Abstract

One- and two-dimensional high-spatial-frequency dielectric surface-relief gratings on a Au substrate are used to design a high-reflectance quarter-wave retarder at 70° angle of incidence and 10.6-μm light wavelength. The equivalent homogeneous anisotropic layer model is used. It is shown that equal and high reflectances (>98.5%) for the p and the s polarizations and quarter-wave retardation can be achieved with two-dimensional ZnS surface-relief gratings. Sensitivities to changes of incidence angle, light wavelength, grating filling factor, and grating layer thickness are considered.

© 1996 Optical Society of America

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References

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  1. R. M. A. Azzam, B. E. Perilloux, “Constraint on the optical constants of a film–substrate system for operation as an external-reflection retarder at a given angle of incidence,” Appl. Opt. 24, 1171–1179 (1985).
    [CrossRef] [PubMed]
  2. M. M. K. Howlader, R. M. A. Azzam, “Periodic and quasi-periodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence,” Opt. Eng. 34, 869–874 (1995).
    [CrossRef]
  3. W. H. Southwell, “Multilayer coating design achieving a broadband 90° phase shift,” Appl. Opt. 19, 2688–2692 (1980).
    [CrossRef] [PubMed]
  4. J. H. Apfel, “Phase retardance of periodic multilayer mirrors,” Appl. Opt. 21, 733–738 (1982).
    [CrossRef] [PubMed]
  5. R. M. A. Azzam, M. E. R. Khan, “Single-reflection film–substrate half-wave retarders with nearly stationary reflection properties over a wide range of incidence angles,” J. Opt. Soc. Am. 73, 160–166 (1983).
    [CrossRef]
  6. A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990).
  7. R. M. A. Azzam, A.-R. M. Zaghloul, N. M. Bashara, “Ellipsometric function of a film–substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am. 65, 252–260 (1975).
    [CrossRef]
  8. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugation,” Appl. Opt. 22, 3220–3228 (1983).
    [CrossRef] [PubMed]
  9. K. Gaylord, E. N. Glytsis, M. G. Moharam, “Zero-reflectivity homogeneous layers and high spatial-frequency surface-relief gratings on lossy materials,” Appl. Opt. 26, 3123–3135 (1987).
    [CrossRef] [PubMed]
  10. K. Gaylord, E. N. Glytsis, M. G. Moharam, W. E. Baird, “Technique for producing antireflection grating surfaces on dielectrics, semiconductors, and metals,” U.S. Patent5,007,708 (16April1991).
  11. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous-layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
    [CrossRef] [PubMed]
  12. D. C. Flanders, “Submicrometer-periodicity gratings as artificial dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
    [CrossRef]
  13. E. B. Grann, M. G. Moharam, D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994).
    [CrossRef]
  14. M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Anti-reflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
    [CrossRef] [PubMed]
  15. A. M. Kan’an, R. M. A. Azzam, “In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism,” Opt. Eng. 33, 2029–2033 (1994).
    [CrossRef]
  16. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  17. D. D. Engelsen, “Ellipsometry of anisotropic films,” J. Opt. Soc. Am. 61, 1460–1466 (1971).
    [CrossRef]
  18. J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys.: Condens. Matter 3, 6121–6133 (1991).
    [CrossRef]
  19. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  20. M. A. Ordal, L. L. Long, R. J. Bell, S. 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, Ti, and W in the infrared and far infrared,” Appl. Opt. 22, 1099–1119 (1983).
    [CrossRef] [PubMed]
  21. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).

1995 (1)

M. M. K. Howlader, R. M. A. Azzam, “Periodic and quasi-periodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence,” Opt. Eng. 34, 869–874 (1995).
[CrossRef]

1994 (3)

1992 (1)

1991 (1)

J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys.: Condens. Matter 3, 6121–6133 (1991).
[CrossRef]

1987 (1)

1985 (1)

1983 (4)

1982 (1)

1980 (1)

1975 (1)

1971 (1)

Alexander, R. W.

Apfel, J. H.

Azzam, R. M. A.

M. M. K. Howlader, R. M. A. Azzam, “Periodic and quasi-periodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence,” Opt. Eng. 34, 869–874 (1995).
[CrossRef]

A. M. Kan’an, R. M. A. Azzam, “In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism,” Opt. Eng. 33, 2029–2033 (1994).
[CrossRef]

R. M. A. Azzam, B. E. Perilloux, “Constraint on the optical constants of a film–substrate system for operation as an external-reflection retarder at a given angle of incidence,” Appl. Opt. 24, 1171–1179 (1985).
[CrossRef] [PubMed]

R. M. A. Azzam, M. E. R. Khan, “Single-reflection film–substrate half-wave retarders with nearly stationary reflection properties over a wide range of incidence angles,” J. Opt. Soc. Am. 73, 160–166 (1983).
[CrossRef]

R. M. A. Azzam, A.-R. M. Zaghloul, N. M. Bashara, “Ellipsometric function of a film–substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am. 65, 252–260 (1975).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Baird, W. E.

