Abstract

A stochastic, semiclassical model is developed for a multimode, homogeneously broadened laser with rapid dipole dephasing, appropriate for semiconductor, Ti:sapphire, or dye lasers. The theory self-consistently incorporates population dynamics including temporal beating effects and relaxation oscillations, spatial hole burning, coherent-wave mixing, and quantum noise. The model is valid for single- and compound-cavity lasers in which the mode frequencies are well defined. We pay particular attention to finding a useful mode basis in the case that the gain medium does not completely fill the cavity. This situation can lead to coupled-cavity effects. For typical systems the model is valid for pump rates up to several times threshold and is tractable for numerical simulations. The theoretical development described in this paper is applied to an experimental system in a companion paper (J. Opt. Soc. Am. B 14, 180 (1997)].

© 1997 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref]
  45. G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147–159 (1988).
    [Crossref]
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    [Crossref]
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    [Crossref]
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1997 (1)

1994 (1)

1993 (1)

1992 (1)

1991 (6)

S. Ciuchi, M. San Miguel, N. B. Abraham, and F. de Pasquale, “Phase and amplitude correlations induced by the switch-on chirp of a detuned laser,” Phys. Rev. A 44, 7657–7668 (1991).
[Crossref] [PubMed]

P. D. Drummond and M. G. Raymer, “Quantum theory of propagation of nonclassical radiation in a near-resonant medium,” Phys. Rev. A 44, 2072–2085 (1991).
[Crossref] [PubMed]

U. Herzog, “Longitudinal mode interaction in semiconductor lasers due to nonlinear gain suppression and four-wave mixing,” Opt. Commun. 82, 390–405 (1991).
[Crossref]

K. Hsu, C. M. Verber, and R. Roy, “Stochastic mode-locking theory for external-cavity semiconductor lasers,” J. Opt. Soc. Am. B 8, 262–275 (1991).
[Crossref]

G. Gray and G. P. Agrawal, “Effect of cross saturation on frequency fluctuations in a nearly single-mode semiconductor laser,” IEEE Photon. Technol. Lett. 3, 204–206 (1991).
[Crossref]

L. F. Tiemeijer, “Effects of nonlinear gain on four-wave mixing and asymmetric gain saturation in a semiconductor laser amplifier,” Appl. Phys. Lett. 59, 499–501 (1991).
[Crossref]

1990 (2)

G. P. Agrawal, “Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers,” IEEE J. Quantum Electron. 26, 1901–1909 (1990).
[Crossref]

C. Ning and H. Haken, “Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hoff bifurcations,” Phys. Rev. A 41, 3826–3837 (1990).
[Crossref] [PubMed]

1989 (4)

D. R. Hjelme and A. R. Mickelson, “Gain nonlinearities due to carrier density dependent dispersion in semiconductor lasers,” IEEE J. Quantum Electron. 25, 1625–1631 (1989).
[Crossref]

G. Gray and R. Roy, “Noise in nearly single-mode semiconductor lasers,” Phys. Rev. A 40, 2452–2462 (1989).
[Crossref] [PubMed]

M. Beck, I. McMackin, 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]

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
[Crossref]

1988 (6)

1987 (4)

W. R. Christian and L. Mandel, “Allowed detuning range of the third order laser theory for an inhomogenously broadened laser,” Opt. Commun. 64, 537–538 (1987).
[Crossref]

A. W. Yu, G. P. Agarwal, and R. Roy, “Noise propagation from pump to secondary laser,” Opt. Lett. 12, 806–808 (1987).
[Crossref] [PubMed]

R. F. Fox and R. Roy, “Steady-state analysis of strongly colored multiplicative noise in a dye laser,” Phys. Rev. A 41, 1838–1842 (1987).
[Crossref]

T. H. Chyba, E. C. Gage, R. Ghosh, P. Lett, L. Mandel, and I. McMackin, “Chaos in a good-cavity single-mode dye laser due to turbulent dye flow,” Opt. Lett. 12, 422–424 (1987).
[Crossref] [PubMed]

1986 (3)

R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5 micrometer distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[Crossref]

H. Atmanspacher and H. Scheingraber, “Deterministic chaos and dynamical instabilities in a multimode cw dye laser,” Phys. Rev. A 34, 253–263 (1986).
[Crossref] [PubMed]

W. W. Chow, “A composite-resonator mode description of coupled lasers,” IEEE J. Quantum Electron. QE-22, 1174–1183 (1986).
[Crossref]

1985 (5)

1984 (1)

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and T. R. Treddicce, “Deterministic chaos in laser with injected signal,” Opt. Commun. 51, 308–314 (1984).
[Crossref]

1972 (1)

M. B. Spencer and W. E. Lamb, “Laser with a transmitting window,” Phys. Rev. A 5, 884–892 (1972); “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
[Crossref]

1971 (1)

