Abstract

An idea is proposed for detecting a weak laser signal from a remote source in the presence of strong background noise. The scheme exploits dynamical nonlinearities arising from heterodyning signal and reference fields inside an active reference laser cavity. This paper shows that for certain reference laser configurations, the resulting bifurcations in the reference laser may be used as warning of irradiation by a laser source.

© 2009 Optical Society of America

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References

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  1. B. Krauskopf and D. Lenstra (Eds.), Fundamental Issues of Nonlinear Laser Dynamics, AIP Conference Proceedings, vol. 548, 2000.
  2. D. M. Kane and K. A. Shore (Eds.), Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, (Wiley, 2005, pp. 147-183).
  3. S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep. 416, 1-128 (20050.
  4. G. Vemuri and R. Roy, "Super-regenerative laser receiver: Transient dynamics of a laser with an external signal," Phys. Rev. A 39, 2539-2543 (1989).
    [CrossRef] [PubMed]
  5. I. Littler, S. Balle, K. Bergmann, G. Vemuri, and R. Roy, "Detection of weak signals via the decay of an unstable state: Initiation of an injection-seeded laser," Phys. Rev. A 41, 4131-4134 (1990).
    [CrossRef] [PubMed]
  6. E. Lacot, R. Day, and F. Stoeckel, "Coherent laser detection by frequency-shifted optical feedback," Phys. Rev. A 64, 043815-043825 (2001).
    [CrossRef]
  7. E. Lacot, O. Hugon, and F. Stoeckel, "Hopf amplification of frequency-shifted optical feedback," Phys. Rev. A 67, 053806-053815 (2003).
    [CrossRef]
  8. M. B. Spencer and W. E. Lamb, Jr., "Laser with a Transmitting Mirror," Phys. Rev. A 5, 884-892 (1972).
    [CrossRef]
  9. R. Lang, "Injection locking properties of a semiconductor laser," IEEE J. Quantum Electron. 18, 976-983 (1982).
    [CrossRef]
  10. F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Deterministic chaos in lasers with injected signal," Opt. Commun. 51, 308-314 (1984).
    [CrossRef]
  11. T. B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A 51, 4181-4185 (1995).
    [CrossRef] [PubMed]
  12. T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, "Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection," Phys. Rev. A 53, 4372-4380 (1996).
    [CrossRef] [PubMed]
  13. T. B. Simpson, "Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection," Opt. Commun. 215, 135-151 (2003).
    [CrossRef]
  14. N. Shunk and K. Peterman, "Noise analysis of injection-locked semiconductor injection lasers," IEEE J. Quantum Electron. 22, 642-650 (1986).
    [CrossRef]
  15. W. A. van der Graaf, A. M. Levine, and D. Lenstra, "Diode lasers locked to noisy injection," IEEE J. Quantum Electron. 33, 434-442 (1997).
    [CrossRef]
  16. S. K. Hwang, J. B. Gao, and J. M. Liu, "Noise-induced chaos in an optically injected semiconductor laser model," Phys. Rev. E 61, 5162-5170 (2000).
    [CrossRef]
  17. C. H. Henry, "Theory of the linewidth of semiconductor laser," IEEE J. Quantum Electron. 18, 259-264 (1982).
    [CrossRef]
  18. G. Vemuri and R. Roy, "Effect of injected field statistics on transient dynamics of an injection seeded laser," Opt. Commun. 77, 471-493 (1990).
    [CrossRef]
  19. E. Doedel, A. Champneys, T. Fairgrieve, Yu. Kuznetsov, B. Sandstede, and X. Wang, "AUTO 2000: Continuation and bifurcation software for ordinary differential equations," http://sourceforge.net/projects/auto2000/.
  20. S. Valling, T. Fordell, and A. M. Lindberg, "Maps of the dynamics of an optically injected solid-state laser," Phys. Rev. A 72, 033810-33818 (2005).
    [CrossRef]

