Abstract

The dynamics of the total intensity and of each individual mode of a microchip laser have been studied. Because of the nonlinear mode coupling by spatial hole burning, the intensity fluctuation of each longitudinal mode can be described by N relaxation frequencies, where N is the number of lasing modes. Owing to the small cross-saturation coefficient between the longitudinal modes, the total intensity exhibits a behavior much more complex than the regular relaxation oscillations usually observed. As a result of the short photon lifetime of the microchip laser this unstable behavior of the total intensity can easily be observed even when the number of modes is small. For each longitudinal mode, we also observed beating and antiphase dynamics between two coupled states of orthogonal polarization. Numerical simulations permit a good description of the experimental results.

© 1996 Optical Society of America

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  2. K. Otsuka, “High sensitive measurement of Doppler-shift with microchip solid-state laser,” Jpn. J. Appl. Phys. 32, L1546–L1548 (1993).
  3. K. Otsuka, M. Georgiou, and P. Mandel, “Intensity fluctuations in multimode lasers with spatial hole burning,” Jpn. J. Appl. Phys. 31, L1250–L1252 (1992).
    [Crossref]
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  5. K. Otsuka, “Transverse effects on antiphase laser dynamics,” Jpn. J. Appl. Phys. 32, L1414–L1417 (1993).
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    [Crossref]
  7. D. Pieroux, P. Mandel, and K. Otuka, “Modulation dynamics in a multimode laser with feedback,” Opt. Commun. 108, 273–277 (1994).
    [Crossref]
  8. P. Mandel, M. Georgiou, K. Otsuka, and D. Pieroux, “Transient and modulation dynamics of a multimode Fabry–Perot laser,” Opt. Commun. 100, 341–350 (1993).
    [Crossref]
  9. K. Otsuka, “Winner takes all dynamics and antiphase states in modulated multimode lasers,” Phys. Rev. Lett. 67, 1090–1093 (1991).
    [Crossref] [PubMed]
  10. C. L. Tang, H. Statz, and G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
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  11. J. A. Fleck and R. E. Kidder, “Coupled mode laser oscillation,” J. Appl. Phys. 35, 2825–2831 (1964).
    [Crossref]
  12. H. Risken and K. Nummedal, “Instability of off resonance mode in lasers,” Phys. Lett. A 26, 275–276 (1968).
    [Crossref]
  13. L. A. Ostrovskii, “Interaction of laser modes,” Soviet Phys. JETP 21, 727–732 (1965).
  14. N. G. Basov, V. N. Morozov, and A. N. Oraevskii, “Non linear mode interaction in lasers,” Soviet Phys. JETP 22, 622–628 (1966).
  15. C. Bracikowski and R. Roy, “Energy sharing in a chaotic multimode laser,” Phys. Rev. A 43, 6455–6457 (1991).
    [Crossref] [PubMed]
  16. K. Otsuka and J. L. Chern, “Dynamical spatial pattern memory in global coupled lasers,” Phys. Rev. A 45, 8288–8291 (1992).
    [Crossref] [PubMed]
  17. P. Mandel, C. Etrich, and K. Otsuka, “Laser rate equations with phase sensitive interactions,” IEEE J. Quantum Electron. 29, 836–843 (1993).
    [Crossref]
  18. K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, “Observation of antiphase states in a multimode laser,” Phys. Rev. Lett. 65, 1749–1752 (1990).
    [Crossref] [PubMed]
  19. S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2811–2822 (1988).
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  22. I. MacMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode standing wave laser,” Phys. Rev. A 38, 820–832 (1988).
    [Crossref]
  23. L. Fabiny, P. Colet, and R. Roy, “Coherence and phase dynamics of spatially coupled solid state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
    [Crossref] [PubMed]
  24. W. Jingyi and P. Mandel, “Antiphase dynamics of multimode intracavity second-harmonic generation,” Phys. Rev. A 48, 671–680 (1993).
    [Crossref] [PubMed]
  25. M. Beck, I. MacMackin, and M. G. Raymer, “Transition from quantum noise driven dynamics to deterministic dynamics in a multimode laser,” Phys. Rev. A 40, 2410–2416 (1989).
    [Crossref] [PubMed]
  26. E. Lacot, F. Stoeckel, and M. Chenevier, “Dynamics of an Erbium-doped fiber laser,” Phys. Rev. A 49, 3997–4008 (1994).
    [Crossref] [PubMed]
  27. E. Lacot and F. Stoeckel, “Two is enough: spectro-temporal dynamics of a two coupled mode laser,” Phys. Rev. A (to be published).
  28. A. E. Siegmann, Lasers (University Science, Mill Valley, Calif., 1986).
  29. T. Baer, “Large-amplitude fluctuations due to longitudinal mode coupling in diode-pumped intracavity-doubled Nd:YAG lasers,” J. Opt. Soc. Am. B 3, 1175–1180 (1986).
    [Crossref]
  30. K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46, 1692–1695 (1992).
    [Crossref] [PubMed]
  31. F. T. Arecchi and R. G. Harrison, Instabilities and Chaos in Quantum Optics (Springer-Verlag, Berlin, 1987).
    [Crossref]
  32. K. Otsuka, D. Pieroux, and P. Mandel, “Modulation dynamics and spatio-temporal pattern generation in a microchip multimode laser,” Opt. Commun. 108, 265–271 (1994).
    [Crossref]
  33. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [Crossref]
  34. M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974).
  35. V. M. Baev, J. Eschner, and A. Weiler, “Intracavity spectroscopy with modulated multimode lasers,” Appl. Phys. B 49, 315–322 (1989).
    [Crossref]
  36. P. Besnard, X. Jia, R. Dalgliesh, A. D. May, and G. Stephan, “Polarization switching in a microchip Nd:YAG laser using polarized feedback,” J. Opt. Soc. Am. B 10, 1605–1609 (1993).
    [Crossref]
  37. P. Berge, Y. Pomeau, and Ch. Vidal, L’Ordre dans le Chaos (Hermann, Paris, 1986).
  38. N. B. Abraham, L. L. Everett, C. Iwata, and M. B. Janicki, “Multimode dynamics of a sinusoidally modulated diode-pumped Nd:YAG laser,” in Proceedings of the Conference Laser Optics ’93, A. Mak, ed., Proc. SPIE2095, 16–24 (1994).
    [Crossref]
  39. O. N. Evdokimova and L. N. Kaptsov, “Quasiperiodic transition to chaos in a multimode YAG:Nd3+ laser with modulated parameters,” Sov. J. Quantum Electron. 20, 824–827 (1990).
    [Crossref]
  40. E. A. Viktorov, V. A. Sokolov, E. V. Tkachenko, and V. I. Ustyugov, “Violation of stability and randomization of the radiation spectra of solid-state lasers due to frequency non-equidistance of modes,” Opt. Spectrosc. (USSR) 68, 537–538 (1990).
  41. E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).
  42. H. Lin and N. B. Abraham, “Low-frequency pulsations in a He–Xe laser with several transverses modes: experimental and numerical results,” Phys. Rev. A 49, 2076–2086 (1994).
    [Crossref] [PubMed]
  43. A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52, 918–921 (1984).
    [Crossref]

