Abstract

The transient dynamics and the kinetics of switching between two stable states in Cr:LiSrGaF6 laser crystal, a material with thermally induced intrinsic optical bistability, have been studied. It has been shown that the characteristic switching time τswitch can be shorter than that determined by the heat transfer in a linear regime. In the quasi-steady-state regime, the rate of switching (τswitch-1) in the system studied is proportional to the square root of the area of the steady-state hysteresis loop. The switching time τswitch can be controlled by changing system parameters, such as the temperature of the heat sink, the heat sinking efficiency, the rate of the pumping power increase, etc. When the pumping power is continuously changed at the rate R, the increment in the switching rate Δτswitch-1 is proportional to R2/3.

© 2003 Optical Society of America

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  1. M. A. Noginov, M. Vondrova, and B. D. Lucas, “Thermally induced optical bistability in Cr-doped Colquiriite crystals,” Phys. Rev. B 65, 035112 (2002).
    [CrossRef]
  2. C. M. Bowden and C. C. Sung, “First- and second-order phase transitions in the Dicke model: relation to optical bistability,” Phys. Rev. A 19, 2392–2401 (1979).
    [CrossRef]
  3. F. A. Hopf and C. M. Bowden, “Heuristic stochastic model of mirrorless optical bistability,” Phys. Rev. A 32, 268–275 (1985).
    [CrossRef] [PubMed]
  4. Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, pp. 3917–3926 (1986).
    [CrossRef]
  5. M. E. Crenshaw and C. M. Bowden, “Local-field effects in a dense collection of two-level atoms embedded in a dielectric medium: Intrinsic optical bistability enhancement and local field correction effects,” Phys. Rev. A 53, 1139–1142 (1996).
    [CrossRef] [PubMed]
  6. M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express 1, 153–159 (1997).
    [CrossRef]
  7. M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, and S. C. Rand, “Cooperative bistability in dense, excited atomic systems,” Phys. Rev. Lett. 73, 1103–1106 (1994).
    [CrossRef] [PubMed]
  8. M. P. Hehlen, H. U. Güdel, Q. Shu, and S. C. Rand, “Cooperative optical bistability in the dimer system Cs3Y2Br9:10%Yb,” J. Chem. Phys. 104, 1232–1244 (1996).
    [CrossRef]
  9. S. R. Lüthi, M. P. Hehlen, T. Reidener, and H. U. Güdel, “Excited-state dynamics and optical bistability in the dimer system Cs3Lu2Br9:Yb3+,” J. Lumin. 77, 447–450 (1998).
    [CrossRef]
  10. M. P. Hehlen, A. Kuditcher, S. C. Rand, and S. R. Lüthi, “Site-selective, intrinsically bistable luminescence of Yb3+ in pairs in CsCdBr3,” Phys. Rev. Lett. 82, 3050–3053 (1999).
    [CrossRef]
  11. A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, “Intrinsic bistability of luminescence and stimulated emission in Yb- and Tm-doped glass,” Phys. Rev. Lett. 84, 1898–1901 (2000).
    [CrossRef] [PubMed]
  12. D. R. Gamelin, S. R. Lüthi, and H. U. Güdel, “The role of laser heating in the intrinsic optical bistability of Yb3+-doped bromide lattices,” J. Chem. Phys. 104, 11045–11057 (2000).
    [CrossRef]
  13. M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switch in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
    [CrossRef] [PubMed]
  14. P. Jung, G. Gray, R. Roy, and P. Mandel, “Scaling law for dynamical hysteresis,” Phys. Rev. Lett. 65, 1873–1876 (1990).
    [CrossRef] [PubMed]
  15. N. E. Fettouhi, B. Segard, and J. Zemmouti, “Scaling of hysteresis in a multidimensional all-optical bistable system,” Eur. Phys. J. D 6, 425–429 (1999).
    [CrossRef]
  16. G. H. Goldsztein, F. Broner, and S. H. Strogatz, “Dynamical hysteresis without static hysteresis: scaling laws and asymptotic expansions,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 57, 1163–1187 (1997).
    [CrossRef]
  17. A. Hohl, H. J. C. van der Linden, and R. Roy, “Scaling laws for dynamical hysteresis in a multidimensional laser system,” Phys. Rev. Lett. 74, 2220–2223 (1995).
    [CrossRef] [PubMed]
  18. L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, “Investigation of the Laser Properties of Cr3+:LiSrGaF6,” IEEE J. Quantum Electron. 28, 2612–2618 (1992).
    [CrossRef]
  19. I. T. Sorokina, E. Sorokin, and R. Szipocs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Physics B 65, 245–254 (1997).
    [CrossRef]
  20. M. Stadler, B. H. T. Chai, and M. Bass, “Crystal growth and spectroscopy of Cr:LiBaAlF6,” in Advanced Solid-State Lasers, G. Dubé and L. Chase, eds., Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington D.C., 1991), pp. 18–20.
  21. M. A. Noginov, V. G. Ostroumov, I. A. Shcherbakov, V. A. Smirnov, and D. A. Zubenko, “Interaction of excited Cr3+ ions in laser crystals,” in Advanced Solid-State Lasers, G. Dubé and L. Chase, eds., Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington D.C., 1991), pp. 21–24.
  22. The numerical values of C and ρ corresponded to those for Cr:LiSrAlF6, a material whose properties are close to those of Cr:LiSrGaF6. The values for Cr:LiSrAlF6 were found in the paper: S. A. Payne, L. K. Smith, J. R. Beach, and B. H. T. Chai, “Properties of Cr:LiSrAlF6 crystals for laser operation,” Applied Optics 33, 5526–5536 (1994).
    [CrossRef]
  23. M. A. Noginov, B. D. Lucas, and M. Vondrova, “Optical bistability in Cr:LiSrGaF6 laser,” J. Opt. Soc. Am. B 19, 1999–2006 (2002).
    [CrossRef]

