Abstract

A new method for design of multilayer antireflection coatings (ARCs) which makes use of a specified reflectance value R0, either zero or nonzero at a particular wavelength λ0, is developed. It offers an explicit scheme for evaluation of the optical/geometrical thickness of each layer, and the design variables are optimized with respect to integrated reflection loss R* over a specified bandwidth. It has been found that the method can be applied for design of wideband ARCs useful in the visible and IR regions, and the resulting bandwidth and residual reflection losses can be controlled as a function of R0. The method is found to be comprehensive so that more useful designs can be worked out, and it can be directly adopted to the design of single- and double-layer ARCs.

© 1985 Optical Society of America

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References

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  1. J. T. Cox, G. Hass, “Antireflection Coatings for Optical and Infrared Optical Materials,” Phys. Thin Films 2, 239 (1969).
  2. A. Mussett, A. Thelen, “Multilayer Antireflection Coatings,” Prog. Opt. 8, 203 (1970).
  3. H. M. Liddell, Computer Aided Design Techniques for Multilayer Filters, (Adam Hilgers, Bristol, 1981).
  4. J. Mouchart, “Thin Film Optical Coatings. 2: Three-Layer Antireflection Coating Theory,” Appl. Opt. 16, 2722 (1977).
    [CrossRef] [PubMed]
  5. J. A. Dobrowlski, F. Ho, “High Performance Step-Down AR Coatings for High Refractive-Index IR Materials,” Appl. Opt 21, 288 (1982).
    [CrossRef]
  6. A. L. Bloom, “Refining and Optimization in Multilayers,” Appl. Opt. 20, 66 (1981).
    [CrossRef] [PubMed]
  7. J. F. Tang, Q. Zheng, “Automatic Design of Optical Thin Film Systems—Merit Function and Numerical Optimization Method,” J. Opt. Soc, Am. 72, 1522 (1982).
    [CrossRef]
  8. C. L. Nagendra, G. K. M. Thutupalli, “Three-Layer Antireflection Coatings: A New Method for Design and Optimization,” Appl. Opt. 22, 4118 (1983).
    [CrossRef] [PubMed]
  9. H. K. Pulker, “Characterization of Optical Thin Films,” Appl. Opt. 18, 1969 (1979).
    [CrossRef] [PubMed]
  10. C. L. Nagendra, G. K. M. Thutupalli, “Single and Doubler Layer Anti-reflection Coatings for Application in the Infrared Region (15 μm),” Vacuum 31, 137 (1981).
    [CrossRef]
  11. H. T. Cox, G. Hass, R. F. Rowntree, “Two Layer Antireflection Coatings for Glass in the Near Infrared,” Vacuum 5, 445 (1954).
    [CrossRef]

1983 (1)

1982 (2)

J. F. Tang, Q. Zheng, “Automatic Design of Optical Thin Film Systems—Merit Function and Numerical Optimization Method,” J. Opt. Soc, Am. 72, 1522 (1982).
[CrossRef]

J. A. Dobrowlski, F. Ho, “High Performance Step-Down AR Coatings for High Refractive-Index IR Materials,” Appl. Opt 21, 288 (1982).
[CrossRef]

1981 (2)

A. L. Bloom, “Refining and Optimization in Multilayers,” Appl. Opt. 20, 66 (1981).
[CrossRef] [PubMed]

C. L. Nagendra, G. K. M. Thutupalli, “Single and Doubler Layer Anti-reflection Coatings for Application in the Infrared Region (15 μm),” Vacuum 31, 137 (1981).
[CrossRef]

1979 (1)

1977 (1)

1970 (1)

A. Mussett, A. Thelen, “Multilayer Antireflection Coatings,” Prog. Opt. 8, 203 (1970).

1969 (1)

J. T. Cox, G. Hass, “Antireflection Coatings for Optical and Infrared Optical Materials,” Phys. Thin Films 2, 239 (1969).

