Abstract

We explore the ultrafast spatio-temporal dynamics of whispering-gallery micro-cavity lasers. To model the dynamics of the nonlinear whispering-gallery modes we develop a three-dimensional Finite-Difference Time-Domain modelling framework based on the spin and therefore optical polarisation resolved Maxwell-Bloch equations. The numerical algorithm brings together a real value form of the optical Bloch equations with the curl part of Maxwell’s equations. The Hamiltonian of the two-level system contains either linear or circular polarised transitions. In cylindrical micro-cavity lasers the coherent, nonlinear emission process leads to ultrafast fan-like rotational phase dynamics of the degenerate whispering-gallery modes. This rotation is shown to be arrested in gear-shaped micro-cavity lasers followed by an over-damped relaxation oscillation.

© 2006 Optical Society of America

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References

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  1. K. J. Vahala, “Optical microcavities,” Nature 424, 939 (2003).
    [Crossref]
  2. A. F. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1667 (1993).
    [Crossref]
  3. M. Fujita and T. Baba, “Microgear Laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
    [Crossref]
  4. M. S. Skolnick, T. A. Fisher, and D. M. Whittaker “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. 13, 645–669 (1998).
    [Crossref]
  5. K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14, 1094–1105 (2006).
    [Crossref] [PubMed]
  6. W. Zakowicz, “Whispering-Gallery-Mode Resonances: A New Way to Accelerate Charged Particles,” Phys. Rev. Lett. 95, 114801 (2005).
    [Crossref] [PubMed]
  7. A. Klaedtke, J. Hamm, and O. Hess, “Simulation of Active and Nonlinear Photonic Nano-Materials in the Finite-Difference Time-Domain (FDTD) Framework,” Lecture Notes in Physics 642, Computational Material Science – From Basic Principles to Material Properties, 75–101, Springer (2004).
  8. P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
    [Crossref]
  9. P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
    [Crossref] [PubMed]
  10. E. Gehrig, O. Hess, C. Ribbat, R. L. Sellin, and D. Bimberg, “Dynamic filamentation and beam quality of quantum-dot lasers,” Appl. Phys. Lett. 84, 1650 (2004).
    [Crossref]
  11. A. Taflove and S. C. Hagness, “Computational Electrodynamics: the FDTD method” 2nd ed. (Artech House, Boston, London, 2000)
  12. K. P. Huy, A. Morand, D. Amans, and P. Benech, “Analytical study of the whispering-gallery mode in two-dimensional microgear cavity using coupled-mode theory,” J. Opt. Soc. Am. B 22, 1793–1803 (2005).
    [Crossref]
  13. R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
    [Crossref]
  14. M. Pelton and Y. Yamamoto, “Ultralow threshold laser using a single quantum dot and a microsphere cavity,” Phys. Rev. A 59, 2418–2421 (1999).
    [Crossref]
  15. K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, “Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photoic Crystals,” IEEE J. Select. Top. Quantum Electron. 91355–1360 (2003).
    [Crossref]
  16. A. Klaedtke research white paper, “Nanolasers,” (University of Surrey, Advanced Technology Institute, Theory and Advanced Computation, 2006), http://www.ati.surrey.ac.uk/TAC/research/nanolasers.

2006 (1)

2005 (2)

2004 (1)

E. Gehrig, O. Hess, C. Ribbat, R. L. Sellin, and D. Bimberg, “Dynamic filamentation and beam quality of quantum-dot lasers,” Appl. Phys. Lett. 84, 1650 (2004).
[Crossref]

2003 (2)

K. J. Vahala, “Optical microcavities,” Nature 424, 939 (2003).
[Crossref]

K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, “Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photoic Crystals,” IEEE J. Select. Top. Quantum Electron. 91355–1360 (2003).
[Crossref]

2002 (1)

M. Fujita and T. Baba, “Microgear Laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
[Crossref]

2001 (1)

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

2000 (1)

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

1999 (1)

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

1998 (1)

M. S. Skolnick, T. A. Fisher, and D. M. Whittaker “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. 13, 645–669 (1998).
[Crossref]

1993 (2)

A. F. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1667 (1993).
[Crossref]

R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
[Crossref]

Amans, D.

Baba, T.

K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, “Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photoic Crystals,” IEEE J. Select. Top. Quantum Electron. 91355–1360 (2003).
[Crossref]

M. Fujita and T. Baba, “Microgear Laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
[Crossref]

Benech, P.

Bimberg, D.

E. Gehrig, O. Hess, C. Ribbat, R. L. Sellin, and D. Bimberg, “Dynamic filamentation and beam quality of quantum-dot lasers,” Appl. Phys. Lett. 84, 1650 (2004).
[Crossref]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

Borri, P.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

Borselli, M.

Eliseev, P. G.

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

Fisher, T. A.