2005

S. Valling, T. Fordell, and A. M. Lindberg, "Maps of the dynamics of an optically injected solid-state laser," Phys. Rev. A 72, 033810-33818 (2005).
[CrossRef]

2003

T. B. Simpson, "Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection," Opt. Commun. 215, 135-151 (2003).
[CrossRef]

E. Lacot, O. Hugon, and F. Stoeckel, "Hopf amplification of frequency-shifted optical feedback," Phys. Rev. A 67, 053806-053815 (2003).
[CrossRef]

2001

E. Lacot, R. Day, and F. Stoeckel, "Coherent laser detection by frequency-shifted optical feedback," Phys. Rev. A 64, 043815-043825 (2001).
[CrossRef]

2000

S. K. Hwang, J. B. Gao, and J. M. Liu, "Noise-induced chaos in an optically injected semiconductor laser model," Phys. Rev. E 61, 5162-5170 (2000).
[CrossRef]

1997

W. A. van der Graaf, A. M. Levine, and D. Lenstra, "Diode lasers locked to noisy injection," IEEE J. Quantum Electron. 33, 434-442 (1997).
[CrossRef]

1996

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, "Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection," Phys. Rev. A 53, 4372-4380 (1996).
[CrossRef] [PubMed]

1995

T. B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A 51, 4181-4185 (1995).
[CrossRef] [PubMed]

1990

I. Littler, S. Balle, K. Bergmann, G. Vemuri, and R. Roy, "Detection of weak signals via the decay of an unstable state: Initiation of an injection-seeded laser," Phys. Rev. A 41, 4131-4134 (1990).
[CrossRef] [PubMed]

G. Vemuri and R. Roy, "Effect of injected field statistics on transient dynamics of an injection seeded laser," Opt. Commun. 77, 471-493 (1990).
[CrossRef]

1989

G. Vemuri and R. Roy, "Super-regenerative laser receiver: Transient dynamics of a laser with an external signal," Phys. Rev. A 39, 2539-2543 (1989).
[CrossRef] [PubMed]

1986

N. Shunk and K. Peterman, "Noise analysis of injection-locked semiconductor injection lasers," IEEE J. Quantum Electron. 22, 642-650 (1986).
[CrossRef]

1984

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Deterministic chaos in lasers with injected signal," Opt. Commun. 51, 308-314 (1984).
[CrossRef]

1982

R. Lang, "Injection locking properties of a semiconductor laser," IEEE J. Quantum Electron. 18, 976-983 (1982).
[CrossRef]

C. H. Henry, "Theory of the linewidth of semiconductor laser," IEEE J. Quantum Electron. 18, 259-264 (1982).
[CrossRef]

1972

M. B. Spencer and W. E. Lamb, Jr., "Laser with a Transmitting Mirror," Phys. Rev. A 5, 884-892 (1972).
[CrossRef]

Alsing, P. M.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, "Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection," Phys. Rev. A 53, 4372-4380 (1996).
[CrossRef] [PubMed]

T. B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A 51, 4181-4185 (1995).
[CrossRef] [PubMed]

Arecchi, F. T.

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Deterministic chaos in lasers with injected signal," Opt. Commun. 51, 308-314 (1984).
[CrossRef]

Balle, S.

I. Littler, S. Balle, K. Bergmann, G. Vemuri, and R. Roy, "Detection of weak signals via the decay of an unstable state: Initiation of an injection-seeded laser," Phys. Rev. A 41, 4131-4134 (1990).
[CrossRef] [PubMed]

Bergmann, K.

I. Littler, S. Balle, K. Bergmann, G. Vemuri, and R. Roy, "Detection of weak signals via the decay of an unstable state: Initiation of an injection-seeded laser," Phys. Rev. A 41, 4131-4134 (1990).
[CrossRef] [PubMed]

Day, R.