K. Gaylord, E. N. Glytsis, M. G. Moharam, W. E. Baird, “Technique for producing antireflection grating surfaces on dielectrics, semiconductors, and metals,” U.S. Patent5,007,708 (16April1991).

Bashara, N. M.

Bell, R. J.

Bell, R. R.

Bell, S. E.

Brundrett, D. L.

Case, S. K.

Engelsen, D. D.

Enger, R. C.

Flanders, D. C.

D. C. Flanders, “Submicrometer-periodicity gratings as artificial dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

Gaylord, K.

K. Gaylord, E. N. Glytsis, M. G. Moharam, “Zero-reflectivity homogeneous layers and high spatial-frequency surface-relief gratings on lossy materials,” Appl. Opt. 26, 3123–3135 (1987).
[CrossRef] [PubMed]

K. Gaylord, E. N. Glytsis, M. G. Moharam, W. E. Baird, “Technique for producing antireflection grating surfaces on dielectrics, semiconductors, and metals,” U.S. Patent5,007,708 (16April1991).

Gaylord, T. K.

Glytsis, E. N.

Grann, E. B.

Gunning, W. J.

Howlader, M. M. K.

M. M. K. Howlader, R. M. A. Azzam, “Periodic and quasi-periodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence,” Opt. Eng. 34, 869–874 (1995).
[CrossRef]

Kan’an, A. M.

A. M. Kan’an, R. M. A. Azzam, “In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism,” Opt. Eng. 33, 2029–2033 (1994).
[CrossRef]

Khan, M. E. R.

Lekner, J.

J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys.: Condens. Matter 3, 6121–6133 (1991).
[CrossRef]

Long, L. L.

Moharam, M. G.

Motamedi, M. E.

Ordal, M. A.

Perilloux, B. E.

Pommet, D. A.

Röseler, A.

A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990).

Southwell, W. H.

Ward, C. A.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Zaghloul, A.-R. M.

Appl. Opt. (8)

J. H. Apfel, “Phase retardance of periodic multilayer mirrors,” Appl. Opt. 21, 733–738 (1982).
[CrossRef] [PubMed]

M. A. Ordal, L. L. Long, R. J. Bell, S. 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, Ti, and W in the infrared and far infrared,” Appl. Opt. 22, 1099–1119 (1983).
[CrossRef] [PubMed]

R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugation,” Appl. Opt. 22, 3220–3228 (1983).
[CrossRef] [PubMed]

R. M. A. Azzam, B. E. Perilloux, “Constraint on the optical constants of a film–substrate system for operation as an external-reflection retarder at a given angle of incidence,” Appl. Opt. 24, 1171–1179 (1985).
[CrossRef] [PubMed]

K. Gaylord, E. N. Glytsis, M. G. Moharam, “Zero-reflectivity homogeneous layers and high spatial-frequency surface-relief gratings on lossy materials,” Appl. Opt. 26, 3123–3135 (1987).
[CrossRef] [PubMed]

M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Anti-reflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
[CrossRef] [PubMed]

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous-layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
[CrossRef] [PubMed]

W. H. Southwell, “Multilayer coating design achieving a broadband 90° phase shift,” Appl. Opt. 19, 2688–2692 (1980).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

D. C. Flanders, “Submicrometer-periodicity gratings as artificial dielectrics,” Appl. Phys. Lett. 42, 492–494 (1983).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

J. Phys.: Condens. Matter (1)

J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys.: Condens. Matter 3, 6121–6133 (1991).
[CrossRef]

Opt. Eng. (2)

A. M. Kan’an, R. M. A. Azzam, “In-line quarter-wave retarders for the infrared using total refraction and total internal reflection in a prism,” Opt. Eng. 33, 2029–2033 (1994).
[CrossRef]

M. M. K. Howlader, R. M. A. Azzam, “Periodic and quasi-periodic nonquarterwave multilayer coatings for 90-deg reflection phase retardance at 45-deg angle of incidence,” Opt. Eng. 34, 869–874 (1995).
[CrossRef]

Other (5)

A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, Berlin, 1990).

K. Gaylord, E. N. Glytsis, M. G. Moharam, W. E. Baird, “Technique for producing antireflection grating surfaces on dielectrics, semiconductors, and metals,” U.S. Patent5,007,708 (16April1991).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985).

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Figures (10)

Fig. 1
Fig. 1

Cross section of a 1-D dielectric surface-relief grating on a Au substrate.

Fig. 2
Fig. 2

Geometry of a 2-D dielectric surface-relief grating with square pillars.

Fig. 3
Fig. 3

Differential reflection phase shift Δ versus angle of incidence for a bare Au substrate at light wavelength λ = 10.6 μm.

