![](bg5.png)
(ground-, first-excited and second-excited states) are
shown in color map. It refers again to the 150 mA
driving condition.
According to this figure we can see that the
exponents associated to the confined states are all
negative (thus being essential for the dissipative
feature of the system), and that there is a clear
dependence of the exponents on the quantum dot
grouping (carriers from the quantum dots more
likely in the ensemble lead to less negative
exponents). Additionally, if ES2 carriers are
compared to ES1 and GS ones, it can be pointed out
that carriers resonant with the spectral window of
lower material gain (that containing ES2 states)
contribute to less negative values of Lyapunov
exponents. This suggests that the way to get other
positive Lyapunov exponents is to operate with
shallow dots, favoring carrier escape up to wetting
layer, a scenario in which higher energy confined
states are less populated.
Figure 6: Time-domain evolution of the Lyapunov
exponents associated to the carrier number equations of
confined states. Color indicates magnitude of the
Lyapunov exponents.
4 CONCLUSIONS
In this work a numerical model for the direct capture
scattering process in quantum dot lasers under
optical feedback has been developed, and an
analysis of the possibility of chaotic operation has
been done after numerical calculation of the
Lyapunov exponents of the system.
Simulation results revealed that positive
Lyapunov exponents are achieved at different
driving conditions, for both direct capture and
cascade only models. Comparison between these
models showed different sensitivity to initial
conditions at different electrical driving levels: with
the direct capture included in the model, higher
positive exponents are obtained at lower currents,
and an inverse trend is obtained for the cascade
model.
Finally, results of the Lyapunov exponents
associated to the carriers in the dot confined states
showed that there is major tendency to negative
values and that the threshold of positive values may
be related to the spectrum window of lower material
gain.
ACKNOWLEDGEMENTS
Brazilian agency CNPq supported this work;
reference number 482393/2011-4.
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