E. Lacot, R. Day, and F. Stoeckel, "Coherent laser detection by frequency-shifted optical feedback," Phys. Rev. A 64, 043815-043825 (2001).
[CrossRef]

Erneux, T.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, "Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection," Phys. Rev. A 53, 4372-4380 (1996).
[CrossRef] [PubMed]

Fordell, T.

S. Valling, T. Fordell, and A. M. Lindberg, "Maps of the dynamics of an optically injected solid-state laser," Phys. Rev. A 72, 033810-33818 (2005).
[CrossRef]

Gao, J. B.

S. K. Hwang, J. B. Gao, and J. M. Liu, "Noise-induced chaos in an optically injected semiconductor laser model," Phys. Rev. E 61, 5162-5170 (2000).
[CrossRef]

Gavrielides, A.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, "Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection," Phys. Rev. A 53, 4372-4380 (1996).
[CrossRef] [PubMed]

T. B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A 51, 4181-4185 (1995).
[CrossRef] [PubMed]

Henry, C. H.

C. H. Henry, "Theory of the linewidth of semiconductor laser," IEEE J. Quantum Electron. 18, 259-264 (1982).
[CrossRef]

Hugon, O.

E. Lacot, O. Hugon, and F. Stoeckel, "Hopf amplification of frequency-shifted optical feedback," Phys. Rev. A 67, 053806-053815 (2003).
[CrossRef]

Hwang, S. K.

S. K. Hwang, J. B. Gao, and J. M. Liu, "Noise-induced chaos in an optically injected semiconductor laser model," Phys. Rev. E 61, 5162-5170 (2000).
[CrossRef]

Kovanis, V.

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, "Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection," Phys. Rev. A 53, 4372-4380 (1996).
[CrossRef] [PubMed]

T. B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A 51, 4181-4185 (1995).
[CrossRef] [PubMed]

Lacot, E.

E. Lacot, O. Hugon, and F. Stoeckel, "Hopf amplification of frequency-shifted optical feedback," Phys. Rev. A 67, 053806-053815 (2003).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, "Coherent laser detection by frequency-shifted optical feedback," Phys. Rev. A 64, 043815-043825 (2001).
[CrossRef]

Lamb, W. E.

M. B. Spencer and W. E. Lamb, Jr., "Laser with a Transmitting Mirror," Phys. Rev. A 5, 884-892 (1972).
[CrossRef]

Lang, R.

R. Lang, "Injection locking properties of a semiconductor laser," IEEE J. Quantum Electron. 18, 976-983 (1982).
[CrossRef]

Lenstra, D.

W. A. van der Graaf, A. M. Levine, and D. Lenstra, "Diode lasers locked to noisy injection," IEEE J. Quantum Electron. 33, 434-442 (1997).
[CrossRef]

Levine, A. M.

W. A. van der Graaf, A. M. Levine, and D. Lenstra, "Diode lasers locked to noisy injection," IEEE J. Quantum Electron. 33, 434-442 (1997).
[CrossRef]

Lindberg, A. M.

S. Valling, T. Fordell, and A. M. Lindberg, "Maps of the dynamics of an optically injected solid-state laser," Phys. Rev. A 72, 033810-33818 (2005).
[CrossRef]

Littler, I.

I. Littler, S. Balle, K. Bergmann, G. Vemuri, and R. Roy, "Detection of weak signals via the decay of an unstable state: Initiation of an injection-seeded laser," Phys. Rev. A 41, 4131-4134 (1990).
[CrossRef] [PubMed]

Liu, J. M.

S. K. Hwang, J. B. Gao, and J. M. Liu, "Noise-induced chaos in an optically injected semiconductor laser model," Phys. Rev. E 61, 5162-5170 (2000).
[CrossRef]

Liu, J.M.

T. B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A 51, 4181-4185 (1995).
[CrossRef] [PubMed]

Meucci, R.

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Deterministic chaos in lasers with injected signal," Opt. Commun. 51, 308-314 (1984).
[CrossRef]

Peterman, K.

