Abstract

A theoretical and experimental investigation of inhomogeneous CeO2–MgF2 and ZnS–Na3AlF6 antireflection coatings for the visible spectral region has been made. By a proper choice of the refractive index profile, the reflectance may be considerably reduced. In the infrared region, Ge–MgF2 films on Ge substrates are shown to give a low reflectance with a small wavelength dependence.

© 1966 Optical Society of America

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References

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  1. G. Bauer, Ann. Physik 19, 434 (1934).
    [CrossRef]
  2. R. Jacobsson, Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. V.
  3. R. E. Thun, K. H. Behrndt, M. Beckermann, K. B. Scow, Autom. Contr. 14, 26 (1961).
  4. R. Jacobsson, J. Phys. (Paris) 25, 46 (1964).
    [CrossRef]
  5. R. Jacobsson, Opt. Acta 10, 309 (1963).
    [CrossRef]
  6. R. Jacobsson, J. O. Mårtensson, Japan J. Appl. Phys., to be published.
  7. R. Jacobsson, J. Opt. Soc. Am. 54, 422 (1964).
    [CrossRef]
  8. A. Vašiček, Optics of Thin Films (North-Holland, Amsterdam, 1960), p. 155.
  9. G. Hass, J. B. Ramsey, R. Thun, J. Opt. Soc. Am. 48, 324 (1958).
    [CrossRef]
  10. A. Ross, Vakuum-Tech. 8, 1 (1959).

1964 (2)

R. Jacobsson, J. Phys. (Paris) 25, 46 (1964).
[CrossRef]

R. Jacobsson, J. Opt. Soc. Am. 54, 422 (1964).
[CrossRef]

1963 (1)

R. Jacobsson, Opt. Acta 10, 309 (1963).
[CrossRef]

1961 (1)

R. E. Thun, K. H. Behrndt, M. Beckermann, K. B. Scow, Autom. Contr. 14, 26 (1961).

1959 (1)

A. Ross, Vakuum-Tech. 8, 1 (1959).

1958 (1)

1934 (1)

G. Bauer, Ann. Physik 19, 434 (1934).
[CrossRef]

Bauer, G.

G. Bauer, Ann. Physik 19, 434 (1934).
[CrossRef]

Beckermann, M.

R. E. Thun, K. H. Behrndt, M. Beckermann, K. B. Scow, Autom. Contr. 14, 26 (1961).

Behrndt, K. H.

R. E. Thun, K. H. Behrndt, M. Beckermann, K. B. Scow, Autom. Contr. 14, 26 (1961).

Hass, G.

Jacobsson, R.

R. Jacobsson, J. Opt. Soc. Am. 54, 422 (1964).
[CrossRef]

R. Jacobsson, J. Phys. (Paris) 25, 46 (1964).
[CrossRef]

R. Jacobsson, Opt. Acta 10, 309 (1963).
[CrossRef]

R. Jacobsson, J. O. Mårtensson, Japan J. Appl. Phys., to be published.

R. Jacobsson, Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. V.

Mårtensson, J. O.

R. Jacobsson, J. O. Mårtensson, Japan J. Appl. Phys., to be published.

Ramsey, J. B.

Ross, A.

A. Ross, Vakuum-Tech. 8, 1 (1959).

Scow, K. B.

R. E. Thun, K. H. Behrndt, M. Beckermann, K. B. Scow, Autom. Contr. 14, 26 (1961).

Thun, R.

Thun, R. E.

R. E. Thun, K. H. Behrndt, M. Beckermann, K. B. Scow, Autom. Contr. 14, 26 (1961).

Vašicek, A.