2002 (2)

M. A. Noginov, M. Vondrova, and B. D. Lucas, “Thermally induced optical bistability in Cr-doped Colquiriite crystals,” Phys. Rev. B 65, 035112 (2002).
[CrossRef]

M. A. Noginov, B. D. Lucas, and M. Vondrova, “Optical bistability in Cr:LiSrGaF6 laser,” J. Opt. Soc. Am. B 19, 1999–2006 (2002).
[CrossRef]

2000 (2)

A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, “Intrinsic bistability of luminescence and stimulated emission in Yb- and Tm-doped glass,” Phys. Rev. Lett. 84, 1898–1901 (2000).
[CrossRef] [PubMed]

D. R. Gamelin, S. R. Lüthi, and H. U. Güdel, “The role of laser heating in the intrinsic optical bistability of Yb3+-doped bromide lattices,” J. Chem. Phys. 104, 11045–11057 (2000).
[CrossRef]

1999 (2)

N. E. Fettouhi, B. Segard, and J. Zemmouti, “Scaling of hysteresis in a multidimensional all-optical bistable system,” Eur. Phys. J. D 6, 425–429 (1999).
[CrossRef]

M. P. Hehlen, A. Kuditcher, S. C. Rand, and S. R. Lüthi, “Site-selective, intrinsically bistable luminescence of Yb3+ in pairs in CsCdBr3,” Phys. Rev. Lett. 82, 3050–3053 (1999).
[CrossRef]

1998 (1)

S. R. Lüthi, M. P. Hehlen, T. Reidener, and H. U. Güdel, “Excited-state dynamics and optical bistability in the dimer system Cs3Lu2Br9:Yb3+,” J. Lumin. 77, 447–450 (1998).
[CrossRef]

1997 (3)

I. T. Sorokina, E. Sorokin, and R. Szipocs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Physics B 65, 245–254 (1997).
[CrossRef]

G. H. Goldsztein, F. Broner, and S. H. Strogatz, “Dynamical hysteresis without static hysteresis: scaling laws and asymptotic expansions,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 57, 1163–1187 (1997).
[CrossRef]

M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express 1, 153–159 (1997).
[CrossRef]

1996 (2)

M. E. Crenshaw and C. M. Bowden, “Local-field effects in a dense collection of two-level atoms embedded in a dielectric medium: Intrinsic optical bistability enhancement and local field correction effects,” Phys. Rev. A 53, 1139–1142 (1996).
[CrossRef] [PubMed]

M. P. Hehlen, H. U. Güdel, Q. Shu, and S. C. Rand, “Cooperative optical bistability in the dimer system Cs3Y2Br9:10%Yb,” J. Chem. Phys. 104, 1232–1244 (1996).
[CrossRef]

1995 (1)

A. Hohl, H. J. C. van der Linden, and R. Roy, “Scaling laws for dynamical hysteresis in a multidimensional laser system,” Phys. Rev. Lett. 74, 2220–2223 (1995).
[CrossRef] [PubMed]

1994 (2)

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, and S. C. Rand, “Cooperative bistability in dense, excited atomic systems,” Phys. Rev. Lett. 73, 1103–1106 (1994).
[CrossRef] [PubMed]

The numerical values of C and ρ corresponded to those for Cr:LiSrAlF6, a material whose properties are close to those of Cr:LiSrGaF6. The values for Cr:LiSrAlF6 were found in the paper: S. A. Payne, L. K. Smith, J. R. Beach, and B. H. T. Chai, “Properties of Cr:LiSrAlF6 crystals for laser operation,” Applied Optics 33, 5526–5536 (1994).
[CrossRef]

1992 (2)

