Abstract

Equations and tables are provided for designing high reflectors with reduced peak electric field intensity. This approach should enhance the laser damage threshold for reflectors in which the damage is correlated with peak electric field intensity in one of the two coating materials.

© 1977 Optical Society of America

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References

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  1. J. H. Apfel, J. S. Matteucci, B. E. Newnam, D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 301.
  2. B. E. Newnam, Damage Resistance of Dielectric Reflectors for Picosecond Pulses (U.S. Government Printing Office, Washington D.C., 1974), NBS Special Publication 414, p. 39.
  3. A. L. Bloom, V. R. Costich, Design for High Power Resistance, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 435, p. 248.
  4. D. Milam, Can a Model Which Describes Gas Breakdown Also Describe Laser Damage to the Bulk and Surfaces of Solid Dielectrics, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 350.
  5. J. R. Bettis, R. A. House, A. H. Guenther, Spot Size and Pulse Duration Dependence of Laser-Induced Damage, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 338.
  6. B. E. Newnam, D. H. Gill, J. Opt. Soc. Am. 66, 166 (1976).
  7. P. H. Berning, in Physics of Thin Films, G. Haas, Ed. (Academic, New York, 1963), Vol. 1, pp. 69–121.
  8. J. H. Apfel, Appl. Opt. 15, 2339 (1976).
    [CrossRef] [PubMed]
  9. J. H. Apfel, Appl. Opt. 11, 1303 (1972).
    [CrossRef] [PubMed]

1976 (2)

B. E. Newnam, D. H. Gill, J. Opt. Soc. Am. 66, 166 (1976).

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

1972 (1)

Apfel, J. H.

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

J. H. Apfel, Appl. Opt. 11, 1303 (1972).
[CrossRef] [PubMed]

J. H. Apfel, J. S. Matteucci, B. E. Newnam, D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 301.

Berning, P. H.

P. H. Berning, in Physics of Thin Films, G. Haas, Ed. (Academic, New York, 1963), Vol. 1, pp. 69–121.

Bettis, J. R.

J. R. Bettis, R. A. House, A. H. Guenther, Spot Size and Pulse Duration Dependence of Laser-Induced Damage, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 338.

Bloom, A. L.

A. L. Bloom, V. R. Costich, Design for High Power Resistance, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 435, p. 248.

Costich, V. R.

A. L. Bloom, V. R. Costich, Design for High Power Resistance, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 435, p. 248.

Gill, D. H.

B. E. Newnam, D. H. Gill, J. Opt. Soc. Am. 66, 166 (1976).

J. H. Apfel, J. S. Matteucci, B. E. Newnam, D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 301.

Guenther, A. H.

J. R. Bettis, R. A. House, A. H. Guenther, Spot Size and Pulse Duration Dependence of Laser-Induced Damage, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 338.

House, R. A.

J. R. Bettis, R. A. House, A. H. Guenther, Spot Size and Pulse Duration Dependence of Laser-Induced Damage, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 338.

Matteucci, J. S.

J. H. Apfel, J. S. Matteucci, B. E. Newnam, D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 301.

Milam, D.

D. Milam, Can a Model Which Describes Gas Breakdown Also Describe Laser Damage to the Bulk and Surfaces of Solid Dielectrics, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 350.

Newnam, B. E.

B. E. Newnam, D. H. Gill, J. Opt. Soc. Am. 66, 166 (1976).

B. E. Newnam, Damage Resistance of Dielectric Reflectors for Picosecond Pulses (U.S. Government Printing Office, Washington D.C., 1974), NBS Special Publication 414, p. 39.

J. H. Apfel, J. S. Matteucci, B. E. Newnam, D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 301.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

B. E. Newnam, D. H. Gill, J. Opt. Soc. Am. 66, 166 (1976).

Other (6)

P. H. Berning, in Physics of Thin Films, G. Haas, Ed. (Academic, New York, 1963), Vol. 1, pp. 69–121.

J. H. Apfel, J. S. Matteucci, B. E. Newnam, D. H. Gill, The Role of Electric Field Strength in Laser Damage of Dielectric Multilayers, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 301.

B. E. Newnam, Damage Resistance of Dielectric Reflectors for Picosecond Pulses (U.S. Government Printing Office, Washington D.C., 1974), NBS Special Publication 414, p. 39.