1995 (1)

1994 (5)

E. Lacot, F. Stoeckel, and M. Chenevier, “Dynamics of an Erbium-doped fiber laser,” Phys. Rev. A 49, 3997–4008 (1994).
[Crossref] [PubMed]

K. Otsuka, D. Pieroux, and P. Mandel, “Modulation dynamics and spatio-temporal pattern generation in a microchip multimode laser,” Opt. Commun. 108, 265–271 (1994).
[Crossref]

H. Lin and N. B. Abraham, “Low-frequency pulsations in a He–Xe laser with several transverses modes: experimental and numerical results,” Phys. Rev. A 49, 2076–2086 (1994).
[Crossref] [PubMed]

S. Longhi, “Theory of transverse modes in end-pumped microchip lasers,” J. Opt. Soc. Am. B 11, 1098–1107 (1994).
[Crossref]

D. Pieroux, P. Mandel, and K. Otuka, “Modulation dynamics in a multimode laser with feedback,” Opt. Commun. 108, 273–277 (1994).
[Crossref]

1993 (8)

P. Mandel, M. Georgiou, K. Otsuka, and D. Pieroux, “Transient and modulation dynamics of a multimode Fabry–Perot laser,” Opt. Commun. 100, 341–350 (1993).
[Crossref]

K. Otsuka, “High sensitive measurement of Doppler-shift with microchip solid-state laser,” Jpn. J. Appl. Phys. 32, L1546–L1548 (1993).

K. Otsuka, P. Mandel, M. Georgiou, and C. Etrich, “Antiphase dynamics in a modulated multimode laser,” Jpn. J. Appl. Phys. 32, L318–L321 (1993).

K. Otsuka, “Transverse effects on antiphase laser dynamics,” Jpn. J. Appl. Phys. 32, L1414–L1417 (1993).

P. Mandel, C. Etrich, and K. Otsuka, “Laser rate equations with phase sensitive interactions,” IEEE J. Quantum Electron. 29, 836–843 (1993).
[Crossref]

P. Besnard, X. Jia, R. Dalgliesh, A. D. May, and G. Stephan, “Polarization switching in a microchip Nd:YAG laser using polarized feedback,” J. Opt. Soc. Am. B 10, 1605–1609 (1993).
[Crossref]

L. Fabiny, P. Colet, and R. Roy, “Coherence and phase dynamics of spatially coupled solid state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref] [PubMed]

W. Jingyi and P. Mandel, “Antiphase dynamics of multimode intracavity second-harmonic generation,” Phys. Rev. A 48, 671–680 (1993).
[Crossref] [PubMed]

1992 (3)

K. Otsuka and J. L. Chern, “Dynamical spatial pattern memory in global coupled lasers,” Phys. Rev. A 45, 8288–8291 (1992).
[Crossref] [PubMed]

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46, 1692–1695 (1992).
[Crossref] [PubMed]

K. Otsuka, M. Georgiou, and P. Mandel, “Intensity fluctuations in multimode lasers with spatial hole burning,” Jpn. J. Appl. Phys. 31, L1250–L1252 (1992).
[Crossref]

1991 (2)

K. Otsuka, “Winner takes all dynamics and antiphase states in modulated multimode lasers,” Phys. Rev. Lett. 67, 1090–1093 (1991).
[Crossref] [PubMed]

C. Bracikowski and R. Roy, “Energy sharing in a chaotic multimode laser,” Phys. Rev. A 43, 6455–6457 (1991).
[Crossref] [PubMed]

1990 (4)

O. N. Evdokimova and L. N. Kaptsov, “Quasiperiodic transition to chaos in a multimode YAG:Nd3+ laser with modulated parameters,” Sov. J. Quantum Electron. 20, 824–827 (1990).
[Crossref]

E. A. Viktorov, V. A. Sokolov, E. V. Tkachenko, and V. I. Ustyugov, “Violation of stability and randomization of the radiation spectra of solid-state lasers due to frequency non-equidistance of modes,” Opt. Spectrosc. (USSR) 68, 537–538 (1990).