L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, “Investigation of the Laser Properties of Cr3+:LiSrGaF6,” IEEE J. Quantum Electron. 28, 2612–2618 (1992).
[CrossRef]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switch in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef] [PubMed]

1990 (1)

P. Jung, G. Gray, R. Roy, and P. Mandel, “Scaling law for dynamical hysteresis,” Phys. Rev. Lett. 65, 1873–1876 (1990).
[CrossRef] [PubMed]

1986 (1)

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, pp. 3917–3926 (1986).
[CrossRef]

1985 (1)

F. A. Hopf and C. M. Bowden, “Heuristic stochastic model of mirrorless optical bistability,” Phys. Rev. A 32, 268–275 (1985).
[CrossRef] [PubMed]

1979 (1)

C. M. Bowden and C. C. Sung, “First- and second-order phase transitions in the Dicke model: relation to optical bistability,” Phys. Rev. A 19, 2392–2401 (1979).
[CrossRef]

Beach, J. R.

The numerical values of C and ρ corresponded to those for Cr:LiSrAlF6, a material whose properties are close to those of Cr:LiSrGaF6. The values for Cr:LiSrAlF6 were found in the paper: S. A. Payne, L. K. Smith, J. R. Beach, and B. H. T. Chai, “Properties of Cr:LiSrAlF6 crystals for laser operation,” Applied Optics 33, 5526–5536 (1994).
[CrossRef]

Ben-Aryeh, Y.

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, pp. 3917–3926 (1986).
[CrossRef]

Bowden, C. M.

M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express 1, 153–159 (1997).
[CrossRef]

M. E. Crenshaw and C. M. Bowden, “Local-field effects in a dense collection of two-level atoms embedded in a dielectric medium: Intrinsic optical bistability enhancement and local field correction effects,” Phys. Rev. A 53, 1139–1142 (1996).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switch in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef] [PubMed]

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, pp. 3917–3926 (1986).
[CrossRef]

F. A. Hopf and C. M. Bowden, “Heuristic stochastic model of mirrorless optical bistability,” Phys. Rev. A 32, 268–275 (1985).
[CrossRef] [PubMed]

C. M. Bowden and C. C. Sung, “First- and second-order phase transitions in the Dicke model: relation to optical bistability,” Phys. Rev. A 19, 2392–2401 (1979).
[CrossRef]

Broner, F.

G. H. Goldsztein, F. Broner, and S. H. Strogatz, “Dynamical hysteresis without static hysteresis: scaling laws and asymptotic expansions,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 57, 1163–1187 (1997).
[CrossRef]

Chai, B. H. T.

The numerical values of C and ρ corresponded to those for Cr:LiSrAlF6, a material whose properties are close to those of Cr:LiSrGaF6. The values for Cr:LiSrAlF6 were found in the paper: S. A. Payne, L. K. Smith, J. R. Beach, and B. H. T. Chai, “Properties of Cr:LiSrAlF6 crystals for laser operation,” Applied Optics 33, 5526–5536 (1994).
[CrossRef]

L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, “Investigation of the Laser Properties of Cr3+:LiSrGaF6,” IEEE J. Quantum Electron. 28, 2612–2618 (1992).
[CrossRef]

Chase, L. L.

L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, “Investigation of the Laser Properties of Cr3+:LiSrGaF6,” IEEE J. Quantum Electron. 28, 2612–2618 (1992).
[CrossRef]

Crenshaw, M. E.

M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express 1, 153–159 (1997).
[CrossRef]

M. E. Crenshaw and C. M. Bowden, “Local-field effects in a dense collection of two-level atoms embedded in a dielectric medium: Intrinsic optical bistability enhancement and local field correction effects,” Phys. Rev. A 53, 1139–1142 (1996).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switch in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef] [PubMed]

Englund, J. C.

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, pp. 3917–3926 (1986).
[CrossRef]

Fettouhi, N. E.

N. E. Fettouhi, B. Segard, and J. Zemmouti, “Scaling of hysteresis in a multidimensional all-optical bistable system,” Eur. Phys. J. D 6, 425–429 (1999).
[CrossRef]

Florea, C. M.

A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, “Intrinsic bistability of luminescence and stimulated emission in Yb- and Tm-doped glass,” Phys. Rev. Lett. 84, 1898–1901 (2000).
[CrossRef] [PubMed]

Gamelin, D. R.

D. R. Gamelin, S. R. Lüthi, and H. U. Güdel, “The role of laser heating in the intrinsic optical bistability of Yb3+-doped bromide lattices,” J. Chem. Phys. 104, 11045–11057 (2000).
[CrossRef]

Goldsztein, G. H.

G. H. Goldsztein, F. Broner, and S. H. Strogatz, “Dynamical hysteresis without static hysteresis: scaling laws and asymptotic expansions,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 57, 1163–1187 (1997).
[CrossRef]

Gray, G.

