Abstract

Transparent bilayer coatings that produce total refraction (TR) of obliquely incident monochromatic light into an underlying substrate are considered. When the substrate is transparent, it is shown that TR takes place without any accompanying change of polarization. Totally refracting bilayers are realizable in the IR where high-refractive-index substrates are available. This is illustrated by a BaF2–ZnSe bilayer on a Ge substrate at a 10.6-μm (CO2 laser) wavelength and 45° angle of incidence. Limited changes of the angle of incidence, wavelength, and refractive indices and thicknesses of the two films of the bilayer are introduced, and their effects on the condition of TR are determined. TR (hence absorption) is also possible for absorbing (semiconductor or metallic) substrates using transparent bilayers of films of nonquarter-wave optical thickness, as is further demonstrated in this paper.

© 1985 Optical Society of America

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References

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  1. See, for example, R. M. A. Azzam, “Single-Layer Antireflection Coatings on Absorbing Substrates for the Parallel and Perpendicular Polarizations at Oblique Incidence,” Appl. Opt. 24, 513 (1985).
    [CrossRef] [PubMed]
  2. H. Pohlack, “Zum Problem der Reflexionsminderung Optischer Glaser bei Nichtsenkrechtem Lichteinfall,” in Jenaer Jahrbuch 1952, P. Gorlich, Ed. (Fischer, Jena, 1952), pp. 103–118.
  3. K. Javily, R. M. A. Azzam, “Coating a Transparent or Absorbing Substrate by a Transparent Thin Film for Minimum Reflectance of Unpolarized Light at Oblique Incidence,” Optik, in press.
  4. P. Baumeister, “The Transmission and Degree of Polarization of Quarter-Wave Stacks at Non-Normal Incidence,” Opt. Acta 8, 105 (1961).
    [CrossRef]
  5. R. M. A. Azzam, K. Javily, “Antireflecting and Polarizing Transparent Bilayer Coatings on Absorbing Substrates at Oblique Incidence,” Appl. Opt. 24, 519 (1985).
    [CrossRef] [PubMed]
  6. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977); Eq. (4.186) must be corrected to have the same denominator as Eq. (4.185). This correction follows because S21 should be replaced by S11 in Eq. (4.170).
  7. M. Herzberger, C. D. Salzberg, “Refractive Indices of Infrared Optical Materials and Color Correction of Infrared Lenses,” J. Opt. Soc. Am. 52, 420 (1962).
    [CrossRef]
  8. P. C. Kemeny, “Refractive Index of Thin Films of Barium Fluoride,” Appl. Opt. 21, 2052 (1982).
    [CrossRef] [PubMed]
  9. M. E. Pedinoff, M. Braunstein, O. M. Stafsudd, “Refractive Indices of Materials: 10.6-μm Ellipsometer Measurements,” Appl. Opt. 16, 2849 (1977).
    [CrossRef] [PubMed]
  10. M. A. Ordal, L. L. Long, R. J. Bell, J. E. Bell, R. R. Bell, R. W. Alexander, C. A. Ward, “Optical Properties of the Metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, and W in the Infrared and Far Infrared,” Appl. Opt. 22, 1099 (1983).
    [CrossRef] [PubMed]
  11. D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaSb, InP, InAs, and InSb from 1.5 to 6.0eV,” Phys. Rev. B 27, 985 (1983).
    [CrossRef]
  12. H. K. Pulker, “Characterization of Optical Thin Films,” Appl. Opt. 18, 1969 (1979).
    [CrossRef] [PubMed]
  13. H. K. Pulker, G. Paesold, E. Ritter, “Refractive Indices of TiO2 Films Produced by Reactive Evaporation of Various Titanium-Oxygen Phases,” Appl. Opt. 15, 2987 (1976).
    [CrossRef]

1985

1983

1982

1979

1977

1976

H. K. Pulker, G. Paesold, E. Ritter, “Refractive Indices of TiO2 Films Produced by Reactive Evaporation of Various Titanium-Oxygen Phases,” Appl. Opt. 15, 2987 (1976).
[CrossRef]

1962

1961

P. Baumeister, “The Transmission and Degree of Polarization of Quarter-Wave Stacks at Non-Normal Incidence,” Opt. Acta 8, 105 (1961).
[CrossRef]

Alexander, R. W.

Aspnes, D. E.

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaSb, InP, InAs, and InSb from 1.5 to 6.0eV,” Phys. Rev. B 27, 985 (1983).
[CrossRef]

Azzam, R. M. A.

See, for example, R. M. A. Azzam, “Single-Layer Antireflection Coatings on Absorbing Substrates for the Parallel and Perpendicular Polarizations at Oblique Incidence,” Appl. Opt. 24, 513 (1985).
[CrossRef] [PubMed]

R. M. A. Azzam, K. Javily, “Antireflecting and Polarizing Transparent Bilayer Coatings on Absorbing Substrates at Oblique Incidence,” Appl. Opt. 24, 519 (1985).
[CrossRef] [PubMed]

K. Javily, R. M. A. Azzam, “Coating a Transparent or Absorbing Substrate by a Transparent Thin Film for Minimum Reflectance of Unpolarized Light at Oblique Incidence,” Optik, in press.

