Abstract

An experiment has been performed to find evidence and analyze a nonlinear diverging lensing effect occurring in a flash-lamp-pumped Cr3+:LiSAF laser. The effect is assigned to a refractive-index change of the material that is proportional to the Cr3+-excited ion population, the corresponding constant of proportionality being determined from the time variation of the laser-pulse far-field divergence.

© 2004 Optical Society of America

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References

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  1. B. C. Weber and A. Hirth, “Efficient single-pulse emission with submicrosecond duration from a Cr:LiSAF laser,” Opt. Commun. 128, 158–165 (1996).
    [CrossRef]
  2. B. C. Weber and A. Hirth, “Presentation of a new and simple technique of Q-switching with a LiSAF: Cr oscillator,” Opt. Commun. 149, 301–306 (1998).
    [CrossRef]
  3. M. Fromager and K. Aït-Ameur, “Modeling of the self-Q-switching behavior of lasers based on chromium doped active material,” Opt. Commun. 191, 305–314 (2001).
    [CrossRef]
  4. D. A. Berkley and G. J. Wolga, “Transient interference studies of emission from a pulsed ruby laser,” J. Appl. Phys. 38, 3231–3241 (1967).
    [CrossRef]
  5. A. Flamholz and G. J. Wolga, “Transient interference studies of passively Q-switched ruby laser emission,” J. Appl. Phys. 39, 2723–2731 (1968).
    [CrossRef]
  6. K. Aït-Ameur, T. Kerdja, and D. Louhibi, “Dynamical optical distortions in ruby lasers,” J. Phys. D 15, 1667–1672 (1982).
    [CrossRef]
  7. K. Aït-Ameur, “Divergence temporal dynamics of a Q-switched laser,” Appl. Opt. 36, 7809–7817 (1997).
    [CrossRef]
  8. S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, “Laser performance of LiSrAlF6:Cr3+,” J. Appl. Phys. 66, 1051–1056 (1989).
    [CrossRef]
  9. P. Beaud, Y. F. Chen, B. H. T. Chai, and M. C. Richardson, “Gain properties of LiSrAlF6:Cr3+,” Opt. Lett. 17, 1064–1066 (1992).
    [CrossRef] [PubMed]
  10. H. Kogelnik, “Imaging of optical modes: resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
    [CrossRef]
  11. K. Aït-Ameur, D. Louhibi, and T. Kerdja, “Measurement of the pumping coefficient dependence upon flashlamp opacity in a Nd:YAG laser,” Opt. Commun. 217, 351–355 (2003).
    [CrossRef]
  12. D. S. Hamilton, D. Heiman, J. Feinberg, and R. W. Hellwarth, “Spatial-diffusion measurements in impurity-doped solids by degenerate four-wave mixing,” Opt. Lett. 4, 124–125 (1979).
    [CrossRef] [PubMed]
  13. T. Catunda, J. P. Andreeta, and J. C. Castro, “Differential interferometric technique for the measurement of the nonlinear index of refraction of ruby,” Appl. Opt. 25, 2391–2395 (1986) and references therein.
    [CrossRef]
  14. T. Catunda and J. C. Castro, “Phase conjugation in GdAlO3:Cr3+ and ruby,” Opt. Commun. 63, 185–190 (1987).
    [CrossRef]
  15. R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser materials,” Opt. Lett. 14, 1204–1206 (1989).
    [CrossRef] [PubMed]
  16. S. C. Weaver and S. A. Payne, “Determination of excited-state polarizabilities of Cr3+-doped materials by degenerate four-wave mixing,” Phys. Rev. B 40, 10727–10740 (1989).
    [CrossRef]
  17. K. F. Wall, R. L. Aggarwal, M. D. Sciacca, H. J. Zeiger, R. E. Fahey, and A. J. Strauss, “Optically induced nonresonant changes in the refractive index of Ti:Al2O3,” Opt. Lett. 14, 180–182 (1989).
    [CrossRef] [PubMed]
  18. R. C. Powell and S. A. Payne, “Dispersion effects in four-wave mixing measurement of ions in solids,” Opt. Lett. 15, 1233–1235 (1990).
    [CrossRef] [PubMed]
  19. E. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38, 2720–2725 (1967).
    [CrossRef]
  20. J. F. Sabatini, A. E. Salwin, and D. S. McClure, “High-energy optical-absorption bands of transition-metal ions in fluoride host crystals,” Phys. Rev. B 11, 3832–3841 (1975).
    [CrossRef]
  21. C. K. Jörgensen, Modern Aspects of Ligand-Field Theory (North-Holland, Amsterdam, 1971).
  22. R. Reisfeld and C. K. Jörgensen, Lasers and Excited State of Rare Earths (Springer, Berlin, 1977).