P. Jung, G. Gray, R. Roy, and P. Mandel, “Scaling law for dynamical hysteresis,” Phys. Rev. Lett. 65, 1873–1876 (1990).
[CrossRef] [PubMed]

Güdel, H. U.

D. R. Gamelin, S. R. Lüthi, and H. U. Güdel, “The role of laser heating in the intrinsic optical bistability of Yb3+-doped bromide lattices,” J. Chem. Phys. 104, 11045–11057 (2000).
[CrossRef]

S. R. Lüthi, M. P. Hehlen, T. Reidener, and H. U. Güdel, “Excited-state dynamics and optical bistability in the dimer system Cs3Lu2Br9:Yb3+,” J. Lumin. 77, 447–450 (1998).
[CrossRef]

M. P. Hehlen, H. U. Güdel, Q. Shu, and S. C. Rand, “Cooperative optical bistability in the dimer system Cs3Y2Br9:10%Yb,” J. Chem. Phys. 104, 1232–1244 (1996).
[CrossRef]

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, and S. C. Rand, “Cooperative bistability in dense, excited atomic systems,” Phys. Rev. Lett. 73, 1103–1106 (1994).
[CrossRef] [PubMed]

Hehlen, M. P.

A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, “Intrinsic bistability of luminescence and stimulated emission in Yb- and Tm-doped glass,” Phys. Rev. Lett. 84, 1898–1901 (2000).
[CrossRef] [PubMed]

M. P. Hehlen, A. Kuditcher, S. C. Rand, and S. R. Lüthi, “Site-selective, intrinsically bistable luminescence of Yb3+ in pairs in CsCdBr3,” Phys. Rev. Lett. 82, 3050–3053 (1999).
[CrossRef]

S. R. Lüthi, M. P. Hehlen, T. Reidener, and H. U. Güdel, “Excited-state dynamics and optical bistability in the dimer system Cs3Lu2Br9:Yb3+,” J. Lumin. 77, 447–450 (1998).
[CrossRef]

M. P. Hehlen, H. U. Güdel, Q. Shu, and S. C. Rand, “Cooperative optical bistability in the dimer system Cs3Y2Br9:10%Yb,” J. Chem. Phys. 104, 1232–1244 (1996).
[CrossRef]

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, and S. C. Rand, “Cooperative bistability in dense, excited atomic systems,” Phys. Rev. Lett. 73, 1103–1106 (1994).
[CrossRef] [PubMed]

Hohl, A.

A. Hohl, H. J. C. van der Linden, and R. Roy, “Scaling laws for dynamical hysteresis in a multidimensional laser system,” Phys. Rev. Lett. 74, 2220–2223 (1995).
[CrossRef] [PubMed]

Hopf, F. A.

F. A. Hopf and C. M. Bowden, “Heuristic stochastic model of mirrorless optical bistability,” Phys. Rev. A 32, 268–275 (1985).
[CrossRef] [PubMed]

Jung, P.

P. Jung, G. Gray, R. Roy, and P. Mandel, “Scaling law for dynamical hysteresis,” Phys. Rev. Lett. 65, 1873–1876 (1990).
[CrossRef] [PubMed]

Kuditcher, A.

A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, “Intrinsic bistability of luminescence and stimulated emission in Yb- and Tm-doped glass,” Phys. Rev. Lett. 84, 1898–1901 (2000).
[CrossRef] [PubMed]

M. P. Hehlen, A. Kuditcher, S. C. Rand, and S. R. Lüthi, “Site-selective, intrinsically bistable luminescence of Yb3+ in pairs in CsCdBr3,” Phys. Rev. Lett. 82, 3050–3053 (1999).
[CrossRef]

Kway, W. L.

L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, “Investigation of the Laser Properties of Cr3+:LiSrGaF6,” IEEE J. Quantum Electron. 28, 2612–2618 (1992).
[CrossRef]

Lucas, B. D.

M. A. Noginov, M. Vondrova, and B. D. Lucas, “Thermally induced optical bistability in Cr-doped Colquiriite crystals,” Phys. Rev. B 65, 035112 (2002).
[CrossRef]

M. A. Noginov, B. D. Lucas, and M. Vondrova, “Optical bistability in Cr:LiSrGaF6 laser,” J. Opt. Soc. Am. B 19, 1999–2006 (2002).
[CrossRef]

Lüthi, S. R.

D. R. Gamelin, S. R. Lüthi, and H. U. Güdel, “The role of laser heating in the intrinsic optical bistability of Yb3+-doped bromide lattices,” J. Chem. Phys. 104, 11045–11057 (2000).
[CrossRef]

M. P. Hehlen, A. Kuditcher, S. C. Rand, and S. R. Lüthi, “Site-selective, intrinsically bistable luminescence of Yb3+ in pairs in CsCdBr3,” Phys. Rev. Lett. 82, 3050–3053 (1999).
[CrossRef]

S. R. Lüthi, M. P. Hehlen, T. Reidener, and H. U. Güdel, “Excited-state dynamics and optical bistability in the dimer system Cs3Lu2Br9:Yb3+,” J. Lumin. 77, 447–450 (1998).
[CrossRef]

Mandel, P.

