Abstract

The passage of a high-power laser pulse through a material window can result in optical distortion that significantly reduces the far-field irradiance. Optical distortion due to pulses having durations on the order of the acoustic wave propagation time through the thickness of the window is a result of heating by the absorbed laser energy and thermally induced plane-strain stress waves. For a given laser pulse duration and axially symmetric irradiance distribution, expressions are derived for the evolution of the window’s aberation function. It is shown that, in this pulse regime, there is no stress induced birefringence and the evolution of the beam profile is such that the Gaussian focus always propagates towards the window aperture. Expressions are derived for the threshold for fracturing. It is shown that in the case of KBr fracturing occurs before lensing whereas for CdTe, Ge, and TI-1173 glass, lensing occurs before fracturing.

© 1974 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Sparks, J. Appl. Phys. 42, 5029 (1971).
    [CrossRef]
  2. F. A. Horrigan, T. F. Deutch, QPR No. 3 Contract DAAH01-70-C-1251, Raytheon Corporation (1970).
  3. F. A. Horrigan, Conference on High Power Infrared Laser Window Materials, AFCLL-71-0592 (1971).
  4. B. Bendow, P. D. Gianino, Appl. Opt. 12, 710 (1973).
    [CrossRef] [PubMed]
  5. J. Marburger, M. Flannery, Conference of High Power Infrared Laser Window Materials, AFCRL-71-0592, p. 11 (1971).
  6. D. A. Holmes, J. E. Korka, P. Avizonis, Appl. Opt. 11, 565 (1972).
    [CrossRef] [PubMed]
  7. J. R. Jasperse, P. D. Gianino, J. Appl. Phys. 43, 1686 (1972).
    [CrossRef]
  8. J. D. O’Keefe, R. L. Johnson, D. A. Evensen, Conference on High Power Infrared Laser Window Materials, AFC-TR-73-0372(1), 19June1973.
  9. M. Born, E. Wolf, Principles of Optics (Interscience Publishers, New York, 1964), Chap. 9.
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  11. L. N. Morland, AIAA J. 6, 1063 (1968).
    [CrossRef]
  12. B. Bendow, J. R. Jasperse, P. D. Gianino, Opt. Commun. 5, 98 (1972).
    [CrossRef]

1973 (1)

1972 (3)

J. R. Jasperse, P. D. Gianino, J. Appl. Phys. 43, 1686 (1972).
[CrossRef]

B. Bendow, J. R. Jasperse, P. D. Gianino, Opt. Commun. 5, 98 (1972).
[CrossRef]

D. A. Holmes, J. E. Korka, P. Avizonis, Appl. Opt. 11, 565 (1972).
[CrossRef] [PubMed]

1971 (1)

M. Sparks, J. Appl. Phys. 42, 5029 (1971).
[CrossRef]

1968 (1)

L. N. Morland, AIAA J. 6, 1063 (1968).
[CrossRef]

Avizonis, P.

Bendow, B.

B. Bendow, P. D. Gianino, Appl. Opt. 12, 710 (1973).
[CrossRef] [PubMed]

B. Bendow, J. R. Jasperse, P. D. Gianino, Opt. Commun. 5, 98 (1972).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Interscience Publishers, New York, 1964), Chap. 9.

Deutch, T. F.

F. A. Horrigan, T. F. Deutch, QPR No. 3 Contract DAAH01-70-C-1251, Raytheon Corporation (1970).

Evensen, D. A.

J. D. O’Keefe, R. L. Johnson, D. A. Evensen, Conference on High Power Infrared Laser Window Materials, AFC-TR-73-0372(1), 19June1973.

Flannery, M.

J. Marburger, M. Flannery, Conference of High Power Infrared Laser Window Materials, AFCRL-71-0592, p. 11 (1971).

Gianino, P. D.

B. Bendow, P. D. Gianino, Appl. Opt. 12, 710 (1973).
[CrossRef] [PubMed]

J. R. Jasperse, P. D. Gianino, J. Appl. Phys. 43, 1686 (1972).
[CrossRef]

B. Bendow, J. R. Jasperse, P. D. Gianino, Opt. Commun. 5, 98 (1972).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Holmes, D. A.

Horrigan, F. A.

F. A. Horrigan, T. F. Deutch, QPR No. 3 Contract DAAH01-70-C-1251, Raytheon Corporation (1970).

F. A. Horrigan, Conference on High Power Infrared Laser Window Materials, AFCLL-71-0592 (1971).

Jasperse, J. R.

