Abstract

We present a factorization scheme that is particularly suited to multilayer optics, and we exploit it to develop a consistent description of the action of a multilayer in terms of three basic matrices. Connections with equivalent behaviors in geometrical optics are discussed.

© 2001 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1999).
    [CrossRef]
  2. H. A. Macleod, Thin-Film Optical Filters (Adam-Hilger, Bristol, UK, 1986).
    [CrossRef]
  3. J. J. Monzón and L. L. Sánchez-Soto, J. Opt. Soc. Am. A 16, 2013 (1999).
    [CrossRef]
  4. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  5. J. J. Monzón and L. L. Sánchez-Soto, Opt. Commun. 162, 1 (1999).
    [CrossRef]
  6. J. J. Monzón and L. L. Sánchez-Soto, J. Opt. Soc. Am. A 16, 2786 (1999).
    [CrossRef]
  7. J. Lekner, Theory of Reflection (Kluwer Scientific, Dordrecht, The Netherlands, 1987).
  8. H. H. Arsenault and B. Macukow, J. Opt. Soc. Am. 73, 1350 (1983).
  9. S. Abe and J. T. Sheridan, Opt. Lett. 19, 1801 (1994).
    [CrossRef]
  10. J. Shamir and N. Cohen, J. Opt. Soc. Am. A 12, 560 (1995).
    [CrossRef]
  11. A. O. Barut and R. Ra̧czka, Theory of Group Representations and Applications (PWN–Polish Scientific, Warsaw, 1977).
  12. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces (Academic, New York, 1978).
  13. H. Bacry and M. Cadilhac, Phys. Rev. A 23, 2533 (1981).
    [CrossRef]
  14. M. Nazarathy and J. Shamir, J. Opt. Soc. Am. 72, 356 (1982).
  15. E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
    [CrossRef]
  16. R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
    [CrossRef]
  17. R. Simon and N. Mukunda, Phys. Rev. Lett. 70, 880 (1993).
    [CrossRef] [PubMed]
  18. G. S. Agarwal and R. Simon, Opt. Commun. 100, 411 (1993).
    [CrossRef]
  19. R. Simon and N. Mukunda, J. Opt. Soc. Am. A 15, 2146 (1998).
    [CrossRef]
  20. R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 3273 (1984).
    [CrossRef]

1999 (3)

1998 (1)

1995 (1)

1994 (1)

1993 (2)

R. Simon and N. Mukunda, Phys. Rev. Lett. 70, 880 (1993).
[CrossRef] [PubMed]

G. S. Agarwal and R. Simon, Opt. Commun. 100, 411 (1993).
[CrossRef]

1988 (1)

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

1985 (1)

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

1984 (1)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 3273 (1984).
[CrossRef]

1983 (1)

1982 (1)

1981 (1)

H. Bacry and M. Cadilhac, Phys. Rev. A 23, 2533 (1981).
[CrossRef]

Abe, S.

Agarwal, G. S.

G. S. Agarwal and R. Simon, Opt. Commun. 100, 411 (1993).
[CrossRef]

Arsenault, H. H.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

Bacry, H.

H. Bacry and M. Cadilhac, Phys. Rev. A 23, 2533 (1981).
[CrossRef]

Barut, A. O.

A. O. Barut and R. Ra̧czka, Theory of Group Representations and Applications (PWN–Polish Scientific, Warsaw, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

Cadilhac, M.

H. Bacry and M. Cadilhac, Phys. Rev. A 23, 2533 (1981).
[CrossRef]

Cohen, N.

Helgason, S.

S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces (Academic, New York, 1978).

Lekner, J.

J. Lekner, Theory of Reflection (Kluwer Scientific, Dordrecht, The Netherlands, 1987).

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Adam-Hilger, Bristol, UK, 1986).
[CrossRef]

Macukow, B.

Monzón, J. J.

Mukunda, N.