2003 (1)

K. Aït-Ameur, D. Louhibi, and T. Kerdja, “Measurement of the pumping coefficient dependence upon flashlamp opacity in a Nd:YAG laser,” Opt. Commun. 217, 351–355 (2003).
[CrossRef]

2001 (1)

M. Fromager and K. Aït-Ameur, “Modeling of the self-Q-switching behavior of lasers based on chromium doped active material,” Opt. Commun. 191, 305–314 (2001).
[CrossRef]

1998 (1)

B. C. Weber and A. Hirth, “Presentation of a new and simple technique of Q-switching with a LiSAF: Cr oscillator,” Opt. Commun. 149, 301–306 (1998).
[CrossRef]

1997 (1)

1996 (1)

B. C. Weber and A. Hirth, “Efficient single-pulse emission with submicrosecond duration from a Cr:LiSAF laser,” Opt. Commun. 128, 158–165 (1996).
[CrossRef]

1992 (1)

1990 (1)

1989 (4)

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser materials,” Opt. Lett. 14, 1204–1206 (1989).
[CrossRef] [PubMed]

S. C. Weaver and S. A. Payne, “Determination of excited-state polarizabilities of Cr3+-doped materials by degenerate four-wave mixing,” Phys. Rev. B 40, 10727–10740 (1989).
[CrossRef]

K. F. Wall, R. L. Aggarwal, M. D. Sciacca, H. J. Zeiger, R. E. Fahey, and A. J. Strauss, “Optically induced nonresonant changes in the refractive index of Ti:Al2O3,” Opt. Lett. 14, 180–182 (1989).
[CrossRef] [PubMed]

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, “Laser performance of LiSrAlF6:Cr3+,” J. Appl. Phys. 66, 1051–1056 (1989).
[CrossRef]

1987 (1)

T. Catunda and J. C. Castro, “Phase conjugation in GdAlO3:Cr3+ and ruby,” Opt. Commun. 63, 185–190 (1987).
[CrossRef]

1986 (1)

1982 (1)

K. Aït-Ameur, T. Kerdja, and D. Louhibi, “Dynamical optical distortions in ruby lasers,” J. Phys. D 15, 1667–1672 (1982).
[CrossRef]

1979 (1)

1975 (1)

J. F. Sabatini, A. E. Salwin, and D. S. McClure, “High-energy optical-absorption bands of transition-metal ions in fluoride host crystals,” Phys. Rev. B 11, 3832–3841 (1975).
[CrossRef]

1968 (1)

A. Flamholz and G. J. Wolga, “Transient interference studies of passively Q-switched ruby laser emission,” J. Appl. Phys. 39, 2723–2731 (1968).
[CrossRef]

1967 (2)

D. A. Berkley and G. J. Wolga, “Transient interference studies of emission from a pulsed ruby laser,” J. Appl. Phys. 38, 3231–3241 (1967).
[CrossRef]

E. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38, 2720–2725 (1967).
[CrossRef]

1965 (1)

H. Kogelnik, “Imaging of optical modes: resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

Aggarwal, R. L.

Aït-Ameur, K.

K. Aït-Ameur, D. Louhibi, and T. Kerdja, “Measurement of the pumping coefficient dependence upon flashlamp opacity in a Nd:YAG laser,” Opt. Commun. 217, 351–355 (2003).
[CrossRef]

M. Fromager and K. Aït-Ameur, “Modeling of the self-Q-switching behavior of lasers based on chromium doped active material,” Opt. Commun. 191, 305–314 (2001).
[CrossRef]

K. Aït-Ameur, “Divergence temporal dynamics of a Q-switched laser,” Appl. Opt. 36, 7809–7817 (1997).
[CrossRef]

K. Aït-Ameur, T. Kerdja, and D. Louhibi, “Dynamical optical distortions in ruby lasers,” J. Phys. D 15, 1667–1672 (1982).
[CrossRef]

Andreeta, J. P.

