Abstract

Two-beam coupling measurements of an avalanche upconversion transition in concentrated Tm:LiYF4 confirm that, despite the resonant nature of the excited-state optical interaction, the induced response is strongly dispersive. This surprising characteristic is shown to be a general feature of avalanche polarization, with an off-resonant process dominating the resonant response.

© 1997 Optical Society of America

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References

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  1. M. A. Kramer, W. R. Tompkin, and R. W. Boyd, Phys. Rev. A 34, 2026 (1986); I. McMichael, P. Yeh, and P. Beckwith, Opt. Lett. 13, 500 (1988).
    [CrossRef] [PubMed]
  2. S. A. Boothroyd, J. Chrostowski, and M. S. O’Sullivan, J. Opt. Soc. Am. B 6, 766 (1989).
    [CrossRef]
  3. D. Redman, Q. Shu, A. Lenef, and S. C. Rand, Opt. Lett. 17, 175 (1992).
    [CrossRef] [PubMed]
  4. J. Chivian, W. Case, and D. Eden, Appl. Phys. Lett. 35, 124 (1979).
    [CrossRef]
  5. H. Ni, “Avalanche upconversion in Tm:LiYF4, TmYAlO3 and Tm:YAG,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1994).
  6. See, for example, Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  7. A. Kueny, W. E. Case, and M. E. Koch, J. Opt. Soc. Am. B 6, 639 (1989).
    [CrossRef]
  8. W. E. Case, M. E. Koch, and A. W. Kueny, J. Lumin. 45351 (1990); U. Oetliker, M. J. Riley, P. S. May, and H. U. Gudel, Coord. Chem. Rev. 111, 125 (1991); M. F. Joubert, S. Guy, and B. Jacquier, Phys. Rev. B 48, 10031 (1993).
    [CrossRef]
  9. H. Ni and S. C. Rand, Opt. Lett. 16, 1424 (1991).
    [CrossRef] [PubMed]
  10. T. Hebert, R. Wannemacher, R. M. Macfarlane, and W. Lenth, Appl. Phys. Lett. 60, 2592 (1992); Y. H. Chen and F. Auzel, Electron. Lett. 30, 1602 (1994); M. Pollnau, W. Luthy, and H. P. Weber, J. Appl. Phys. 77, 6128 (1995); R. Scheps, IEEE J. Quantum Electron. 31, 309 (1995).
    [CrossRef]
  11. T. Sandrock, E. Heumann, and G. Huber, in International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1996).
  12. L. M. Yang, T. Sonsnowski, M. L. Stock, T. B. Norris, J. Squier, G. Mourou, M. L. Dennis, and I. Duling, Opt. Lett. 20, 1044 (1995).
    [CrossRef]
  13. H. Ni and S. C. Rand, Opt. Lett. 17, 1222 (1992).
    [CrossRef] [PubMed]
  14. Q. Shu, “Cooperative optical nonlinearities,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1996).
  15. ρr can be calculated by use of the standard four-level model,8 as we have done, or it can be treated as a free parameter.

1995

1992

T. Hebert, R. Wannemacher, R. M. Macfarlane, and W. Lenth, Appl. Phys. Lett. 60, 2592 (1992); Y. H. Chen and F. Auzel, Electron. Lett. 30, 1602 (1994); M. Pollnau, W. Luthy, and H. P. Weber, J. Appl. Phys. 77, 6128 (1995); R. Scheps, IEEE J. Quantum Electron. 31, 309 (1995).
[CrossRef]

D. Redman, Q. Shu, A. Lenef, and S. C. Rand, Opt. Lett. 17, 175 (1992).
[CrossRef] [PubMed]

H. Ni and S. C. Rand, Opt. Lett. 17, 1222 (1992).
[CrossRef] [PubMed]

1991

1990

W. E. Case, M. E. Koch, and A. W. Kueny, J. Lumin. 45351 (1990); U. Oetliker, M. J. Riley, P. S. May, and H. U. Gudel, Coord. Chem. Rev. 111, 125 (1991); M. F. Joubert, S. Guy, and B. Jacquier, Phys. Rev. B 48, 10031 (1993).
[CrossRef]

1989

1986

M. A. Kramer, W. R. Tompkin, and R. W. Boyd, Phys. Rev. A 34, 2026 (1986); I. McMichael, P. Yeh, and P. Beckwith, Opt. Lett. 13, 500 (1988).
[CrossRef] [PubMed]

1979

J. Chivian, W. Case, and D. Eden, Appl. Phys. Lett. 35, 124 (1979).
[CrossRef]

Boothroyd, S. A.

Boyd, R. W.