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, “Observation of antiphase states in a multimode laser,” Phys. Rev. Lett. 65, 1749–1752 (1990).
[Crossref] [PubMed]

J. J. Zayhowski, “Microchip lasers,” Lincoln Lab. J. 3, 427–446 (1990).

1989 (2)

V. M. Baev, J. Eschner, and A. Weiler, “Intracavity spectroscopy with modulated multimode lasers,” Appl. Phys. B 49, 315–322 (1989).
[Crossref]

M. Beck, I. MacMackin, and M. G. Raymer, “Transition from quantum noise driven dynamics to deterministic dynamics in a multimode laser,” Phys. Rev. A 40, 2410–2416 (1989).
[Crossref] [PubMed]

1988 (2)

I. MacMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode standing wave laser,” Phys. Rev. A 38, 820–832 (1988).
[Crossref]

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2811–2822 (1988).
[Crossref]

1986 (1)

1985 (1)

1984 (1)

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52, 918–921 (1984).
[Crossref]

1968 (1)

H. Risken and K. Nummedal, “Instability of off resonance mode in lasers,” Phys. Lett. A 26, 275–276 (1968).
[Crossref]

1966 (1)

N. G. Basov, V. N. Morozov, and A. N. Oraevskii, “Non linear mode interaction in lasers,” Soviet Phys. JETP 22, 622–628 (1966).

1965 (1)

L. A. Ostrovskii, “Interaction of laser modes,” Soviet Phys. JETP 21, 727–732 (1965).

1964 (1)

J. A. Fleck and R. E. Kidder, “Coupled mode laser oscillation,” J. Appl. Phys. 35, 2825–2831 (1964).
[Crossref]

1963 (1)

C. L. Tang, H. Statz, and G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[Crossref]

Abraham, N. B.

H. Lin and N. B. Abraham, “Low-frequency pulsations in a He–Xe laser with several transverses modes: experimental and numerical results,” Phys. Rev. A 49, 2076–2086 (1994).
[Crossref] [PubMed]

N. B. Abraham, L. A. Lugiato, and L. M. Narducci, “Overview of instabilities in laser systems,” J. Opt. Soc. Am. B 2, 7–13 (1985).
[Crossref]

N. B. Abraham, L. L. Everett, C. Iwata, and M. B. Janicki, “Multimode dynamics of a sinusoidally modulated diode-pumped Nd:YAG laser,” in Proceedings of the Conference Laser Optics ’93, A. Mak, ed., Proc. SPIE2095, 16–24 (1994).
[Crossref]

Ackerhalt, J. R.

Arecchi, F. T.

F. T. Arecchi and R. G. Harrison, Instabilities and Chaos in Quantum Optics (Springer-Verlag, Berlin, 1987).
[Crossref]

Baer, T.

Baev, V. M.

V. M. Baev, J. Eschner, and A. Weiler, “Intracavity spectroscopy with modulated multimode lasers,” Appl. Phys. B 49, 315–322 (1989).
[Crossref]

Basov, N. G.

N. G. Basov, V. N. Morozov, and A. N. Oraevskii, “Non linear mode interaction in lasers,” Soviet Phys. JETP 22, 622–628 (1966).

Beck, M.

M. Beck, I. MacMackin, and M. G. Raymer, “Transition from quantum noise driven dynamics to deterministic dynamics in a multimode laser,” Phys. Rev. A 40, 2410–2416 (1989).
[Crossref] [PubMed]

I. MacMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode standing wave laser,” Phys. Rev. A 38, 820–832 (1988).
[Crossref]

Berge, P.

P. Berge, Y. Pomeau, and Ch. Vidal, L’Ordre dans le Chaos (Hermann, Paris, 1986).

Besnard, P.

Bielawski, S.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46, 1692–1695 (1992).
[Crossref] [PubMed]

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2811–2822 (1988).
[Crossref]

Bracikowski, C.

C. Bracikowski and R. Roy, “Energy sharing in a chaotic multimode laser,” Phys. Rev. A 43, 6455–6457 (1991).
[Crossref] [PubMed]

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, “Observation of antiphase states in a multimode laser,” Phys. Rev. Lett. 65, 1749–1752 (1990).
[Crossref] [PubMed]

Chenevier, M.

E. Lacot, F. Stoeckel, and M. Chenevier, “Dynamics of an Erbium-doped fiber laser,” Phys. Rev. A 49, 3997–4008 (1994).
[Crossref] [PubMed]

Chern, J. L.

K. Otsuka and J. L. Chern, “Dynamical spatial pattern memory in global coupled lasers,” Phys. Rev. A 45, 8288–8291 (1992).
[Crossref] [PubMed]

Colet, P.

