Abstract

The characteristic matrix method is used to compute the electric field distribution in a multilayer. The use of optically inhomogeneous films is suggested to lessen discontinuity in the material properties and in the absorption distribution at interfaces between the high-index and the low-index layers, thereby enhancing the laser damage threshold.

© 1980 Optical Society of America

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References

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  1. B. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing-Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U. S. Spec. Publ. 435 (1975), p. 254.
  2. J. H. Apfel, J. S. Mateucci, B. E. Newnam, D. H. Gill, “The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers,” Nat. Bur. Stand. U.S. Spec. Publ. 462 (1976), p. 301.
  3. J. H. Apfel, Appl. Opt. 16, 1880 (1977).
    [CrossRef] [PubMed]
  4. D. H. Gill, B. E. Newnam, J. McLeod, “Use of Nonquarter-wave Designs to Increase the Damage Resistance of Reflectors at 532 and 1064 nanometer,” at NBS Ninth Symposium on Materials for High Power Lasers, Boulder, Colo., October 1977.
  5. A. L. Bloom, V. R. Costich, “Design for High Power Resistance,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976), p. 248.
  6. J. R. Bettis, A. H. Guenther, R. A. House, Opt. Lett. 4, 8 (1979).
    [CrossRef]
  7. B. E. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976).
  8. J. H. Apfel, Appl. Opt. 15, 2339 (1976).
    [CrossRef] [PubMed]
  9. R. Jacobsson, “Light Reflection from Films of Continuously Varying Refractive Index,” in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1966), Vol. 5.
    [CrossRef]
  10. F. Abelés, “Optics of Thin Films,” in Advanced Optical Techniques, A. C. S. Van Heel, Ed. (North-Holland, Amsterdam, 1967).
  11. R. R. Austin, R. Michaud, A. Guenther, J. Putman, Appl. Opt. 12, 665 (1973).
    [CrossRef] [PubMed]
  12. O. Arnon, Appl. Opt. 16, 2147 (1977).
    [CrossRef] [PubMed]
  13. V. V. Veremei, I. M. Minkov, Opt. Spectrosc. 33, 640 (1972).
  14. W. Hansen, J. Opt. Soc. Am. 58, 380 (1968).
    [CrossRef]

1979 (1)

J. R. Bettis, A. H. Guenther, R. A. House, Opt. Lett. 4, 8 (1979).
[CrossRef]

1977 (2)

1976 (4)

A. L. Bloom, V. R. Costich, “Design for High Power Resistance,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976), p. 248.

B. E. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976).

J. H. Apfel, J. S. Mateucci, B. E. Newnam, D. H. Gill, “The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers,” Nat. Bur. Stand. U.S. Spec. Publ. 462 (1976), p. 301.

J. H. Apfel, Appl. Opt. 15, 2339 (1976).
[CrossRef] [PubMed]

1975 (1)

B. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing-Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U. S. Spec. Publ. 435 (1975), p. 254.

1973 (1)

1972 (1)

V. V. Veremei, I. M. Minkov, Opt. Spectrosc. 33, 640 (1972).

1968 (1)

Abelés, F.

F. Abelés, “Optics of Thin Films,” in Advanced Optical Techniques, A. C. S. Van Heel, Ed. (North-Holland, Amsterdam, 1967).

Apfel, J. H.

J. H. Apfel, Appl. Opt. 16, 1880 (1977).
[CrossRef] [PubMed]

J. H. Apfel, Appl. Opt. 15, 2339 (1976).
[CrossRef] [PubMed]

J. H. Apfel, J. S. Mateucci, B. E. Newnam, D. H. Gill, “The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers,” Nat. Bur. Stand. U.S. Spec. Publ. 462 (1976), p. 301.

Arnon, O.

Austin, R. R.

Bettis, J. R.

J. R. Bettis, A. H. Guenther, R. A. House, Opt. Lett. 4, 8 (1979).
[CrossRef]

Bloom, A. L.

A. L. Bloom, V. R. Costich, “Design for High Power Resistance,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976), p. 248.

Costich, V. R.

A. L. Bloom, V. R. Costich, “Design for High Power Resistance,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976), p. 248.

Faulkner, G.

B. E. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976).

B. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing-Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U. S. Spec. Publ. 435 (1975), p. 254.

Gill, D. H.

J. H. Apfel, J. S. Mateucci, B. E. Newnam, D. H. Gill, “The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers,” Nat. Bur. Stand. U.S. Spec. Publ. 462 (1976), p. 301.

B. E. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976).

B. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing-Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U. S. Spec. Publ. 435 (1975), p. 254.

D. H. Gill, B. E. Newnam, J. McLeod, “Use of Nonquarter-wave Designs to Increase the Damage Resistance of Reflectors at 532 and 1064 nanometer,” at NBS Ninth Symposium on Materials for High Power Lasers, Boulder, Colo., October 1977.

Guenther, A.

Guenther, A. H.

J. R. Bettis, A. H. Guenther, R. A. House, Opt. Lett. 4, 8 (1979).
[CrossRef]

Hansen, W.

House, R. A.

J. R. Bettis, A. H. Guenther, R. A. House, Opt. Lett. 4, 8 (1979).
[CrossRef]

Jacobsson, R.

