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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.
Locus of the polarization-state transformation factor
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