F. T. Arecchi and V. Degiorgio, “Statistical properties of laser radiation during a transient buildup,” Phys. Rev. A 3, 1108–1124 (1971).
[Crossref]

1968 (1)

H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[Crossref]

1967 (1)

F. T. Arecchi, V. Degiorgio, and B. Querzola, “Time-dependent statistical properties of the laser radiation,” Phys. Rev. Lett. 19, 1168–1171 (1967).
[Crossref]

1966 (3)

H. Haken, “Theory of intensity and phase fluctuations of a homogeneously broadened laser,” Z. Phys. 190, 327–356 (1966).
[Crossref]

D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev. 141, 306–322 (1966).
[Crossref]

A. Yariv, “Parametric interactions of optical modes,” IEEE J. Quantum Electron. QE-2, 30–37 (1966).
[Crossref]

1964 (1)

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. 134, A1429–A1450 (1964).
[Crossref]

1963 (1)

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

Abraham, N. B.

S. Ciuchi, M. San Miguel, N. B. Abraham, and F. de Pasquale, “Phase and amplitude correlations induced by the switch-on chirp of a detuned laser,” Phys. Rev. A 44, 7657–7668 (1991).
[Crossref] [PubMed]

N. B. Abraham, P. Mandel, and L. M. Narducci, “Dynamical instabilities and pulsations in lasers,” in Progress in Optics XXV, E. Wolf, ed. (Elsevier, Amsterdam, 1988), pp. 25–28.

N. B. Abraham, “An overview of optical instabilities and chaos and an introduction to some models and current areas of research in laser instabilities,” in Dynamics of Non-Linear Optical Systems, L. Pesquera and F. J. Bermejo, eds. (World Scientific, Singapore, 1989), pp. 3–28.

Adkison, D.

Agarwal, G. P.

Agrawal, G. P.

G. Gray and G. P. Agrawal, “Effect of cross saturation on frequency fluctuations in a nearly single-mode semiconductor laser,” IEEE Photon. Technol. Lett. 3, 204–206 (1991).
[Crossref]

G. P. Agrawal, “Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers,” IEEE J. Quantum Electron. 26, 1901–1909 (1990).
[Crossref]

G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147–159 (1988).
[Crossref]

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986), Chap. 6, p. 247.

Arecchi, F. T.

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and T. R. Treddicce, “Deterministic chaos in laser with injected signal,” Opt. Commun. 51, 308–314 (1984).
[Crossref]

F. T. Arecchi and V. Degiorgio, “Statistical properties of laser radiation during a transient buildup,” Phys. Rev. A 3, 1108–1124 (1971).
[Crossref]

F. T. Arecchi, V. Degiorgio, and B. Querzola, “Time-dependent statistical properties of the laser radiation,” Phys. Rev. Lett. 19, 1168–1171 (1967).
[Crossref]

Atmanspacher, H.

H. Atmanspacher and H. Scheingraber, “Deterministic chaos and dynamical instabilities in a multimode cw dye laser,” Phys. Rev. A 34, 253–263 (1986).
[Crossref] [PubMed]

Beck, M.

M. Beck, I. McMackin, 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]

M. G. Raymer, Z. Deng, and M. Beck, “Strong-field dynamics of a multimode, standing-wave dye laser,” J. Opt. Soc. Am. B 5, 1588–1595 (1988).
[Crossref]

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. 8, p. 375.

Boyd, R. W.

Brunner, W.

Chakmakjian, S.

C. R. Stroud, K. Koch, and S. Chakmakjian, “Instabilities and higher-order states of cw ring dye lasers,” in Optical Instabilities, R. W. Boyd, M. G. Raymer, and L. M. Narducci, eds. (Cambridge U. Press, Cambridge, 1986), Chap. II, pp. 274–276.

Chow, W. W.

W. W. Chow, “A composite-resonator mode description of coupled lasers,” IEEE J. Quantum Electron. QE-22, 1174–1183 (1986).
[Crossref]

Chraplyvy, A. R.

R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5 micrometer distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[Crossref]

Christian, W. R.

W. R. Christian and L. Mandel, “Allowed detuning range of the third order laser theory for an inhomogenously broadened laser,” Opt. Commun. 64, 537–538 (1987).
[Crossref]

Chyba, T. H.

Ciuchi, S.

S. Ciuchi, M. San Miguel, N. B. Abraham, and F. de Pasquale, “Phase and amplitude correlations induced by the switch-on chirp of a detuned laser,” Phys. Rev. A 44, 7657–7668 (1991).
[Crossref] [PubMed]

Cooper, J.

de Pasquale, F.

S. Ciuchi, M. San Miguel, N. B. Abraham, and F. de Pasquale, “Phase and amplitude correlations induced by the switch-on chirp of a detuned laser,” Phys. Rev. A 44, 7657–7668 (1991).
[Crossref] [PubMed]

Degiorgio, V.