L. Fabiny, P. Colet, and R. Roy, “Coherence and phase dynamics of spatially coupled solid state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref] [PubMed]

Dalgliesh, R.

de Mars, G.

C. L. Tang, H. Statz, and G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[Crossref]

Derozier, D.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46, 1692–1695 (1992).
[Crossref] [PubMed]

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2811–2822 (1988).
[Crossref]

Eschner, J.

V. M. Baev, J. Eschner, and A. Weiler, “Intracavity spectroscopy with modulated multimode lasers,” Appl. Phys. B 49, 315–322 (1989).
[Crossref]

Etrich, C.

P. Mandel, C. Etrich, and K. Otsuka, “Laser rate equations with phase sensitive interactions,” IEEE J. Quantum Electron. 29, 836–843 (1993).
[Crossref]

K. Otsuka, P. Mandel, M. Georgiou, and C. Etrich, “Antiphase dynamics in a modulated multimode laser,” Jpn. J. Appl. Phys. 32, L318–L321 (1993).

Evdokimova, O. N.

O. N. Evdokimova and L. N. Kaptsov, “Quasiperiodic transition to chaos in a multimode YAG:Nd3+ laser with modulated parameters,” Sov. J. Quantum Electron. 20, 824–827 (1990).
[Crossref]

Everett, L. L.

N. B. Abraham, L. L. Everett, C. Iwata, and M. B. Janicki, “Multimode dynamics of a sinusoidally modulated diode-pumped Nd:YAG laser,” in Proceedings of the Conference Laser Optics ’93, A. Mak, ed., Proc. SPIE2095, 16–24 (1994).
[Crossref]

Fabiny, L.

L. Fabiny, P. Colet, and R. Roy, “Coherence and phase dynamics of spatially coupled solid state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref] [PubMed]

Fleck, J. A.

J. A. Fleck and R. E. Kidder, “Coupled mode laser oscillation,” J. Appl. Phys. 35, 2825–2831 (1964).
[Crossref]

Georgiou, M.

P. Mandel, M. Georgiou, K. Otsuka, and D. Pieroux, “Transient and modulation dynamics of a multimode Fabry–Perot laser,” Opt. Commun. 100, 341–350 (1993).
[Crossref]

K. Otsuka, P. Mandel, M. Georgiou, and C. Etrich, “Antiphase dynamics in a modulated multimode laser,” Jpn. J. Appl. Phys. 32, L318–L321 (1993).

K. Otsuka, M. Georgiou, and P. Mandel, “Intensity fluctuations in multimode lasers with spatial hole burning,” Jpn. J. Appl. Phys. 31, L1250–L1252 (1992).
[Crossref]

Glorieux, P.

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46, 1692–1695 (1992).
[Crossref] [PubMed]

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2811–2822 (1988).
[Crossref]

Harrison, R. G.

F. T. Arecchi and R. G. Harrison, Instabilities and Chaos in Quantum Optics (Springer-Verlag, Berlin, 1987).
[Crossref]

Iwata, C.

N. B. Abraham, L. L. Everett, C. Iwata, and M. B. Janicki, “Multimode dynamics of a sinusoidally modulated diode-pumped Nd:YAG laser,” in Proceedings of the Conference Laser Optics ’93, A. Mak, ed., Proc. SPIE2095, 16–24 (1994).
[Crossref]

James, G.

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, “Observation of antiphase states in a multimode laser,” Phys. Rev. Lett. 65, 1749–1752 (1990).
[Crossref] [PubMed]

Janicki, M. B.

N. B. Abraham, L. L. Everett, C. Iwata, and M. B. Janicki, “Multimode dynamics of a sinusoidally modulated diode-pumped Nd:YAG laser,” in Proceedings of the Conference Laser Optics ’93, A. Mak, ed., Proc. SPIE2095, 16–24 (1994).
[Crossref]

Jia, X.

Jingyi, W.

W. Jingyi and P. Mandel, “Antiphase dynamics of multimode intracavity second-harmonic generation,” Phys. Rev. A 48, 671–680 (1993).
[Crossref] [PubMed]

Kaptsov, L. N.

O. N. Evdokimova and L. N. Kaptsov, “Quasiperiodic transition to chaos in a multimode YAG:Nd3+ laser with modulated parameters,” Sov. J. Quantum Electron. 20, 824–827 (1990).
[Crossref]

Khaleev, M. M.

E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Kidder, R. E.

J. A. Fleck and R. E. Kidder, “Coupled mode laser oscillation,” J. Appl. Phys. 35, 2825–2831 (1964).
[Crossref]

Lacot, E.

E. Lacot, F. Stoeckel, and M. Chenevier, “Dynamics of an Erbium-doped fiber laser,” Phys. Rev. A 49, 3997–4008 (1994).
[Crossref] [PubMed]

E. Lacot and F. Stoeckel, “Two is enough: spectro-temporal dynamics of a two coupled mode laser,” Phys. Rev. A (to be published).

Lamb, W. E.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974).

Le Floch, A.

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52, 918–921 (1984).
[Crossref]

Le Naour, R.

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52, 918–921 (1984).
[Crossref]

Lenormand, J. M.

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52, 918–921 (1984).
[Crossref]

Lin, H.