1954 (1)

H. T. Cox, G. Hass, R. F. Rowntree, “Two Layer Antireflection Coatings for Glass in the Near Infrared,” Vacuum 5, 445 (1954).
[CrossRef]

Bloom, A. L.

Cox, H. T.

H. T. Cox, G. Hass, R. F. Rowntree, “Two Layer Antireflection Coatings for Glass in the Near Infrared,” Vacuum 5, 445 (1954).
[CrossRef]

Cox, J. T.

J. T. Cox, G. Hass, “Antireflection Coatings for Optical and Infrared Optical Materials,” Phys. Thin Films 2, 239 (1969).

Dobrowlski, J. A.

J. A. Dobrowlski, F. Ho, “High Performance Step-Down AR Coatings for High Refractive-Index IR Materials,” Appl. Opt 21, 288 (1982).
[CrossRef]

Hass, G.

J. T. Cox, G. Hass, “Antireflection Coatings for Optical and Infrared Optical Materials,” Phys. Thin Films 2, 239 (1969).

H. T. Cox, G. Hass, R. F. Rowntree, “Two Layer Antireflection Coatings for Glass in the Near Infrared,” Vacuum 5, 445 (1954).
[CrossRef]

Ho, F.

J. A. Dobrowlski, F. Ho, “High Performance Step-Down AR Coatings for High Refractive-Index IR Materials,” Appl. Opt 21, 288 (1982).
[CrossRef]

Liddell, H. M.

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

Mouchart, J.

Mussett, A.

A. Mussett, A. Thelen, “Multilayer Antireflection Coatings,” Prog. Opt. 8, 203 (1970).

Nagendra, C. L.

C. L. Nagendra, G. K. M. Thutupalli, “Three-Layer Antireflection Coatings: A New Method for Design and Optimization,” Appl. Opt. 22, 4118 (1983).
[CrossRef] [PubMed]

C. L. Nagendra, G. K. M. Thutupalli, “Single and Doubler Layer Anti-reflection Coatings for Application in the Infrared Region (15 μm),” Vacuum 31, 137 (1981).
[CrossRef]

Pulker, H. K.

Rowntree, R. F.

H. T. Cox, G. Hass, R. F. Rowntree, “Two Layer Antireflection Coatings for Glass in the Near Infrared,” Vacuum 5, 445 (1954).
[CrossRef]

Tang, J. F.

J. F. Tang, Q. Zheng, “Automatic Design of Optical Thin Film Systems—Merit Function and Numerical Optimization Method,” J. Opt. Soc, Am. 72, 1522 (1982).
[CrossRef]

Thelen, A.

A. Mussett, A. Thelen, “Multilayer Antireflection Coatings,” Prog. Opt. 8, 203 (1970).

Thutupalli, G. K. M.

C. L. Nagendra, G. K. M. Thutupalli, “Three-Layer Antireflection Coatings: A New Method for Design and Optimization,” Appl. Opt. 22, 4118 (1983).
[CrossRef] [PubMed]

C. L. Nagendra, G. K. M. Thutupalli, “Single and Doubler Layer Anti-reflection Coatings for Application in the Infrared Region (15 μm),” Vacuum 31, 137 (1981).
[CrossRef]

Zheng, Q.

J. F. Tang, Q. Zheng, “Automatic Design of Optical Thin Film Systems—Merit Function and Numerical Optimization Method,” J. Opt. Soc, Am. 72, 1522 (1982).
[CrossRef]

Appl. Opt (1)

J. A. Dobrowlski, F. Ho, “High Performance Step-Down AR Coatings for High Refractive-Index IR Materials,” Appl. Opt 21, 288 (1982).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc, Am. (1)

J. F. Tang, Q. Zheng, “Automatic Design of Optical Thin Film Systems—Merit Function and Numerical Optimization Method,” J. Opt. Soc, Am. 72, 1522 (1982).
[CrossRef]

Phys. Thin Films (1)

J. T. Cox, G. Hass, “Antireflection Coatings for Optical and Infrared Optical Materials,” Phys. Thin Films 2, 239 (1969).