F. T. Arecchi and V. Degiorgio, “Statistical properties of laser radiation during a transient buildup,” Phys. Rev. A 3, 1108–1124 (1971).
[Crossref]

F. T. Arecchi, V. Degiorgio, and B. Querzola, “Time-dependent statistical properties of the laser radiation,” Phys. Rev. Lett. 19, 1168–1171 (1967).
[Crossref]

deMars, G.

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

Deng, Z.

Drummond, P. D.

P. D. Drummond and M. G. Raymer, “Quantum theory of propagation of nonclassical radiation in a near-resonant medium,” Phys. Rev. A 44, 2072–2085 (1991).
[Crossref] [PubMed]

Dutta, N. K.

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986), Chap. 6, p. 247.

Fader, W. J.

W. J. Fader, “Theory of two coupled lasers,” IEEE J. Quantum Electron. QE-21, 1838–1844 (1985).
[Crossref]

Fischer, R.

Fox, R. F.

R. F. Fox and R. Roy, “Steady-state analysis of strongly colored multiplicative noise in a dye laser,” Phys. Rev. A 41, 1838–1842 (1987).
[Crossref]

Frey, R.

B. Thedrez, A. Jones, and R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” IEEE J. Quantum Electron. 24, 1499–1506 (1988).
[Crossref]

Fu, H.

Gadomski, W.

Gage, E. C.

Gardiner, C. W.

C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983), Chap. 4, pp. 80–85.

Ghosh, R.

Gray, G.

G. Gray and G. P. Agrawal, “Effect of cross saturation on frequency fluctuations in a nearly single-mode semiconductor laser,” IEEE Photon. Technol. Lett. 3, 204–206 (1991).
[Crossref]

G. Gray and R. Roy, “Noise in nearly single-mode semiconductor lasers,” Phys. Rev. A 40, 2452–2462 (1989).
[Crossref] [PubMed]

Haken, H.

C. Ning and H. Haken, “Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hoff bifurcations,” Phys. Rev. A 41, 3826–3837 (1990).
[Crossref] [PubMed]

H. Fu and H. Haken, “Semiclassical theory of dye lasers: the single-frequency and multifrequency steady states of operation,” J. Opt. Soc. Am. B 5, 899–908 (1988).
[Crossref]

H. Haken, “Theory of intensity and phase fluctuations of a homogeneously broadened laser,” Z. Phys. 190, 327–356 (1966).
[Crossref]

H. Haken, Light, Vol. 2 (North Holland, Amsterdam, 1985), Chap. 10, p. 248.

H. Haken, “The adiabatic elimination principle in dynamical theories,” in Optical Instabilities, R. W. Boyd, M. G. Raymer, and L. M. Narducci, eds. (Cambridge U. Press, Cambridge, 1986), pp. 1–19.

Henry, C. W.

C. W. Henry, “Line broadening of semiconductor lasers,” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), Chap. 2, p. 66.

Herzog, U.

U. Herzog, “Longitudinal mode interaction in semiconductor lasers due to nonlinear gain suppression and four-wave mixing,” Opt. Commun. 82, 390–405 (1991).
[Crossref]

Hillman, L. W.

Hjelme, D. R.

D. R. Hjelme and A. R. Mickelson, “Gain nonlinearities due to carrier density dependent dispersion in semiconductor lasers,” IEEE J. Quantum Electron. 25, 1625–1631 (1989).
[Crossref]

Hodges, S. E.

Hsu, K.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chap. 7, p. 282.

Jones, A.

B. Thedrez, A. Jones, and R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” IEEE J. Quantum Electron. 24, 1499–1506 (1988).
[Crossref]

Knight, P. L.

P. L. Knight, “Non-Markovian effects in spontaneous emission: deviations from the exponential decay law,” in Coherence and Quantum Optics IV, L. Mandel and E. Wolf, eds. (Plenum, New York, 1978), pp. 635–647.

Koch, K.

C. R. Stroud, K. Koch, and S. Chakmakjian, “Instabilities and higher-order states of cw ring dye lasers,” in Optical Instabilities, R. W. Boyd, M. G. Raymer, and L. M. Narducci, eds. (Cambridge U. Press, Cambridge, 1986), Chap. II, pp. 274–276.

Krasinski, J.

Lamb, W. E.

M. B. Spencer and W. E. Lamb, “Laser with a transmitting window,” Phys. Rev. A 5, 884–892 (1972); “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
[Crossref]

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. 134, A1429–A1450 (1964).
[Crossref]

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1977), Chap. 9, p. 119; Chap. 20, p. 134.

Lax, M.

M. Lax, “The theory of laser noise,” in Laser Noise, R. Roy, ed., Proc. SPIE1376, 2–20 (1990).
[Crossref]

Lett, P.

Lippi, G. L.

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and T. R. Treddicce, “Deterministic chaos in laser with injected signal,” Opt. Commun. 51, 308–314 (1984).
[Crossref]

Liu, P. L.

