Solitons in Nonlocal Media

(a) (b)
5.4 Role of Gain Saturation
Figure 5.2: Numerically simulated beam propagation in the cell of fig. 5.1, in the presence
of a constant gain γ. Fig. 5.2(a) and 5.2(b) show the results for γ = 0m −1 (passive medium)
and γ = 100m −1 (active medium), respectively. The input profile is Gaussian with a waist
equal to 2.8µm. Wavelength is 633nm.
a numerical aperture large enough to confine all the input light and prevent losses
due to the coupling to the radiation modes. Therefore, at low input powers only
part of the excitation gets trapped and G is reduced by a constant factor (i.e. I can
write G(s)|Pin = ηcoupling(Pin)exp(2γs) with ηcoupling the initial coupling to modes
of the self-induced guide, which clearly depends on the initial beam power), whereas
above threshold (dependent on wavelength through diffraction), the power amplifica-
tion reaches a maximum and saturates (i.e. ηcoupling saturates to 1) for large enough
Pin. Figure 5.6 shows the calculated G versus γ for various input powers at two differ-
ent wavelengths: the gain is higher and saturates above Pin = 0.5mW at λ = 633nm
[fig. 5.6(a)], while at λ = 1064nm it keeps increasing with power [fig. 5.6(b)] until
Pin = 3.0mW due to the stronger diffraction.
5.4 Role of Gain Saturation
5.4.1 Mechanism for Dye Luminescence: a Simple Model
The simplest way to model optical gain in the interaction between signal, pump and
luminescent dye is to consider the dye as a three level system (four level systems are
similar but more involved to compute), as in laser theory (111).
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