Abstract

Recent developments of laser materials have advanced the state of the art to a point where the optical quality of many of these materials is approaching the diffraction limit. Using such components in a laser does not necessarily guarantee the generation of diffraction-limited laser beams. One of the severe problems is thermal distortion introduced in the optical cavity by the flash lamps. Ruby and glass lasers require a minimum of 0.6 J of heat deposition per joule of population inversion. Typical figures are 4–6 J per joule of population inversion.1 Nonuniformities in the deposition of this heat cause optical distortions which virtually preclude diffraction-limited laser operation even if the materials themselves are of diffraction-limited optical quality. This paper will investigate these thermal effects in detail, and the relative sensitivity of a variety of materials to nonuniform energy depositions will be discussed. Water close to its point of maximum density and a certain special type of glass known as Pockels glass will be shown to have properties of particular interest for use in diffraction-limited lasers.

© 1966 Optical Society of America

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References

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  1. E. Dixon, American Optical Company, and J. Boyden, Korad (private communication).
  2. G. Morey, Properties of Glass (Reinhold Publishing Co., York, 1954).
  3. H. Hovestadt, Jena Glass (The MacMillan Co., New York, 1902).
  4. F. E. Neumann, Ann. Physik 54, 449 (1841).
    [CrossRef]
  5. B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (John Wiley & Sons, Inc., New York, 1960).
  6. E. Snitzer (private communication).
  7. Owens-Illinois Glass Company (private communication).
  8. F. Pockels, Ann. Phys., 7, 745, 202 (1902); Ann. Phys. 11, 651 (1903).
    [CrossRef]
  9. F. Molby, J. Opt. Soc. Am. 39, 600 (1949).
    [CrossRef]
  10. L. Filon, Proc. Roy. Soc. (London), A89, 587 (1913); L. Filon, F. Harris, ibid., A106, 718 (1924).
  11. L. Filon, H. Jessop, Proc. Roy. Soc. (London), A101, 165 (1922). H. Jessop, Trans. Roy. Soc. (London) A223, 89 (1922).
  12. D. Gray, ed. American Institute of Physics Handbook (McGraw–Hill Book Co., Inc., New York. 1963), 2nd ed.

1949 (1)

1922 (1)

L. Filon, H. Jessop, Proc. Roy. Soc. (London), A101, 165 (1922). H. Jessop, Trans. Roy. Soc. (London) A223, 89 (1922).

1913 (1)

L. Filon, Proc. Roy. Soc. (London), A89, 587 (1913); L. Filon, F. Harris, ibid., A106, 718 (1924).

1902 (1)

F. Pockels, Ann. Phys., 7, 745, 202 (1902); Ann. Phys. 11, 651 (1903).
[CrossRef]

1841 (1)

F. E. Neumann, Ann. Physik 54, 449 (1841).
[CrossRef]

Boley, B. A.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (John Wiley & Sons, Inc., New York, 1960).

Boyden, J.

E. Dixon, American Optical Company, and J. Boyden, Korad (private communication).

Dixon, E.

E. Dixon, American Optical Company, and J. Boyden, Korad (private communication).

Filon, L.

L. Filon, H. Jessop, Proc. Roy. Soc. (London), A101, 165 (1922). H. Jessop, Trans. Roy. Soc. (London) A223, 89 (1922).

L. Filon, Proc. Roy. Soc. (London), A89, 587 (1913); L. Filon, F. Harris, ibid., A106, 718 (1924).

Hovestadt, H.

H. Hovestadt, Jena Glass (The MacMillan Co., New York, 1902).

Jessop, H.

L. Filon, H. Jessop, Proc. Roy. Soc. (London), A101, 165 (1922). H. Jessop, Trans. Roy. Soc. (London) A223, 89 (1922).

Molby, F.

Morey, G.

G. Morey, Properties of Glass (Reinhold Publishing Co., York, 1954).

Neumann, F. E.

F. E. Neumann, Ann. Physik 54, 449 (1841).
[CrossRef]

Pockels, F.

