Abstract

A theoretical model and its experimental realization for the temperature grating relaxation time constant and its impact on the temporal and the spectral profiles of a Q-switched and modelocked Nd:YAG laser pumped distributed feedback dye laser (DFDL) is reported. Boundary conditions for different types of excitation pulses have been established to predict the effect of temperature phase gratings on laser gain build-up and temporal elongation of the DFDL pulses. The proposed transient grating method is useful in measuring grating relaxation time constants for lasing dye solutions. The proposed mathematical model is demonstrated by measurement of the relaxation time constant of R6G in ethanol at 10-3M. The measured relaxation time constant of 16±0.2 ns is very close to the tabulated values determined using other techniques.

© 2003 Optical Society of America

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References

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  1. V. Yu. Kurstak and S. S. Anufrick “Influence of thermal phase lattice on ultrashort pulses characteristics generated by DFDL”, LFNM, Kharkiv, Ukraine, 3–5 (2002).
  2. J. Liang, H. Sun, and Y. Hu et.al, “The observation of lasing wavelength shift from the reflection center of an Ytterbium doped fiber grating laser,” Opt. Commun. 216, 173 (2003).
    [Crossref]
  3. A. A. Afanas’ev et al. “Effect of a thermal lattice on the generated line width of a dye laser with distributed feedback,” J. Appl. Spectr. 37, 899 (1982)
    [Crossref]
  4. A. W. Broerman, D.C. Venerus, and J. D. Schiebler, “Evidence of the stress thermal rule in an elastomer subjected to simple elongation,” J. Chem. Phys. 11, 6955 (1999).
  5. R. Y. Choie, T.H. Barnes, and W.J. Sandle et al, “Observation of a thermal phase grating contribution to diffraction in erythrosine doped gelatin films,” Opt. Commun. 186, 43 (2000).
    [Crossref]
  6. Laser induced dynamic gratings, edited by H.J Eichler, P. Gunter, and D.W. Pohl, Springer Verlag Series on Opt. Sciences, 50, 17 (1986).
  7. A. Bosh, M. Brodin, N. Orchair, S. Odulov, and S. Soskin, Soviet Physics, JEPT Lett.18, 397 (1973).
  8. H. J. Eichler, Ch. Hartig, and J. Knof, Phys Status Solidi (a)45, 433, 1978.
    [Crossref]
  9. Zs. Bor, A. Muller, and B. Racz, “UV and blue ps pulse generation by a N-laser pumped DFDL,” Optic. Commun. 40, 294 (1982).
    [Crossref]
  10. M. Fogiel, ‘Handbook of Mathematical Scientific and Engineering Formulas, Tables, Functions, Graphs and Transforms,’ TEA New York, 304, 7 (1986).
  11. A. Penzkofer and W. Falkenstein et al, Chem. Phys. Lett, 44, 82 (1976).
    [Crossref]
  12. D.Y. Key, ‘The scattering of light from light induced structures in liquids,’ Ph.D. Thesis, London University, (1977).
  13. P.Y. Key and R.G. Harrison, IEEE. J. Quant. Electron.QE-6, 645 (1970).

2003 (1)

J. Liang, H. Sun, and Y. Hu et.al, “The observation of lasing wavelength shift from the reflection center of an Ytterbium doped fiber grating laser,” Opt. Commun. 216, 173 (2003).
[Crossref]

2000 (1)

R. Y. Choie, T.H. Barnes, and W.J. Sandle et al, “Observation of a thermal phase grating contribution to diffraction in erythrosine doped gelatin films,” Opt. Commun. 186, 43 (2000).
[Crossref]

1999 (1)

A. W. Broerman, D.C. Venerus, and J. D. Schiebler, “Evidence of the stress thermal rule in an elastomer subjected to simple elongation,” J. Chem. Phys. 11, 6955 (1999).

1982 (2)

Zs. Bor, A. Muller, and B. Racz, “UV and blue ps pulse generation by a N-laser pumped DFDL,” Optic. Commun. 40, 294 (1982).
[Crossref]

A. A. Afanas’ev et al. “Effect of a thermal lattice on the generated line width of a dye laser with distributed feedback,” J. Appl. Spectr. 37, 899 (1982)
[Crossref]

Afanas’ev, A. A.

