Abstract

Approximations are developed for the refractive indices of nonabsorbing layers with equal optical thickness producing an antireflection coating for a dielectric substrate that has a Chebyshev spectral response.

© 1986 Optical Society of America

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References

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  1. J. S. Seeley, H. M. Liddell, T. C. Chen, “Extraction of Chebyshev Design Data for the Lowpass Dielectric Multilayer,” Opt. Acta 20, 641 (1973).
    [Crossref]
  2. L. Young, “Antireflection Coatings on Glass,” Appl. Opt. 4, 366 (1965).
    [Crossref]
  3. L. Young, “Synthesis of Multiple Antireflection Films over a Prescribed Frequency Band,” J. Opt. Soc. Am. 51, 967 (1961).
    [Crossref]
  4. H. Riblet, “General synthesis of quarterwave Impedance Transformers,” IRE Trans. Microwave Theory Tech. MTT-5, 36 (1957).
    [Crossref]
  5. R. Levy, “Table sof Element Values for the Distributed LowPass Prototype Filter,” IEEE Trans. Microwave Theory Tech. MTT-13, 514 (1965).
    [Crossref]
  6. H. Pohlack, “Synthesis of Optical Coatings with Prescribed Spectral Characteristics,” in Jenaer Jahrbuch (VEB Carl Zeiss, Jena, 1952), in German.
  7. P. Kard, Analysis and Synthesis of Multilayer Interference Coatings (Valgus, Tallinn, Estonia, 1971), in Russian.
  8. P. Baumeister, R. Moore, K. Walsh: “Application of Linear Programming to Antireflection Coating Design,” J. Opt. Soc. Am. 67, 1039 (1977).
    [Crossref]
  9. P. Baumeister, “Optical Interference Coating Technology,” lecture notes for the five-day short course engineering 823.17 at the UCLA Extension (1985), Sec. 2.7.4.3.
  10. G. Matthaei, L. Young, E. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964).
  11. R. G. Muchmore, “Optimum Bandwidth for Two Layer Antireflection Films,” J. Opt. Soc. Am. 38, 20 (1948).
    [Crossref]

1985 (1)

P. Baumeister, “Optical Interference Coating Technology,” lecture notes for the five-day short course engineering 823.17 at the UCLA Extension (1985), Sec. 2.7.4.3.

1977 (1)

1973 (1)

J. S. Seeley, H. M. Liddell, T. C. Chen, “Extraction of Chebyshev Design Data for the Lowpass Dielectric Multilayer,” Opt. Acta 20, 641 (1973).
[Crossref]

1965 (2)

L. Young, “Antireflection Coatings on Glass,” Appl. Opt. 4, 366 (1965).
[Crossref]

R. Levy, “Table sof Element Values for the Distributed LowPass Prototype Filter,” IEEE Trans. Microwave Theory Tech. MTT-13, 514 (1965).
[Crossref]

1961 (1)

1957 (1)

H. Riblet, “General synthesis of quarterwave Impedance Transformers,” IRE Trans. Microwave Theory Tech. MTT-5, 36 (1957).
[Crossref]

1948 (1)

Baumeister, P.

P. Baumeister, “Optical Interference Coating Technology,” lecture notes for the five-day short course engineering 823.17 at the UCLA Extension (1985), Sec. 2.7.4.3.

P. Baumeister, R. Moore, K. Walsh: “Application of Linear Programming to Antireflection Coating Design,” J. Opt. Soc. Am. 67, 1039 (1977).
[Crossref]

Chen, T. C.

J. S. Seeley, H. M. Liddell, T. C. Chen, “Extraction of Chebyshev Design Data for the Lowpass Dielectric Multilayer,” Opt. Acta 20, 641 (1973).
[Crossref]

Jones, E.

G. Matthaei, L. Young, E. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964).

Kard, P.

P. Kard, Analysis and Synthesis of Multilayer Interference Coatings (Valgus, Tallinn, Estonia, 1971), in Russian.

Levy, R.

R. Levy, “Table sof Element Values for the Distributed LowPass Prototype Filter,” IEEE Trans. Microwave Theory Tech. MTT-13, 514 (1965).
[Crossref]

Liddell, H. M.

J. S. Seeley, H. M. Liddell, T. C. Chen, “Extraction of Chebyshev Design Data for the Lowpass Dielectric Multilayer,” Opt. Acta 20, 641 (1973).
[Crossref]

Matthaei, G.

G. Matthaei, L. Young, E. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964).

Moore, R.

Muchmore, R. G.

Pohlack, H.