A. L. Bloom, V. R. Costich, Design for High Power Resistance, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 435, p. 248.

D. Milam, Can a Model Which Describes Gas Breakdown Also Describe Laser Damage to the Bulk and Surfaces of Solid Dielectrics, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 350.

J. R. Bettis, R. A. House, A. H. Guenther, Spot Size and Pulse Duration Dependence of Laser-Induced Damage, (U.S. Government Printing Office, Washington, D.C., 1976), NBS Special Publication 462, p. 338.

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Figures (8)

Fig. 1
Fig. 1

The time averaged square of the electric field in a thirteen-layer quarterwave stack (Table I) as a function of distance measured normal to the surface of the layers for radiation incident from the left. The high index layers are indicated by cross-hatch shading.

Fig. 2
Fig. 2

Electric field intensity profile of a fifteen-layer reflector (Table II) in which the peak value in the high index material is lower than for a conventional quarterwave stack reflector.

Fig. 3
Fig. 3

The recursion formula for the tangential component of the electric field strength at the interfaces of a multilayer for radiation incident from the left.

Fig. 4
Fig. 4

Definition of terms used in Eq. (2).

Fig. 5
Fig. 5

Electric field intensity profile of a twenty-one layer reflector (Table III) in which the peak value is the same for the first five high index layers as seen by radiation incident from the left.

Fig. 6
Fig. 6

The optical thickness of the low index layer as a function of the reflectance amplitude of the multilayer before addition of the modifying pair. Curves are presented for various ratios of the high to low index coating materials.

Fig. 7
Fig. 7

The optical thickness of the high index layer as a function of the reflectance amplitude of the multilayer before addition of the modifying pair. Curves are presented for various ratios of the high to low index materials.

Fig. 8
Fig. 8

Circle diagram of the complex reflectance amplitude for an eleven-layer reflector with four modifying pairs of layers. The reflectance vector extends from the origin (+) to the curve starting with the uncoated substrate (S) and follows through successive high (H) and low (L) index layers to the final position on the negative real axis. The intersections between the layers of the four modifying pairs fall on the circle of constant admittance passing through point P on the real axis.

Tables (3)

Tables Icon

Table I Design of Thirteen-Layer QW Stack (Fig. 1)a

Tables Icon

Table II Design of Fifteen Layer-Modified Stack (Fig. 2)a

Tables Icon

Table III Design of Twenty-one-Layer Modified Stack (Fig. 5)a

Equations (14)

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E j / E j - 1 = [ 1 + r exp ( i 2 ϕ ) ] / ( 1 + r ) exp ( i ϕ ) ,
| 1 + r exp ( - 2 i θ ) ( 1 + r ) exp ( - i θ ) | 2 = | ( 1 - f r ) + ( r - f ) exp ( 2 i ϕ ) ( 1 - f r + r - f ) exp ( i ϕ ) | 2 ,
( n 1 - n 2 ) / ( n 1 + n 2 ) = ( 1 - n ) / ( 1 + n ) ,
cos 2 θ = f ( 1 - r ) 2 + ( 1 - f r ) ( r - f ) cos 2 ϕ r ( 1 - f ) 2 .
r exp ( - i 2 θ ) = u + i v ,
tan 2 ϕ = v ( 1 - f 2 ) u ( 1 + f 2 ) - f ( 1 + u 2 + v 2 ) ,
r = - B + S G N ( v ) ( B 2 - 4 A C ) 1 / 2 2 A ,
cos 2 θ = ( n 2 - 2 ) / n 2 ,
tan 2 ϕ = - 2 n ( n 2 - 1 ) 1 / 2 .
E j / E j - 1 = 2 exp ( - i ϕ ) / [ ( 1 + Y j / n j ) + ( 1 - Y j / n j ) exp ( - 2 i ϕ ) ] .
E j - 1 / E j 2 = E j + 1 / E j 2 .
Re ( Y j - 1 ) = Re ( Y j + 1 )
Re ( Y j - 1 ) = 2 Y j / { [ 1 + ( Y j / n j ) 2 ] + [ 1 - ( Y j / n j ) 2 ] cos 2 θ } ,
Re ( Y j + 1 ) = 2 Y j / { [ 1 + ( Y j / n j + 1 ) 2 ] + [ 1 - ( Y j / n j + 1 ) 2 ] cos 2 ϕ } .

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