P. Jung, G. Gray, R. Roy, and P. Mandel, “Scaling law for dynamical hysteresis,” Phys. Rev. Lett. 65, 1873–1876 (1990).
[CrossRef] [PubMed]

Noginov, M. A.

M. A. Noginov, B. D. Lucas, and M. Vondrova, “Optical bistability in Cr:LiSrGaF6 laser,” J. Opt. Soc. Am. B 19, 1999–2006 (2002).
[CrossRef]

M. A. Noginov, M. Vondrova, and B. D. Lucas, “Thermally induced optical bistability in Cr-doped Colquiriite crystals,” Phys. Rev. B 65, 035112 (2002).
[CrossRef]

Payne, S. A.

The numerical values of C and ρ corresponded to those for Cr:LiSrAlF6, a material whose properties are close to those of Cr:LiSrGaF6. The values for Cr:LiSrAlF6 were found in the paper: S. A. Payne, L. K. Smith, J. R. Beach, and B. H. T. Chai, “Properties of Cr:LiSrAlF6 crystals for laser operation,” Applied Optics 33, 5526–5536 (1994).
[CrossRef]

L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, “Investigation of the Laser Properties of Cr3+:LiSrGaF6,” IEEE J. Quantum Electron. 28, 2612–2618 (1992).
[CrossRef]

Rai, J.

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, and S. C. Rand, “Cooperative bistability in dense, excited atomic systems,” Phys. Rev. Lett. 73, 1103–1106 (1994).
[CrossRef] [PubMed]

Rand, S. C.

A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, “Intrinsic bistability of luminescence and stimulated emission in Yb- and Tm-doped glass,” Phys. Rev. Lett. 84, 1898–1901 (2000).
[CrossRef] [PubMed]

M. P. Hehlen, A. Kuditcher, S. C. Rand, and S. R. Lüthi, “Site-selective, intrinsically bistable luminescence of Yb3+ in pairs in CsCdBr3,” Phys. Rev. Lett. 82, 3050–3053 (1999).
[CrossRef]

M. P. Hehlen, H. U. Güdel, Q. Shu, and S. C. Rand, “Cooperative optical bistability in the dimer system Cs3Y2Br9:10%Yb,” J. Chem. Phys. 104, 1232–1244 (1996).
[CrossRef]

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, and S. C. Rand, “Cooperative bistability in dense, excited atomic systems,” Phys. Rev. Lett. 73, 1103–1106 (1994).
[CrossRef] [PubMed]

Reidener, T.

S. R. Lüthi, M. P. Hehlen, T. Reidener, and H. U. Güdel, “Excited-state dynamics and optical bistability in the dimer system Cs3Lu2Br9:Yb3+,” J. Lumin. 77, 447–450 (1998).
[CrossRef]

Roy, R.

A. Hohl, H. J. C. van der Linden, and R. Roy, “Scaling laws for dynamical hysteresis in a multidimensional laser system,” Phys. Rev. Lett. 74, 2220–2223 (1995).
[CrossRef] [PubMed]

P. Jung, G. Gray, R. Roy, and P. Mandel, “Scaling law for dynamical hysteresis,” Phys. Rev. Lett. 65, 1873–1876 (1990).
[CrossRef] [PubMed]

Scalora, M.

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switch in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef] [PubMed]

Segard, B.

N. E. Fettouhi, B. Segard, and J. Zemmouti, “Scaling of hysteresis in a multidimensional all-optical bistable system,” Eur. Phys. J. D 6, 425–429 (1999).
[CrossRef]

Shu, Q.

M. P. Hehlen, H. U. Güdel, Q. Shu, and S. C. Rand, “Cooperative optical bistability in the dimer system Cs3Y2Br9:10%Yb,” J. Chem. Phys. 104, 1232–1244 (1996).
[CrossRef]

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, and S. C. Rand, “Cooperative bistability in dense, excited atomic systems,” Phys. Rev. Lett. 73, 1103–1106 (1994).
[CrossRef] [PubMed]

Smith, L. K.

The numerical values of C and ρ corresponded to those for Cr:LiSrAlF6, a material whose properties are close to those of Cr:LiSrGaF6. The values for Cr:LiSrAlF6 were found in the paper: S. A. Payne, L. K. Smith, J. R. Beach, and B. H. T. Chai, “Properties of Cr:LiSrAlF6 crystals for laser operation,” Applied Optics 33, 5526–5536 (1994).
[CrossRef]

L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, “Investigation of the Laser Properties of Cr3+:LiSrGaF6,” IEEE J. Quantum Electron. 28, 2612–2618 (1992).
[CrossRef]

Sorokin, E.

