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)

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]

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]

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)

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

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]

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]

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]

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]

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

Opt. Lett. (5)

Phys. Rev. B (2)

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]

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]

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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