P. L. Liu, “Photon statistics and mode partition noise of semiconductor lasers,” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), Chap. 10, p. 444.

Mandel, L.

W. R. Christian and L. Mandel, “Allowed detuning range of the third order laser theory for an inhomogenously broadened laser,” Opt. Commun. 64, 537–538 (1987).
[Crossref]

T. H. Chyba, E. C. Gage, R. Ghosh, P. Lett, L. Mandel, and I. McMackin, “Chaos in a good-cavity single-mode dye laser due to turbulent dye flow,” Opt. Lett. 12, 422–424 (1987).
[Crossref] [PubMed]

Mandel, P.

H. Zeghlache and P. Mandel, “Influence of detuning on the properties of laser equations,” J. Opt. Soc. Am. B 2, 18–22 (1985).
[Crossref]

N. B. Abraham, P. Mandel, and L. M. Narducci, “Dynamical instabilities and pulsations in lasers,” in Progress in Optics XXV, E. Wolf, ed. (Elsevier, Amsterdam, 1988), pp. 25–28.

Marcuse, D.

D. Marcuse, “Computer simulation of laser photon fluctuations: coupled-cavity lasers,” IEEE J. Quantum Electron. QE-21, 154–161 (1985).
[Crossref]

McCumber, D. E.

D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev. 141, 306–322 (1966).
[Crossref]

McMackin, I.

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

T. H. Chyba, E. C. Gage, R. Ghosh, P. Lett, L. Mandel, and I. McMackin, “Chaos in a good-cavity single-mode dye laser due to turbulent dye flow,” Opt. Lett. 12, 422–424 (1987).
[Crossref] [PubMed]

Mickelson, A. R.

D. R. Hjelme and A. R. Mickelson, “Gain nonlinearities due to carrier density dependent dispersion in semiconductor lasers,” IEEE J. Quantum Electron. 25, 1625–1631 (1989).
[Crossref]

Munroe, M.

Narducci, L. M.

N. B. Abraham, P. Mandel, and L. M. Narducci, “Dynamical instabilities and pulsations in lasers,” in Progress in Optics XXV, E. Wolf, ed. (Elsevier, Amsterdam, 1988), pp. 25–28.

Ning, C.

C. Ning and H. Haken, “Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hoff bifurcations,” Phys. Rev. A 41, 3826–3837 (1990).
[Crossref] [PubMed]

Nummedal, K.

H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[Crossref]

Paul, H.

Puccioni, G. P.

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and T. R. Treddicce, “Deterministic chaos in laser with injected signal,” Opt. Commun. 51, 308–314 (1984).
[Crossref]

Querzola, B.

F. T. Arecchi, V. Degiorgio, and B. Querzola, “Time-dependent statistical properties of the laser radiation,” Phys. Rev. Lett. 19, 1168–1171 (1967).
[Crossref]

Radzewicz, C.

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

Raymer, M. G.

S. E. Hodges, M. Munroe, W. Gadomski, J. Cooper, and M. G. Raymer, “Turn-on transient dynamics in a multimode, compound-cavity laser,” J. Opt. Soc. Am. B 14, 180–190 (1997).
[Crossref]

M. Munroe, S. E. Hodges, J. Cooper, and M. G. Raymer, “Total intensity modulation and mode hopping in a coupled-cavity laser as a result of external-cavity length variations,” Opt. Lett. 19, 105–107 (1994).
[Crossref]

S. E. Hodges, M. Munroe, J. Cooper, and M. G. Raymer, “Compound cavity laser modes for arbitrary interface reflectivity,” Opt. Lett. 18, 1481–1483 (1993).
[Crossref]

S. E. Hodges, M. Munroe, D. Adkison, W. Gadomski, and M. G. Raymer, “Turn-on transient statistics and dynamics in a multimode, short-cavity laser,” Opt. Lett. 17, 931–933 (1992).
[Crossref] [PubMed]

P. D. Drummond and M. G. Raymer, “Quantum theory of propagation of nonclassical radiation in a near-resonant medium,” Phys. Rev. A 44, 2072–2085 (1991).
[Crossref] [PubMed]

M. Beck, I. McMackin, 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]

M. G. Raymer, Z. Deng, and M. Beck, “Strong-field dynamics of a multimode, standing-wave dye laser,” J. Opt. Soc. Am. B 5, 1588–1595 (1988).
[Crossref]

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

Risken, H.

H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[Crossref]

Roy, R.