A. A. Afanas’ev et al. “Effect of a thermal lattice on the generated line width of a dye laser with distributed feedback,” J. Appl. Spectr. 37, 899 (1982)
[Crossref]

Anufrick, S. S.

V. Yu. Kurstak and S. S. Anufrick “Influence of thermal phase lattice on ultrashort pulses characteristics generated by DFDL”, LFNM, Kharkiv, Ukraine, 3–5 (2002).

Barnes, T.H.

R. Y. Choie, T.H. Barnes, and W.J. Sandle et al, “Observation of a thermal phase grating contribution to diffraction in erythrosine doped gelatin films,” Opt. Commun. 186, 43 (2000).
[Crossref]

Bor, Zs.

Zs. Bor, A. Muller, and B. Racz, “UV and blue ps pulse generation by a N-laser pumped DFDL,” Optic. Commun. 40, 294 (1982).
[Crossref]

Bosh, A.

A. Bosh, M. Brodin, N. Orchair, S. Odulov, and S. Soskin, Soviet Physics, JEPT Lett.18, 397 (1973).

Brodin, M.

A. Bosh, M. Brodin, N. Orchair, S. Odulov, and S. Soskin, Soviet Physics, JEPT Lett.18, 397 (1973).

Broerman, A. W.

A. W. Broerman, D.C. Venerus, and J. D. Schiebler, “Evidence of the stress thermal rule in an elastomer subjected to simple elongation,” J. Chem. Phys. 11, 6955 (1999).

Choie, R. Y.

R. Y. Choie, T.H. Barnes, and W.J. Sandle et al, “Observation of a thermal phase grating contribution to diffraction in erythrosine doped gelatin films,” Opt. Commun. 186, 43 (2000).
[Crossref]

Eichler, H. J.

H. J. Eichler, Ch. Hartig, and J. Knof, Phys Status Solidi (a)45, 433, 1978.
[Crossref]

Falkenstein, W.

A. Penzkofer and W. Falkenstein et al, Chem. Phys. Lett, 44, 82 (1976).
[Crossref]

Fogiel, M.

M. Fogiel, ‘Handbook of Mathematical Scientific and Engineering Formulas, Tables, Functions, Graphs and Transforms,’ TEA New York, 304, 7 (1986).

Harrison, R.G.

P.Y. Key and R.G. Harrison, IEEE. J. Quant. Electron.QE-6, 645 (1970).

Hartig, Ch.

H. J. Eichler, Ch. Hartig, and J. Knof, Phys Status Solidi (a)45, 433, 1978.
[Crossref]

Hu, Y.

J. Liang, H. Sun, and Y. Hu et.al, “The observation of lasing wavelength shift from the reflection center of an Ytterbium doped fiber grating laser,” Opt. Commun. 216, 173 (2003).
[Crossref]

Key, D.Y.

D.Y. Key, ‘The scattering of light from light induced structures in liquids,’ Ph.D. Thesis, London University, (1977).

Key, P.Y.

P.Y. Key and R.G. Harrison, IEEE. J. Quant. Electron.QE-6, 645 (1970).

Knof, J.

H. J. Eichler, Ch. Hartig, and J. Knof, Phys Status Solidi (a)45, 433, 1978.
[Crossref]

Kurstak, V. Yu.

V. Yu. Kurstak and S. S. Anufrick “Influence of thermal phase lattice on ultrashort pulses characteristics generated by DFDL”, LFNM, Kharkiv, Ukraine, 3–5 (2002).

Liang, J.

J. Liang, H. Sun, and Y. Hu et.al, “The observation of lasing wavelength shift from the reflection center of an Ytterbium doped fiber grating laser,” Opt. Commun. 216, 173 (2003).
[Crossref]

Muller, A.

Zs. Bor, A. Muller, and B. Racz, “UV and blue ps pulse generation by a N-laser pumped DFDL,” Optic. Commun. 40, 294 (1982).
[Crossref]

Odulov, S.

