. Lett. 91, 227402-(4) (2003).
[CrossRef] [PubMed]

Bid???egaray-Fesquet, B.

B. Bid???egaray-Fesquet, F. Castella, and P. Degond, "From Bloch model to the rate equations," Disc. Cont. Dyn. Sys. 11, 1-26 (2004).
[CrossRef]

Castella, F.

B. Bid???egaray-Fesquet, F. Castella, and P. Degond, "From Bloch model to the rate equations," Disc. Cont. Dyn. Sys. 11, 1-26 (2004).
[CrossRef]

Chen-Tsay, C. T.

Y. Y. Lee and C. T. Chen-Tsay, "The fifteenfold way of the SU(4) symmetry scheme of strongly interacting particles," Chinese Journal of Physics 3, 45-68 (1965).

Conti, C.

C. Conti, L. Angelani, and G. Ruocco, "Light diffusion and localization in three-dimensional nonlinear disordered media," Phys. Rev. A 75, 033812-(5) (2007).
[CrossRef]

Cummings, F. W.

E. T. Jaynes and F. W. Cummings, "Comparison of Quantum and Semiclassical Radiation Theory with Application to the Beam Maser," Proc. IEEE. 51, 89-109 (1963).
[CrossRef]

Degond, P.

B. Bid???egaray-Fesquet, F. Castella, and P. Degond, "From Bloch model to the rate equations," Disc. Cont. Dyn. Sys. 11, 1-26 (2004).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, "Observation of Resonances in the Radiation Pressure on Dielectric Spheres," Phys. Rev. Lett. 38, 1351-1354 (1977).
[CrossRef]

Eberly, J. H.

F. T. Hioe and J. H. Eberly, "N-Level Coherence Vector and Higher Conservation Laws in Quantum Optics and Quantum Mechanics," Phys. Rev. Lett. 47, 838-(4) (1981).
[CrossRef]

Hahn, E. L.

S. L. McCall and E. L. Hahn, "Self-Induced Transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

Hare, J.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefvre-Seguin, and J. -M. Raimond, "Very low threshold whisperinggallery- mode microsphere laser," Phys. Rev. A 54, R1777-(4) (1996).
[CrossRef] [PubMed]

Hioe, F. T.

F. T. Hioe and J. H. Eberly, "N-Level Coherence Vector and Higher Conservation Laws in Quantum Optics and Quantum Mechanics," Phys. Rev. Lett. 47, 838-(4) (1981).
[CrossRef]

Ihlein, G.

U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
[CrossRef]

Jaynes, E. T.

E. T. Jaynes and F. W. Cummings, "Comparison of Quantum and Semiclassical Radiation Theory with Application to the Beam Maser," Proc. IEEE. 51, 89-109 (1963).
[CrossRef]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-(3) (2002).
[CrossRef] [PubMed]

Krau, O.

U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
[CrossRef]

Laeri, F.

U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
[CrossRef]

Lamb, W. E.

W. E. Lamb, "Theory of an Optical Maser," Phys. Rev. 134, A1429-A1450 (1964).
[CrossRef]

Lee, Y. Y.

Y. Y. Lee and C. T. Chen-Tsay, "The fifteenfold way of the SU(4) symmetry scheme of strongly interacting particles," Chinese Journal of Physics 3, 45-68 (1965).

Lefvre-Seguin, V.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefvre-Seguin, and J. -M. Raimond, "Very low threshold whisperinggallery- mode microsphere laser," Phys. Rev. A 54, R1777-(4) (1996).
[CrossRef] [PubMed]

Li, K.

K. Li, M. I. Stockman, and D. J. Bergman, "Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens," Phys. Rev. Lett. 91, 227402-(4) (2003).
[CrossRef] [PubMed]

Limburg, B.

U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
[CrossRef]

McCall, S. L.

S. L. McCall and E. L. Hahn, "Self-Induced Transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

Mendez-Alcaraz, J.

