Abstract

A new algorithm for the design of multilayer antireflection coatings (ARC) is developed. This makes use of a closed-loop nonlinear approximation technique to arrive at the exact thickness of each layer. The method offers a simpler and faster optimization procedure. It has been successfully used in the design of broadband ARCs on substrates with a wide range of refractive indices. Detailed analysis of the effect of errors in the refractive index and thickness of each layer, individually and collectively on the ultimate performance of the system, is discussed in detail. To minimize the effects of these errors, in situ correction (dynamic correction) procedure at each stage of development of the system is suggested.

© 1983 Optical Society of America

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References

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  1. J. T. Cox, G. Hass, Phys. Thin Films, 2, 239 (1969).
  2. A. Mussett, A. Thelen, Prog. Opt. 8, 203 (1970).
  3. H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969).
  4. H. M. Liddell, Computer Aided Design Techniques for the Design of Multilayer Filters (Adam Hilger, Bristol, 1981).
  5. A. Thetford, Opt. Acta 16, 37 (1969).
    [CrossRef]
  6. J. A. Dobrowolski, Appl. Opt. 20, 74 (1981).
    [CrossRef] [PubMed]
  7. J. A. Dobrowolski, F. Ho, Appl. Opt. 21, 288 (1982).
    [CrossRef] [PubMed]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).
  9. C. L. Nagendra, G. K. M. Thutupalli, Vacuum 31, 137 (1981).
    [CrossRef]
  10. J. Mouchart, Appl. Opt. 16, 2722 (1977).
    [CrossRef] [PubMed]
  11. H. K. Pulker, Appl. Opt. 18, 1969 (1979).
    [CrossRef] [PubMed]
  12. E. Ritter, Phys. Thin Films 8, 1 (1975).

1982

1981

C. L. Nagendra, G. K. M. Thutupalli, Vacuum 31, 137 (1981).
[CrossRef]

J. A. Dobrowolski, Appl. Opt. 20, 74 (1981).
[CrossRef] [PubMed]

1979

1977

1975

E. Ritter, Phys. Thin Films 8, 1 (1975).

1970

A. Mussett, A. Thelen, Prog. Opt. 8, 203 (1970).

1969

A. Thetford, Opt. Acta 16, 37 (1969).
[CrossRef]

J. T. Cox, G. Hass, Phys. Thin Films, 2, 239 (1969).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Cox, J. T.

J. T. Cox, G. Hass, Phys. Thin Films, 2, 239 (1969).

Dobrowolski, J. A.

Hass, G.

J. T. Cox, G. Hass, Phys. Thin Films, 2, 239 (1969).

Ho, F.

Liddell, H. M.

H. M. Liddell, Computer Aided Design Techniques for the Design of Multilayer Filters (Adam Hilger, Bristol, 1981).

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969).

Mouchart, J.

Mussett, A.

A. Mussett, A. Thelen, Prog. Opt. 8, 203 (1970).

Nagendra, C. L.

C. L. Nagendra, G. K. M. Thutupalli, Vacuum 31, 137 (1981).
[CrossRef]

Pulker, H. K.

Ritter, E.

E. Ritter, Phys. Thin Films 8, 1 (1975).

Thelen, A.

A. Mussett, A. Thelen, Prog. Opt. 8, 203 (1970).

Thetford, A.

A. Thetford, Opt. Acta 16, 37 (1969).
[CrossRef]

Thutupalli, G. K. M.

C. L. Nagendra, G. K. M. Thutupalli, Vacuum 31, 137 (1981).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Appl. Opt.

Opt. Acta

A. Thetford, Opt. Acta 16, 37 (1969).
[CrossRef]

Phys. Thin Films

E. Ritter, Phys. Thin Films 8, 1 (1975).

J. T. Cox, G. Hass, Phys. Thin Films, 2, 239 (1969).

Prog. Opt.

A. Mussett, A. Thelen, Prog. Opt. 8, 203 (1970).

Vacuum

C. L. Nagendra, G. K. M. Thutupalli, Vacuum 31, 137 (1981).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969).

H. M. Liddell, Computer Aided Design Techniques for the Design of Multilayer Filters (Adam Hilger, Bristol, 1981).

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Figures (8)

Fig. 1
Fig. 1

Reflection losses of ARCs on high-index systems.

Fig. 2
Fig. 2

Reflection losses of ARCs on low-index systems. (Tho2 should read ThO2.)

Fig. 3
Fig. 3

Effect on spectral stability of a low-index system due to errors in thicknesses and refractive indices.

Fig. 4
Fig. 4

Effect on spectral stability of a high-index system due to errors in thicknesses and refractive indices.