A. Bosh, M. Brodin, N. Orchair, S. Odulov, and S. Soskin, Soviet Physics, JEPT Lett.18, 397 (1973).

Orchair, N.

A. Bosh, M. Brodin, N. Orchair, S. Odulov, and S. Soskin, Soviet Physics, JEPT Lett.18, 397 (1973).

Penzkofer, A.

A. Penzkofer and W. Falkenstein et al, Chem. Phys. Lett, 44, 82 (1976).
[Crossref]

Racz, B.

Zs. Bor, A. Muller, and B. Racz, “UV and blue ps pulse generation by a N-laser pumped DFDL,” Optic. Commun. 40, 294 (1982).
[Crossref]

Sandle, W.J.

R. Y. Choie, T.H. Barnes, and W.J. Sandle et al, “Observation of a thermal phase grating contribution to diffraction in erythrosine doped gelatin films,” Opt. Commun. 186, 43 (2000).
[Crossref]

Schiebler, J. D.

A. W. Broerman, D.C. Venerus, and J. D. Schiebler, “Evidence of the stress thermal rule in an elastomer subjected to simple elongation,” J. Chem. Phys. 11, 6955 (1999).

Soskin, S.

A. Bosh, M. Brodin, N. Orchair, S. Odulov, and S. Soskin, Soviet Physics, JEPT Lett.18, 397 (1973).

Sun, H.

J. Liang, H. Sun, and Y. Hu et.al, “The observation of lasing wavelength shift from the reflection center of an Ytterbium doped fiber grating laser,” Opt. Commun. 216, 173 (2003).
[Crossref]

Venerus, D.C.

A. W. Broerman, D.C. Venerus, and J. D. Schiebler, “Evidence of the stress thermal rule in an elastomer subjected to simple elongation,” J. Chem. Phys. 11, 6955 (1999).

J. Appl. Spectr. (1)

A. A. Afanas’ev et al. “Effect of a thermal lattice on the generated line width of a dye laser with distributed feedback,” J. Appl. Spectr. 37, 899 (1982)
[Crossref]

J. Chem. Phys. (1)

A. W. Broerman, D.C. Venerus, and J. D. Schiebler, “Evidence of the stress thermal rule in an elastomer subjected to simple elongation,” J. Chem. Phys. 11, 6955 (1999).

Opt. Commun. (2)

R. Y. Choie, T.H. Barnes, and W.J. Sandle et al, “Observation of a thermal phase grating contribution to diffraction in erythrosine doped gelatin films,” Opt. Commun. 186, 43 (2000).
[Crossref]

J. Liang, H. Sun, and Y. Hu et.al, “The observation of lasing wavelength shift from the reflection center of an Ytterbium doped fiber grating laser,” Opt. Commun. 216, 173 (2003).
[Crossref]

Optic. Commun. (1)

Zs. Bor, A. Muller, and B. Racz, “UV and blue ps pulse generation by a N-laser pumped DFDL,” Optic. Commun. 40, 294 (1982).
[Crossref]

Other (8)

M. Fogiel, ‘Handbook of Mathematical Scientific and Engineering Formulas, Tables, Functions, Graphs and Transforms,’ TEA New York, 304, 7 (1986).

A. Penzkofer and W. Falkenstein et al, Chem. Phys. Lett, 44, 82 (1976).
[Crossref]

D.Y. Key, ‘The scattering of light from light induced structures in liquids,’ Ph.D. Thesis, London University, (1977).

P.Y. Key and R.G. Harrison, IEEE. J. Quant. Electron.QE-6, 645 (1970).

Laser induced dynamic gratings, edited by H.J Eichler, P. Gunter, and D.W. Pohl, Springer Verlag Series on Opt. Sciences, 50, 17 (1986).

A. Bosh, M. Brodin, N. Orchair, S. Odulov, and S. Soskin, Soviet Physics, JEPT Lett.18, 397 (1973).

H. J. Eichler, Ch. Hartig, and J. Knof, Phys Status Solidi (a)45, 433, 1978.
[Crossref]

V. Yu. Kurstak and S. S. Anufrick “Influence of thermal phase lattice on ultrashort pulses characteristics generated by DFDL”, LFNM, Kharkiv, Ukraine, 3–5 (2002).

