Abstract

The equality of the transmitted and reflected irradiances by a symmetric, absorbing beam splitter consisting of three media is considered. The condition of minimum absorptance and the phase difference between the transmitted and reflected fields are studied as well.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. H. Steel, Interferometry (Cambridge U. Press, London, 1983), Sec. 8.6.
  2. A. L. Fymat, “Jones's matrix representation of optical instruments. I: Beam splitters,” Appl. Opt. 10, 2499–2505 (1971).
    [CrossRef] [PubMed]
  3. J. J. Monzón, L. L. Sánchez-Soto, “Some properties of absorbing beam splitters,” Optik 97, 71–74 (1994).
  4. H. A. Macleod, Thin-film Optical Filters (Hilger, Bristol, UK, 1986), p. 148.
  5. F. Pi, G. Orriols, “Energy balance in the superposition of light waves with lossless beam splitters,” Am. J. Phys. 53, 667–670 (1985).
    [CrossRef]
  6. Z. Y. Ou, L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. 57, 66–67 (1989).
    [CrossRef]
  7. J. J. Monzón, L. L. Sánchez-Soto, “Absorbing beam splitter in a Michelson interferometer,” Appl. Opt. 34, 7834–7839 (1995).
    [CrossRef] [PubMed]
  8. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Sec. 4.6.
  9. J. J. Monzón, L. L. Sánchez-Soto, “On the concept of absorption for a Fabry–Perot interferometer,” Am. J. Phys. 63 (1995).
  10. J. J. Monzón, L. L. Sánchez-Soto, E. Bernabeu, “Influence of coating thickness on the performance of a Fabry–Perot interferometer,” Appl. Opt. 30, 4126–4132 (1991).
    [CrossRef] [PubMed]
  11. J. J. Monzón, L. L. Sánchez-Soto, “Reflected fringes in a Fabry–Perot interferometer with absorbing coatings,” J. Opt. Soc. Am. A 12, 132–136 (1995).
    [CrossRef]
  12. J. J. Monzón, L. L. Sánchez-Soto, “On the definition of absorption for a Fabry–Perot interferometer,” Pure Appl. Opt. 1, 219–226 (1992);“Optical performance of absorber structures for thermal detectors,” Appl. Opt. 33, 5137–5141 (1994).
    [CrossRef] [PubMed]
  13. K. W. Raine, M. J. Downs, “Beam-splitter coatings for producing phase quadrature interferometer outputs,” Opt. Acta 25, 549–558 (1978).
    [CrossRef]
  14. F. Parmigiani, “Phase dependence of the Michelson interferometer outputs on the absorbing beam splitter thickness,” Opt. Commun. 38, 319–324 (1981).
    [CrossRef]
  15. J. H. Apfel, “Triangular coordinate graphical presentation of the optical performance of a semitransparent metal film,” Appl. Opt. 29, 4272–4275 (1990).
    [CrossRef] [PubMed]
  16. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

1995 (3)

1994 (1)

J. J. Monzón, L. L. Sánchez-Soto, “Some properties of absorbing beam splitters,” Optik 97, 71–74 (1994).

1992 (1)

J. J. Monzón, L. L. Sánchez-Soto, “On the definition of absorption for a Fabry–Perot interferometer,” Pure Appl. Opt. 1, 219–226 (1992);“Optical performance of absorber structures for thermal detectors,” Appl. Opt. 33, 5137–5141 (1994).
[CrossRef] [PubMed]

1991 (1)

1990 (1)

1989 (1)

Z. Y. Ou, L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. 57, 66–67 (1989).
[CrossRef]

1985 (1)

F. Pi, G. Orriols, “Energy balance in the superposition of light waves with lossless beam splitters,” Am. J. Phys. 53, 667–670 (1985).
[CrossRef]

1981 (1)

F. Parmigiani, “Phase dependence of the Michelson interferometer outputs on the absorbing beam splitter thickness,” Opt. Commun. 38, 319–324 (1981).
[CrossRef]

1978 (1)

K. W. Raine, M. J. Downs, “Beam-splitter coatings for producing phase quadrature interferometer outputs,” Opt. Acta 25, 549–558 (1978).
[CrossRef]

1971 (1)

Apfel, J. H.