B. Bendow, J. R. Jasperse, P. D. Gianino, Opt. Commun. 5, 98 (1972).
[CrossRef]

J. R. Jasperse, P. D. Gianino, J. Appl. Phys. 43, 1686 (1972).
[CrossRef]

Johnson, R. L.

J. D. O’Keefe, R. L. Johnson, D. A. Evensen, Conference on High Power Infrared Laser Window Materials, AFC-TR-73-0372(1), 19June1973.

Korka, J. E.

Marburger, J.

J. Marburger, M. Flannery, Conference of High Power Infrared Laser Window Materials, AFCRL-71-0592, p. 11 (1971).

Morland, L. N.

L. N. Morland, AIAA J. 6, 1063 (1968).
[CrossRef]

O’Keefe, J. D.

J. D. O’Keefe, R. L. Johnson, D. A. Evensen, Conference on High Power Infrared Laser Window Materials, AFC-TR-73-0372(1), 19June1973.

Sparks, M.

M. Sparks, J. Appl. Phys. 42, 5029 (1971).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Interscience Publishers, New York, 1964), Chap. 9.

AIAA J. (1)

L. N. Morland, AIAA J. 6, 1063 (1968).
[CrossRef]

Appl. Opt. (2)

J. Appl. Phys. (2)

M. Sparks, J. Appl. Phys. 42, 5029 (1971).
[CrossRef]

J. R. Jasperse, P. D. Gianino, J. Appl. Phys. 43, 1686 (1972).
[CrossRef]

Opt. Commun. (1)

B. Bendow, J. R. Jasperse, P. D. Gianino, Opt. Commun. 5, 98 (1972).
[CrossRef]

Other (6)

J. Marburger, M. Flannery, Conference of High Power Infrared Laser Window Materials, AFCRL-71-0592, p. 11 (1971).

F. A. Horrigan, T. F. Deutch, QPR No. 3 Contract DAAH01-70-C-1251, Raytheon Corporation (1970).

F. A. Horrigan, Conference on High Power Infrared Laser Window Materials, AFCLL-71-0592 (1971).

J. D. O’Keefe, R. L. Johnson, D. A. Evensen, Conference on High Power Infrared Laser Window Materials, AFC-TR-73-0372(1), 19June1973.

M. Born, E. Wolf, Principles of Optics (Interscience Publishers, New York, 1964), Chap. 9.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Cross-section schematic of the response of a circular laser window to an ultrashort laser pulse.

Fig. 2
Fig. 2

Aberration function/irradiance and various components of the aberration function as a function of nondimensional time in the ultrashort pulse regime. Thickness h = 1.0 cm. Wavelength is 10.6 μm. Window material is Ge.

Fig. 3
Fig. 3

Aberration function/irradiance and various components of the aberration function as a function of nondimensional time in the ultrashort pulse regime. Thickness h = 1.0 cm. Wavelength is 10.6 νm. Window material is KBr.

Fig. 4
Fig. 4

The on-axis normalized intensity as a function of normalized range. The intensity at the window aperture is Gaussian [exp(−2μ2ρ2)], with μ2 = 0.5 (Ref 4).

Fig. 5
Fig. 5

The on-axis normalized intensity as a function of normalized range. The intensity at the window aperture is Gaussian [exp(−2μ2ρ2)], with μ2 = 3.0 (Ref. 4).

Fig. 6
Fig. 6

Aberration function as a function of irradiance for various window materials. The termination of the curves indicates fracturing of the window.

Fig. 7
Fig. 7

Evolution of the through-the-thickness stress wave. The nondimensional time increment between wave profiles, Δηz, is equal to 1.0; the nondimensional thickness, h, is equal to 10; and the nondimensional laser pulse duration time, ηd, is equal to 1.0.

Fig. 8
Fig. 8

Evolution of the through-the-thickness stress wave. The nondimensional time increment between wave profiles, Δηz, is equal to 1.0; the nondimensional thickness, h, is equal to 10; and the nondimensional laser pulse duration time, ηd, is equal to 4.0.