M. S. Skolnick, T. A. Fisher, and D. M. Whittaker “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. 13, 645–669 (1998).
[Crossref]

Fujita, M.

M. Fujita and T. Baba, “Microgear Laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
[Crossref]

Gehrig, E.

E. Gehrig, O. Hess, C. Ribbat, R. L. Sellin, and D. Bimberg, “Dynamic filamentation and beam quality of quantum-dot lasers,” Appl. Phys. Lett. 84, 1650 (2004).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, “Computational Electrodynamics: the FDTD method” 2nd ed. (Artech House, Boston, London, 2000)

Hamm, J.

A. Klaedtke, J. Hamm, and O. Hess, “Simulation of Active and Nonlinear Photonic Nano-Materials in the Finite-Difference Time-Domain (FDTD) Framework,” Lecture Notes in Physics 642, Computational Material Science – From Basic Principles to Material Properties, 75–101, Springer (2004).

Hess, O.

E. Gehrig, O. Hess, C. Ribbat, R. L. Sellin, and D. Bimberg, “Dynamic filamentation and beam quality of quantum-dot lasers,” Appl. Phys. Lett. 84, 1650 (2004).
[Crossref]

A. Klaedtke, J. Hamm, and O. Hess, “Simulation of Active and Nonlinear Photonic Nano-Materials in the Finite-Difference Time-Domain (FDTD) Framework,” Lecture Notes in Physics 642, Computational Material Science – From Basic Principles to Material Properties, 75–101, Springer (2004).

Huy, K. P.

Klaedtke, A.

A. Klaedtke research white paper, “Nanolasers,” (University of Surrey, Advanced Technology Institute, Theory and Advanced Computation, 2006), http://www.ati.surrey.ac.uk/TAC/research/nanolasers.

A. Klaedtke, J. Hamm, and O. Hess, “Simulation of Active and Nonlinear Photonic Nano-Materials in the Finite-Difference Time-Domain (FDTD) Framework,” Lecture Notes in Physics 642, Computational Material Science – From Basic Principles to Material Properties, 75–101, Springer (2004).

Krishna, S.

Langbein, W.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

Lester, L. F.

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

Levi, A. F.

A. F. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1667 (1993).
[Crossref]

R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
[Crossref]

Li, H.

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

Liu, G. T.

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

Logan, R. A.

A. F. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1667 (1993).
[Crossref]

R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
[Crossref]

Malloy, K. J.

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

McCall, S. L.

A. F. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1667 (1993).
[Crossref]

R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
[Crossref]

Mohideen, U.

R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
[Crossref]

Morand, A.

Nakagawa, A.

K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, “Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photoic Crystals,” IEEE J. Select. Top. Quantum Electron. 91355–1360 (2003).
[Crossref]

Newell, T. C.

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

Nozaki, K.

K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, “Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photoic Crystals,” IEEE J. Select. Top. Quantum Electron. 91355–1360 (2003).
[Crossref]

Ouyang, D.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

Painter, O.

Pearton, S. J.

R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
[Crossref]

A. F. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1667 (1993).
[Crossref]

Pelton, M.

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

Ribbat, C.

E. Gehrig, O. Hess, C. Ribbat, R. L. Sellin, and D. Bimberg, “Dynamic filamentation and beam quality of quantum-dot lasers,” Appl. Phys. Lett. 84, 1650 (2004).
[Crossref]

Sano, D.

K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, “Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photoic Crystals,” IEEE J. Select. Top. Quantum Electron. 91355–1360 (2003).
[Crossref]

Schneider, S.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

Sellin, R. L.

E. Gehrig, O. Hess, C. Ribbat, R. L. Sellin, and D. Bimberg, “Dynamic filamentation and beam quality of quantum-dot lasers,” Appl. Phys. Lett. 84, 1650 (2004).
[Crossref]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

Skolnick, M. S.

M. S. Skolnick, T. A. Fisher, and D. M. Whittaker “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. 13, 645–669 (1998).
[Crossref]

Slusher, R. E.

R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
[Crossref]

Srinivasan, K.

Stintz, A.

K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14, 1094–1105 (2006).
[Crossref] [PubMed]

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, “Computational Electrodynamics: the FDTD method” 2nd ed. (Artech House, Boston, London, 2000)

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424, 939 (2003).
[Crossref]

Whittaker, D. M.

M. S. Skolnick, T. A. Fisher, and D. M. Whittaker “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. 13, 645–669 (1998).
[Crossref]

Woggon, U.

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

Yamamoto, Y.

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

Zakowicz, W.