H. Pohlack, “Synthesis of Optical Coatings with Prescribed Spectral Characteristics,” in Jenaer Jahrbuch (VEB Carl Zeiss, Jena, 1952), in German.

Riblet, H.

H. Riblet, “General synthesis of quarterwave Impedance Transformers,” IRE Trans. Microwave Theory Tech. MTT-5, 36 (1957).
[Crossref]

Seeley, J. S.

J. S. Seeley, H. M. Liddell, T. C. Chen, “Extraction of Chebyshev Design Data for the Lowpass Dielectric Multilayer,” Opt. Acta 20, 641 (1973).
[Crossref]

Walsh, K.

Young, L.

Appl. Opt. (1)

IEEE Trans. Microwave Theory Tech. (1)

R. Levy, “Table sof Element Values for the Distributed LowPass Prototype Filter,” IEEE Trans. Microwave Theory Tech. MTT-13, 514 (1965).
[Crossref]

IRE Trans. Microwave Theory Tech. (1)

H. Riblet, “General synthesis of quarterwave Impedance Transformers,” IRE Trans. Microwave Theory Tech. MTT-5, 36 (1957).
[Crossref]

J. Opt. Soc. Am. (3)

lecture notes for the five-day short course engineering 823.17 at the UCLA Extension (1)

P. Baumeister, “Optical Interference Coating Technology,” lecture notes for the five-day short course engineering 823.17 at the UCLA Extension (1985), Sec. 2.7.4.3.

Opt. Acta (1)

J. S. Seeley, H. M. Liddell, T. C. Chen, “Extraction of Chebyshev Design Data for the Lowpass Dielectric Multilayer,” Opt. Acta 20, 641 (1973).
[Crossref]

Other (3)

G. Matthaei, L. Young, E. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures (McGraw-Hill, New York, 1964).

H. Pohlack, “Synthesis of Optical Coatings with Prescribed Spectral Characteristics,” in Jenaer Jahrbuch (VEB Carl Zeiss, Jena, 1952), in German.

P. Kard, Analysis and Synthesis of Multilayer Interference Coatings (Valgus, Tallinn, Estonia, 1971), in Russian.

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Figures (1)

Fig. 1
Fig. 1

Computed reflectance vs normalized frequency of (a) two nonabsorbing layers, (b) a three-layer coating, and (c) a four-layer coating on a substrate of refractive index 4.0. Each layer is 0.25 wave in optical thickness at λ0. The indices of the layers are shown in the figure.

Tables (3)

Tables Icon

Table I Coefficients Appearing in Eq. (19)

Tables Icon

Table II Comparison of Approximate and Exact Index Values

Tables Icon

Table III Approximate Indices for Maximally Flat AR Coatings

Equations (20)

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β = 2 π n i h i λ - 1 ,
R T = R s T s P m 2 ( C / C 0 ) P m 2 ( 1 / C 0 ) ,
F R / T , F s R s / T s .
0 F F s [ P m ( 1 / C 0 ) ] - 2 .
λ 0 - 1 = 0.5 [ ( λ 1 ) - 1 + ( λ 2 ) - 1 ] .
β 1 : β 2 : : ( λ 1 ) - 1 : ( λ 1 ) - 1 .
C 0 cos β 1 cos β 2 .
F = i = 0 m a i ( cos β ) m - i ( sin β ) i ( - 1 ) i / 2 ,
n 1 = n m ,             n 2 = n m - 1 ,             n 3 = n m - 2 .
n j = n s n 0 ,
[ C 4 ( a 0 + a 2 + a 4 ) - C 2 ( a 2 + 2 a 4 ) + a 4 ] = F s C 0 4 [ 8 ( C / C 0 ) 4 - 8 ( C / C 0 ) 2 + 1 ] P 0 - 1 ,
P 0 C 0 4 - 8 C 0 2 + 8.
a 2 = F s P 0 - 1 ( 8 C 0 2 - 2 C 0 4 ) 14 F s - 12 u 1 - 4 u 2 ,
a 4 = F s P 0 - 1 C 0 4 F s - 4 u 1 + 4 u 2 .
u 1 F s 16 [ 15 - C 0 2 ( 8 - C 0 2 ) C 0 4 - 8 C 0 2 + 8 ] ,
u 2 F s 16 [ 11 - C 0 2 ( 8 - 5 C 0 2 ) C 0 4 - 8 C 0 2 + 8 ] .
n 1 n s exp ( - 2 u 1 ) ,
n 2 n s exp ( - 2 u 2 ) .
u i F s κ 1 [ κ 2 - C 0 2 P ( C 0 ) Q ( C 0 ) ] ,
n i = n s exp ( - 2 u i ) .

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