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Sec. 4.6.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Sec. 4.6.

Bernabeu, E.

Downs, M. J.

K. W. Raine, M. J. Downs, “Beam-splitter coatings for producing phase quadrature interferometer outputs,” Opt. Acta 25, 549–558 (1978).
[CrossRef]

Fymat, A. L.

Macleod, H. A.

H. A. Macleod, Thin-film Optical Filters (Hilger, Bristol, UK, 1986), p. 148.

Mandel, L.

Z. Y. Ou, L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. 57, 66–67 (1989).
[CrossRef]

Monzón, J. J.

J. J. Monzón, L. L. Sánchez-Soto, “Absorbing beam splitter in a Michelson interferometer,” Appl. Opt. 34, 7834–7839 (1995).
[CrossRef] [PubMed]

J. J. Monzón, L. L. Sánchez-Soto, “Reflected fringes in a Fabry–Perot interferometer with absorbing coatings,” J. Opt. Soc. Am. A 12, 132–136 (1995).
[CrossRef]

J. J. Monzón, L. L. Sánchez-Soto, “On the concept of absorption for a Fabry–Perot interferometer,” Am. J. Phys. 63 (1995).

J. J. Monzón, L. L. Sánchez-Soto, “Some properties of absorbing beam splitters,” Optik 97, 71–74 (1994).

J. J. Monzón, L. L. Sánchez-Soto, “On the definition of absorption for a Fabry–Perot interferometer,” Pure Appl. Opt. 1, 219–226 (1992);“Optical performance of absorber structures for thermal detectors,” Appl. Opt. 33, 5137–5141 (1994).
[CrossRef] [PubMed]

J. J. Monzón, L. L. Sánchez-Soto, E. Bernabeu, “Influence of coating thickness on the performance of a Fabry–Perot interferometer,” Appl. Opt. 30, 4126–4132 (1991).
[CrossRef] [PubMed]

Orriols, G.

F. Pi, G. Orriols, “Energy balance in the superposition of light waves with lossless beam splitters,” Am. J. Phys. 53, 667–670 (1985).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou, L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. 57, 66–67 (1989).
[CrossRef]

Parmigiani, F.

F. Parmigiani, “Phase dependence of the Michelson interferometer outputs on the absorbing beam splitter thickness,” Opt. Commun. 38, 319–324 (1981).
[CrossRef]

Pi, F.

F. Pi, G. Orriols, “Energy balance in the superposition of light waves with lossless beam splitters,” Am. J. Phys. 53, 667–670 (1985).
[CrossRef]

Raine, K. W.

K. W. Raine, M. J. Downs, “Beam-splitter coatings for producing phase quadrature interferometer outputs,” Opt. Acta 25, 549–558 (1978).
[CrossRef]

Sánchez-Soto, L. L.

J. J. Monzón, L. L. Sánchez-Soto, “Absorbing beam splitter in a Michelson interferometer,” Appl. Opt. 34, 7834–7839 (1995).
[CrossRef] [PubMed]

J. J. Monzón, L. L. Sánchez-Soto, “Reflected fringes in a Fabry–Perot interferometer with absorbing coatings,” J. Opt. Soc. Am. A 12, 132–136 (1995).
[CrossRef]

J. J. Monzón, L. L. Sánchez-Soto, “On the concept of absorption for a Fabry–Perot interferometer,” Am. J. Phys. 63 (1995).