F. Pockels, Ann. Phys., 7, 745, 202 (1902); Ann. Phys. 11, 651 (1903).
[CrossRef]

Snitzer, E.

E. Snitzer (private communication).

Weiner, J. H.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (John Wiley & Sons, Inc., New York, 1960).

Ann. Phys. (1)

F. Pockels, Ann. Phys., 7, 745, 202 (1902); Ann. Phys. 11, 651 (1903).
[CrossRef]

Ann. Physik (1)

F. E. Neumann, Ann. Physik 54, 449 (1841).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. Roy. Soc. (London) (2)

L. Filon, Proc. Roy. Soc. (London), A89, 587 (1913); L. Filon, F. Harris, ibid., A106, 718 (1924).

L. Filon, H. Jessop, Proc. Roy. Soc. (London), A101, 165 (1922). H. Jessop, Trans. Roy. Soc. (London) A223, 89 (1922).

Other (7)

D. Gray, ed. American Institute of Physics Handbook (McGraw–Hill Book Co., Inc., New York. 1963), 2nd ed.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (John Wiley & Sons, Inc., New York, 1960).

E. Snitzer (private communication).

Owens-Illinois Glass Company (private communication).

E. Dixon, American Optical Company, and J. Boyden, Korad (private communication).

G. Morey, Properties of Glass (Reinhold Publishing Co., York, 1954).

H. Hovestadt, Jena Glass (The MacMillan Co., New York, 1902).

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Figures (1)

Fig. 1
Fig. 1

Schematic of the electric field distribution of the three lowest order modes. The arrows indicate the direction of the electric field in these modes. The strength of the transverse components of the electric field follow a J0 (ur/a) dependence for the HE11 mode and a J1 (ur/a dependence for the TE01 and TM11 modes. The parameter u fixes the scale of the Bessel function so that the first zero of the Bessel function occurs at r = a.

Tables (2)

Tables Icon

Table I Thermal Optical Properties of Gases and Liquids

Tables Icon

Table II Numerical Values of the Coefficients in Eqs.(12) for a Variety of Glasses (The data are for a wavelength of 5890 Å and a temperature of 50°C)

Equations (24)