L. Rojas-Ochas, J. Mendez-Alcaraz, P. S. J.J. Saenz, and F. Scheffold, "Photonic Properties of Strongly Correlated Colloidal Liquids," Phys.Rev.Lett. 93, 073903-(4) (2004).
[CrossRef]

Mie, G.

G. Mie, "Beitrge zur Optik trber Medien, speziell kolloidaler Metallsungen," Ann. Phys. 330, 377-445 (1908).
[CrossRef]

Miyano, K.

H. Yukawa, S. Arnold, and K. Miyano, "Microcavity effect of dyes adsorbed on a levitated droplet," Phys. Rev. A 60, 2491-2496 (1999).
[CrossRef]

Raimond, J. -M.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefvre-Seguin, and J. -M. Raimond, "Very low threshold whisperinggallery- mode microsphere laser," Phys. Rev. A 54, R1777-(4) (1996).
[CrossRef] [PubMed]

Rojas-Ochas, L.

L. Rojas-Ochas, J. Mendez-Alcaraz, P. S. J.J. Saenz, and F. Scheffold, "Photonic Properties of Strongly Correlated Colloidal Liquids," Phys.Rev.Lett. 93, 073903-(4) (2004).
[CrossRef]

Ruocco, G.

C. Conti, L. Angelani, and G. Ruocco, "Light diffusion and localization in three-dimensional nonlinear disordered media," Phys. Rev. A 75, 033812-(5) (2007).
[CrossRef]

Saenz, P. S. J.J.

L. Rojas-Ochas, J. Mendez-Alcaraz, P. S. J.J. Saenz, and F. Scheffold, "Photonic Properties of Strongly Correlated Colloidal Liquids," Phys.Rev.Lett. 93, 073903-(4) (2004).
[CrossRef]

Sandoghdar, V.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefvre-Seguin, and J. -M. Raimond, "Very low threshold whisperinggallery- mode microsphere laser," Phys. Rev. A 54, R1777-(4) (1996).
[CrossRef] [PubMed]

Scheffold, F.

L. Rojas-Ochas, J. Mendez-Alcaraz, P. S. J.J. Saenz, and F. Scheffold, "Photonic Properties of Strongly Correlated Colloidal Liquids," Phys.Rev.Lett. 93, 073903-(4) (2004).
[CrossRef]

Schth, F.

U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
[CrossRef]

Slavcheva, G.

G. Slavcheva, J. Arnold, and R. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Top. Quantum Electron. 10, 1052-1062 (2004).
[CrossRef]

Slusher, R. E.

Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46, 66-73 (1993).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-(3) (2002).
[CrossRef] [PubMed]

Stockman, M. I.

K. Li, M. I. Stockman, and D. J. Bergman, "Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens," Phys. Rev. Lett. 91, 227402-(4) (2003).
[CrossRef] [PubMed]

Treussart, F.

V. Sandoghdar, F. Treussart, J. Hare, V. Lefvre-Seguin, and J. -M. Raimond, "Very low threshold whisperinggallery- mode microsphere laser," Phys. Rev. A 54, R1777-(4) (1996).
[CrossRef] [PubMed]

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-(3) (2002).
[CrossRef] [PubMed]

L. Yang and K. J. Vahala, "Gain functionalization of silica microresonators," Opt. Lett. 28, 592-(3) (2003).
[CrossRef] [PubMed]

Vietze, U.

U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
[CrossRef]

Wyatt, P. J.

P. J. Wyatt, "Scattering of Electromagnetic Plane Waves from Inhomogeneous Spherically Symmetric Objects," Phys. Rev. 127, 1837-1843 (1962).
[CrossRef]

Xu, M.

M. Xu and R. R. Alfano, "Random Walk of Polarized Light in Turbid Media," Phys. Rev. Lett. 95, 213901-(4) (2005).
[CrossRef] [PubMed]

Yamamoto, Y.

Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46, 66-73 (1993).
[CrossRef]

Yang, L.

L. Yang and K. J. Vahala, "Gain functionalization of silica microresonators," Opt. Lett. 28, 592-(3) (2003).
[CrossRef] [PubMed]

Yukawa, H.