I. T. Sorokina, E. Sorokin, and R. Szipocs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Physics B 65, 245–254 (1997).
[CrossRef]

Sorokina, I. T.

I. T. Sorokina, E. Sorokin, and R. Szipocs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Physics B 65, 245–254 (1997).
[CrossRef]

Strogatz, S. H.

G. H. Goldsztein, F. Broner, and S. H. Strogatz, “Dynamical hysteresis without static hysteresis: scaling laws and asymptotic expansions,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 57, 1163–1187 (1997).
[CrossRef]

Sullivan, K. U.

M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express 1, 153–159 (1997).
[CrossRef]

Sung, C. C.

C. M. Bowden and C. C. Sung, “First- and second-order phase transitions in the Dicke model: relation to optical bistability,” Phys. Rev. A 19, 2392–2401 (1979).
[CrossRef]

Szipocs, R.

I. T. Sorokina, E. Sorokin, and R. Szipocs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Physics B 65, 245–254 (1997).
[CrossRef]

van der Linden, H. J. C.

A. Hohl, H. J. C. van der Linden, and R. Roy, “Scaling laws for dynamical hysteresis in a multidimensional laser system,” Phys. Rev. Lett. 74, 2220–2223 (1995).
[CrossRef] [PubMed]

Vondrova, M.

M. A. Noginov, M. Vondrova, and B. D. Lucas, “Thermally induced optical bistability in Cr-doped Colquiriite crystals,” Phys. Rev. B 65, 035112 (2002).
[CrossRef]

M. A. Noginov, B. D. Lucas, and M. Vondrova, “Optical bistability in Cr:LiSrGaF6 laser,” J. Opt. Soc. Am. B 19, 1999–2006 (2002).
[CrossRef]

Winick, K. W.

A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, “Intrinsic bistability of luminescence and stimulated emission in Yb- and Tm-doped glass,” Phys. Rev. Lett. 84, 1898–1901 (2000).
[CrossRef] [PubMed]

Zemmouti, J.

N. E. Fettouhi, B. Segard, and J. Zemmouti, “Scaling of hysteresis in a multidimensional all-optical bistable system,” Eur. Phys. J. D 6, 425–429 (1999).
[CrossRef]

Appl. Physics B (1)

I. T. Sorokina, E. Sorokin, and R. Szipocs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Physics B 65, 245–254 (1997).
[CrossRef]

Applied Optics (1)

The numerical values of C and ρ corresponded to those for Cr:LiSrAlF6, a material whose properties are close to those of Cr:LiSrGaF6. The values for Cr:LiSrAlF6 were found in the paper: S. A. Payne, L. K. Smith, J. R. Beach, and B. H. T. Chai, “Properties of Cr:LiSrAlF6 crystals for laser operation,” Applied Optics 33, 5526–5536 (1994).
[CrossRef]

Eur. Phys. J. D (1)

N. E. Fettouhi, B. Segard, and J. Zemmouti, “Scaling of hysteresis in a multidimensional all-optical bistable system,” Eur. Phys. J. D 6, 425–429 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, “Investigation of the Laser Properties of Cr3+:LiSrGaF6,” IEEE J. Quantum Electron. 28, 2612–2618 (1992).
[CrossRef]

J. Chem. Phys. (2)

D. R. Gamelin, S. R. Lüthi, and H. U. Güdel, “The role of laser heating in the intrinsic optical bistability of Yb3+-doped bromide lattices,” J. Chem. Phys. 104, 11045–11057 (2000).
[CrossRef]

M. P. Hehlen, H. U. Güdel, Q. Shu, and S. C. Rand, “Cooperative optical bistability in the dimer system Cs3Y2Br9:10%Yb,” J. Chem. Phys. 104, 1232–1244 (1996).
[CrossRef]

J. Lumin. (1)

S. R. Lüthi, M. P. Hehlen, T. Reidener, and H. U. Güdel, “Excited-state dynamics and optical bistability in the dimer system Cs3Lu2Br9:Yb3+,” J. Lumin. 77, 447–450 (1998).
[CrossRef]

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

Opt. Express (1)

M. E. Crenshaw, K. U. Sullivan, and C. M. Bowden, “Local field effects in multicomponent media,” Opt. Express 1, 153–159 (1997).
[CrossRef]

Phys. Rev. A (4)

C. M. Bowden and C. C. Sung, “First- and second-order phase transitions in the Dicke model: relation to optical bistability,” Phys. Rev. A 19, 2392–2401 (1979).
[CrossRef]