H. Lin and N. B. Abraham, “Low-frequency pulsations in a He–Xe laser with several transverses modes: experimental and numerical results,” Phys. Rev. A 49, 2076–2086 (1994).
[Crossref] [PubMed]

Longhi, S.

Lugiato, L. A.

MacMackin, I.

M. Beck, I. MacMackin, and M. G. Raymer, “Transition from quantum noise driven dynamics to deterministic dynamics in a multimode laser,” Phys. Rev. A 40, 2410–2416 (1989).
[Crossref] [PubMed]

I. MacMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode standing wave laser,” Phys. Rev. A 38, 820–832 (1988).
[Crossref]

Mak, A. A.

E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[Crossref]

Mandel, P.

K. Otsuka, D. Pieroux, and P. Mandel, “Modulation dynamics and spatio-temporal pattern generation in a microchip multimode laser,” Opt. Commun. 108, 265–271 (1994).
[Crossref]

D. Pieroux, P. Mandel, and K. Otuka, “Modulation dynamics in a multimode laser with feedback,” Opt. Commun. 108, 273–277 (1994).
[Crossref]

P. Mandel, M. Georgiou, K. Otsuka, and D. Pieroux, “Transient and modulation dynamics of a multimode Fabry–Perot laser,” Opt. Commun. 100, 341–350 (1993).
[Crossref]

P. Mandel, C. Etrich, and K. Otsuka, “Laser rate equations with phase sensitive interactions,” IEEE J. Quantum Electron. 29, 836–843 (1993).
[Crossref]

W. Jingyi and P. Mandel, “Antiphase dynamics of multimode intracavity second-harmonic generation,” Phys. Rev. A 48, 671–680 (1993).
[Crossref] [PubMed]

K. Otsuka, P. Mandel, M. Georgiou, and C. Etrich, “Antiphase dynamics in a modulated multimode laser,” Jpn. J. Appl. Phys. 32, L318–L321 (1993).

K. Otsuka, M. Georgiou, and P. Mandel, “Intensity fluctuations in multimode lasers with spatial hole burning,” Jpn. J. Appl. Phys. 31, L1250–L1252 (1992).
[Crossref]

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46, 1692–1695 (1992).
[Crossref] [PubMed]

May, A. D.

Milonni, D. W.

Morozov, V. N.

N. G. Basov, V. N. Morozov, and A. N. Oraevskii, “Non linear mode interaction in lasers,” Soviet Phys. JETP 22, 622–628 (1966).

Narducci, L. M.

Novikov, G. E.

E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Nummedal, K.

H. Risken and K. Nummedal, “Instability of off resonance mode in lasers,” Phys. Lett. A 26, 275–276 (1968).
[Crossref]

Oraevskii, A. N.

N. G. Basov, V. N. Morozov, and A. N. Oraevskii, “Non linear mode interaction in lasers,” Soviet Phys. JETP 22, 622–628 (1966).

Orlov, O. A.

E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Ostrovskii, L. A.

L. A. Ostrovskii, “Interaction of laser modes,” Soviet Phys. JETP 21, 727–732 (1965).

Otsuka, K.

K. Otsuka, D. Pieroux, and P. Mandel, “Modulation dynamics and spatio-temporal pattern generation in a microchip multimode laser,” Opt. Commun. 108, 265–271 (1994).
[Crossref]

P. Mandel, M. Georgiou, K. Otsuka, and D. Pieroux, “Transient and modulation dynamics of a multimode Fabry–Perot laser,” Opt. Commun. 100, 341–350 (1993).
[Crossref]

P. Mandel, C. Etrich, and K. Otsuka, “Laser rate equations with phase sensitive interactions,” IEEE J. Quantum Electron. 29, 836–843 (1993).
[Crossref]

K. Otsuka, “Transverse effects on antiphase laser dynamics,” Jpn. J. Appl. Phys. 32, L1414–L1417 (1993).

K. Otsuka, P. Mandel, M. Georgiou, and C. Etrich, “Antiphase dynamics in a modulated multimode laser,” Jpn. J. Appl. Phys. 32, L318–L321 (1993).

K. Otsuka, “High sensitive measurement of Doppler-shift with microchip solid-state laser,” Jpn. J. Appl. Phys. 32, L1546–L1548 (1993).

K. Otsuka, M. Georgiou, and P. Mandel, “Intensity fluctuations in multimode lasers with spatial hole burning,” Jpn. J. Appl. Phys. 31, L1250–L1252 (1992).
[Crossref]

K. Otsuka and J. L. Chern, “Dynamical spatial pattern memory in global coupled lasers,” Phys. Rev. A 45, 8288–8291 (1992).
[Crossref] [PubMed]

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46, 1692–1695 (1992).
[Crossref] [PubMed]

K. Otsuka, “Winner takes all dynamics and antiphase states in modulated multimode lasers,” Phys. Rev. Lett. 67, 1090–1093 (1991).
[Crossref] [PubMed]

Otuka, K.

D. Pieroux, P. Mandel, and K. Otuka, “Modulation dynamics in a multimode laser with feedback,” Opt. Commun. 108, 273–277 (1994).
[Crossref]

Pieroux, D.

