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t 12 =<br />

2k 1x<br />

k 1x + k 2x<br />

and t 12 =<br />

2n 2 1k 2x<br />

n 2 1k 2x + n 2 2k 2x<br />

for s wave and p wave respectively Eqn<br />

(xii)<br />

Knowing all these relations, the amplitu<strong>de</strong> of the eld from medium 1 to medium<br />

3 can be simply expressed ( by, )<br />

A 1<br />

B 1<br />

(<br />

= D1 −1 D 2 P 2 D2 −1 D 3<br />

A ′ 3<br />

B ′ 3<br />

)<br />

Eqn (xiii)<br />

Thus the column vectors that represent the plane wave in each medium is related<br />

by a product of 2x2 matrices in sequence. Each si<strong>de</strong> of the interface is linked by<br />

dynamical matric and within the thickness of the thin lm by the propagation<br />

matrix. Such a recipe can be applied to a multilayer structure and also be exten<strong>de</strong>d<br />

to a (3 x 3) matrix.<br />

tel-00916300, version 1 - 10 Dec 2013<br />

190

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