A. Vašiček, Optics of Thin Films (North-Holland, Amsterdam, 1960), p. 155.

Ann. Physik (1)

G. Bauer, Ann. Physik 19, 434 (1934).
[CrossRef]

Autom. Contr. (1)

R. E. Thun, K. H. Behrndt, M. Beckermann, K. B. Scow, Autom. Contr. 14, 26 (1961).

J. Opt. Soc. Am. (2)

J. Phys. (Paris) (1)

R. Jacobsson, J. Phys. (Paris) 25, 46 (1964).
[CrossRef]

Opt. Acta (1)

R. Jacobsson, Opt. Acta 10, 309 (1963).
[CrossRef]

Vakuum-Tech. (1)

A. Ross, Vakuum-Tech. 8, 1 (1959).

Other (3)

R. Jacobsson, J. O. Mårtensson, Japan J. Appl. Phys., to be published.

A. Vašiček, Optics of Thin Films (North-Holland, Amsterdam, 1960), p. 155.

R. Jacobsson, Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. V.

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Figures (12)

Fig. 1
Fig. 1

Refractive index profiles according to the Lorentz–Lorenz theory for n1 = 1.35 and n2 = 2.35.

Fig. 2
Fig. 2

(a) Average index n ¯ and position of first reflectance minimum ( n ¯d/λ)min as functions of α for films with n1 = 1.35, n2 = 2.35, and ns = 1.5. (b) Reflectance at first maximum, Rmax, and at first minimum, Rmin, for films with n1 = 1.35, n2 = 2.35, and ns = 1.5.

Fig. 3
Fig. 3

Contours of equal minimum reflectance for films with n1 = 1.35, n2 = 2.35, projected on the αns plane.

Fig. 4
Fig. 4

Reflectance and position of first minimum as functions of index of substrate for films with n1 = 1.35, n2 = 2.35, and α = 0.3.

Fig. 5
Fig. 5

Reflectance as a function of fraction of deposition time for films with n1 = 1.35, n2 = 2.35, and with ns = 1.5.

Fig. 6
Fig. 6

Calculated and experimental reflectance of inhomogeneous CeO2–MgF2 film on glass with ns = 1.5.

Fig. 7
Fig. 7

Measured refractive index of homogeneous CeO2–MgF2 films on glass as a function of CeO2 concentration, calculated from expected deposition rates. Broken curve according to the L–L theory with n1 = 1.38, n2 = 2.25.

Fig. 8
Fig. 8

Calculated reflectance of inhomogeneous CeO2–MgF2 film and measured reflectance of inhomogeneous CeO2–MgF2 film plus homogeneous MgF2 film. Substrate of glass with ns = 1.5.

Fig. 9
Fig. 9

Measured refractive index of homogeneous ZnS–Na3AlF6 films on glass with ns = 1.5 as a function of ZnS concentration, calculated from expected deposition rates. Broken curve according to the L–L theory with n1 = 1.35, n2 = 2.35.

Fig. 10
Fig. 10

Reflectance of inhomogeneous ZnS–Na3AlF6 films on glass with ns = 1.5 and minimum at (a) 0.555 μ and at (b) 1.274 μ.

Fig. 11
Fig. 11

Measured refractive index of homogeneous Ge–MgF2 films on glass as a function of Ge concentration, calculated from expected deposition rates.

Fig. 12
Fig. 12

Measured transmittance of Ge plate, coated on both sides with inhomogeneous Ge–MgF2 film with α = 0.64 and thickness 1.2 μ.

Equations (5)

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n 2 ( z ) = n 2 - β n 2 2 1 - β + β ( 1 - α ) ( n 1 2 - n 2 2 ) ( 1 - β ) { ( α - β ) - ( 1 - β ) [ 1 + ( α 2 - 1 ) z d ] ½ } ,
α = β · a 1 a 2 = v 2 ( 0 ) v 1 ( T ) .
n ¯ d = ( 2 ν + 1 ) λ 4             ( ν = 0 , 1 , 2 ) , n 0 n s = n 1 n 2 ,
n ¯ d = 2 ν · λ 4             ( ν = 1 , 2 ) , n 0 n 2 = n 1 n s ,
S 1 = ( 2 d K 1 A 1 1 + α ) ½ , S 2 = α S 1 · K 2 K 1 ,

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