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977); Eq. (4.186) must be corrected to have the same denominator as Eq. (4.185). This correction follows because S21 should be replaced by S11 in Eq. (4.170).

Bashara, N. M.

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977); Eq. (4.186) must be corrected to have the same denominator as Eq. (4.185). This correction follows because S21 should be replaced by S11 in Eq. (4.170).

Baumeister, P.

P. Baumeister, “The Transmission and Degree of Polarization of Quarter-Wave Stacks at Non-Normal Incidence,” Opt. Acta 8, 105 (1961).
[CrossRef]

Bell, J. E.

Bell, R. J.

Bell, R. R.

Braunstein, M.

Herzberger, M.

Javily, K.

R. M. A. Azzam, K. Javily, “Antireflecting and Polarizing Transparent Bilayer Coatings on Absorbing Substrates at Oblique Incidence,” Appl. Opt. 24, 519 (1985).
[CrossRef] [PubMed]

K. Javily, R. M. A. Azzam, “Coating a Transparent or Absorbing Substrate by a Transparent Thin Film for Minimum Reflectance of Unpolarized Light at Oblique Incidence,” Optik, in press.

Kemeny, P. C.

Long, L. L.

Ordal, M. A.

Paesold, G.

H. K. Pulker, G. Paesold, E. Ritter, “Refractive Indices of TiO2 Films Produced by Reactive Evaporation of Various Titanium-Oxygen Phases,” Appl. Opt. 15, 2987 (1976).
[CrossRef]

Pedinoff, M. E.

Pohlack, H.

H. Pohlack, “Zum Problem der Reflexionsminderung Optischer Glaser bei Nichtsenkrechtem Lichteinfall,” in Jenaer Jahrbuch 1952, P. Gorlich, Ed. (Fischer, Jena, 1952), pp. 103–118.

Pulker, H. K.

H. K. Pulker, “Characterization of Optical Thin Films,” Appl. Opt. 18, 1969 (1979).
[CrossRef] [PubMed]

H. K. Pulker, G. Paesold, E. Ritter, “Refractive Indices of TiO2 Films Produced by Reactive Evaporation of Various Titanium-Oxygen Phases,” Appl. Opt. 15, 2987 (1976).
[CrossRef]

Ritter, E.

H. K. Pulker, G. Paesold, E. Ritter, “Refractive Indices of TiO2 Films Produced by Reactive Evaporation of Various Titanium-Oxygen Phases,” Appl. Opt. 15, 2987 (1976).
[CrossRef]

Salzberg, C. D.

Stafsudd, O. M.

Studna, A. A.

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaSb, InP, InAs, and InSb from 1.5 to 6.0eV,” Phys. Rev. B 27, 985 (1983).
[CrossRef]

Ward, C. A.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Acta

P. Baumeister, “The Transmission and Degree of Polarization of Quarter-Wave Stacks at Non-Normal Incidence,” Opt. Acta 8, 105 (1961).
[CrossRef]

Phys. Rev. B

D. E. Aspnes, A. A. Studna, “Dielectric Functions and Optical Parameters of Si, Ge, GaP, GaSb, InP, InAs, and InSb from 1.5 to 6.0eV,” Phys. Rev. B 27, 985 (1983).
[CrossRef]

Other

See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977); Eq. (4.186) must be corrected to have the same denominator as Eq. (4.185). This correction follows because S21 should be replaced by S11 in Eq. (4.170).

H. Pohlack, “Zum Problem der Reflexionsminderung Optischer Glaser bei Nichtsenkrechtem Lichteinfall,” in Jenaer Jahrbuch 1952, P. Gorlich, Ed. (Fischer, Jena, 1952), pp. 103–118.

K. Javily, R. M. A. Azzam, “Coating a Transparent or Absorbing Substrate by a Transparent Thin Film for Minimum Reflectance of Unpolarized Light at Oblique Incidence,” Optik, in press.

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Figures (8)

Fig. 1
Fig. 1

p and s intensity reflectances (on a logarithmic scale) plotted vs the angle of incidence ϕ (in degrees) for a bilayer of two films of refractive indices n1 = 1.20697 and n2 = 2.41394 and thicknesses d1 = 2.70920 μm and d2 = 1.14815 μm, respectively, on a Ge substrate of refractive index n3 = 4. A 10.6-μm (CO2-laser) beam is assumed to be incident from air (N0 = 1). At ϕ = 45°, R p = R s = 0, and total refraction takes place.