Baldwin, G. D.

E. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38, 2720–2725 (1967).
[CrossRef]

Beaud, P.

Berkley, D. A.

D. A. Berkley and G. J. Wolga, “Transient interference studies of emission from a pulsed ruby laser,” J. Appl. Phys. 38, 3231–3241 (1967).
[CrossRef]

Castro, J. C.

Catunda, T.

Chai, B. H. T.

Chase, L. L.

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser materials,” Opt. Lett. 14, 1204–1206 (1989).
[CrossRef] [PubMed]

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, “Laser performance of LiSrAlF6:Cr3+,” J. Appl. Phys. 66, 1051–1056 (1989).
[CrossRef]

Chen, Y. F.

Fahey, R. E.

Feinberg, J.

Flamholz, A.

A. Flamholz and G. J. Wolga, “Transient interference studies of passively Q-switched ruby laser emission,” J. Appl. Phys. 39, 2723–2731 (1968).
[CrossRef]

Fromager, M.

M. Fromager and K. Aït-Ameur, “Modeling of the self-Q-switching behavior of lasers based on chromium doped active material,” Opt. Commun. 191, 305–314 (2001).
[CrossRef]

Hamilton, D. S.

Heiman, D.

Hellwarth, R. W.

Hirth, A.

B. C. Weber and A. Hirth, “Presentation of a new and simple technique of Q-switching with a LiSAF: Cr oscillator,” Opt. Commun. 149, 301–306 (1998).
[CrossRef]

B. C. Weber and A. Hirth, “Efficient single-pulse emission with submicrosecond duration from a Cr:LiSAF laser,” Opt. Commun. 128, 158–165 (1996).
[CrossRef]

Kerdja, T.

K. Aït-Ameur, D. Louhibi, and T. Kerdja, “Measurement of the pumping coefficient dependence upon flashlamp opacity in a Nd:YAG laser,” Opt. Commun. 217, 351–355 (2003).
[CrossRef]

K. Aït-Ameur, T. Kerdja, and D. Louhibi, “Dynamical optical distortions in ruby lasers,” J. Phys. D 15, 1667–1672 (1982).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Imaging of optical modes: resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

Kway, W. L.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, “Laser performance of LiSrAlF6:Cr3+,” J. Appl. Phys. 66, 1051–1056 (1989).
[CrossRef]

Louhibi, D.

K. Aït-Ameur, D. Louhibi, and T. Kerdja, “Measurement of the pumping coefficient dependence upon flashlamp opacity in a Nd:YAG laser,” Opt. Commun. 217, 351–355 (2003).
[CrossRef]

K. Aït-Ameur, T. Kerdja, and D. Louhibi, “Dynamical optical distortions in ruby lasers,” J. Phys. D 15, 1667–1672 (1982).
[CrossRef]

McClure, D. S.

J. F. Sabatini, A. E. Salwin, and D. S. McClure, “High-energy optical-absorption bands of transition-metal ions in fluoride host crystals,” Phys. Rev. B 11, 3832–3841 (1975).
[CrossRef]

Newkirk, H. W.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, “Laser performance of LiSrAlF6:Cr3+,” J. Appl. Phys. 66, 1051–1056 (1989).
[CrossRef]

Payne, S. A.

R. C. Powell and S. A. Payne, “Dispersion effects in four-wave mixing measurement of ions in solids,” Opt. Lett. 15, 1233–1235 (1990).
[CrossRef] [PubMed]

R. C. Powell, S. A. Payne, L. L. Chase, and G. D. Wilke, “Index-of-refraction change in optically pumped solid-state laser materials,” Opt. Lett. 14, 1204–1206 (1989).
[CrossRef] [PubMed]

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, “Laser performance of LiSrAlF6:Cr3+,” J. Appl. Phys. 66, 1051–1056 (1989).
[CrossRef]

S. C. Weaver and S. A. Payne, “Determination of excited-state polarizabilities of Cr3+-doped materials by degenerate four-wave mixing,” Phys. Rev. B 40, 10727–10740 (1989).
[CrossRef]

Powell, R. C.