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Figures (4)

Fig.1.
Fig.1.

Intensity profile of modelocked laser pump and the DFDL output.

Fig. 2.
Fig. 2.

Impact of pump laser pulse train profile on DFDL output profiles.

Fig.3.
Fig.3.

Experimental layout of Nd:YAG laser pumped DFDL.

Fig.4.
Fig.4.

Microdensitometer scanned streak record of Q-switched and modelocked Nd:YAG laser and corresponding DFDL output together with simulated output from the model.

Equations (37)

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T t = . [ D th ( T ) T ] + α I ( r , t ) QC
T t = D th 2 T + α I ( r , t ) QC
D th = s QC p
I = I av + 2 Δ I cos qx ,
Δ T t + D th q 2 Δ T = 2 α Δ I QC ,
T av t D th 2 T = α I av QC .
τ q 1 D th q 2 ,
τ w w 2 8 D th ,
Δ T = Δ T st ( 1 e t τ q ) , t < t p where
Δ T = 2 α Δ I s q 2
Δ T = Δ T ( t p ) e ( t t p ) τ q , t t p .
Δ T p = ( 2 α Δ I t p QC ) e t τ q .
Δ T ( Ω ) = Δ T st ( 1 + Ω 2 τ q 2 ) 1 2 .
T av ( x , t ) = [ α I av ( x ) QC ] · t , t t p .
T ( x , t ) ( 1 4 π D th t ) exp ( x 2 4 D th t ) .
w th 2 2 = 4 D th t
T ( 0 , t ) 1 4 π D th t .
T av ( x , t ) = [ T 0 ( τ w t + τ w t p ) ] · exp [ ( 2 x w ) 2 ( τ w t + τ w t p ) 2 ] for t > t p .
T = T ( x , t ) · g ( z , t )
( n a ) n = n 1 ( 1 r n ) ( 1 r )
( n a ) n = n o ( 1 r n ) 2 π ( 1 r ) z 1 z 2 e [ ( z z od ) 2 z a ] dz
( n a ) n lim n = n o 2 π ( 1 r ) z 1 z 2 ( Fringe amplitude distribution ) dz
( n a ) n = k = 1 n n 1 ( n k + 1 ) r ( k 1 )
( n o ) n = n op 2 π k = 1 n e [ ( t k t op ) 2 ta ]
( n a ) n = ( n o ) k r ( k 1 ) 2 π ( k = 1 n e [ ( t k t op ) 2 ta ] ) z 1 z 2 e [ ( z z op ) 2 z b ] dz
( n a ) n = r ( k 1 ) ( n o ) k k = 1 n ( The envelope profile ) z 1 z 2 ( Temp fringe profile ) dz
( n a ) n = ( n 1 ) 1 ( 1 r n ) ( 1 r ) + r ( n o ) x [ 1 nr ( n 1 ) + ( n 1 ) r ( n 1 ) ( 1 r ) 2
( n o ) x = ( n op ) k 2 π k = 1 n e [ ( t k t oe ) 2 ta ] z 1 z 2 e [ ( z z op ) 2 z b ] dz
( n a ) k = n o ( 1 r n ) 2 π ( 1 r ) z 1 z 2 e ( z y 2 z b ) dz
+ ( n op ) k r [ 1 nr ( n 1 ) + ( n 1 ) r ( n 1 ) ] 2 π ( 1 r ) 2 k = 1 n e ( t x 2 ta ) z 1 z 2 e ( z y 2 z b ) dz
n 1 = n o exp ( ( t τ q ) )
n 1 = ( n o ) m exp ( ( t t o ) 2 2 )
n 1 = n o exp ( 2 L c c τ q )
τ q = 2 L c c ln ( r )
r = 0.2498 x 10 0.033 τ D
τ q = 2 L c c ( ln ( 0.2498 x 10 0.033 τ D ) )
τ q = c p ρ K t K ¯ 2

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