Abstract

A perfect antireflection (AR) coating would remove completely the reflection from an interface between two media for all wavelengths, polarizations, and angles of incidence. The degree to which this can be achieved is investigated numerically. It is shown that wideband solutions can be found provided that layers can be deposited with refractive indices that are close to that of the low-index medium. Thus realistic solutions exist for interfaces between two solid media. Narrow-band high-angle AR solutions are also possible for polarized light and for unpolarized light in the vicinity of certain reststrahlen bands.

© 2002 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
    [CrossRef] [PubMed]
  4. I. V. Grebenshchikov, L. G. Vlasov, B. S. Neporent, N. V. Suikovskaya, Prosvetlenie Optiki (Antireflection Coating of Optical Surfaces) (State Publishers of Technical and Theoretical Literature, Moscow, 1946).
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    [CrossRef]
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  8. J. A. Dobrowolski, S. H. C. Piotrowski, “Refractive index as a variable in the numerical design of optical thin films,” Appl. Opt. 21, 1502–1510 (1982).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  17. A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1988), pp. 41–55.
  18. J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 8.95–8.102.
  19. H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.
  20. J. A. Dobrowolski, D. Poitras, P. Ma, M. Acree, H. Vakil, “Towards perfect antireflection coatings,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Postconference Digest (Optical Society of America, Washington, D.C., 2001), paper TuA2-1-2.

1998 (1)

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

1997 (1)

1992 (1)

1989 (1)

J. C. Monga, “Anti-reflection coatings for grazing incidence angles,” J. Mod. Opt. 36, 381–387 (1989).
[CrossRef]

1982 (1)

1978 (1)

1977 (1)

1966 (1)

1961 (1)

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
[CrossRef]

1952 (1)

1880 (1)

J. W. S. Rayleigh, “On reflections of vibrations at the confines of two media between which the transition is gradual,” Proc. London Math. Soc. 11, 51–56 (1880).

Acree, M.

J. A. Dobrowolski, D. Poitras, P. Ma, M. Acree, H. Vakil, “Towards perfect antireflection coatings,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Postconference Digest (Optical Society of America, Washington, D.C., 2001), paper TuA2-1-2.

Baumeister, P.

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
[CrossRef]

Baumeister, P. W.

Chen, S.

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Dobrowolski, J. A.

K. V. Popov, J. A. Dobrowolski, A. V. Tikhonravov, B. T. Sullivan, “Broadband high-reflection multilayer coatings at oblique angles of incidence,” Appl. Opt. 36, 2139–2151 (1997).
[CrossRef] [PubMed]

J. A. Dobrowolski, S. H. C. Piotrowski, “Refractive index as a variable in the numerical design of optical thin films,” Appl. Opt. 21, 1502–1510 (1982).
[CrossRef] [PubMed]

J. A. Dobrowolski, D. Poitras, P. Ma, M. Acree, H. Vakil, “Towards perfect antireflection coatings,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Postconference Digest (Optical Society of America, Washington, D.C., 2001), paper TuA2-1-2.

J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 8.95–8.102.

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 42.19–42.34.

Epstein, L. I.

Fan, S.

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Grebenshchikov, I. V.

I. V. Grebenshchikov, L. G. Vlasov, B. S. Neporent, N. V. Suikovskaya, Prosvetlenie Optiki (Antireflection Coating of Optical Surfaces) (State Publishers of Technical and Theoretical Literature, Moscow, 1946).

Joannopoulos, J. D.

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Ma, P.

J. A. Dobrowolski, D. Poitras, P. Ma, M. Acree, H. Vakil, “Towards perfect antireflection coatings,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Postconference Digest (Optical Society of America, Washington, D.C., 2001), paper TuA2-1-2.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (Institute of Physics, Bristol, UK, 2001), p. 154.

Michel, J.

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Minot, M. J.

Monga, J. C.

J. C. Monga, “Double-layer broadband antireflection coatings for grazing incidence angles,” Appl. Opt. 31, 546–553 (1992).
[CrossRef] [PubMed]

J. C. Monga, “Anti-reflection coatings for grazing incidence angles,” J. Mod. Opt. 36, 381–387 (1989).
[CrossRef]

Neporent, B. S.

I. V. Grebenshchikov, L. G. Vlasov, B. S. Neporent, N. V. Suikovskaya, Prosvetlenie Optiki (Antireflection Coating of Optical Surfaces) (State Publishers of Technical and Theoretical Literature, Moscow, 1946).

Ohmer, M. C.

Philipp, H. R.

H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.

Piotrowski, S. H. C.

Pohlack, H.

H. Pohlack, “Zum Problem der Reflexionsverminderung optischer Gläser bei nichtsenkrechtem Lichteinfall,” in Jenaer Jahrbuch 1952, P. Görlich, ed. (Fischer, Jena, Germany, 1952), pp. 103–118.

Poitras, D.

J. A. Dobrowolski, D. Poitras, P. Ma, M. Acree, H. Vakil, “Towards perfect antireflection coatings,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Postconference Digest (Optical Society of America, Washington, D.C., 2001), paper TuA2-1-2.

Popov, K. V.

Rayleigh, J. W. S.

J. W. S. Rayleigh, “On reflections of vibrations at the confines of two media between which the transition is gradual,” Proc. London Math. Soc. 11, 51–56 (1880).

Sawaki, T.