H. Yukawa, S. Arnold, and K. Miyano, "Microcavity effect of dyes adsorbed on a levitated droplet," Phys. Rev. A 60, 2491-2496 (1999).
[CrossRef]

Ziolkowski, R.

G. Slavcheva, J. Arnold, and R. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Top. Quantum Electron. 10, 1052-1062 (2004).
[CrossRef]

Ann. Phys. (1)

G. Mie, "Beitrge zur Optik trber Medien, speziell kolloidaler Metallsungen," Ann. Phys. 330, 377-445 (1908).
[CrossRef]

Chinese Journal of Physics (1)

Y. Y. Lee and C. T. Chen-Tsay, "The fifteenfold way of the SU(4) symmetry scheme of strongly interacting particles," Chinese Journal of Physics 3, 45-68 (1965).

Disc. Cont. Dyn. Sys. (1)

B. Bid???egaray-Fesquet, F. Castella, and P. Degond, "From Bloch model to the rate equations," Disc. Cont. Dyn. Sys. 11, 1-26 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

G. Slavcheva, J. Arnold, and R. Ziolkowski, "FDTD simulation of the nonlinear gain dynamics in active optical waveguides and semiconductor microcavities," IEEE J. Sel. Top. Quantum Electron. 10, 1052-1062 (2004).
[CrossRef]

Phys. Rev. (3)

S. L. McCall and E. L. Hahn, "Self-Induced Transparency," Phys. Rev. 183, 457-485 (1969).
[CrossRef]

P. J. Wyatt, "Scattering of Electromagnetic Plane Waves from Inhomogeneous Spherically Symmetric Objects," Phys. Rev. 127, 1837-1843 (1962).
[CrossRef]

W. E. Lamb, "Theory of an Optical Maser," Phys. Rev. 134, A1429-A1450 (1964).
[CrossRef]

Phys. Rev. A (1)

H. Yukawa, S. Arnold, and K. Miyano, "Microcavity effect of dyes adsorbed on a levitated droplet," Phys. Rev. A 60, 2491-2496 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

A. Ashkin and J. M. Dziedzic, "Observation of Resonances in the Radiation Pressure on Dielectric Spheres," Phys. Rev. Lett. 38, 1351-1354 (1977).
[CrossRef]

Phys. Today (1)

Y. Yamamoto and R. E. Slusher, "Optical processes in microcavities," Phys. Today 46, 66-73 (1993).
[CrossRef]

Proc. IEEE. (1)

E. T. Jaynes and F. W. Cummings, "Comparison of Quantum and Semiclassical Radiation Theory with Application to the Beam Maser," Proc. IEEE. 51, 89-109 (1963).
[CrossRef]

Other (19)

G. W. Gardiner and P. Zoller, Quantum noise (Springer, Berlin, 2000).

A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).

U. Vietze, O. Krau, F. Laeri, G. Ihlein, F. Schth, B. Limburg, and M. Abraham, "Zeolite-Dye Microlasers," Phys. Rev. Lett. 81, 4628-(4) (1998).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415, 621-(3) (2002).
[CrossRef] [PubMed]

V. Sandoghdar, F. Treussart, J. Hare, V. Lefvre-Seguin, and J. -M. Raimond, "Very low threshold whisperinggallery- mode microsphere laser," Phys. Rev. A 54, R1777-(4) (1996).
[CrossRef] [PubMed]

L. Yang and K. J. Vahala, "Gain functionalization of silica microresonators," Opt. Lett. 28, 592-(3) (2003).
[CrossRef] [PubMed]

P. W. Barber and K. Chang, Optical Effects Associated with Small Particles (World Scientific, Singapore, 1988).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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

M. Xu and R. R. Alfano, "Random Walk of Polarized Light in Turbid Media," Phys. Rev. Lett. 95, 213901-(4) (2005).
[CrossRef] [PubMed]

Y. Yamamoto, F. Tassone, and H. Cao, Semiconductor Cavity Quantum Electrodynamics (Springer, Berlin, 2000).

E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1997).