R. Simon and N. Mukunda, J. Opt. Soc. Am. A 15, 2146 (1998).
[CrossRef]

R. Simon and N. Mukunda, Phys. Rev. Lett. 70, 880 (1993).
[CrossRef] [PubMed]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 3273 (1984).
[CrossRef]

Nazarathy, M.

Ra¸czka, R.

A. O. Barut and R. Ra̧czka, Theory of Group Representations and Applications (PWN–Polish Scientific, Warsaw, 1977).

Sánchez-Soto, L. L.

Shamir, J.

Sheridan, J. T.

Simon, R.

R. Simon and N. Mukunda, J. Opt. Soc. Am. A 15, 2146 (1998).
[CrossRef]

G. S. Agarwal and R. Simon, Opt. Commun. 100, 411 (1993).
[CrossRef]

R. Simon and N. Mukunda, Phys. Rev. Lett. 70, 880 (1993).
[CrossRef] [PubMed]

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 3273 (1984).
[CrossRef]

Sudarshan, E. C. G.

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 3273 (1984).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

Opt. Acta (1)

E. C. G. Sudarshan, N. Mukunda, and R. Simon, Opt. Acta 32, 855 (1985).
[CrossRef]

Opt. Commun. (3)

R. Simon, N. Mukunda, and E. C. G. Sudarshan, Opt. Commun. 65, 322 (1988).
[CrossRef]

J. J. Monzón and L. L. Sánchez-Soto, Opt. Commun. 162, 1 (1999).
[CrossRef]

G. S. Agarwal and R. Simon, Opt. Commun. 100, 411 (1993).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 3273 (1984).
[CrossRef]

H. Bacry and M. Cadilhac, Phys. Rev. A 23, 2533 (1981).
[CrossRef]

Phys. Rev. Lett. (1)

R. Simon and N. Mukunda, Phys. Rev. Lett. 70, 880 (1993).
[CrossRef] [PubMed]

Other (6)

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1999).
[CrossRef]

H. A. Macleod, Thin-Film Optical Filters (Adam-Hilger, Bristol, UK, 1986).
[CrossRef]

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).

J. Lekner, Theory of Reflection (Kluwer Scientific, Dordrecht, The Netherlands, 1987).

A. O. Barut and R. Ra̧czka, Theory of Group Representations and Applications (PWN–Polish Scientific, Warsaw, 1977).

S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces (Academic, New York, 1978).

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Figures (1)

Fig. 1
Fig. 1

Wave vectors of the input [Ea+ and Es-] and the output [Ea- and Es+] fields in a multilayer sandwiched between two semi-infinite ambient (0) and substrate m+1 media. The angle of refraction in the jth medium is denoted θj.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

Ea-=RasEa++TsaEs-,Es+=TasEa++RsaEs-,
E=E+E-,
Ea=MasEs,
Mas=1/Tas-Rsa/TasRas/TasX/Tas,
Ras=Rasexpiρ,Tas=Tasexpiτ.
X=expi2τ,Rsa=-Ras*expi2τ,
Mas=1/TasRas*/Tas*Ras/Tas1/Tas*αββ*α*,
Mas=KϕAξNν,
Kϕ=expiϕ/200exp-iϕ/2,Aξ=coshξ/2isinhξ/2-isinhξ/2coshξ/2,Nν=1-iν/2ν/2ν/21+iν/2.
ϕ/2=argα+iβ,ξ/2=lnl/α+iβ,ν/2=Reαβ*/α+iβ2.
U=121ii1
E=MasEs,
E=E+E-=UE=12E++iE-E-+iE+,
Mas=UMasU-1=abcd,
a=Reα+Imβ,b=Imα+Reβ,c=-Imα+Reβ,d=Reα-Imβ.
Mas=KϕAξNν,
Kϕ=cosϕ/2sinϕ/2-sinϕ/2cosϕ/2,Aξ=expξ/200exp-ξ/2,Nν=10ν1.

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