Richardson, M. C.

Riedel, E.

E. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38, 2720–2725 (1967).
[CrossRef]

Sabatini, J. F.

J. F. Sabatini, A. E. Salwin, and D. S. McClure, “High-energy optical-absorption bands of transition-metal ions in fluoride host crystals,” Phys. Rev. B 11, 3832–3841 (1975).
[CrossRef]

Salwin, A. E.

J. F. Sabatini, A. E. Salwin, and D. S. McClure, “High-energy optical-absorption bands of transition-metal ions in fluoride host crystals,” Phys. Rev. B 11, 3832–3841 (1975).
[CrossRef]

Sciacca, M. D.

Smith, L. K.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, “Laser performance of LiSrAlF6:Cr3+,” J. Appl. Phys. 66, 1051–1056 (1989).
[CrossRef]

Strauss, A. J.

Wall, K. F.

Weaver, S. C.

S. C. Weaver and S. A. Payne, “Determination of excited-state polarizabilities of Cr3+-doped materials by degenerate four-wave mixing,” Phys. Rev. B 40, 10727–10740 (1989).
[CrossRef]

Weber, B. C.

B. C. Weber and A. Hirth, “Presentation of a new and simple technique of Q-switching with a LiSAF: Cr oscillator,” Opt. Commun. 149, 301–306 (1998).
[CrossRef]

B. C. Weber and A. Hirth, “Efficient single-pulse emission with submicrosecond duration from a Cr:LiSAF laser,” Opt. Commun. 128, 158–165 (1996).
[CrossRef]

Wilke, G. D.

Wolga, G. J.

A. Flamholz and G. J. Wolga, “Transient interference studies of passively Q-switched ruby laser emission,” J. Appl. Phys. 39, 2723–2731 (1968).
[CrossRef]

D. A. Berkley and G. J. Wolga, “Transient interference studies of emission from a pulsed ruby laser,” J. Appl. Phys. 38, 3231–3241 (1967).
[CrossRef]

Zeiger, H. J.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Imaging of optical modes: resonators with internal lenses,” Bell Syst. Tech. J. 44, 455–494 (1965).
[CrossRef]

J. Appl. Phys. (4)

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and H. W. Newkirk, “Laser performance of LiSrAlF6:Cr3+,” J. Appl. Phys. 66, 1051–1056 (1989).
[CrossRef]

D. A. Berkley and G. J. Wolga, “Transient interference studies of emission from a pulsed ruby laser,” J. Appl. Phys. 38, 3231–3241 (1967).
[CrossRef]

A. Flamholz and G. J. Wolga, “Transient interference studies of passively Q-switched ruby laser emission,” J. Appl. Phys. 39, 2723–2731 (1968).
[CrossRef]

E. Riedel and G. D. Baldwin, “Theory of dynamic optical distortion in isotropic laser materials,” J. Appl. Phys. 38, 2720–2725 (1967).
[CrossRef]

J. Phys. D (1)

K. Aït-Ameur, T. Kerdja, and D. Louhibi, “Dynamical optical distortions in ruby lasers,” J. Phys. D 15, 1667–1672 (1982).
[CrossRef]

Opt. Commun. (5)

B. C. Weber and A. Hirth, “Efficient single-pulse emission with submicrosecond duration from a Cr:LiSAF laser,” Opt. Commun. 128, 158–165 (1996).
[CrossRef]

B. C. Weber and A. Hirth, “Presentation of a new and simple technique of Q-switching with a LiSAF: Cr oscillator,” Opt. Commun. 149, 301–306 (1998).
[CrossRef]

M. Fromager and K. Aït-Ameur, “Modeling of the self-Q-switching behavior of lasers based on chromium doped active material,” Opt. Commun. 191, 305–314 (2001).
[CrossRef]

K. Aït-Ameur, D. Louhibi, and T. Kerdja, “Measurement of the pumping coefficient dependence upon flashlamp opacity in a Nd:YAG laser,” Opt. Commun. 217, 351–355 (2003).
[CrossRef]