K. Li, M. I. Stockman, and D. J. Bergman, "Self-Similar Chain of Metal Nanospheres as an Efficient Nanolens," Phys. Rev. Lett. 91, 227402-(4) (2003).
[CrossRef] [PubMed]

C. Conti, L. Angelani, and G. Ruocco, "Light diffusion and localization in three-dimensional nonlinear disordered media," Phys. Rev. A 75, 033812-(5) (2007).
[CrossRef]

L. Rojas-Ochas, J. Mendez-Alcaraz, P. S. J.J. Saenz, and F. Scheffold, "Photonic Properties of Strongly Correlated Colloidal Liquids," Phys.Rev.Lett. 93, 073903-(4) (2004).
[CrossRef]

F. T. Hioe and J. H. Eberly, "N-Level Coherence Vector and Higher Conservation Laws in Quantum Optics and Quantum Mechanics," Phys. Rev. Lett. 47, 838-(4) (1981).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2005).

G. Slavcheva, J. M. Arnold, I. Wallace, and R. W. Ziolkowski, "Coupled Maxwell-pseudospin equations for investigation of self-induced transparency effects in a degenerate three-level quantum system in two dimensions: Finite-difference time-domain study," Phys. Rev. A 66, 063418-(21) (2002).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Press, New York, 1995).

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Figures (5)

Fig. 1.
Fig. 1.

(Color online). (left) Energy diagram of a four-level atomic system with a triply-degenerate excited state; (right) sketch of a single Mie nanoresonator with a d-thick layer of amplifying material.

Fig. 2.
Fig. 2.

(Color online). MB-FDTD results for Na =1026 m-3: (a)-(c) time evolution of the electric field components (sampled in proximity of the sphere center, to avoid symmetry effects), (d) energy density (isosurface plot) with xy (down) xz (left) and yz (right) slices in the sphere middle plane.

Fig. 3.
Fig. 3.

(Color online). (a) Time series spectrogram computed from MB-FDTD analysis for Na =1026 m-3 (the mode-competition dynamics is denoted by the beating modeamplitudes); (b, solid line) Mie theory extinction factor Qext for a single nanosphere of diameter 600 nm and εr =8.41; (b, dashed line) active medium gain bandwidth.

Fig. 4.
Fig. 4.

(Color online). Frequency demodulation analysis: time evolution of modal amplitude a 1(t) (a) and phases ϕ 1,2(t) (c–d); (b) 1D map obtained with a Poincaré surface of section of (a 1,a 2) at a 1=180 kV/m.

Fig. 5.
Fig. 5.

(Color online). Spectrograms for increasing pumping rates: Na =1026 m-3 (a), Na =1027 m-3; (c) Power density spectrum for various Na .

Equations (14)

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H t = 1 μ 0 × E ,
E t = 1 ε 0 [ × H P t ] ,
H ̂ = H ̂ 0 + H ̂ I
H ̂ 0 = h ¯ ω 0 [ 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] ,
Q ̂ = q 0 [ 0 x y z x 0 0 0 y 0 0 0 z 0 0 0 ] ,
i h ¯ ρ ̂ t = [ H ̂ , ρ ̂ ] ,
S j = Tr [ ρ ̂ s ̂ j ] , j [ 1 , 15 ]
S t = Γ ̂ S γ ̂ ( S S ( 0 ) ) ,
Γ jh = i 2 h ¯ Tr ( H ̂ [ s ̂ j , s ̂ h ] ) ,
Γ 1,2 = Γ 4,5 = Γ 9,10 = ω 0 ,
Γ 1,7 = Γ 2,6 = Γ 3,5 = Γ 8,5 3 = Γ 14,9 = Γ 10,13 = Ω y ,
Γ 3,2 2 = Γ 7,4 = Γ 5,6 = Γ 12,9 = Γ 10,11 = Ω x ,
Γ 1,12 = Γ 2,11 = Γ 3,10 = Γ 4,14 = Γ 5,13 = 2 2 Γ 15,10 3 = Ω z ,
Q ̂ = Tr [ ρ ̂ Q ̂ ] = q 0 ( x S 1 + y S 4 + z S 9 ) .

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