Prog. Opt. (1)

A. Mussett, A. Thelen, “Multilayer Antireflection Coatings,” Prog. Opt. 8, 203 (1970).

Vacuum (2)

C. L. Nagendra, G. K. M. Thutupalli, “Single and Doubler Layer Anti-reflection Coatings for Application in the Infrared Region (15 μm),” Vacuum 31, 137 (1981).
[CrossRef]

H. T. Cox, G. Hass, R. F. Rowntree, “Two Layer Antireflection Coatings for Glass in the Near Infrared,” Vacuum 5, 445 (1954).
[CrossRef]

Other (1)

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

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Figures (10)

Fig. 1
Fig. 1

Influence of the layer thickness d3 on the spectral profile of the infrared ARC having system configuration 1.7/2.56/3.45/4.4, λ0 = 15.0 μm, for a given set of values of R0 ranging from 0.000 to 0.015.

Fig. 2
Fig. 2

Typical behavior of the integrated reflection loss R* with respect to layer thicknesses d1,d2, and d3 for different R0 values.

Fig. 3
Fig. 3

Optimized spectral profile for each set value of R0 corresponding to Fig. 1; in the inset is shown the variation of R* with R0 corresponding to the optimized system.

Fig. 4
Fig. 4

Spectral profiles of visible region ARC with system configuration 1.23/1.38/1.45/1.52, λ0 = 0.7 μm, for different d3 and R0 values.

Fig. 5
Fig. 5

Dependence of integrated reflection loss R* with respect to layer thicknesses for a given R0 value.

Fig. 6
Fig. 6

Spectral characteristics of optimized designs for different R0 values corresponding to Fig. 4; in the inset is shown the variation of R* with respect to R0.

Fig. 7
Fig. 7

Summary of the results of the system 1.38/1.45/1.63/1.52, λ0 = 0.6 μm: (1) R0 = 0.002, d3 = 0.103; (2) R0 = 0.005, d3 = 0.138; (3) R0 = 0.010, d3 = 0.162; (4) R0 = 0.015; d3 = 0.168.

Fig. 8
Fig. 8

Characteristic features of the results for an IR stepped sequence ARC with system configuration 1.465/4.021/1.465/4.02, λ0 = 10.0 μm: (1) R0 = 0.000, d3 = 0.3; (2) R0 = 0.0003, d3 = 0.28; (3) R0 = 0.0005; d3 = 0.28; (4) R0 = 0.005; d3 = 0.23.

Fig. 9
Fig. 9

Typical behavior of the results for a stepped sequence visible region ARC with system configuration 1.38/2.1/1.88/1.52, λ0 = 0.6 μm: (1) R0 = 000, d3 = 0.96; (2) R0 = 0.002, d3 = 0.084; (3) R0 = 0.005, d3 = 0.076.

Fig. 10
Fig. 10

Reflectance characteristics of double-layer ARCs in IR and visible regions with system configurations 1.7/2.56/4.4, λ0 = 15.0 μm, and 1.23/ 1.38/1.52, λ0 = 0.6 μm, respectively.

Tables (1)

Tables Icon

Table I Summary of the Design Results of Wideband ARCs

Equations (4)

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R = ( M 11 P 0 P L M 22 ) 2 + ( M 12 P 0 P L M 21 ) 2 ( M 11 P 0 + P L M 22 ) 2 + ( M 12 P 0 P L + M 21 ) 2 ,
( 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 ) ,
( 1 R 0 ) ( M 11 2 P 0 2 + M 12 2 P 0 2 P L 2 + M 21 2 + M 22 2 P L 2 ) 2 P 0 P L ( 1 + R 0 ) ( M 11 M 22 + M 12 M 21 ) = 0 ,
R * = λ 1 λ 2 R ( λ ) d λ / λ 1 λ 2 d λ .

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