Films minces à base de Si nanostructuré pour des cellules ...

5.3.1 Single emitter modeling
In the same scheme as illustrated in gure 5.1 we now introduce a single emitter
placed at position x e below the sample surface (Fig. 5.9).
tel-00916300, version 1 - 10 Dec 2013
Figure 5.9: Schematic representation of the various components of the incident wave and
the wave from a single emitter placed at a distance x e in the thin lm.
The emitter is considered as a source travelling in the positive and negative
directions of x, the amplitude of which are given by S + and S − respectively.
Let A t = A(x = x − e ), B t = B(x = x −+
e ) be the amplitude of the waves on top
of the emitter and A b = A(x = x + e ) & B b = B(x = x + e ) the amplitudes below the
emitter. Then at x = x e , we may write,
A b = A t + S + Eqn (5.15)
B b = B t − S − Eqn (5.16)
Equations 5.15 and 5.16 reect that the total amplitude of waves travelling in
the positive and negative directions is a combined contribution from the pump and
the source.
The eld amplitude at the top and bottom of the source can be linked using
matrix formulation as follows:
⎛ ⎞ ⎛
⎞⎛
⎞
⎜
⎝
A t
B t
1
⎟ ⎜
⎠ = ⎝
1 0 −S +
0 1 +S −
0 0 1
⎟⎜
⎠⎝
A b
B b
1
⎟
⎠ Eqn (5.17)
The elds near the top interface in medium 2 can be linked to that near the
bottom interface using a product of matrices between x = 0 and x e , at x e and
between x = x e and d. This is written as,
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