J. J. Monzón, L. L. Sánchez-Soto, “Some properties of absorbing beam splitters,” Optik 97, 71–74 (1994).

J. J. Monzón, L. L. Sánchez-Soto, “On the definition of absorption for a Fabry–Perot interferometer,” Pure Appl. Opt. 1, 219–226 (1992);“Optical performance of absorber structures for thermal detectors,” Appl. Opt. 33, 5137–5141 (1994).
[CrossRef] [PubMed]

J. J. Monzón, L. L. Sánchez-Soto, E. Bernabeu, “Influence of coating thickness on the performance of a Fabry–Perot interferometer,” Appl. Opt. 30, 4126–4132 (1991).
[CrossRef] [PubMed]

Steel, W. H.

W. H. Steel, Interferometry (Cambridge U. Press, London, 1983), Sec. 8.6.

Am. J. Phys. (3)

F. Pi, G. Orriols, “Energy balance in the superposition of light waves with lossless beam splitters,” Am. J. Phys. 53, 667–670 (1985).
[CrossRef]

Z. Y. Ou, L. Mandel, “Derivation of reciprocity relations for a beam splitter from energy balance,” Am. J. Phys. 57, 66–67 (1989).
[CrossRef]

J. J. Monzón, L. L. Sánchez-Soto, “On the concept of absorption for a Fabry–Perot interferometer,” Am. J. Phys. 63 (1995).

Appl. Opt. (4)

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

Opt. Acta (1)

K. W. Raine, M. J. Downs, “Beam-splitter coatings for producing phase quadrature interferometer outputs,” Opt. Acta 25, 549–558 (1978).
[CrossRef]

Opt. Commun. (1)

F. Parmigiani, “Phase dependence of the Michelson interferometer outputs on the absorbing beam splitter thickness,” Opt. Commun. 38, 319–324 (1981).
[CrossRef]

Optik (1)

J. J. Monzón, L. L. Sánchez-Soto, “Some properties of absorbing beam splitters,” Optik 97, 71–74 (1994).

Pure Appl. Opt. (1)

J. J. Monzón, L. L. Sánchez-Soto, “On the definition of absorption for a Fabry–Perot interferometer,” Pure Appl. Opt. 1, 219–226 (1992);“Optical performance of absorber structures for thermal detectors,” Appl. Opt. 33, 5137–5141 (1994).
[CrossRef] [PubMed]

Other (4)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Sec. 4.6.

H. A. Macleod, Thin-film Optical Filters (Hilger, Bristol, UK, 1986), p. 148.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

W. H. Steel, Interferometry (Cambridge U. Press, London, 1983), Sec. 8.6.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Symmetric BS's: (a) a configuration consisting of a doubly coated transparent plate with two identical metal films, and (b) a metal film sandwiched between two identical transparent plates.

Fig. 2
Fig. 2

Transmittance T , reflectance ℛ, and absorptance A for a symmetric BS in air (N 0 = 1) and with silver coatings (λ = 6888 Å, N 1 = 0.14 − 4.44i) on a glass plate (N 2 = 1.5) versus the plate phase thickness β2 (in radians) for a coating thickness d 1 = 200 Å. The angle of incidence is θ0 = 45°, and the polarization is p.

Fig. 3
Fig. 3

Plots of the condition T = ℛ: (a) Curves of equal transmittance and reflectance T = ℛ versus the coating thickness d 1 (in angstroms) and the plate phase thickness β2 (in radians) for the same BS described for Fig. 2 and for p and s polarizations, and (b) projection of the curves shown in (a) onto the horizontal plane.

Fig. 4
Fig. 4

Phase difference τ − ρ (in degrees) versus d 1 (in angstroms) for the same BS and conditions described for Fig. 2 and p polarization.

Fig. 5
Fig. 5

Behavior of the BS from Fig. 2, for p polarization and all conditions the same, in a triangular coordinate system. The coating thickness varies between 0 and 600 Å. Curve A corresponds to β2 = (Φ210 + Δ210)/2 and curve B to β2 = (Φ210 + Δ210)/2 + (π/2). The numbers indicate some typical thicknesses for the coatings.

Fig. 6
Fig. 6

Response of the BS from Fig. 2 when β2 varies between 0 and π radians for coating thicknesses of 50 and 200 Å (a) for p polarization, and (b) for s polarization. The other data are the same as for Fig. 2.