Fig. 5
Fig. 5

Flow chart for in situ thickness corrections (dynamic correction procedure).

Fig. 6
Fig. 6

Effect of angle of incidence on spectral losses of ARCs on high-index systems.

Fig. 7
Fig. 7

Comparison of spectral characteristics obtained by different methods.

Fig. 8
Fig. 8

Spectral characteristics when d3 is set to different values.

Equations (11)

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r = ( M 11 P 0 M 22 P 1 ) + i ( M 12 P 0 P 1 M 21 ) ( M 11 P 0 + M 22 P 1 ) + i ( M 12 P 0 P 1 + M 21 ) ,
[ M 11 i M 12 i M 21 M 22 ] = j = 1 n [ cos x j i sin x j P j i P j sin x j cos x j ] ,
n 0 sin θ 0 = n 1 sin θ 1 n j 1 sin θ j 1 = n j sin θ j = n n sin θ n = n s sin θ s .
R = r r * = ( M 11 P 0 M 22 P 1 ) 2 + ( M 12 P 0 P 1 M 21 ) 2 ( M 11 P 0 + M 22 P 1 ) 2 + ( M 12 P 0 P 1 + M 21 ) 2 .
M 11 2 P 0 2 + M 22 2 P 1 2 + M 12 2 P 0 2 P 1 2 + 2 P 0 P 1 ( M 11 M 22 M 12 M 21 ) = 0 .
[ M 11 i M 12 i M 21 M 22 ] = j = 1 3 [ cos x j i sin x j P j i P j sin x j cos x j ] ,
A cos 2 x 1 + B sin 2 x 1 + C = 0 , A = ( a 1 + a 2 cos 2 x 3 ) cos 2 x 2 a 3 sin 2 x 2 sin 2 x 3 + a 4 + a 5 cos 2 x 3 , B = ( a 6 cos 2 x 2 sin 2 x 3 + a 7 sin 2 x 2 + a 8 sin 2 x 2 cos 2 x 3 ) C = ( a 9 + a 10 cos 2 x 3 ) cos 2 x 2 a 11 sin 2 x 2 sin 2 x 3 + a 12 + a 13 cos 2 x 3 a 14 .
A 2 + B 2 C 2 = 0 .
x i + 1 = x i f ( x i ) f ( x i ) ,
n 1 d 1 = λ 0 4 π cos 1 ( A / C ) .
a 1 = ( n 0 2 n 1 2 ) ( n 1 2 + n 2 2 ) ( n 2 2 n 3 2 ) ( n 3 2 + n s 2 ) , a 2 = ( n 0 2 n 1 2 ) ( n 1 2 + n 2 2 ) ( n 2 2 + n 3 2 ) ( n 3 2 n s 2 ) , a 3 = 2 n 2 n 3 ( n 0 2 n 1 2 ) ( n 1 2 + n 2 2 ) ( n 3 2 n s 2 ) , a 4 = ( n 0 2 n 1 2 ) ( n 1 2 n 2 2 ) ( n 2 2 + n 3 2 ) ( n 3 2 + n s 2 ) , a 5 = ( n 0 2 n 1 2 ) ( n 1 2 n 2 2 ) ( n 2 2 n 3 2 ) ( n 3 2 n s 2 ) , a 6 = 4 n 1 n 3 n 2 2 ( n 0 2 n 1 2 ) ( n 3 2 n s 2 ) , a 7 = 2 n 1 n 2 ( n 0 2 n 1 2 ) ( n 2 2 n 3 2 ) ( n 3 2 + n s 2 ) , a 8 = 2 n 1 n 2 ( n 0 2 n 1 2 ) ( n 2 2 + n 3 2 ) ( n 3 2 n s 2 ) , a 9 = ( n 0 2 + n 1 2 ) ( n 1 2 n 2 2 ) ( n 2 2 n 3 2 ) ( n 3 2 + n s 2 ) , a 10 = ( n 0 2 + n 1 2 ) ( n 1 2 n 2 2 ) ( n 2 2 + n 3 2 ) ( n 3 2 n s 2 ) , a 11 = 2 n 2 n 3 ( n 0 2 + n 1 2 ) ( n 1 2 n 2 2 ) ( n 3 2 n s 2 ) , a 12 = ( n 0 2 + n 1 2 ) ( n 1 2 + n 2 2 ) ( n 2 2 + n 3 2 ) ( n 3 2 + n s 2 ) , a 13 = ( n 0 2 + n 1 2 ) ( n 1 2 + n 2 2 ) ( n 2 2 n 3 2 ) ( n 3 2 n s 2 ) , a 14 = 16 n 0 n s n 1 2 n 2 2 n 3 2 .

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