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  1. D. A. Holmes, J. Opt. Soc. Am. 54, 1340 (1964). Wherever possible in the present work, I continue the notation used in this reference.
    [Crossref]
  2. Here I define tanψ≡T, where T is the electric field amplitude ratio factor introduced in Ref. 1.
  3. The elimination of tanβd between Eqs. (24) and (25) is most easily accomplished as follows. Take the tangent of both sides of Eq. (24), then square both sides and call the resultant (24a). Solve Eq. (25) for tan2βd and substitute tan2βd and tan4βd into Eq. (24a). After some manipulation, Eqs. (4) and (5) can be obtained.
  4. For 0< K<1, two positive real values of ∊ will satisfy Eq. (7). However, it can be shown that one of the solutions for ∊ will lie somewhere in the interval 0<∊<1 and therefore can be discarded.
  5. D. K. Burge and H. E. Bennett, J. Opt. Soc. Am. 54, 1428 (1964).
    [Crossref]

1964 (2)

J. Opt. Soc. Am. (2)

Other (3)

Here I define tanψ≡T, where T is the electric field amplitude ratio factor introduced in Ref. 1.

The elimination of tanβd between Eqs. (24) and (25) is most easily accomplished as follows. Take the tangent of both sides of Eq. (24), then square both sides and call the resultant (24a). Solve Eq. (25) for tan2βd and substitute tan2βd and tan4βd into Eq. (24a). After some manipulation, Eqs. (4) and (5) can be obtained.

For 0< K<1, two positive real values of ∊ will satisfy Eq. (7). However, it can be shown that one of the solutions for ∊ will lie somewhere in the interval 0<∊<1 and therefore can be discarded.

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Figures (1)

Fig. 1
Fig. 1

Locus of the polarization-state transformation factor ρ with βd as the changing factor and with the angle of incidence fixed at i=60°. The real part of ρ is measured along the horizontal axis and the imaginary part of ρ is measured along the vertical axis. The curve numbers specify the slab refractive index as follows: (1) n=1.5; (2) n=2.0; (3) n=2.5; (4) n=3.0; (5) n=3.5; (6) n=4.0; (7) n=4.5; (8) n=5.0. The arrow indicates the direction of travel around a circle when βd is increased from zero. All curves begin at the real point ρ=1 when βd=0. When βd=π/2, then ρ=Ks/Kp, a real number. When βd=π, all curves then arrive back at the starting point ρ=1. The cycle is repeated as βd passes through successive intervals of π. The dashed circle (– – –) has a radius of 1.5 and is centered on the real axis at 2.5; all points ρ≠1, corresponding to finite values of n, must lie within this circle.

Equations (10)

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ρ = [ 1 + j K s tan β d ] / [ 1 + j K p tan β d ] .
ρ = ( K s + K p ) / 2 K p + ( K s - K p ) / 2 K p · exp [ j π - j 2 tan - 1 ( K p tan β d ) ] .
r = ( 1 2 ) ( - 1 ) 2 / [ ( + 1 ) cot 2 i + ( - 1 ) ] ,
C 1 K 2 + C 2 K + C 3 = 0 ,
C 1 = tan 2 ψ - cos 2 Δ ,
C 2 = 2 sin 2 Δ ,
C 3 - cot 2 ψ - cos 2 Δ .
K = ( - sin 2 Δ - 2 cos Δ cot 2 ψ ) / ( tan 2 ψ - cos 2 Δ ) .
K = ( 2 cos 2 i + - sin 2 i ) / ( 2 + cos 2 i ) .
= 1 - K cos 2 i + [ ( 1 - K ) 2 + ( 1 - K 2 ) sin 2 2 i ] 1 2 2 ( K - cos 2 i ) .