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

As seen from gure 5.1, a part of the incident light is transmitted within the
thin lm and a part is reected back. Therefore the total electric eld −→ E (x) is
a superposition of two waves travelling opposite to each other in the positive and
negative directions of x with elds E + and E − . This can be represented by,
E y (x) = E + e −ikxx + E − e ikxx =A(x) + B(x) Eqn (5.2)
where ±k x represent the x component of wave vector, A(x) and B(x) are constants
in the positive and negative directions of x. We consider A(x) and B(x)
at four positions for simplicity: top and bottom of interfaces at x = 0 and x = d
repectively as shown in gure 5.1. These can be written as,
A 1 = A(x = 0 − ) and B 1 = B(x = 0 − ) Eqn (5.3)
tel-00916300, version 1 - 10 Dec 2013
A ′ 2 = A(x = 0 + ) and B ′ 2 = B(x = 0 + ) Eqn (5.4)
A 2 = A(x = d − ) and B 2 = B(x = d − ) Eqn (5.5)
A ′ 3 = A(x = d + ) and B ′ 3 = B(x = d + ) Eqn (5.6)
Therefore, we can quantitatively describe the pump prole depending upon transmission
and reection of the incident wave using Fresnel's equations. For this, the
components A 1 which corresponds to the incident pump eld and B 1 the eld of the
reected wave can be linked using the following equation, detailed in Appendix I,
(
) (
A 1
= M
B 1
A ′ 3
B ′ 3
)
Eqn (5.7)
where B ′ 3=0, considering a semi-innite medium (no wave travelling towards
the negative direction of x) and M is a product of matrices that link the elds in
medium 1 and 3. The ratio of A 1 to B 1 gives the reected amplitude and A 1 to A ′ 3
the transmitted amplitude. For a known input eld A 1 , the reected amplitude B 1
can be calculated with the global reection coecient of all the structure (r glob ) due
to the propagation of the wave inside the thin lm.
The pump eld repartition in the thin lm is thus obtained by connecting each
of the components mentioned in gure 5.1 as follows,
(
(
) (
A 1
= D1 −1 D 2
B 1
) (
A 2
= D2 −1 D 3
B 2
A ′ 2
B ′ 2
A ′ 3
B ′ 3
)
= D 12
(
)
= D 23
(
A ′ 2
B ′ 2
A ′ 3
B ′ 3
)
)
Eqn (5.8)
Eqn (5.9)
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