M. A. Kramer, W. R. Tompkin, and R. W. Boyd, Phys. Rev. A 34, 2026 (1986); I. McMichael, P. Yeh, and P. Beckwith, Opt. Lett. 13, 500 (1988).
[CrossRef] [PubMed]

Case, W.

J. Chivian, W. Case, and D. Eden, Appl. Phys. Lett. 35, 124 (1979).
[CrossRef]

Case, W. E.

W. E. Case, M. E. Koch, and A. W. Kueny, J. Lumin. 45351 (1990); U. Oetliker, M. J. Riley, P. S. May, and H. U. Gudel, Coord. Chem. Rev. 111, 125 (1991); M. F. Joubert, S. Guy, and B. Jacquier, Phys. Rev. B 48, 10031 (1993).
[CrossRef]

A. Kueny, W. E. Case, and M. E. Koch, J. Opt. Soc. Am. B 6, 639 (1989).
[CrossRef]

Chivian, J.

J. Chivian, W. Case, and D. Eden, Appl. Phys. Lett. 35, 124 (1979).
[CrossRef]

Chrostowski, J.

Dennis, M. L.

Duling, I.

Eden, D.

J. Chivian, W. Case, and D. Eden, Appl. Phys. Lett. 35, 124 (1979).
[CrossRef]

Hebert, T.

T. Hebert, R. Wannemacher, R. M. Macfarlane, and W. Lenth, Appl. Phys. Lett. 60, 2592 (1992); Y. H. Chen and F. Auzel, Electron. Lett. 30, 1602 (1994); M. Pollnau, W. Luthy, and H. P. Weber, J. Appl. Phys. 77, 6128 (1995); R. Scheps, IEEE J. Quantum Electron. 31, 309 (1995).
[CrossRef]

Heumann, E.

T. Sandrock, E. Heumann, and G. Huber, in International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1996).

Huber, G.

T. Sandrock, E. Heumann, and G. Huber, in International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1996).

Koch, M. E.

W. E. Case, M. E. Koch, and A. W. Kueny, J. Lumin. 45351 (1990); U. Oetliker, M. J. Riley, P. S. May, and H. U. Gudel, Coord. Chem. Rev. 111, 125 (1991); M. F. Joubert, S. Guy, and B. Jacquier, Phys. Rev. B 48, 10031 (1993).
[CrossRef]

A. Kueny, W. E. Case, and M. E. Koch, J. Opt. Soc. Am. B 6, 639 (1989).
[CrossRef]

Kramer, M. A.

M. A. Kramer, W. R. Tompkin, and R. W. Boyd, Phys. Rev. A 34, 2026 (1986); I. McMichael, P. Yeh, and P. Beckwith, Opt. Lett. 13, 500 (1988).
[CrossRef] [PubMed]

Kueny, A.

Kueny, A. W.

W. E. Case, M. E. Koch, and A. W. Kueny, J. Lumin. 45351 (1990); U. Oetliker, M. J. Riley, P. S. May, and H. U. Gudel, Coord. Chem. Rev. 111, 125 (1991); M. F. Joubert, S. Guy, and B. Jacquier, Phys. Rev. B 48, 10031 (1993).
[CrossRef]

Lenef, A.

Lenth, W.

T. Hebert, R. Wannemacher, R. M. Macfarlane, and W. Lenth, Appl. Phys. Lett. 60, 2592 (1992); Y. H. Chen and F. Auzel, Electron. Lett. 30, 1602 (1994); M. Pollnau, W. Luthy, and H. P. Weber, J. Appl. Phys. 77, 6128 (1995); R. Scheps, IEEE J. Quantum Electron. 31, 309 (1995).
[CrossRef]

Macfarlane, R. M.

T. Hebert, R. Wannemacher, R. M. Macfarlane, and W. Lenth, Appl. Phys. Lett. 60, 2592 (1992); Y. H. Chen and F. Auzel, Electron. Lett. 30, 1602 (1994); M. Pollnau, W. Luthy, and H. P. Weber, J. Appl. Phys. 77, 6128 (1995); R. Scheps, IEEE J. Quantum Electron. 31, 309 (1995).
[CrossRef]

Mourou, G.

Ni, H.

H. Ni and S. C. Rand, Opt. Lett. 17, 1222 (1992).
[CrossRef] [PubMed]

H. Ni and S. C. Rand, Opt. Lett. 16, 1424 (1991).
[CrossRef] [PubMed]

H. Ni, “Avalanche upconversion in Tm:LiYF4, TmYAlO3 and Tm:YAG,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1994).

Norris, T. B.

O’Sullivan, M. S.

Rand, S. C.

Redman, D.

Sandrock, T.

T. Sandrock, E. Heumann, and G. Huber, in International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1996).

Shen, Y. R.