Fig. 2
Fig. 2

p and s intensity reflectances (on a logarithmic scale) vs wavelength λ (in microns) at 45° angle of incidence for a bilayer of two films of refractive indices n1 = 1.20697 and n2 = 2.41394 and thicknesses d1 = 2.70920 μm and d2 = 1.14815 μm, respectively, on a Ge substrate of refractive index n3 = 4. At the design wavelength λ = 10.6 μm, R p = R s = 0, and total refraction takes place from air into Ge. The effect of material dispersion is ignored.

Fig. 3
Fig. 3

p and s reflectances (on a logarithmic scale) vs the refractive-index n1 of the first film with thickness d1 = 2.70920 μm. The second film has n2 = 2.41394 and d2 = 1.14815 μm. Films 1 and 2 form a bilayer on a Ge substrate (n3 = 4) on which 10.6-μm radiation is incident from air (N0 = 1) at 45° angle of incidence. When n1 = 1.20697, R p = R s = 0, and total refraction occurs.

Fig. 4
Fig. 4

Same as in Fig. 3 except that now the refractive index of film 2 is being shifted (by ±0.1) around the design value n2 = 2.41394.

Fig. 5
Fig. 5

p and s intensity reflectances (on a logarithmic scale) vs the thickness d1 of film 1 of a bilayer (n1 = 1.20697, n2 = 2.41394, d2 = 1.4815 μm) on a Ge substrate (n3 = 4) on which 10.6-μm radiation is incident from air (N0 = 1) at 45° angle of incidence. When d1 = 2.70920 μm, R p = R s = 0, and total refraction takes place.

Fig. 6
Fig. 6

Same as in Fig. 5 except that the thickness of film 2 is now being shifted (by ±0.01 μm) around the design value d2 = 1.14815 μm.

Fig. 7
Fig. 7

Refractive indices n1 and n2 of the two films of a totally refracting bilayer on an absorbing substrate with complex refractive index N3 = 4 − jk3 plotted vs the extinction coefficient k3. Light is assumed to be incident from air (N0 = 1) at 45° angle of incidence.

Fig. 8
Fig. 8

Normalized thicknesses ζ1 and ζ2 of the two films of a totally refracting bilayer (with refractive indices given by Fig. 7) on an absorbing substrate with complex refractive index N3 = 4 − jk3 plotted vs the extinction coefficient k3. Light is assumed to be incident from air (N0 = 1) at 45° angle of incidence.

Tables (2)

Tables Icon

Table I Characteristics of Totally Refracting Transparent Bilayer Coatings on a Ti Substrate (N3 = 4 − j2) for 10.6-μm CO2-Laser Radiation at Three Angles of Incidencea

Tables Icon

Table II Characteristics of Totally Refracting Transparent Bilayer Coatings on a Si Substrate at 45° Angle of Incidence for Five Ar+-Laser Lines and the 632.8-nm He-Ne-Laser Linea

Equations (21)

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R ν = r 01 ν + r 12 ν X 1 + r 01 ν r 12 ν r 23 ν X 2 + r 23 ν X 1 X 2 1 + r 01 ν r 12 ν X 1 + r 12 ν r 23 ν X 2 + r 01 ν r 23 ν X 1 X 2 , ν = p , s ,
X i = exp ( j 2 π ζ i ) , i = 1,2 ,
ζ i = d i / D ϕ i , i = 1,2 ,
D ϕ i = λ 2 ( N i 2 N 0 2 sin 2 ϕ ) 1 / 2 , i = 1,2 .
r 01 ν r 12 ν + r 23 ν = r 01 ν r 12 ν r 23 ν ,
S 0 S 2 2 = S 1 2 S 3 ,
S i = ( N i 2 N 0 2 sin 2 ϕ ) 1 / 2 , i = 0,1,2,3 .
N 1 4 N 3 2 S 0 S 2 2 = N 0 2 N 2 4 S 1 2 S 3 .
n 2 4 = n 1 4 n 3 2 .
n 1 2 = { ( n 3 + u ) + [ ( n 3 + u ) 2 ( n 3 + 1 ) 2 u ] 1 / 2 } / ( n 3 + 1 ) .
n 1 = 2 cos ( ϕ / 2 ) ,
n 1 2 = 2 n 3 / ( n 3 + 1 ) .
t s = 2 S 0 S 1 S 2 / ( S 0 S 2 2 + S 1 2 S 3 ) ,
t p = 2 n 1 2 n 2 2 n 3 S 0 S 1 S 2 / ( n 1 4 n 3 2 S 0 S 2 2 + n 2 4 S 1 2 S 3 ) .
t p = t s .
n 1 = ( 0.9 + 0.31 ) 1 / 2 = 1.20697 ,
n 2 = 2.41394 .
d 1 = 2.70920 μ m , d 2 = 1.14815 μ m .
R ν = | R ν | 2 ,
R u = 1 2 ( R p + R s ) ,
R u = f ( n 1 , ζ 1 , n 2 , ζ 2 ; n 3 , k 3 , ϕ ) .

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