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Δ P = L ( d n / d T ) Δ T ,
Δ P ( r ) = L ( d n / d T ) Δ T ( r ) .
Δ P = L Δ n + ( n - 1 ) Δ L , = L [ Δ n + ( n - 1 ) ɛ z z ] ,
Δ n = ( n / T ) ɛ = 0 Δ T + ( n ¯ / ɛ ¯ ) T Δ ɛ ¯ .
V x = V 0 + q ɛ x x + p ɛ y y + p ɛ z z , V y = V 0 + p ɛ x x + q ɛ y y + p ɛ z z , V z = V 0 + p ɛ x x + p ɛ y y + q ɛ z z ,
V r = V 0 + q ɛ r r + p ɛ θ θ + p ɛ z z , V θ = V 0 + p ɛ r r + q ɛ θ θ + p ɛ z z , V z = V 0 + p ɛ r r + p ɛ θ θ + q ɛ z z ,
( n / ɛ ¯ ) Δ ɛ ¯ r = Δ n r = n r - n 0 = ( n r / V 0 ) ( V 0 - V r ) ( - n 0 / V 0 ) [ q ɛ r r + p ( ɛ θ θ + ɛ z z ) ] , ( n / ɛ ¯ ) Δ ɛ ¯ θ = Δ n θ = n θ - n 0 = ( n θ / V 0 ) ( V 0 - V θ ) ( - n 0 / V 0 ) [ q ɛ θ θ + p ( ɛ r r + ɛ z z ) ] .
ɛ r r = ( 1 / E ) [ σ r r - ν ( σ θ θ + σ z z ) ] + α T , ɛ θ θ = ( 1 / E ) [ σ θ θ - ν ( σ r r + σ z z ) ] + α T , ɛ z z = ( 1 / E ) [ σ z z - ν ( σ r r + σ θ θ ) ] + α T .
Δ n r = ( n T ) ɛ = 0 Δ T + n 0 σ r r E [ 2 ν p V 0 - q V 0 ] + n 0 σ θ θ E [ ν q V 0 - ( 1 - ν ) p V 0 ] + n 0 σ z z E [ ν q V 0 - ( 1 - ν ) p V 0 ] - n 0 α Δ T [ 2 p V 0 + q V 0 ] , Δ n θ = ( n T ) ɛ = 0 Δ T + n 0 σ r r E [ ν q V 0 - ( 1 - ν ) p V 0 ] + n 0 σ θ θ E [ 2 ν p V 0 - q V 0 ] + n 0 σ z z E [ ν q V 0 - ( 1 - ν ) p V 0 ] - n 0 α Δ T [ 2 p V 0 + q V 0 ] .
B = n 0 E [ q V 0 - 2 ν p V 0 ]             and             B = n 0 E [ ( 1 - ν ) p V 0 - ν q V 0 ]
Δ P r = L { ( n - 1 ) ɛ z z + [ ( n T ) ɛ = 0 - n 0 α ( 2 p V 0 + q V 0 ) ] Δ T - σ r r B - ( σ θ θ + σ z z ) B } , Δ P θ = L { ( n - 1 ) ɛ z z + [ ( n T ) ɛ = 0 - n 0 α ( 2 p V 0 + q V 0 ) ] Δ T - ( σ r r + σ z z ) B - σ θ θ B } .
[ ( n T ) ɛ = 0 - n 0 α ( 2 p V 0 + q V 0 ) ] Δ T
σ r r ( r ) = α E 1 - ν [ 1 A 2 0 A T ( r ) r d r - 1 r 2 0 r T ( r ) r d r ] , σ θ θ ( r ) = α E 1 - ν [ 1 A 2 0 A T ( r ) r d r + 1 r 2 0 r T ( r ) r d r - T ( r ) ] , σ z z ( r ) = α E 1 - ν [ 2 A 2 0 A T ( r ) r d r - T ( r ) ] , ɛ z z ( r ) = constant = 2 α A 2 0 A T ( r ) r d r .
Δ P r ( r ) = L { [ n α n + α E 1 - ν ( 2 B ) ] T ( r ) + α E 1 - ν ( B - B ) 1 r 2 0 r T ( r ) r d r + [ 2 α ( n - 1 ) - α E 1 - ν ( 3 B + B ) ] 1 A 2 0 A T ( r ) r d r } , Δ P θ ( r ) = L { [ n α n + α E 1 - ν ( B + B ) ] T ( r ) + α E 1 - ν ( B - B ) 1 r 2 0 r T ( r ) r d r + [ 2 α ( n - 1 ) - α E 1 - ν ( 3 B + B ) ] 1 A 2 0 A T ( r ) r d r } .
Δ P r ( r ) - Δ P θ ( r ) = α E 1 - ν ( B - B ) { T ( r ) - 2 r 2 0 r T ( r ) r d r } .
Δ P ( r ) = L { [ n α n + 2 α E 1 - ν B ] T ( r ) + [ 2 α ( n - 1 ) - α E 1 - ν 4 B ] 1 A 2 0 A T ( r ) r d r } .
{ n α n + [ 2 α E / ( 1 - ν ) ] B } = 0 ;
[ n α n + 2 α E 1 - ν B ] 1.0 × 10 - 5
Δ T ( r ) = Q ( r ) / ( L ρ q ) ,
Δ P ( r 1 ) - Δ P ( r 2 ) = λ = L d n d T [ Δ T ( r 1 ) - Δ T ( r 2 ) ] = L d n d T Q ( r 1 ) - Q ( r 2 ) L ρ q = d n d T Δ Q ρ q ;
Δ Q = λ ρ q ( d n / d T ) .
d n d T | λ = 5890 Å ,
Δ Q = λ ρ q / [ n α n + 2 α E 1 - ν B ] ,
n α n + [ 2 α E / ( 1 - ν ) ] B

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