K. Hsu, C. M. Verber, and R. Roy, “Stochastic mode-locking theory for external-cavity semiconductor lasers,” J. Opt. Soc. Am. B 8, 262–275 (1991).
[Crossref]

G. Gray and R. Roy, “Noise in nearly single-mode semiconductor lasers,” Phys. Rev. A 40, 2452–2462 (1989).
[Crossref] [PubMed]

A. W. Yu, G. P. Agarwal, and R. Roy, “Noise propagation from pump to secondary laser,” Opt. Lett. 12, 806–808 (1987).
[Crossref] [PubMed]

R. F. Fox and R. Roy, “Steady-state analysis of strongly colored multiplicative noise in a dye laser,” Phys. Rev. A 41, 1838–1842 (1987).
[Crossref]

San Miguel, M.

S. Ciuchi, M. San Miguel, N. B. Abraham, and F. de Pasquale, “Phase and amplitude correlations induced by the switch-on chirp of a detuned laser,” Phys. Rev. A 44, 7657–7668 (1991).
[Crossref] [PubMed]

Sargent, M.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1977), Chap. 9, p. 119; Chap. 20, p. 134.

Scheingraber, H.

H. Atmanspacher and H. Scheingraber, “Deterministic chaos and dynamical instabilities in a multimode cw dye laser,” Phys. Rev. A 34, 253–263 (1986).
[Crossref] [PubMed]

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1977), Chap. 9, p. 119; Chap. 20, p. 134.

Shimoda, K.

K. Shimoda, Introduction to Laser Physics (Springer-Verlag, Berlin, 1986), Chap. 9, p. 176.

Siegman, A.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 3, p. 120.

Spencer, M. B.

M. B. Spencer and W. E. Lamb, “Laser with a transmitting window,” Phys. Rev. A 5, 884–892 (1972); “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
[Crossref]

Statz, H.

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

Stroud, C. R.

L. W. Hillman, J. Krasinski, R. W. Boyd, and C. R. Stroud, “Dynamics of homogeneously broadened lasers: higher-order bichromatic states of operation,” J. Opt. Soc. Am. B 2, 211–217 (1985).
[Crossref]

C. R. Stroud, K. Koch, and S. Chakmakjian, “Instabilities and higher-order states of cw ring dye lasers,” in Optical Instabilities, R. W. Boyd, M. G. Raymer, and L. M. Narducci, eds. (Cambridge U. Press, Cambridge, 1986), Chap. II, pp. 274–276.

Svelto, O.

O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1989), Chap. 6, pp. 331–339.

Tang, C. L.

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

Thedrez, B.

B. Thedrez, A. Jones, and R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” IEEE J. Quantum Electron. 24, 1499–1506 (1988).
[Crossref]

Tiemeijer, L. F.

L. F. Tiemeijer, “Effects of nonlinear gain on four-wave mixing and asymmetric gain saturation in a semiconductor laser amplifier,” Appl. Phys. Lett. 59, 499–501 (1991).
[Crossref]

Tkach, R. W.

R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5 micrometer distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[Crossref]

Treddicce, T. R.

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and T. R. Treddicce, “Deterministic chaos in laser with injected signal,” Opt. Commun. 51, 308–314 (1984).
[Crossref]

Verber, C. M.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. 8, p. 375.

Yamada, M.

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
[Crossref]

Yariv, A.

A. Yariv, “Parametric interactions of optical modes,” IEEE J. Quantum Electron. QE-2, 30–37 (1966).
[Crossref]

Yu, A. W.

Zeghlache, H.

Appl. Phys. Lett. (1)

L. F. Tiemeijer, “Effects of nonlinear gain on four-wave mixing and asymmetric gain saturation in a semiconductor laser amplifier,” Appl. Phys. Lett. 59, 499–501 (1991).
[Crossref]

IEEE J. Quantum Electron. (7)

D. R. Hjelme and A. R. Mickelson, “Gain nonlinearities due to carrier density dependent dispersion in semiconductor lasers,” IEEE J. Quantum Electron. 25, 1625–1631 (1989).
[Crossref]

W. J. Fader, “Theory of two coupled lasers,” IEEE J. Quantum Electron. QE-21, 1838–1844 (1985).
[Crossref]

W. W. Chow, “A composite-resonator mode description of coupled lasers,” IEEE J. Quantum Electron. QE-22, 1174–1183 (1986).
[Crossref]

D. Marcuse, “Computer simulation of laser photon fluctuations: coupled-cavity lasers,” IEEE J. Quantum Electron. QE-21, 154–161 (1985).
[Crossref]

B. Thedrez, A. Jones, and R. Frey, “Two-level description of gain and mixing susceptibilities in amplifying semiconductor materials,” IEEE J. Quantum Electron. 24, 1499–1506 (1988).
[Crossref]

G. P. Agrawal, “Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers,” IEEE J. Quantum Electron. 26, 1901–1909 (1990).
[Crossref]

A. Yariv, “Parametric interactions of optical modes,” IEEE J. Quantum Electron. QE-2, 30–37 (1966).
[Crossref]

IEEE Photon. Technol. Lett. (1)

G. Gray and G. P. Agrawal, “Effect of cross saturation on frequency fluctuations in a nearly single-mode semiconductor laser,” IEEE Photon. Technol. Lett. 3, 204–206 (1991).
[Crossref]