F. A. Hopf and C. M. Bowden, “Heuristic stochastic model of mirrorless optical bistability,” Phys. Rev. A 32, 268–275 (1985).
[CrossRef] [PubMed]

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, pp. 3917–3926 (1986).
[CrossRef]

M. E. Crenshaw and C. M. Bowden, “Local-field effects in a dense collection of two-level atoms embedded in a dielectric medium: Intrinsic optical bistability enhancement and local field correction effects,” Phys. Rev. A 53, 1139–1142 (1996).
[CrossRef] [PubMed]

Phys. Rev. B (1)

M. A. Noginov, M. Vondrova, and B. D. Lucas, “Thermally induced optical bistability in Cr-doped Colquiriite crystals,” Phys. Rev. B 65, 035112 (2002).
[CrossRef]

Phys. Rev. Lett. (6)

A. Hohl, H. J. C. van der Linden, and R. Roy, “Scaling laws for dynamical hysteresis in a multidimensional laser system,” Phys. Rev. Lett. 74, 2220–2223 (1995).
[CrossRef] [PubMed]

M. P. Hehlen, H. U. Güdel, Q. Shu, J. Rai, and S. C. Rand, “Cooperative bistability in dense, excited atomic systems,” Phys. Rev. Lett. 73, 1103–1106 (1994).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, “Ultrafast intrinsic optical switch in a dense medium of two-level atoms,” Phys. Rev. Lett. 68, 911–914 (1992).
[CrossRef] [PubMed]

P. Jung, G. Gray, R. Roy, and P. Mandel, “Scaling law for dynamical hysteresis,” Phys. Rev. Lett. 65, 1873–1876 (1990).
[CrossRef] [PubMed]

M. P. Hehlen, A. Kuditcher, S. C. Rand, and S. R. Lüthi, “Site-selective, intrinsically bistable luminescence of Yb3+ in pairs in CsCdBr3,” Phys. Rev. Lett. 82, 3050–3053 (1999).
[CrossRef]

A. Kuditcher, M. P. Hehlen, C. M. Florea, K. W. Winick, and S. C. Rand, “Intrinsic bistability of luminescence and stimulated emission in Yb- and Tm-doped glass,” Phys. Rev. Lett. 84, 1898–1901 (2000).
[CrossRef] [PubMed]

SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. (1)

G. H. Goldsztein, F. Broner, and S. H. Strogatz, “Dynamical hysteresis without static hysteresis: scaling laws and asymptotic expansions,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 57, 1163–1187 (1997).
[CrossRef]

Other (2)

M. Stadler, B. H. T. Chai, and M. Bass, “Crystal growth and spectroscopy of Cr:LiBaAlF6,” in Advanced Solid-State Lasers, G. Dubé and L. Chase, eds., Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington D.C., 1991), pp. 18–20.

M. A. Noginov, V. G. Ostroumov, I. A. Shcherbakov, V. A. Smirnov, and D. A. Zubenko, “Interaction of excited Cr3+ ions in laser crystals,” in Advanced Solid-State Lasers, G. Dubé and L. Chase, eds., Vol. 10 of OSA Proceedings Series (Optical Society of America, Washington D.C., 1991), pp. 21–24.

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Figures (14)

Fig. 1
Fig. 1

(a) Steady-state hysteresis loop n(Wa) in Cr:LiSGaF crystal. (b) Response times calculated at different positions on the n(Wa) curve at positive (gray triangles) and negative (black diamonds) power steps. Positive steps were equal to 0.001 W and negative steps were equal to -0.001 W. Both curves were calculated at T0=200 K, α=1×10-17 cm3/s, λp=488 nm, λe=834 nm, χ=6×10-3 W/deg, l=0.1 cm, and s=3.3×10-3 cm2.

Fig. 2
Fig. 2

Transient dynamics of Cr-excited-state concentration n after 1% step increase of the absorbed pumping power in the linear part of the n(Wa) curve (Wa0.665 W, point E in Fig. 1a). The curve was calculated at the same values of parameters as in Fig. 1.

Fig. 3
Fig. 3

Transient dynamics of Cr-excited-state concentration n after step increase of the absorbed pumping power (trace 2, step=0.1%; trace 3, step=0.2%; trace 4, step=0.3%; trace 5, step=0.4%) in Cr:LiSGaF calculated at the starting value of the absorbed pumping power Wa0.995 W. Trace 1 is the curve similar to that of Fig. 2 corresponding to the linear part of the dependence n(Wa). All curves were calculated at the same values of parameters as in Fig. 1.

Fig. 4
Fig. 4

Dynamics of the switching from the upper branch to the lower branch of the hysteresis loop in Cr:LiSGaF calculated at the starting value of the absorbed pumping power equal to Wa0.995 W with the values of the power steps equal to (trace 1) 0.8%, (trace 2) 0.7%, (trace 3) 0.6%, (trace 4) 0.5%. In the calculations, the delay times [stage (a)] were longer than they appear in the figure. In the figure, we intentionally modified the delay times to make all four traces viewable in the same plot. The curves were calculated at the same values of parameters as in Fig. 1.

