Abstract

The recursion equation for electric field strength in a multilayer thin film system yields only the tangential component of the field. This paper discusses the relationship between the tangential component, the peak value, and the time average value of the total electric field for the two planes of polarization. This approach leads to easy understanding of the discontinuous field strength for p polarization and the relationship between the peak and time average field strengths. The results are applied to a polarizing beam splitter of the type used with high energy lasers.

© 1976 Optical Society of America

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References

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  1. D. Kossel, K. Deutscher, K. Hirschberg, Physics of Thin Films (Academic, New York, 1969), Vol. 5, pp. 1–45.
  2. W. W. Buchman, Appl. Opt. 14, 1220 (1975).
  3. R. H. Miller, Opt. Spectra 9 (7), 32 (1975).
  4. B. F. Newnam, D. H. Gill, G. Faulkner, NBS Special Publication No. 435, 254 (1976).
  5. L. Levi, Applied Optics (Wiley, New York, 1968), p. 51.
  6. P. H. Berning, Physics of Thin Films (Academic, New York, 1963), Vol. 1, pp. 69–121.
  7. J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963), p. 394.

1976 (1)

B. F. Newnam, D. H. Gill, G. Faulkner, NBS Special Publication No. 435, 254 (1976).

1975 (2)

W. W. Buchman, Appl. Opt. 14, 1220 (1975).

R. H. Miller, Opt. Spectra 9 (7), 32 (1975).

Berning, P. H.

P. H. Berning, Physics of Thin Films (Academic, New York, 1963), Vol. 1, pp. 69–121.

Buchman, W. W.

Deutscher, K.

D. Kossel, K. Deutscher, K. Hirschberg, Physics of Thin Films (Academic, New York, 1969), Vol. 5, pp. 1–45.

Faulkner, G.

B. F. Newnam, D. H. Gill, G. Faulkner, NBS Special Publication No. 435, 254 (1976).

Gill, D. H.

B. F. Newnam, D. H. Gill, G. Faulkner, NBS Special Publication No. 435, 254 (1976).

Hirschberg, K.

D. Kossel, K. Deutscher, K. Hirschberg, Physics of Thin Films (Academic, New York, 1969), Vol. 5, pp. 1–45.

Kossel, D.

D. Kossel, K. Deutscher, K. Hirschberg, Physics of Thin Films (Academic, New York, 1969), Vol. 5, pp. 1–45.

Levi, L.

L. Levi, Applied Optics (Wiley, New York, 1968), p. 51.

Miller, R. H.

R. H. Miller, Opt. Spectra 9 (7), 32 (1975).

Newnam, B. F.

B. F. Newnam, D. H. Gill, G. Faulkner, NBS Special Publication No. 435, 254 (1976).

Stone, J. M.

J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963), p. 394.

Appl. Opt. (1)

NBS Special Publication No. 435 (1)

B. F. Newnam, D. H. Gill, G. Faulkner, NBS Special Publication No. 435, 254 (1976).

Opt. Spectra (1)

R. H. Miller, Opt. Spectra 9 (7), 32 (1975).

Other (4)

L. Levi, Applied Optics (Wiley, New York, 1968), p. 51.

P. H. Berning, Physics of Thin Films (Academic, New York, 1963), Vol. 1, pp. 69–121.

J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963), p. 394.

D. Kossel, K. Deutscher, K. Hirschberg, Physics of Thin Films (Academic, New York, 1969), Vol. 5, pp. 1–45.

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Figures (4)

Fig. 1
Fig. 1

Sketch of radiation passing through a slab at oblique incidence to show that the beam intensity is not constant.

Fig. 2
Fig. 2

Indentification of the positions for which the maximum value of E 2 ¯ is given in Table I.

Fig. 3
Fig. 3

Profile of E 2 ¯ in Buchman beam splitter with radiation incident from the substrate. The maximum values in the different materials are indicated.

Fig. 4
Fig. 4

Profile of E 2 ¯ in Buchman beam splitter with radiation incident from air. The maximum values in the different materials are indicated.

Tables (1)

Tables Icon

Table I Maximum Values of E 2 ¯ for Buchman Beam splitter

Equations (26)

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M = ( μ ) 1 / 2 E 2 ¯ ,
M ( W / cm 2 ) = 0.0013 n E 2 max ,
E max ( V / cm ) = 27.4 ( M / n ) 1 / 2 .
M 0 cos θ 0 = M cos θ ,
T = ( cos θ 0 / cos θ ) T ,
tangential component : E = E p cos θ 0 , normal component : E = E p sin θ 0 .
tangential component : E = E s , normal component : E = 0.
E j / E j - 1 = ( 1 + r e 2 i ϕ ) / ( 1 + r ) e i ϕ ,
E j 2 ¯ = ½ E j 2 .
parallel : E = E i cos θ ( 1 + r ) , perpendicular : E = E i sin θ ( 1 - r ) ,
E E = sin θ cos θ ( 1 - r 1 + r ) .
E 2 = ( E sin ω t ) 2 + [ E sin ( ω t + ρ ) ] 2 ,
E 2 ¯ = 1 τ t t + τ E 2 d t = ½ ( E 2 + E 2 ) .
( E 2 + E 2 ) 1 / 2 .
E 2 peak = ½ [ E 2 + E 2 + ( E 4 + 2 E 2 E 2 cos 2 ρ + E 4 ) 1 / 2 ] .
L E peak 2 L .
E 2 peak 2 E 2 ¯ ,
E 2 = E j - 1 / ( 1 + r ) 2 ( A + B ) ,
E 2 = E j - 1 tan θ / ( 1 - r ) 2 ( A - B ) ,
E j s 2 ¯ = ½ E j - 1 / ( 1 + r ) 2 ( A + B ) ,
E j p 2 ¯ = ½ E j - 1 / ( 1 + r ) 2 [ A ( 1 + tan θ 2 ) + B ( 1 - tan θ 2 ) ] .
n E 2 cos θ = Tn 0 E 0 2 cos θ 0 .
absorption ( n k E 2 ¯ d t ) / ( n 0 E 0 2 ¯ cos θ 0 ) ,
E 2 ¯ = 1 T E 2 ¯ d t ,
E 2 s ¯ = ½ E 1 / ( 1 + r ) 2 ( C - D ) ,
E 2 p ¯ = ½ E 1 / ( 1 + r ) 2 [ C ( 1 + tan θ 2 ) - D ( 1 - tan θ 2 ) ] , C = [ ( 1 - e - α ) - r r * ( 1 - e α ) ] / α , D = [ ( 1 - e β ) - r * ( 1 - e - β ) ] / β .

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