N. Shunk and K. Peterman, "Noise analysis of injection-locked semiconductor injection lasers," IEEE J. Quantum Electron. 22, 642-650 (1986).
[CrossRef]

Puccioni, G.

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Deterministic chaos in lasers with injected signal," Opt. Commun. 51, 308-314 (1984).
[CrossRef]

Roy, R.

I. Littler, S. Balle, K. Bergmann, G. Vemuri, and R. Roy, "Detection of weak signals via the decay of an unstable state: Initiation of an injection-seeded laser," Phys. Rev. A 41, 4131-4134 (1990).
[CrossRef] [PubMed]

G. Vemuri and R. Roy, "Effect of injected field statistics on transient dynamics of an injection seeded laser," Opt. Commun. 77, 471-493 (1990).
[CrossRef]

G. Vemuri and R. Roy, "Super-regenerative laser receiver: Transient dynamics of a laser with an external signal," Phys. Rev. A 39, 2539-2543 (1989).
[CrossRef] [PubMed]

Shunk, N.

N. Shunk and K. Peterman, "Noise analysis of injection-locked semiconductor injection lasers," IEEE J. Quantum Electron. 22, 642-650 (1986).
[CrossRef]

Simpson, T. B.

T. B. Simpson, "Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection," Opt. Commun. 215, 135-151 (2003).
[CrossRef]

T. B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A 51, 4181-4185 (1995).
[CrossRef] [PubMed]

Spencer, M. B.

M. B. Spencer and W. E. Lamb, Jr., "Laser with a Transmitting Mirror," Phys. Rev. A 5, 884-892 (1972).
[CrossRef]

Stoeckel, F.

E. Lacot, O. Hugon, and F. Stoeckel, "Hopf amplification of frequency-shifted optical feedback," Phys. Rev. A 67, 053806-053815 (2003).
[CrossRef]

E. Lacot, R. Day, and F. Stoeckel, "Coherent laser detection by frequency-shifted optical feedback," Phys. Rev. A 64, 043815-043825 (2001).
[CrossRef]

Tredicce, J.

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Deterministic chaos in lasers with injected signal," Opt. Commun. 51, 308-314 (1984).
[CrossRef]

Valling, S.

S. Valling, T. Fordell, and A. M. Lindberg, "Maps of the dynamics of an optically injected solid-state laser," Phys. Rev. A 72, 033810-33818 (2005).
[CrossRef]

van der Graaf, W. A.

W. A. van der Graaf, A. M. Levine, and D. Lenstra, "Diode lasers locked to noisy injection," IEEE J. Quantum Electron. 33, 434-442 (1997).
[CrossRef]

Vemuri, G.

I. Littler, S. Balle, K. Bergmann, G. Vemuri, and R. Roy, "Detection of weak signals via the decay of an unstable state: Initiation of an injection-seeded laser," Phys. Rev. A 41, 4131-4134 (1990).
[CrossRef] [PubMed]

G. Vemuri and R. Roy, "Effect of injected field statistics on transient dynamics of an injection seeded laser," Opt. Commun. 77, 471-493 (1990).
[CrossRef]

G. Vemuri and R. Roy, "Super-regenerative laser receiver: Transient dynamics of a laser with an external signal," Phys. Rev. A 39, 2539-2543 (1989).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

R. Lang, "Injection locking properties of a semiconductor laser," IEEE J. Quantum Electron. 18, 976-983 (1982).
[CrossRef]

N. Shunk and K. Peterman, "Noise analysis of injection-locked semiconductor injection lasers," IEEE J. Quantum Electron. 22, 642-650 (1986).
[CrossRef]

W. A. van der Graaf, A. M. Levine, and D. Lenstra, "Diode lasers locked to noisy injection," IEEE J. Quantum Electron. 33, 434-442 (1997).
[CrossRef]

C. H. Henry, "Theory of the linewidth of semiconductor laser," IEEE J. Quantum Electron. 18, 259-264 (1982).
[CrossRef]

Opt. Commun.