J. Appl. Phys. (3)

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

H. Risken and K. Nummedal, “Self-pulsing in lasers,” J. Appl. Phys. 39, 4662–4672 (1968).
[Crossref]

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
[Crossref]

J. Lightwave Technol. (1)

R. W. Tkach and A. R. Chraplyvy, “Regimes of feedback effects in 1.5 micrometer distributed feedback lasers,” J. Lightwave Technol. 4, 1655–1661 (1986).
[Crossref]

J. Opt. Soc. Am. B (9)

S. E. Hodges, M. Munroe, W. Gadomski, J. Cooper, and M. G. Raymer, “Turn-on transient dynamics in a multimode, compound-cavity laser,” J. Opt. Soc. Am. B 14, 180–190 (1997).
[Crossref]

H. Fu and H. Haken, “Semiclassical theory of dye lasers: the single-frequency and multifrequency steady states of operation,” J. Opt. Soc. Am. B 5, 899–908 (1988).
[Crossref]

W. Brunner, R. Fischer, and H. Paul, “Regular and chaotic behavior of multimode lasers,” J. Opt. Soc. Am. B 2, 202–210 (1985).
[Crossref]

K. Hsu, C. M. Verber, and R. Roy, “Stochastic mode-locking theory for external-cavity semiconductor lasers,” J. Opt. Soc. Am. B 8, 262–275 (1991).
[Crossref]

W. Brunner, R. Fischer, and H. Paul, “Time evolution of the total electric-field strength in a multimode laser,” J. Opt. Soc. Am. B 5, 1139–1143 (1988).
[Crossref]

L. W. Hillman, J. Krasinski, R. W. Boyd, and C. R. Stroud, “Dynamics of homogeneously broadened lasers: higher-order bichromatic states of operation,” J. Opt. Soc. Am. B 2, 211–217 (1985).
[Crossref]

M. G. Raymer, Z. Deng, and M. Beck, “Strong-field dynamics of a multimode, standing-wave dye laser,” J. Opt. Soc. Am. B 5, 1588–1595 (1988).
[Crossref]

H. Zeghlache and P. Mandel, “Influence of detuning on the properties of laser equations,” J. Opt. Soc. Am. B 2, 18–22 (1985).
[Crossref]

G. P. Agrawal, “Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers,” J. Opt. Soc. Am. B 5, 147–159 (1988).
[Crossref]

Opt. Commun. (3)

W. R. Christian and L. Mandel, “Allowed detuning range of the third order laser theory for an inhomogenously broadened laser,” Opt. Commun. 64, 537–538 (1987).
[Crossref]

F. T. Arecchi, G. L. Lippi, G. P. Puccioni, and T. R. Treddicce, “Deterministic chaos in laser with injected signal,” Opt. Commun. 51, 308–314 (1984).
[Crossref]

U. Herzog, “Longitudinal mode interaction in semiconductor lasers due to nonlinear gain suppression and four-wave mixing,” Opt. Commun. 82, 390–405 (1991).
[Crossref]

Opt. Lett. (5)

Phys. Rev. (2)

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. 134, A1429–A1450 (1964).
[Crossref]

D. E. McCumber, “Intensity fluctuations in the output of cw laser oscillators. I,” Phys. Rev. 141, 306–322 (1966).
[Crossref]

Phys. Rev. A (10)

P. D. Drummond and M. G. Raymer, “Quantum theory of propagation of nonclassical radiation in a near-resonant medium,” Phys. Rev. A 44, 2072–2085 (1991).
[Crossref] [PubMed]

F. T. Arecchi and V. Degiorgio, “Statistical properties of laser radiation during a transient buildup,” Phys. Rev. A 3, 1108–1124 (1971).
[Crossref]

G. Gray and R. Roy, “Noise in nearly single-mode semiconductor lasers,” Phys. Rev. A 40, 2452–2462 (1989).
[Crossref] [PubMed]

R. F. Fox and R. Roy, “Steady-state analysis of strongly colored multiplicative noise in a dye laser,” Phys. Rev. A 41, 1838–1842 (1987).
[Crossref]

C. Ning and H. Haken, “Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hoff bifurcations,” Phys. Rev. A 41, 3826–3837 (1990).
[Crossref] [PubMed]

S. Ciuchi, M. San Miguel, N. B. Abraham, and F. de Pasquale, “Phase and amplitude correlations induced by the switch-on chirp of a detuned laser,” Phys. Rev. A 44, 7657–7668 (1991).
[Crossref] [PubMed]

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

M. B. Spencer and W. E. Lamb, “Laser with a transmitting window,” Phys. Rev. A 5, 884–892 (1972); “Theory of two coupled lasers,” Phys. Rev. A 5, 893–898 (1972).
[Crossref]