Fig. 7
Fig. 7

Values of T = ℛ for the BS from Fig. 2 versus the coating thickness d 1 in angstroms.

Fig. 8
Fig. 8

Curves of equal transmittance and reflectance for p and s polarizations of a silver film sanwiched between two identical glass plates. The film thickness d 2 is in angstroms, and the plate phase thickness β1 is in radians. Other data are the same as for Fig. 2.

Equations (20)

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

β j = 2 π λ N j d j cos θ j
T = T 012 T 210 exp ( i β 2 ) 1 R 210 2 exp ( i 2 β 2 ) , R = R 012 + T 012 R 210 T 210 exp ( i 2 β 2 ) 1 R 210 2 exp ( i 2 β 2 ) ,
T ijk = t i j t j k exp ( i β j ) 1 + r i j r j k exp ( i 2 β j ) , R ijk = r i j + r j k exp ( i 2 β j ) 1 + r i j r j k exp ( i 2 β j )
z 210 = R 012 R 210 T 012 T 210 R 012 = 1 + r 21 r 10 exp ( i 2 β 1 ) r 21 + r 10 exp ( i 2 β 1 ) = | z 210 | exp ( i Φ 210 ) R 210 = | R 210 | exp ( i Δ 210 ) . ,
T = R 012 ( R 210 z 210 ) exp ( i β 2 ) 1 R 210 2 exp ( i 2 β 2 ) | T | exp ( i τ ) , R = R 012 1 z 210 R 210 exp ( i 2 β 2 ) 1 R 210 2 exp ( i 2 β 2 ) | R | exp ( i ρ ) .
A = 1 T .
T ( β 1 , β 2 ) = ( β 1 , β 2 ) .
T = | R 012 | 2 | R 210 | 2 + | z 210 | 2 2 | z 210 R 210 | cos ( Φ 210 Δ 210 ) 1 + | R 210 | 4 2 | R 210 | 2 cos 2 ( β 2 Δ 210 ) ,
= | R 012 | 2 1 + | z 210 R 210 | 2 2 | z 210 R 210 | cos ( 2 β 2 Φ 210 Δ 210 ) 1 + | R 210 | 4 2 | R 210 | 2 cos 2 ( β 2 Δ 210 ) .
cos ( 2 β 2 Φ 210 Δ 210 ) = Q ( β 1 ) ,
Q ( β 1 ) = cos ( Φ 210 Δ 210 ) + ( 1 | R 210 | 2 ) ( 1 | z 210 | 2 ) 2 | z 210 R 210 | ,
1 Q ( β 1 ) 1 .
β 2 = Φ 210 + Δ 210 2 ± 1 2 arccos Q ( β 1 ) .
τ ρ = arctan [ A sin ( β 2 Φ 210 ) C sin ( β 2 Δ 210 ) B cos ( β 2 Φ 210 ) + D cos ( β 2 Δ 210 ) ] ,
A = | z 210 | ( 1 | R 210 | 2 ) , B = | z 210 | ( 1 + | R 210 | 2 ) , C = | R 210 | ( 1 | z 210 | 2 ) , D = | R 210 | ( 1 + | z 210 | 2 ) .
β 2 = arctan ( A sin Φ 210 C sin Δ 210 A cos Φ 210 C cos Δ 210 ) .
β 2 = arctan ( A sin Φ 210 B cos Φ 210 C sin Δ 210 + D cos Δ 210 A cos Φ 210 + B sin Φ 210 C cos Δ 210 D sin Δ 210 ) ,
exp ( 4 Im β 2 ) + b exp ( 2 Im β 2 ) + c = 0 ,
b = 4 | z 210 R 210 | sin Φ 210 sin Δ 210 | z 210 | 2 | R 210 | 2 | z 210 R 210 | 2 , c = 1 | z 210 R 210 | 2 .
d 2 λ 4 π Im ( N 2 cos θ 2 ) ln ( b + b 2 4 c 2 ) .

Metrics