Equations (26)

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

T ( ρ , z , t ) = T m ( ρ ) t d e - β z [ t U ( t ) - ( t - t d ) U ( t - t d ) ] ,
2 σ z 2 z - 1 C 0 2 2 σ z t 2 = 3 α E C 0 2 T m exp ( - β z ) [ 2 t d δ ( t ) + t t d δ ( t ) t - 2 t d δ ( t - t d ) - 1 t d ( t - t d ) δ t ( t - t d ) ] ,
z z = 1 ρ C 0 2 σ z + 3 α E ρ C 0 2 T .
z z = 3 K T m ( ρ ) ρ C 0 2 ( t t d - z C 0 t d ) U ( z - C 0 t )
w = z = 0 C 0 t z z d z .
n γ = n 0 + ( n T ) T - 1 2 n 0 3 P 12 z z ,
ψ γ = 2 k z = 0 h / 2 ( n - 1 ) d z + k h ,
ψ γ = 2 k ( n γ - 1 ) ( h 2 - C 0 t ) + 2 k ( h / 2 - C 0 t ( h + w ) / 2 ( n γ - 1 ) d z + k h .
T m ( ρ ) = β P ( ρ ) t C ,
Φ γ = [ 2 ( n 0 - 1 ) α K β t d 2 2 ρ C 0 C ( t t d ) 2 - n 0 3 P 12 α K β t d 2 2 ρ C 0 C ( t t d ) 2 + h ( n T ) β t d C ( t t d ) ] P ( ρ )
Φ γ = D ( t ) P ( ρ ) .
u k R 2 ( 1 x 0 - 1 x )
P ^ ( x , t ) x 2 x 0 2 P ¯ ( x , t ) P ( ρ , t )
P ( ρ ) = P M e - 2 μ 2 ρ 2
D k [ 2 ( n 0 - 1 ) α K β t d 2 2 ρ C 0 C ( t t d ) 2 - n 0 3 P 12 α K β t d 2 2 ρ C 0 C ( t t d ) 2 + h ( n T ) β t d C ( t t d ) ] P M .
P c = ρ C σ c α K β t d .
t d = h 2 C 0 ,
Φ γ f = ( n 0 - 1 ) - n 0 3 P 12 σ c h ρ C 0 2 + ( n T ) 2 h σ c α K .
z ξ z / α t η / β C 0 , t d η d / β C 0 , σ z α T m E θ z , θ z T / T m .
2 θ z ξ z 2 - 2 θ z η 2 = exp ( - ξ z ) [ 2 η d δ ( η ) + η η d δ ( η ) η - 2 η d δ ( η - η d ) - 1 η d ( η - η d ) δ ( η - η d ) η ] .
d 2 θ ¯ z ξ z 2 - S 2 θ ¯ z = exp ( - ξ z ) ( 1 η d - 1 η d e - S η d ) ,
θ ¯ z ( ξ z , S ) = A e - S ξ z + B e - S ξ z + ( 1 η d - 1 η d e - S η d ) exp ( - ξ z )
θ ¯ z ( 0 , S ) = 0
θ ¯ z ( h , S ) = 0.
θ ¯ z ( ξ z , S ) = - ( 1 η d - 1 η d e - S η d ) ( e S h - e - h e S h - e - S h ) e - S h + ( 1 η d - 1 η d e - S η d ) + ( e - S h - e - h e S h - e - S h ) e + S h + ( 1 η d - 1 η d e - S η d ) e - ξ z
θ z ( ξ z , η ) = 1 η d m = 0 { sinh ( η - ξ z - 2 h m ) U ( η - ξ z - 2 h m ) - e - h sinh [ η - ξ z - 2 h ( m + 1 2 ) ] × U [ η - ξ z - 2 h ( m + 1 2 ) ] + sinh [ η + ξ z - 2 h ( m + 1 ) ] U [ η + ξ z - 2 h ( m + 1 ) ] - e - h sinh [ η + ξ z - 2 h ( m + 1 2 ) ] × U [ η + ξ z - 2 h ( m + 1 2 ) ] - sinh ( η - ξ z - η d - 2 h m ) U ( η - ξ z - η d - 2 h m ) + e - h sinh [ η - ξ z - η d - 2 h ( m + 1 2 ) ] × U [ η - ξ z - η d - 2 h ( m + 1 2 ) ] - sinh [ η + ξ z - η d - 2 h ( m + 1 ) ] × U [ η + ξ z - η d - 2 h ( m + 1 ) ] + e - h sinh [ η + ξ z - η d - 2 h ( m + 1 2 ) ] × U [ η + ξ z - η d - 2 h ( m + 1 2 ) ] } - e - ξ z [ sinh ( η ) U ( η ) - sinh ( η - η d ) U ( η - η d ) ] .

Metrics