W. Zakowicz, “Whispering-Gallery-Mode Resonances: A New Way to Accelerate Charged Particles,” Phys. Rev. Lett. 95, 114801 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

M. Fujita and T. Baba, “Microgear Laser,” Appl. Phys. Lett. 80, 2051–2053 (2002).
[Crossref]

P. G. Eliseev, H. Li, A. Stintz, G. T. Liu, T. C. Newell, K. J. Malloy, and L. F. Lester, “Transition dipole moment of InAs/InGaAs quantum dots from experiments on ultralow-threshold laser diodes,” Appl. Phys. Lett. 77, 262–264 (2000).
[Crossref]

E. Gehrig, O. Hess, C. Ribbat, R. L. Sellin, and D. Bimberg, “Dynamic filamentation and beam quality of quantum-dot lasers,” Appl. Phys. Lett. 84, 1650 (2004).
[Crossref]

R. E. Slusher, A. F. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63, 1310–1312 (1993).
[Crossref]

Electron. Lett. (1)

A. F. Levi, S. L. McCall, S. J. Pearton, and R. A. Logan, “Room temperature operation of submicrometer radius disk laser,” Electron. Lett. 29, 1666–1667 (1993).
[Crossref]

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

K. Nozaki, A. Nakagawa, D. Sano, and T. Baba, “Ultralow Threshold and Single-Mode Lasing in Microgear Lasers and Its Fusion With Quasi-Periodic Photoic Crystals,” IEEE J. Select. Top. Quantum Electron. 91355–1360 (2003).
[Crossref]

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

Nature (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 939 (2003).
[Crossref]

Opt. Express (1)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (2)

W. Zakowicz, “Whispering-Gallery-Mode Resonances: A New Way to Accelerate Charged Particles,” Phys. Rev. Lett. 95, 114801 (2005).
[Crossref] [PubMed]

P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, “Ultralong Dephasing Time in InGaAs Quantum Dots,” Phys. Rev. Lett. 87, 157401 (2001).
[Crossref] [PubMed]

Semicond. Sci. Technol. (1)

M. S. Skolnick, T. A. Fisher, and D. M. Whittaker “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. 13, 645–669 (1998).
[Crossref]

Other (3)

A. Klaedtke, J. Hamm, and O. Hess, “Simulation of Active and Nonlinear Photonic Nano-Materials in the Finite-Difference Time-Domain (FDTD) Framework,” Lecture Notes in Physics 642, Computational Material Science – From Basic Principles to Material Properties, 75–101, Springer (2004).

A. Taflove and S. C. Hagness, “Computational Electrodynamics: the FDTD method” 2nd ed. (Artech House, Boston, London, 2000)

A. Klaedtke research white paper, “Nanolasers,” (University of Surrey, Advanced Technology Institute, Theory and Advanced Computation, 2006), http://www.ati.surrey.ac.uk/TAC/research/nanolasers.

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Figures (6)

Fig. 1.
Fig. 1.

Discrete, spatially resolved Fourier transforms of the Cartesian electric and magnetic field components of the cold-cavity HEM510 WGM. The contour lines show the logarithmic decay of the field.

Fig. 2.
Fig. 2.

Geometry of the cylindric resonator cavities used in the simulations. The 3D view on the whole dielectric cavity structure, including pedestal and the active region (yellow), is shown on the left. The right shows the corrugation parameters in the gear-like cavity.

Fig. 3.
Fig. 3.

The logarithmic resonance intensity (I) spectrum of the incompatible and compatible (insets from left to right) HEM510 modes in the microgear. The Lorentzian line shape of the dipole resonance is included (dashed curve).

Fig. 4.
Fig. 4.

Snapshot of the spatial variation in the inversion probability of the dipoles in the microdisc cavity and the evolution of the averaged inversion. The end of the red line marks the time of the snapshot. Animations can be found at [16].

Fig. 5.
Fig. 5.

Snapshot of the spatial variation in the inversion probability of the dipoles in the microgear cavity and the evolution of the averaged inversion. The end of the red line marks the time of the snapshot. Animations can be found at [16].

Fig. 6.
Fig. 6.

Ultrafast dynamic behaviour of the HEM510 lasing mode in a disc (a) and gear (b). Shown is the azimuthal part of the electric field in the disc plane (x-y). The contour lines are even spaced on a logarithmic scale to enhance the visibility of the symmetric properties of the field pattern. The corresponding animations can be found at [16].

Tables (1)

Tables Icon

Table 1. The table summarises the two-level material parameters of the laser simulations; density (n a); dipole moment ( d ); transition frequency (ω 0); polarisation damping constant (γ p); non-radiative decay constant (γ nr); thermal equilibrium (ρ bb,0) and initial occupation probability of the upper level (ρ bb(t = 0)); pump strength (Λ).

Equations (4)

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

curlE= t H, curlH= t D.
D= ε r E+2 n a dP
t 2 P=2 γ p t P+ ω 0 2 P= ω 0 2 Ω N|d·E|
t N=2Λ γ nr (N N 0 )4 Ω ω 0 2 |d·E| t P

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