D. Pieroux, P. Mandel, and K. Otuka, “Modulation dynamics in a multimode laser with feedback,” Opt. Commun. 108, 273–277 (1994).
[Crossref]

K. Otsuka, D. Pieroux, and P. Mandel, “Modulation dynamics and spatio-temporal pattern generation in a microchip multimode laser,” Opt. Commun. 108, 265–271 (1994).
[Crossref]

P. Mandel, M. Georgiou, K. Otsuka, and D. Pieroux, “Transient and modulation dynamics of a multimode Fabry–Perot laser,” Opt. Commun. 100, 341–350 (1993).
[Crossref]

Pomeau, Y.

P. Berge, Y. Pomeau, and Ch. Vidal, L’Ordre dans le Chaos (Hermann, Paris, 1986).

Radzewicz, C.

I. MacMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode standing wave laser,” Phys. Rev. A 38, 820–832 (1988).
[Crossref]

Raymer, M. G.

M. Beck, I. MacMackin, and M. G. Raymer, “Transition from quantum noise driven dynamics to deterministic dynamics in a multimode laser,” Phys. Rev. A 40, 2410–2416 (1989).
[Crossref] [PubMed]

I. MacMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode standing wave laser,” Phys. Rev. A 38, 820–832 (1988).
[Crossref]

Risken, H.

H. Risken and K. Nummedal, “Instability of off resonance mode in lasers,” Phys. Lett. A 26, 275–276 (1968).
[Crossref]

Ropars, G.

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52, 918–921 (1984).
[Crossref]

Roy, R.

L. Fabiny, P. Colet, and R. Roy, “Coherence and phase dynamics of spatially coupled solid state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref] [PubMed]

C. Bracikowski and R. Roy, “Energy sharing in a chaotic multimode laser,” Phys. Rev. A 43, 6455–6457 (1991).
[Crossref] [PubMed]

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, “Observation of antiphase states in a multimode laser,” Phys. Rev. Lett. 65, 1749–1752 (1990).
[Crossref] [PubMed]

Sargent, M.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974).

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974).

Shih, M. L.

Siegmann, A. E.

A. E. Siegmann, Lasers (University Science, Mill Valley, Calif., 1986).

Sokolov, V. A.

E. A. Viktorov, V. A. Sokolov, E. V. Tkachenko, and V. I. Ustyugov, “Violation of stability and randomization of the radiation spectra of solid-state lasers due to frequency non-equidistance of modes,” Opt. Spectrosc. (USSR) 68, 537–538 (1990).

Statz, H.

C. L. Tang, H. Statz, and G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[Crossref]

Stephan, G.

Stoeckel, F.

E. Lacot, F. Stoeckel, and M. Chenevier, “Dynamics of an Erbium-doped fiber laser,” Phys. Rev. A 49, 3997–4008 (1994).
[Crossref] [PubMed]

E. Lacot and F. Stoeckel, “Two is enough: spectro-temporal dynamics of a two coupled mode laser,” Phys. Rev. A (to be published).

Tang, C. L.

C. L. Tang, H. Statz, and G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[Crossref]

Tkachenko, E. V.

E. A. Viktorov, V. A. Sokolov, E. V. Tkachenko, and V. I. Ustyugov, “Violation of stability and randomization of the radiation spectra of solid-state lasers due to frequency non-equidistance of modes,” Opt. Spectrosc. (USSR) 68, 537–538 (1990).

Ustyugov, V. I.

E. A. Viktorov, V. A. Sokolov, E. V. Tkachenko, and V. I. Ustyugov, “Violation of stability and randomization of the radiation spectra of solid-state lasers due to frequency non-equidistance of modes,” Opt. Spectrosc. (USSR) 68, 537–538 (1990).

E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Vidal, Ch.

P. Berge, Y. Pomeau, and Ch. Vidal, L’Ordre dans le Chaos (Hermann, Paris, 1986).

Viktorov, E. A.

E. A. Viktorov, V. A. Sokolov, E. V. Tkachenko, and V. I. Ustyugov, “Violation of stability and randomization of the radiation spectra of solid-state lasers due to frequency non-equidistance of modes,” Opt. Spectrosc. (USSR) 68, 537–538 (1990).

E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Vitrishchak, I. B.

E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

Weiler, A.

V. M. Baev, J. Eschner, and A. Weiler, “Intracavity spectroscopy with modulated multimode lasers,” Appl. Phys. B 49, 315–322 (1989).
[Crossref]

Wiesenfeld, K.

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, “Observation of antiphase states in a multimode laser,” Phys. Rev. Lett. 65, 1749–1752 (1990).
[Crossref] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[Crossref]

Zayhowski, J. J.

J. J. Zayhowski, “Microchip lasers,” Lincoln Lab. J. 3, 427–446 (1990).

Appl. Phys. B (1)

V. M. Baev, J. Eschner, and A. Weiler, “Intracavity spectroscopy with modulated multimode lasers,” Appl. Phys. B 49, 315–322 (1989).
[Crossref]

IEEE J. Quantum Electron. (1)

P. Mandel, C. Etrich, and K. Otsuka, “Laser rate equations with phase sensitive interactions,” IEEE J. Quantum Electron. 29, 836–843 (1993).
[Crossref]

J. Appl. Phys. (2)

C. L. Tang, H. Statz, and G. de Mars, “Spectral output and spiking behavior of solid state lasers,” J. Appl. Phys. 34, 2289–2295 (1963).
[Crossref]

J. A. Fleck and R. E. Kidder, “Coupled mode laser oscillation,” J. Appl. Phys. 35, 2825–2831 (1964).
[Crossref]

J. Opt. Soc. Am. B (5)

Jpn. J. Appl. Phys. (4)

K. Otsuka, “High sensitive measurement of Doppler-shift with microchip solid-state laser,” Jpn. J. Appl. Phys. 32, L1546–L1548 (1993).