R. Jacobsson, “Light Reflection from Films of Continuously Varying Refractive Index,” in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1966), Vol. 5.
[CrossRef]

Mateucci, J. S.

J. H. Apfel, J. S. Mateucci, B. E. Newnam, D. H. Gill, “The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers,” Nat. Bur. Stand. U.S. Spec. Publ. 462 (1976), p. 301.

McLeod, J.

D. H. Gill, B. E. Newnam, J. McLeod, “Use of Nonquarter-wave Designs to Increase the Damage Resistance of Reflectors at 532 and 1064 nanometer,” at NBS Ninth Symposium on Materials for High Power Lasers, Boulder, Colo., October 1977.

Michaud, R.

Minkov, I. M.

V. V. Veremei, I. M. Minkov, Opt. Spectrosc. 33, 640 (1972).

Newnam, B.

B. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing-Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U. S. Spec. Publ. 435 (1975), p. 254.

Newnam, B. E.

J. H. Apfel, J. S. Mateucci, B. E. Newnam, D. H. Gill, “The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers,” Nat. Bur. Stand. U.S. Spec. Publ. 462 (1976), p. 301.

B. E. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976).

D. H. Gill, B. E. Newnam, J. McLeod, “Use of Nonquarter-wave Designs to Increase the Damage Resistance of Reflectors at 532 and 1064 nanometer,” at NBS Ninth Symposium on Materials for High Power Lasers, Boulder, Colo., October 1977.

Putman, J.

Veremei, V. V.

V. V. Veremei, I. M. Minkov, Opt. Spectrosc. 33, 640 (1972).

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

Nat. Bur. Stand. U. S. Spec. Publ. 435 (1)

B. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing-Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U. S. Spec. Publ. 435 (1975), p. 254.

Nat. Bur. Stand. U.S. Spec. Publ. 435 (2)

A. L. Bloom, V. R. Costich, “Design for High Power Resistance,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976), p. 248.

B. E. Newnam, D. H. Gill, G. Faulkner, “Influence of Standing Wave Fields on the Laser Damage Resistance of Dielectric Films,” Nat. Bur. Stand. U.S. Spec. Publ. 435 (1976).

Nat. Bur. Stand. U.S. Spec. Publ. 462 (1)

J. H. Apfel, J. S. Mateucci, B. E. Newnam, D. H. Gill, “The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers,” Nat. Bur. Stand. U.S. Spec. Publ. 462 (1976), p. 301.

Opt. Lett. (1)

J. R. Bettis, A. H. Guenther, R. A. House, Opt. Lett. 4, 8 (1979).
[CrossRef]

Opt. Spectrosc. (1)

V. V. Veremei, I. M. Minkov, Opt. Spectrosc. 33, 640 (1972).

Other (3)

D. H. Gill, B. E. Newnam, J. McLeod, “Use of Nonquarter-wave Designs to Increase the Damage Resistance of Reflectors at 532 and 1064 nanometer,” at NBS Ninth Symposium on Materials for High Power Lasers, Boulder, Colo., October 1977.

R. Jacobsson, “Light Reflection from Films of Continuously Varying Refractive Index,” in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1966), Vol. 5.
[CrossRef]

F. Abelés, “Optics of Thin Films,” in Advanced Optical Techniques, A. C. S. Van Heel, Ed. (North-Holland, Amsterdam, 1967).

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Figures (2)

Fig. 1
Fig. 1

Computed relative distribution of n|E|2 at λ0 in quarterwave dielectric stack of Ta2O5/SiO2 (nH = 2.10; nL = 1.46). Square wave index profile (bottom curve) is also shown.

Fig. 2
Fig. 2

Caption to Fig. 1 obtains, but two layers of inhomogeneous refractive index are added to top of stack. Index profile is shown in bottom figure. In computations, each inhomogeneous layer is simulated by ten homogeneous sublayers. Refractive index increases linearly from n = 1.46 to 2.10 from interior to exterior of stack.

Equations (15)

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

N = | E ( z ) | 2 | E 0 + | 2 ,
M i = [ cos β i j q i 1 sin β i j q i sin β i cos β i ] ,
β i = 2 π λ 1 cos θ i n i h i ,
q i = n i
q i = n i cos θ i
q i = n i sec θ i
M = Π i = 1 l M i = [ m 11 j m 12 j m 21 m 22 ]
E 0 + + E 0 = [ m 11 + j m 12 q s ] E s + ,
E 0 + E 0 = [ j m 21 / q 0 + m 22 q s / q 0 ] E s + ,
| E 0 + | 2 = 0.25 [ ( m 11 + m 22 q s / q 0 ) 2 + ( m 21 / q 0 + m 12 q s ) 2 ] | E s | 2 ,
[ m 11 j m 12 j m 21 m 22 ] = [ cos Δ β ( j sin Δ β ) / q 1 j q 1 sin Δ β cos Δ β ] ,
Δ β = Δ h cos θ 1 2 π n 1 / λ .
[ m 11 j m 12 j m 21 m 22 ] × [ m 11 j m 12 j m 21 m 22 ] = [ m 11 j m 12 j m 21 m 22 ] .
| E | 2 = [ ( m 11 ) 2 + ( q s m 12 ) 2 ] | E s | 2 .
[ sec θ i sec θ o ] 2

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