G. Vemuri and R. Roy, "Effect of injected field statistics on transient dynamics of an injection seeded laser," Opt. Commun. 77, 471-493 (1990).
[CrossRef]

T. B. Simpson, "Mapping the nonlinear dynamics of a distributed feedback semiconductor laser subject to external optical injection," Opt. Commun. 215, 135-151 (2003).
[CrossRef]

F. T. Arecchi, R. Meucci, G. Puccioni, and J. Tredicce, "Deterministic chaos in lasers with injected signal," Opt. Commun. 51, 308-314 (1984).
[CrossRef]

Phys. Rev. A

T. B. Simpson, J.M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, "Period-doubling cascades and chaos in a semiconductor laser with optical injection," Phys. Rev. A 51, 4181-4185 (1995).
[CrossRef] [PubMed]

T. Erneux, V. Kovanis, A. Gavrielides, and P. M. Alsing, "Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection," Phys. Rev. A 53, 4372-4380 (1996).
[CrossRef] [PubMed]

G. Vemuri and R. Roy, "Super-regenerative laser receiver: Transient dynamics of a laser with an external signal," Phys. Rev. A 39, 2539-2543 (1989).
[CrossRef] [PubMed]

I. Littler, S. Balle, K. Bergmann, G. Vemuri, and R. Roy, "Detection of weak signals via the decay of an unstable state: Initiation of an injection-seeded laser," Phys. Rev. A 41, 4131-4134 (1990).
[CrossRef] [PubMed]

E. Lacot, R. Day, and F. Stoeckel, "Coherent laser detection by frequency-shifted optical feedback," Phys. Rev. A 64, 043815-043825 (2001).
[CrossRef]

E. Lacot, O. Hugon, and F. Stoeckel, "Hopf amplification of frequency-shifted optical feedback," Phys. Rev. A 67, 053806-053815 (2003).
[CrossRef]

M. B. Spencer and W. E. Lamb, Jr., "Laser with a Transmitting Mirror," Phys. Rev. A 5, 884-892 (1972).
[CrossRef]

S. Valling, T. Fordell, and A. M. Lindberg, "Maps of the dynamics of an optically injected solid-state laser," Phys. Rev. A 72, 033810-33818 (2005).
[CrossRef]

Phys. Rev. E

S. K. Hwang, J. B. Gao, and J. M. Liu, "Noise-induced chaos in an optically injected semiconductor laser model," Phys. Rev. E 61, 5162-5170 (2000).
[CrossRef]

Other

B. Krauskopf and D. Lenstra (Eds.), Fundamental Issues of Nonlinear Laser Dynamics, AIP Conference Proceedings, vol. 548, 2000.

D. M. Kane and K. A. Shore (Eds.), Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, (Wiley, 2005, pp. 147-183).

S. Wieczorek, B. Krauskopf, T.B. Simpson, and D. Lenstra, "The dynamical complexity of optically injected semiconductor lasers," Phys. Rep. 416, 1-128 (20050.

E. Doedel, A. Champneys, T. Fairgrieve, Yu. Kuznetsov, B. Sandstede, and X. Wang, "AUTO 2000: Continuation and bifurcation software for ordinary differential equations," http://sourceforge.net/projects/auto2000/.

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Figures (11)

Fig. 1.
Fig. 1.

Sketch of experimental setup showing the reference laser with intracavity electric field, E. The injected signal, consisting of coherent and incoherent contributions, EI and EB , respectively, mixes with the reference laser field after passing through a resonator mirror of transmission, T. The cavity length is L and the effects of the active medium is represented by a complex susceptibility.

Fig. 2.
Fig. 2.