K. Otsuka, M. Georgiou, and P. Mandel, “Intensity fluctuations in multimode lasers with spatial hole burning,” Jpn. J. Appl. Phys. 31, L1250–L1252 (1992).
[Crossref]

K. Otsuka, P. Mandel, M. Georgiou, and C. Etrich, “Antiphase dynamics in a modulated multimode laser,” Jpn. J. Appl. Phys. 32, L318–L321 (1993).

K. Otsuka, “Transverse effects on antiphase laser dynamics,” Jpn. J. Appl. Phys. 32, L1414–L1417 (1993).

Lincoln Lab. J. (1)

J. J. Zayhowski, “Microchip lasers,” Lincoln Lab. J. 3, 427–446 (1990).

Opt. Commun. (3)

D. Pieroux, P. Mandel, and K. Otuka, “Modulation dynamics in a multimode laser with feedback,” Opt. Commun. 108, 273–277 (1994).
[Crossref]

P. Mandel, M. Georgiou, K. Otsuka, and D. Pieroux, “Transient and modulation dynamics of a multimode Fabry–Perot laser,” Opt. Commun. 100, 341–350 (1993).
[Crossref]

K. Otsuka, D. Pieroux, and P. Mandel, “Modulation dynamics and spatio-temporal pattern generation in a microchip multimode laser,” Opt. Commun. 108, 265–271 (1994).
[Crossref]

Opt. Spectrosc. (USSR) (1)

E. A. Viktorov, V. A. Sokolov, E. V. Tkachenko, and V. I. Ustyugov, “Violation of stability and randomization of the radiation spectra of solid-state lasers due to frequency non-equidistance of modes,” Opt. Spectrosc. (USSR) 68, 537–538 (1990).

Phys. Lett. A (1)

H. Risken and K. Nummedal, “Instability of off resonance mode in lasers,” Phys. Lett. A 26, 275–276 (1968).
[Crossref]

Phys. Rev. A (10)

C. Bracikowski and R. Roy, “Energy sharing in a chaotic multimode laser,” Phys. Rev. A 43, 6455–6457 (1991).
[Crossref] [PubMed]

K. Otsuka and J. L. Chern, “Dynamical spatial pattern memory in global coupled lasers,” Phys. Rev. A 45, 8288–8291 (1992).
[Crossref] [PubMed]

S. Bielawski, D. Derozier, and P. Glorieux, “Antiphase dynamics and polarization effects in the Nd-doped fiber laser,” Phys. Rev. A 46, 2811–2822 (1988).
[Crossref]

K. Otsuka, P. Mandel, S. Bielawski, D. Derozier, and P. Glorieux, “Alternate time scale in multimode lasers,” Phys. Rev. A 46, 1692–1695 (1992).
[Crossref] [PubMed]

I. MacMackin, C. Radzewicz, M. Beck, and M. G. Raymer, “Instabilities and chaos in a multimode standing wave laser,” Phys. Rev. A 38, 820–832 (1988).
[Crossref]

L. Fabiny, P. Colet, and R. Roy, “Coherence and phase dynamics of spatially coupled solid state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[Crossref] [PubMed]

W. Jingyi and P. Mandel, “Antiphase dynamics of multimode intracavity second-harmonic generation,” Phys. Rev. A 48, 671–680 (1993).
[Crossref] [PubMed]

M. Beck, I. MacMackin, and M. G. Raymer, “Transition from quantum noise driven dynamics to deterministic dynamics in a multimode laser,” Phys. Rev. A 40, 2410–2416 (1989).
[Crossref] [PubMed]

E. Lacot, F. Stoeckel, and M. Chenevier, “Dynamics of an Erbium-doped fiber laser,” Phys. Rev. A 49, 3997–4008 (1994).
[Crossref] [PubMed]

H. Lin and N. B. Abraham, “Low-frequency pulsations in a He–Xe laser with several transverses modes: experimental and numerical results,” Phys. Rev. A 49, 2076–2086 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

A. Le Floch, G. Ropars, J. M. Lenormand, and R. Le Naour, “Dynamics of laser eigenstates,” Phys. Rev. Lett. 52, 918–921 (1984).
[Crossref]

K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, “Observation of antiphase states in a multimode laser,” Phys. Rev. Lett. 65, 1749–1752 (1990).
[Crossref] [PubMed]

K. Otsuka, “Winner takes all dynamics and antiphase states in modulated multimode lasers,” Phys. Rev. Lett. 67, 1090–1093 (1991).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

O. N. Evdokimova and L. N. Kaptsov, “Quasiperiodic transition to chaos in a multimode YAG:Nd3+ laser with modulated parameters,” Sov. J. Quantum Electron. 20, 824–827 (1990).
[Crossref]

Soviet Phys. JETP (2)

L. A. Ostrovskii, “Interaction of laser modes,” Soviet Phys. JETP 21, 727–732 (1965).

N. G. Basov, V. N. Morozov, and A. N. Oraevskii, “Non linear mode interaction in lasers,” Soviet Phys. JETP 22, 622–628 (1966).

