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

gure 5.11. It can be seen clearly that the population in the excited state N 3 follows
the pump prole with regularly alternating maxima and minima as suggested before.
5.3.3 Dynamical losses and gain
In the framework of this thesis, it is assumed that the real part of refractive index
is a constant, while the imaginary part may depend on the absorption and gain
dynamics according to the following equation,
ñ = n(λ) − ik(λ, x) + ig(λ, x) Eqn (5.31)
tel-00916300, version 1 - 10 Dec 2013
where n(λ) is the real part of refractive index which we assume to be unchanged
with the absorption dynamics, k(λ, x) accounts for the dynamic losses (absorption)
and g(λ, x) is the dynamic gain (emission).
Gain refers to an increase in the emitted electromagnetic intensity due to energy
transfers within the medium as compared to the incident pump. When the gain is
higher than the absorption in the thin lm, we may expect to see emission. In order
to simulate the gain and losses few assumptions are made:
ˆ Dynamic losses k(λ, x): The dynamic losses which depend on the population
of emitters, can be expressed using the following equation,
k(λ, x)= σ abs(λ).N 1 (x).λ
Eqn (5.32)
4π
where σ abs is the absorption cross section, and N 1 is the population of emitters
in the ground state.
In order to estimate the absorption cross section (σ abs ), and to give a shape to
it, Lorentzian functions are used. Therefore σ abs can be represented by,
σ abs = σ abs.max.
1
1 +
(ω 2 ij(abs) −ω2 ) 2
ω 2 ∆ω 2 (abs)
Eqn (5.33)
where σ abs.max is the maximum value of absorption cross sections, ω ij(abs) is the
frequency of absorption between levels i to j, and ∆ω is the width of the Lorentzian
curve of absorption.
The parameters in equation 5.32 are obtained by giving a shape to k(λ, x) by
tting the experimentally obtained k(λ) with lorentzian function in the energy range
of investigation (1.1 - 2.05 eV) of the emission behaviours (Fig. 5.12).
ˆ Dynamic gain g(λ, x) : Similar to dynamic losses, dynamic gain can also be
represented as a function of emission cross section (σ emis ) and the population
of emitters in the excited state (N 3 ) as follows,
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