Fig. 5
Fig. 5

Switching rate τswitch0-1 (squares), linear response rate τlin-1 (diamonds), response rate in the quenched regime τquench-1 (triangles), and square root of the area of the steady-state hysteresis loop (S0)1/2 (circles) plotted versus the heat-sink temperature T0. The data points were calculated at α=1×10-17 cm3/s, λp=488 nm, λe=834 nm, χ=6×10-3 W/deg, l=0.1 cm, and s=3.3×10-3 cm2. Inset: Switching rate τswitch0-1 versus loop area S0 plotted in log–log scale with T0 being the varying parameter; the slope of the power dependence is equal to 1/2.

Fig. 6
Fig. 6

Dependence of the switching rate τswitch0-1 (squares), linear response rate τlin-1 (diamonds), response rate in the quenched regime τquench-1 (triangles), and square root of the area of the steady-state hysteresis loop S01/2 (circles) on the heat-sink factor χ. The data points were calculated at T0=200 K, α=1×10-17 cm3/s, λp=488 nm, λe=834 nm, l=0.1 cm, and s=3.3×10-3 cm2. Inset: Switching rate τswitch0-1 versus loop area S0 plotted in log–log scale with χ being the varying parameter; the slope of the power dependence is equal to 1/2.

Fig. 7
Fig. 7

The hysteresis loops calculated in a steady-state regime using a static model (trace 1) and in a nonstationary regime, with different rates of the pumping power change R: trace 2, R=0.0005 W/s, τswitch=88.5 ms; trace 3, R=5 W/s, τswitch=15.8 ms; trace 4, R=10 W/s, τswitch=10.8 ms. The black circles mark the points where the switching power was measured. The calculations were done for T0=200 K, α=1×10-17 cm3/s, λp=488 nm, λe=834 nm, l=0.1 cm, and s=3.3×10-3 cm2.

Fig. 8
Fig. 8

The switching-down power Wswitch versus pumping power increase (ramp) R. Diamonds, calculated points; solid curve, fitting according to Eq. (4) (W0=1.517 W/s and K1=0.4077 W1/3 s-2/3). The data points were calculated at T0=200 K, α=1×10-17 cm3/s, λp=488 nm, λe=834 nm, l=0.1 cm, and s=3.3×10-3 cm2. Inset: delay in switching power Wswitch-Wswitch0 plotted in log–log scale.

Fig. 9
Fig. 9

Rate of switching down τswdown-1 versus rate of switching up τswup-1. The data points were calculated at the same parameter values as in Fig. 8.

Fig. 10
Fig. 10

Switching rate τswitch-1 plotted against the rate of power increase. The data points were calculated at the same parameter values as in Fig. 8. Inset: increase in switching rate Δτswitch-1 plotted versus rate of power increase R in log–log scale.

Fig. 11
Fig. 11

Experimental kinetics of Cr:LiSGaF laser emission close to the laser shutoff recorded at different rates of the pumping power increase. Trace 1, R=0.0005 W/s; trace 2, R=0.001 W/s; trace 3, R=0.004 W/s.

Fig. 12
Fig. 12

Switching rate τswitch-1 versus pumping power increase rate R. Diamonds, experimental data; solid curve, fitting with KR2/3, where K=1797 W-2/3 s-1/3 (τswitch0-1 in this case is negligibly small). Inset: same plot in logarithmic scale.

Fig. 13
Fig. 13

Switching power Wswitch versus pumping power increase rate R. Diamonds, experimental data; solid curve, fitting according to Eq. 4 (W0=0.06 W/s and K1=0.267 W1/3 s-2/3). Inset: (Wswitch-W0) versus R plotted in logarithmic scale.

Fig. 14
Fig. 14

Increment in the switching rate versus increment in the area of the loop. Inset: same in log–log scale. The data points were calculated at T0=200 K, α=1×10-17 cm3/s, λp=488 nm, λe=834 nm, l=0.1 cm, s=3.3×10-3 cm2.

Equations (11)

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τ-1=A+B exp(-ΔE/kT),
dQdt=Wa1-η νeνp-(T-T0)χ,
η=AA+αn+B exp(-ΔE/kT),
dndt=Wahνpls-nA-αn2-nB exp(-ΔE/kT).
Q=CρlsT,
dxdt=ax-bx3+F(t),
Fcrit=F0+KΩ2/3,
Wswitch=W0+K1R2/3.
τswitch-1=τswitch0-1+Δτswitch-1(R),
τswitch0-1=ξS01/2,
Δτswitch-1(R)=ςΔS(R)=K2R2/3.

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