M. Beck, I. McMackin, 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]

H. Atmanspacher and H. Scheingraber, “Deterministic chaos and dynamical instabilities in a multimode cw dye laser,” Phys. Rev. A 34, 253–263 (1986).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

F. T. Arecchi, V. Degiorgio, and B. Querzola, “Time-dependent statistical properties of the laser radiation,” Phys. Rev. Lett. 19, 1168–1171 (1967).
[Crossref]

Z. Phys. (1)

H. Haken, “Theory of intensity and phase fluctuations of a homogeneously broadened laser,” Z. Phys. 190, 327–356 (1966).
[Crossref]

Other (21)

M. Lax, “The theory of laser noise,” in Laser Noise, R. Roy, ed., Proc. SPIE1376, 2–20 (1990).
[Crossref]

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, Reading, Mass., 1977), Chap. 9, p. 119; Chap. 20, p. 134.

P. L. Liu, “Photon statistics and mode partition noise of semiconductor lasers,” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), Chap. 10, p. 444.

G. P. Agrawal and N. K. Dutta, Long-Wavelength Semiconductor Lasers (Van Nostrand Reinhold, New York, 1986), Chap. 6, p. 247.

C. W. Henry, “Line broadening of semiconductor lasers,” in Coherence, Amplification and Quantum Effects in Semiconductor Lasers, Y. Yamamoto, ed. (Wiley, New York, 1991), Chap. 2, p. 66.

S. E. Hodges, “Turn-on transient dynamics in a multimode laser,” Ph.D. dissertation (University of Oregon, Eugene, Ore., 1993).

N. B. Abraham, P. Mandel, and L. M. Narducci, “Dynamical instabilities and pulsations in lasers,” in Progress in Optics XXV, E. Wolf, ed. (Elsevier, Amsterdam, 1988), pp. 25–28.

N. B. Abraham, “An overview of optical instabilities and chaos and an introduction to some models and current areas of research in laser instabilities,” in Dynamics of Non-Linear Optical Systems, L. Pesquera and F. J. Bermejo, eds. (World Scientific, Singapore, 1989), pp. 3–28.

O. Svelto, Principles of Lasers, 3rd ed. (Plenum, New York, 1989), Chap. 6, pp. 331–339.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 3, p. 120.

F. P. Schaefer, ed., Dye Lasers, 3rd ed. (Springer-Verlag, Berlin, 1990), Chap. 1, pp. 28, 86–90.

F. J. Duarte and L. W. Hillman, eds., Dye Laser Principles with Applications (Academic, Boston, Mass., 1990), Chap. 5, p. 195.

H. Haken, Light, Vol. 2 (North Holland, Amsterdam, 1985), Chap. 10, p. 248.

K. Shimoda, Introduction to Laser Physics (Springer-Verlag, Berlin, 1986), Chap. 9, p. 176.

H. Haken, “The adiabatic elimination principle in dynamical theories,” in Optical Instabilities, R. W. Boyd, M. G. Raymer, and L. M. Narducci, eds. (Cambridge U. Press, Cambridge, 1986), pp. 1–19.

C. R. Stroud, K. Koch, and S. Chakmakjian, “Instabilities and higher-order states of cw ring dye lasers,” in Optical Instabilities, R. W. Boyd, M. G. Raymer, and L. M. Narducci, eds. (Cambridge U. Press, Cambridge, 1986), Chap. II, pp. 274–276.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. 8, p. 375.

R. W. Boyd, Nonlinear Optics (Academic, Boston, Mass., 1992), Chap. 3, pp. 148–154.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chap. 7, p. 282.

C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983), Chap. 4, pp. 80–85.

P. L. Knight, “Non-Markovian effects in spontaneous emission: deviations from the exponential decay law,” in Coherence and Quantum Optics IV, L. Mandel and E. Wolf, eds. (Plenum, New York, 1978), pp. 635–647.

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Figures (1)

Fig. 1
Fig. 1

Laser system.

Equations (46)