T. Sawaki, “Studies on anti-reflection films,” Research rep. 315 (Osaka Industrial Research Institute, Osaka, Japan, 1960).

Suikovskaya, N. V.

I. V. Grebenshchikov, L. G. Vlasov, B. S. Neporent, N. V. Suikovskaya, Prosvetlenie Optiki (Antireflection Coating of Optical Surfaces) (State Publishers of Technical and Theoretical Literature, Moscow, 1946).

Sullivan, B. T.

Thelen, A.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1988), pp. 41–55.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Tikhonravov, A. V.

Turner, A. F.

Vakil, H.

J. A. Dobrowolski, D. Poitras, P. Ma, M. Acree, H. Vakil, “Towards perfect antireflection coatings,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Postconference Digest (Optical Society of America, Washington, D.C., 2001), paper TuA2-1-2.

Vlasov, L. G.

I. V. Grebenshchikov, L. G. Vlasov, B. S. Neporent, N. V. Suikovskaya, Prosvetlenie Optiki (Antireflection Coating of Optical Surfaces) (State Publishers of Technical and Theoretical Literature, Moscow, 1946).

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Appl. Opt. (4)

J. Mod. Opt. (1)

J. C. Monga, “Anti-reflection coatings for grazing incidence angles,” J. Mod. Opt. 36, 381–387 (1989).
[CrossRef]

J. Opt. Soc. Am. (3)

Opt. Acta (1)

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
[CrossRef]

Proc. London Math. Soc. (1)

J. W. S. Rayleigh, “On reflections of vibrations at the confines of two media between which the transition is gradual,” Proc. London Math. Soc. 11, 51–56 (1880).

Science (1)

Y. Fink, J. N. Winn, S. Fan, S. Chen, J. Michel, J. D. Joannopoulos, E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Other (9)

I. V. Grebenshchikov, L. G. Vlasov, B. S. Neporent, N. V. Suikovskaya, Prosvetlenie Optiki (Antireflection Coating of Optical Surfaces) (State Publishers of Technical and Theoretical Literature, Moscow, 1946).

T. Sawaki, “Studies on anti-reflection films,” Research rep. 315 (Osaka Industrial Research Institute, Osaka, Japan, 1960).

H. Pohlack, “Zum Problem der Reflexionsverminderung optischer Gläser bei nichtsenkrechtem Lichteinfall,” in Jenaer Jahrbuch 1952, P. Görlich, ed. (Fischer, Jena, Germany, 1952), pp. 103–118.

H. A. Macleod, Thin Film Optical Filters (Institute of Physics, Bristol, UK, 2001), p. 154.

A. Thelen, Design of Optical Interference Coatings (McGraw-Hill, New York, 1988), pp. 41–55.

J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp. 8.95–8.102.

H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.

J. A. Dobrowolski, D. Poitras, P. Ma, M. Acree, H. Vakil, “Towards perfect antireflection coatings,” in Optical Interference Coatings, Vol. 63 of OSA Trends in Optics and Photonics Postconference Digest (Optical Society of America, Washington, D.C., 2001), paper TuA2-1-2.

J. A. Dobrowolski, “Optical properties of films and coatings,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), pp. 42.19–42.34.

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Figures (6)

Fig. 1
Fig. 1

Structure and effective refractive-index profiles of various types of AR coating. (a)–(c) Homogeneous single-layer, digital, and multilayer AR coatings; (d)–(f) inhomogeneous single-layer, structured, and complex AR coatings (from Fig. 8, Ref. 11).

Fig. 2
Fig. 2

Reflectance as a function of angle of incidence for s- and p-polarized light of an interface between a substrate of index 3.00 and air.

Fig. 3
Fig. 3

Refractive-index profiles (column 1), angular variation of the average reflectance for unpolarized light (column 2), and spectral variation of the average reflectance for 30°, 50°, 60°, 70°, 80°, and 85° (column 3) of AR coatings for different interfaces. (a)–(c) Conventional 3-layer AR coating for a 3.00–1.00 interface; (d)–(f) 200-layer AR coating for a 3.00–1.00 interface; (g)–(i) 47-layer AR coating for a 1.48–1.00 interface; (j)–(l) single-layer AR coating for a 3.00–1.48 interface; (m)–(o) 6-layer AR coating for a 3.00–1.48 interface; (p)–(r) 53-layer AR coating for a 3.00–1.00 interface; (s)–(u) 7-layer AR coating for a 3.00–1.00 interface; (v)–(x) 4-layer AR coating for a 3.00–1.00 interface.

Fig. 4
Fig. 4

Cosecant of the angle of refraction in layers of different refractive indices as a function of angle of incidence.

Fig. 5
Fig. 5

Refractive-index profiles (column 1), angular variation of the reflectance (column 2), and spectral variation of the reflectance for indicated angles of incidence (column 3) of AR coatings for 3.00–1.00 interfaces. (a)–(c) Herpin equivalent index design for unpolarized light; (d)–(f) Herpin equivalent index design for s-polarized light; (g)–(i) Herpin equivalent index design for p-polarized light; (j)–(l) AR coating for unpolarized light based on use of reststrahlen materials.

Fig. 6
Fig. 6

Optical constants of SiO2 in the reststrahlen region.

Tables (1)

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Table 1 Construction Parameters of Some of the Systems

Equations (3)

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nM sinθ=nsinϕ.
ndϕ=nd0 cosϕ
nd0/ndϕ=secϕ.

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