Fig. 4
Fig. 4

Locus of grating region thickness d versus grating filling factor f for QWR designs with (a) |ρ| = 1.00 ± 0.01 and |Δ| = 90° ± 0.1°, (b) |ρ| = 1.000 ± 0.001 and |Δ| = 90° ± 0.01°.

Fig. 5
Fig. 5

Differential reflection phase shift Δ as a function of incidence angle for the five QWR designs listed in Table 2.

Fig. 6
Fig. 6

Intensity reflectance ratio as a function of incidence angle for the five QWR designs listed in Table 2.

Fig. 7
Fig. 7

Average reflectance as a function of incidence angle for the five QWR designs listed in Table 2.

Fig. 8
Fig. 8

Differential reflection phase shift Δ as a function of the incident-light wavelength λ for the five QWR designs listed in Table 2.

Fig. 9
Fig. 9

Sensitivity of the differential reflection phase shift Δ to error of the grating filling factor f for the five QWR designs listed in Table 2.

Fig. 10
Fig. 10

Sensitivity of the differential reflection phase shift Δ to error of the grating-region thickness d for the five QWR designs listed in Table 2.

Tables (2)

Tables Icon

Table 1 Five Selected QWR’s at 70° Incidence Angle and 10.6-μm Light Wavelength Designed with a Homogeneous Isotropic Film on a Au Substrate

Tables Icon

Table 2 Five QWR’s at 70° Incidence Angle and 10.6-μm Light Wavelength Designed with a 2-D ZnS Grating on a Au Substrate

Equations (29)

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R γ = [ r 12 γ + r 23 γ exp ( - j 2 β γ ) ] / [ 1 + r 12 γ r 23 γ exp ( - j 2 β γ ) ] , γ = p p , s s ,
r 12 p p = ( N o N e cos ϕ 1 - n 1 p 1 ) / ( N o N e cos ϕ 1 + n 1 p 1 ) ,
r 23 p p = ( - N o N e cos ϕ 3 + n 3 p 3 ) / ( N o N e cos ϕ 3 + n 3 p 3 ) ,
r 12 s s = ( n 1 cos ϕ 1 - s 1 ) / ( n 1 cos ϕ 1 + s 1 ) ,
r 23 s s = ( - n 3 cos ϕ 3 + s 3 ) / ( n 3 cos ϕ 3 + s 3 ) ,
p 1 = ( N e 2 - n 1 2 sin 2 ϕ 1 ) 1 / 2 ,
p 3 = ( N e 2 - n 3 2 sin 2 ϕ 3 ) 1 / 2 ,
s 1 = ( N o 2 - n 1 2 sin 2 ϕ 1 ) 1 / 2 ,
s 3 = ( N o 2 - n 3 2 sin 2 ϕ 3 ) 1 / 2 .
β p p = ( 2 π d / λ ) ( N o / N e ) p 1 ,
β s s = ( 2 π d / λ ) s 1 ,
r 12 p p = ( N o N e cos ϕ 1 - n 1 s 1 ) / ( N o N e cos ϕ 1 + n 1 s 1 ) ,
r 23 p p = ( - N o N e cos ϕ 3 + n 3 s 3 ) / ( N o N e cos ϕ 3 + n 3 s 3 ) ,
r 12 s s = ( n 1 cos ϕ 1 - s 1 ) / ( n 1 cos ϕ 1 + s 1 ) ,
r 23 s s = ( - n 3 cos ϕ 3 + s 3 ) / ( n 3 cos ϕ 3 + s 3 ) ;
β p p = ( 2 π d / λ ) ( N e / N o ) s 1 ,
β s s = ( 2 π d / λ ) s 1 .
r 12 p p = ( N o 2 cos ϕ 1 - n 1 s 1 ) / ( N o 2 cos ϕ 1 + n 1 s 1 ) ,
r 23 p p = ( - N o 2 cos ϕ 3 + n 3 s 3 ) / ( N o 2 cos ϕ 3 + n 3 s 3 ) ,
r 12 s s = ( n 1 cos ϕ 1 - p 1 ) / ( n 1 cos ϕ 1 + p 1 ) ,
r 23 s s = ( - n 3 cos ϕ 3 + p 3 ) / ( n 3 cos ϕ 3 + p 3 ) ;
β p p = ( 2 d π / λ ) s 1 ,
β s s = ( 2 d π / λ ) p 1 .
R γ = R γ 2 .
ρ = R p / R s = R p / R s exp ( j Δ ) = ± j ,
N o = ( 1 - f + n c 2 f ) 1 / 2 .
N e = ( 1 - f + f / n c 2 ) - 1 / 2 .
N o = ( { ( 1 - f + f n c 2 ) [ f + ( 1 - f ) n c 2 ] + n c 2 } / { 2 [ f + ( 1 - f ) n c 2 ] } ) 1 / 2 ,
N e = ( 1 - f + f n c 2 ) 1 / 2 .

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