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

tP(r, t)=-(γ+iδ)P(r, t)-iμ2W(r, t)A(r, t)+μρη(r, t),
tW(r, t)=γ[R(r, t)-W(r, t)]+i4[A(r, t)P*(r, t)-A*(r, t)P(r, t)]+ρθ(r, t),
c22-(r) 2t2-κ(r) tE(r, t)exp(-iωt)
=4π(r)+23 2t2P(r, t)exp(-iωt).
η*(r, t)η(r, t)=8γW(r, t)δ(t-t)δ3(r-r)/ρ2,
θ(r, t)θ(r, t)=2γδ(t-t)δ3(r-r)/ρ,
A(r, t)(r)+23E(r, t).
tP(r, t)=-(γ+iδ)P(r, t)-iμ2(r)W(r, t)E(r, t)+μ(r)ρη(r, t),
tW(r, t)=γ[R(r, t)-W(r, t)]+i4[E(r, t)P*(r, t)-E*(r, t)P(r, t)]+ρθ(r, t),
c22-(r) 2t2-κ(r) tE(r, t)exp(-iωt)
=4π 2t2P(r, t)exp(-iωt).
E(r, t)=k uk(r)Ek(t)exp(-iΔkt),
[c22+(r)ωj2]uj(r)=0
C d3r(r)uj*(r)uk(r)=δj,k,
Ek(t)=exp(iΔkt) C d3r(r)uk*(r)E(r, t).
P(r, t)=k uk(r)Pk(t)exp(-iΔkt),
Pk(t)=q Pkq(t)exp[-i(Δq-Δk)t],
W(r, t)=pWp(r, t)exp(-iΔpt),
ddtPjq(t)=-βqPjq(t)-iμ2k fq,k-Eq-k(t)Wj,q-kk(t)+Qjq(t),
fq,k±(t)exp[i(Δq±Δk-Δq±k)t],
Qjq(t)=μρτt-τt dt exp(iΔqt)G d3ruj*(r)η(r, t),
Wj,kp(t)G d3ruj*(r)Wp(r, t)uk(r).
ddtWj,kp(t)=γRj,kp-(γ-iΔp)Wj,kp(t)+ρ 1τt-τt dt exp(iΔpt)θj,k(t)-i4m,n αj,k,m,nfm,p+Em*(t)Pnm+p(t)+i4m,n αj,k,n,mfm,p-*Em(t)[Pnm-p(t)]*,
Rj,kp(t)G d3ruj*(r)Rp(r, t)uk(r),
θj,k(t)Gd3ruj*(r)θ(r, t)uk(r).
αj,k,m,n=Gd3ruj*(r)uk(r)um*(r)un(r)
ddtEq(t)=-12κqEq(t)+i2πωqPqq(t).
κq=C d3r|uq(r)|2κ(r, ωq).
κq=-c ln[R1(ωq)R2(ωq)]/2LC,
κq=cAq2[1-R(ωq)]/4.
Pjq(t)-iμ2βqp fq,p-Eq-p(t)Wj,q-pp(t)+1βqQjq(t).
ddtEj(t)=-½κjEj(t)+gj2βjpfj,p-Wj,j-pp(t)Ej-p(t)+8πωjFjj(t),
Fjq(t)=iβj(πωj/2)1/2Qjq(t)
Fjq*(t)Fkp(t)=2γgjgkβj*βkfk,j-Wk,jp-q(t)δ(t-t).
W(r, t)=N(t)/VG+X(r, t),
N(t)=Gd3rW(r, t).
Wj,kp(t)=δj,kδp,0N(t)/VC+Xj,kp(t),
Wj,kp0(t)1(γ-iΔp)γRj,kp+Gj,kp(t)-μ242m,n αj,k,m,nβm+pfm,p+Em*(t)Em+p(t)×Wn,m+p0(t)-μ242m,n αj,k,n,mβm-p*fm,p-*Em(t)×Em-p*(t)Wm-p,n0(t)
ddtEj(t)=-12κjEj(t)+8πωjFjj(t)+gj2βjWj,j0(t)Ej(t)+p,p0 fj,p-Wj,j-pp(t)Ej-p(t),
ddtWj,k0(t)=γ[Rj,k0-Wj,k0(t)]+Gj,k0(t)-μ242m,n αj,k,m,nβm|Em(t)|2Wn,m0(t)+p,p0 fm,p-Em*(t)Em-p(t)Wn,m-pp(t)-μ242m,n αj,k,n,mβm*|Em(t)|2Wm,n0(t)+p,p0 fm,p-*Em-p*(t)Em(t)Wn,m-pp*(t),
Fjj*(t)Fkk(t)=2γgjgkβj*βkN(t)VCδj,k+fk,j-Xk,jk-j(t)×δ(t-t).
Gj,kp(t)=ρτt-τt dt exp(iΔpt)θj,k(t)-μ2m,nαj,k,m,ngm+pfm,p+Em*(t)Fnm-p(t)+αj,k,n,mgm-pfm,p-*Em(t)Fnm-p*(t)
Wj,j0(t)Rj,j0-μ222γm,n|Em(t)|2 Reαj,j,m,nβmRn,m0+Gj,j0(t)γ.
Wj,j0(t)R LGLC1-μ222γγm αj,j,m,mlm|Em(t)|2+Gj,j0(t)γ,
Wj,j-pp0(t)μ2R42γ(γ-iΔp)LGLCαj,j-p,j-p,j×1βj+1βj-p*Ej-p*(t)Ej(t)+m,mj-p αj,j-p,m,m+pβm+pEm*(t)Em-p(t)+m,mj αj,j-p,m-p,mβm-p*Em(t)Em-p*(t)+Gj,j-ppγ-iΔp,
lj=γ Re(1/βj)=γ2/[γ2+(δ-Δj)2]

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