Other (8)

E. Lacot and F. Stoeckel, “Two is enough: spectro-temporal dynamics of a two coupled mode laser,” Phys. Rev. A (to be published).

A. E. Siegmann, Lasers (University Science, Mill Valley, Calif., 1986).

F. T. Arecchi and R. G. Harrison, Instabilities and Chaos in Quantum Optics (Springer-Verlag, Berlin, 1987).
[Crossref]

P. Berge, Y. Pomeau, and Ch. Vidal, L’Ordre dans le Chaos (Hermann, Paris, 1986).

N. B. Abraham, L. L. Everett, C. Iwata, and M. B. Janicki, “Multimode dynamics of a sinusoidally modulated diode-pumped Nd:YAG laser,” in Proceedings of the Conference Laser Optics ’93, A. Mak, ed., Proc. SPIE2095, 16–24 (1994).
[Crossref]

E. A. Viktorov, I. B. Vitrishchak, G. E. Novikov, O. A. Orlov, A. A. Mak, V. I. Ustyugov, and M. M. Khaleev, “Instabilities and chaos in solid-state lasers as a result of mode coupling,” in Nonlinear Dynamics in Optical Systems, N. B. Abraham, E. Garmire, and P. Mandel, eds., Vol. 7 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1991).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
[Crossref]

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1974).

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Figures (9)

Fig. 1
Fig. 1

Numerical simulation of the transient behaviors of the total intensity for a bimode laser for different values of the pump parameter N0: (a) N0=1.05, (b) N0=2, (c) N0=21, (d) N0 = 100, with the following parameters: g1=1, g2=0.99, C11 = C22=1, C12=C21=2/3, γ=5×103, f1=10-6. η is the number of spikes per damping period.

Fig. 2
Fig. 2

Numerical simulation of the transient behaviors of the total intensity for a bimode laser for different values of γ = T1/T: (a) γ=5×102, (b) γ=5×103, (c)γ=5×104 and with the following parameters: N0=3, g1=1, g2=0.99, C11 = C22=1, C12=C21=2/3, and f1=10-6. η is the number of spikes per damping period.

Fig. 3
Fig. 3

Experimental transient behavior of the total intensity of a coupled eight-longitudinal-mode laser in response to a step pump function. The pump power is 320 mW (two times above the threshold, N0=2) and γ=106 (T=3×10-10 s, T1=300 µs).

Fig. 4
Fig. 4

Numerical simulation of the transient behavior of the total intensity of a coupled eight-longitudinal-mode laser in response to a step pump function with the same parameters as in Fig. 3 and with Cii=1, Cij=2/3, f1=10-9, and gj=1/{1 + [0.085(j-4.6)]2.

Fig. 5
Fig. 5

Power spectrum of the unpolarized intensity of each of the eight individual modes of the microchip laser for a pump power of 400 mW. Vertical lines show how the different modes are coupled to one another. Narrow peaks are parasitic artifacts.

Fig. 6
Fig. 6

Power spectra of the unpolarized and polarized intensities of the mode at 1055.1 nm, showing the high frequency fH, a group of low frequencies fL, and a group of very low frequencies fVL. Narrow peaks are parasitic artifacts.

Fig. 7
Fig. 7

Power spectrum of the polarized intensity of each of the eight modes in the low- and very low-frequency domains. Vertical lines show how the different modes are coupled to one another.

Fig. 8
Fig. 8

Measured relaxation frequencies of the total intensity of the microchip laser as a function of the pump power (top) for the high relaxation frequency, (center) for the low relaxation frequencies that are due to the cross-saturation coupling of the longitudinal mode: f2 (circles), f3 (upward-pointing triangles), f4 (downward-pointing triangles), f5 (diamonds), f6 (+), f7 (*), and f8 (×), and (bottom) for the very low relaxation frequencies that are due to cross-saturation coupling of the two orthogonal states of polarization fII (circles), fIII (upward-pointing triangle), fIV (downward-pointing triangles), fV (diamonds), fVI (+), fVII (*), and fVIII (×).

Fig. 9
Fig. 9

Power spectrum of the total intensity of each of different values of the pump power. This figure shows the high frequency f1 and some of the lower frequencies. The total intensity does not exhibit perfect antiphase dynamics. The narrow peaks marked with asterisks are parasitic artifacts.

Equations (11)

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

ddtn(z,t)=-[n(z,t)-n0¯]T1-iDgiMi(t)×1-cos 2miπzLn(z,t),
ddtMi(t)=-MiT+DgiMi(t)z1-l/2z1+l/2n(z,t)×1-cos 2miπzLdz.
Gi=Dgiz1-l/2z1+l/2n(z,t)1-cos 2miπzLdz,
Kij=n(z,t)sin2 miπzLsin2 mjπzLdzn(z,t)sin2 miπzLdz.
Ni=GiT,  Ii=2DgiT1K11Mi,
ddtIi=γ(Ni-1)Ii+γflNi,
dNidt=N0gi-Ni-j=1mCijgjIjNi,
Nc=1-C12g2-C12.
ωH2ωL2=1+C121-C12.
η=ωLtd2π1-C121+C121/2γ(N0-Nc)N021/2.
Cij=Cji=2/3,  Cii=1.

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