T. Catunda and J. C. Castro, “Phase conjugation in GdAlO3:Cr3+ and ruby,” Opt. Commun. 63, 185–190 (1987).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. B (2)

S. C. Weaver and S. A. Payne, “Determination of excited-state polarizabilities of Cr3+-doped materials by degenerate four-wave mixing,” Phys. Rev. B 40, 10727–10740 (1989).
[CrossRef]

J. F. Sabatini, A. E. Salwin, and D. S. McClure, “High-energy optical-absorption bands of transition-metal ions in fluoride host crystals,” Phys. Rev. B 11, 3832–3841 (1975).
[CrossRef]

Other (2)

C. K. Jörgensen, Modern Aspects of Ligand-Field Theory (North-Holland, Amsterdam, 1971).

R. Reisfeld and C. K. Jörgensen, Lasers and Excited State of Rare Earths (Springer, Berlin, 1977).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for our divergence diagnostic. BS, beam splitter; F1 and F2, neutral-density filters; S, circular stop; D1 and D2, photodiodes.

Fig. 2
Fig. 2

(a) Signal V1 versus time corresponding to a sequence of relaxation pulse characteristics of the free-running mode of the laser. (b) Laser divergence as a function of time from pulse to pulse.

Fig. 3
Fig. 3

Function β(t)=[Ni(t)-Nth]/NT versus time during a sequence of relaxation pulses.

Fig. 4
Fig. 4

(a) Experimental temporal evolutions of signals V1 and V2, (b) divergence θ, (c) function θ˙=dθ(t)/dt during the first laser spike.

Fig. 5
Fig. 5

Function β(t)=[Ni-N(t)]/NT versus time during a single pulse.

Fig. 6
Fig. 6

Theoretical variation of the minimum value of dθ(t)/dt as a function of the constant K.

Fig. 7
Fig. 7

(a) Gain spectra versus reduced population ratio β0=Nexc/NT, as deduced from the measurements of the stimulated emission and the ground-state and excited-state absorption cross-sectional spectra of Cr:LiCAF. (b) Resulting refractive-index variation versus β0.

Equations (33)

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Nt=-NΦσc-Nτ+Rp(NT-N),
Φt=ΦNσc1-δtR+Nτ2,
Nd(r, t)Ni-[Ni-N(t)]exp[-2r2/Wrod2(t)].
Δn(r, t)=KNd(r, t)NT,
exp-2r2Wc2(t)1-4r2Wc2(t),
n(r, t)n01-Kβ(t)4n0Wc2(t)r2,
f(t)=-2Wc2(t)Kβ(t)Lrod.
g(t)=1-L1f(t)+1Rc.
Wp2=λLπg(1-g)1/2,
Wc2=λLπ1g(1-g)1/2.
θ(t)=λπWp(t).
V2=A2P2=A2T2(0.92P)exp(-2r02/W2),
V1=A1P1=A1T1(0.04P),
W=Wp1+λzπWp221/2λzπWp=θz,
V2V1=A0 exp-2r02W2,
θ(t)=r0z-2ln1A0V2(t)V1(t)1/2.
β(t)=Ni(t)-NthNT.
Nit=Rp(NT-Ni)-Niτ.
Ni(t)=RpτNT[1-exp(-t/τ)].
Ni(t0)=δ+γ2σLrod.
Nth=δ2σLrod,
β(t0)=γ2σNTLrod.
g(t)=1-L1f(t)+1fr+1Rc
β(t)=Ni-N(t)NT.
1ΦdΦdt=Nσc1-δtR,
N(t)=1σc11ΦdΦdt+δtR.
1Φ(t)dΦ(t)dt1P(t)dP(t)dt=1V1(t)dV1(t)dt.
N(t0)=RPτNT1-exp-t0τ=δ+γ2σLrod.
g0=β0(σem-σesa)-(1-β0)σgsa,
Δn(λ)=12π2PV0g0(λ)(λ/λ)2-1dλ,
n2-1n2+1=4π3NTαP,
K=2πnfL2NTΔαP,fL=n2+23.
ΔαPq2(2πc)2mfei(ν¯i-ν¯e)2-ν¯P2-fgiν¯i2-ν¯P2,

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