See, for example, Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Shu, Q.

D. Redman, Q. Shu, A. Lenef, and S. C. Rand, Opt. Lett. 17, 175 (1992).
[CrossRef] [PubMed]

Q. Shu, “Cooperative optical nonlinearities,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1996).

Sonsnowski, T.

Squier, J.

Stock, M. L.

Tompkin, W. R.

M. A. Kramer, W. R. Tompkin, and R. W. Boyd, Phys. Rev. A 34, 2026 (1986); I. McMichael, P. Yeh, and P. Beckwith, Opt. Lett. 13, 500 (1988).
[CrossRef] [PubMed]

Wannemacher, R.

T. Hebert, R. Wannemacher, R. M. Macfarlane, and W. Lenth, Appl. Phys. Lett. 60, 2592 (1992); Y. H. Chen and F. Auzel, Electron. Lett. 30, 1602 (1994); M. Pollnau, W. Luthy, and H. P. Weber, J. Appl. Phys. 77, 6128 (1995); R. Scheps, IEEE J. Quantum Electron. 31, 309 (1995).
[CrossRef]

Yang, L. M.

Appl. Phys. Lett.

J. Chivian, W. Case, and D. Eden, Appl. Phys. Lett. 35, 124 (1979).
[CrossRef]

T. Hebert, R. Wannemacher, R. M. Macfarlane, and W. Lenth, Appl. Phys. Lett. 60, 2592 (1992); Y. H. Chen and F. Auzel, Electron. Lett. 30, 1602 (1994); M. Pollnau, W. Luthy, and H. P. Weber, J. Appl. Phys. 77, 6128 (1995); R. Scheps, IEEE J. Quantum Electron. 31, 309 (1995).
[CrossRef]

J. Lumin.

W. E. Case, M. E. Koch, and A. W. Kueny, J. Lumin. 45351 (1990); U. Oetliker, M. J. Riley, P. S. May, and H. U. Gudel, Coord. Chem. Rev. 111, 125 (1991); M. F. Joubert, S. Guy, and B. Jacquier, Phys. Rev. B 48, 10031 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

M. A. Kramer, W. R. Tompkin, and R. W. Boyd, Phys. Rev. A 34, 2026 (1986); I. McMichael, P. Yeh, and P. Beckwith, Opt. Lett. 13, 500 (1988).
[CrossRef] [PubMed]

Other

H. Ni, “Avalanche upconversion in Tm:LiYF4, TmYAlO3 and Tm:YAG,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1994).

See, for example, Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

T. Sandrock, E. Heumann, and G. Huber, in International Quantum Electronics Conference (Optical Society of America, Washington, D.C., 1996).

Q. Shu, “Cooperative optical nonlinearities,” Ph.D. dissertation (University of Michigan, Ann Arbor, Mich., 1996).

ρr can be calculated by use of the standard four-level model,8 as we have done, or it can be treated as a free parameter.

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Figures (4)

Fig. 1
Fig. 1

(a) Reduction of a multilevel avalanche system to a two-level nonlinear system. Cross relaxation (curved arrows) and decay (wiggly arrows) account for incoherent pumping of excited states at large detunings from the ground-state transition. (b) Calculation of the susceptibility from Eq. (4). Solid dashed curves correspond to real and imaginary induced indices, respectively. The parameters used are Γ21=2×1012 s-1 and γ21=2×108 s-1.

Fig. 2
Fig. 2

Experimental two-beam coupling signals in Tm:LiYF4 versus both pump–probe detuning and pump intensity.

Fig. 3
Fig. 3

Real (n2) and imaginary (n2) nonlinear indices versus input intensity from data of Fig. 2.

Fig. 4
Fig. 4

Plot of the dispersive (filled diamonds) and absorptive (open circles) amplitudes of the TBC signals in 5% Tm:LiYF4 versus wavelength over a broad spectral region containing both ground- and excited-state transitions. Inset: Enlargement of the avalanche resonance region at 648 nm. The slight skewing of the dispersive component line shape with respect to the absorptive component is due to the summation of ground- and excited-state polarization contributions. Data are uncorrected for sample absorption.

Equations (4)

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

ρ˙11=γ21ρ22-Ωv-Λ1=0,
ρ˙22=-γ21ρ22+Ωv+Λ2=0,
ρ˜˙21=-Γ21-iΔρ˜21+½iΩρ22-ρ11=0.
χeff3ω=4Nμ124-30-1Δ-iΓ21Γ21/γ21Δ2+Γ212Δ2+Γ212+Ω2Γ21/γ21+4Nμ124-30-1Δ-iΓ211+2f/γ21Δ2+Γ212+Ω2Γ21/γ21ρr/Ω2.

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