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

⎛
⎜
⎝
A ′ 2
B ′ 2
1
⎞
⎛
⎟ ⎜
⎠ = ⎝
e ik2xe 0 0
0 e −ik2xe 0
0 0 1
⎞ ⎛
⎟ ⎜
⎠ ⎝
1 0 −S +
0 1 +S −
0 0 1
⎞ ⎛
⎟ ⎜
⎠ ⎝
e ik2(d−xe) 0 0
0 e −ik2(d−xe) 0
0 0 1
⎞⎛
⎟⎜
⎠⎝
A 2
B 2
1
⎞
⎟
⎠
which on simplication gives,
⎛
⎜
⎝
A ′ 2
B ′ 2
1
⎞
⎛
⎟ ⎜
⎠ = ⎝
e ik 2d
0 −e −ik 2d S +
0 e −ik 2d
e −ik 2d S −
0 0 1
⎞⎛
⎟⎜
⎠⎝
A 2
B 2
1
⎞
⎟
⎠ Eqn (5.18)
tel-00916300, version 1 - 10 Dec 2013
Following the principles as detailed in section 5.2.1, the eld amplitudes between
medium 1 and medium 3 can be linked while taking into account the presence of
source at x = x e now as follows,
⎛
⎜
⎝
A 1
B 1
1
⎞ ⎛
⎟
⎠ = D1 −1 ⎜
D 2 ⎝
e ik 2d
0 −e −ik 2d S +
0 e −ik 2d
e −ik 2d S −
0 0 1
⎞ ⎛
⎟
⎠ D2 −1 ⎜
D 3 ⎝
A ′ 3
B ′ 3
1
⎞
⎟
⎠ Eqn (5.19)
This global matrix formulation links the eld amplitude at each wavelength and
hence when we consider the case of emission wavelength (source wavelength) in
medium 1, the input wave A 1 = 0 (since incident wavelength ≠ emission wavelength).
The outgoing wave B 1 is only due to emission from the source which travels
in the negative x direction towards medium 1. Therefore this can be represented as
B 1 = B0 − . In medium 3, the outgoing wave A ′ 3 is a contribution only from source
and hence A 3 = B s + . As described before, we consider a semi innite medium as the
substrate, therefore there is no wave reecting back from the susbtrate (B 3 = 0).
Using these conditions in Eqn 5.19, the two opposite travelling waves arising from
the source, B0 − and B + S
can be linked as follows:
⎛
⎜
⎝
0
B − 0
1
⎞ ⎛
⎟
⎠ = D1 −1 ⎜
D 2 ⎝
e ik 2d
0 −e −ik 2d S +
0 e −ik 2d
e −ik 2d S −
0 0 1
⎞ ⎛
⎟
⎠ D2 −1 ⎜
D 3 ⎝
B + s
0
1
⎞
⎟
⎠ Eqn. (5.20)
The intensities of the source waves travelling in opposite directions are then
calculated with the following equations,
I + S = cε 0n | B + s | 2
2
and I − O = cε 0n | Bo − | 2
2
Eqn (5.21)
We now consider the amplitudes of the single source at x e at the two opposite
ends of medium 2 as u + and u − , then
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