Bifurcation diagram in plane of coherent injected intensity and frequency detuning for Λ = 4. The laser specification (Table 1) is typical for microcavity laser operating with a quantum-well gain medium. The dashed line indicates a one-dimensional bifurcation transition for Δ = 17 GHz that is illustrated in Figs. 3-9.

Fig. 3.
Fig. 3.

Intensity maxima versus injected intensity for the noise-free case (see top sketch); Λ = 4 and Δ = 17 GHz. The arrows indicate the injected intensities for the spectra in Fig. 4.

Fig. 4.
Fig. 4.

Reference laser spectra for noise-free case and increasing (clockwise direction) injected intensities, (a) 0.015, (b) 0.25, (c) 0.6, (d) 18, (e) 50 and (f) 130 W/cm2; Λ = 4 and Δ = 17 GHz.

Fig. 5.
Fig. 5.

Intensity maxima versus injected intensity for noise-free injection and noisy reference-laser (see top sketch); Λ = 4 and Δ = 17 GHz. The reference-laser linewidths are 70MHz and 5GHz. The arrows indicate the injected intensities for the spectra in Fig. 6.

Fig. 6.
Fig. 6.

Intensity spectra for reference laser linewidths of 70MHz and 5 GHz (left and right columns, respectively); Λ = 4 and Δ = 17 GHz. The injected intensities are (a) 0, (b) 0.015, (c) 0.25, (d) 0.6, (e) 18 and (f) 130 W/cm2.

Fig. 7.
Fig. 7.

Intensity maxima versus coherent injected intensity for 70MHz reference laser and injected signal (see top sketch); Λ = 4 and Δ = 17 GHz. The incoherent injected contributions are 0.06 and 0.6W/cm2. The arrows indicate the coherent injected intensities for the spectra in Figs. 8 and 9.

Fig. 8.
Fig. 8.

Spectral response for 70MHz reference laser and low incoherent injection ; Λ = 4 and Δ = 17 GHz.(Left column) Injected intensity spectra with solid and dashed curves showing coherent and incoherent contributions, respectively. From top to bottom, the coherent contributions are (a) 0.015, (b) 0.6, (c) 18 and (d) 130W/cm2, while the incoherent contribution is clamped at 0.06W/cm2. (Right column) Corresponding reference-laser intensity spectra.

Fig. 9.
Fig. 9.

Spectral response for 70MHz reference laser and high incoherent injection; Λ = 4 and Δ = 17 GHz. (Left column) Injected intensity spectra with solid and dashed curves showing coherent and incoherent contributions, respectively. From top to bottom, the coherent contributions are (a) 0.015, (b) 0.6, (c) 18 and (d) 130W/cm2, while the incoherent contribution is clamped at 0.6W/cm2. (Right column) Corresponding reference-laser intensity spectra.

Fig. 10.
Fig. 10.

Coherent and incoherent normalized peak intensities in reference laser versus injected coherent intensity for background noise of 0.06W/cm2 (solid curve) and 0.6W/cm2 (dashed curve).

Fig. 11.
Fig. 11.

Experimental setup for a remote laser radiation sensor with basic components: (a) light collection optics, (b) reference laser and (c) detection scheme for bifurcations.

Tables (1)

Tables Icon

Table I: Input parameters for numerical simulations

Equations (7)

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

d E d t = i 2 π Δ E γ E E + c n b Γ ξ ( N N t h ) ( 1 i α ) E + F L + c T 2 n b L [ E I + E B ] ,
d N d t = Λ γ N N ε 0 n b c h ̅ v [ g t h + ξ ( N N t h ) ] E 2 ,
F L ( t ) = F ' L ( t ) F " L ( t ' ) = 0
F ' L ( t ) F ' L ( t ' ) = F " L ( t ) F " L ( t ' ) = 2 D L δ ( t t ' )
D L = h ̅ v ε 0 ε b β γ N N t h δ ( t t ' )
d ϕ a d t = F a ( t )
F a ( t ) F a ( t ' ) = 2 π Δ v a δ ( t t ' )

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