Oscillations, Waves, and Interactions - GWDG

428 U. Parlitz
with a clear tendency that control becomes the more effective the more different delay
times are used. In the following two examples of successful application of MDFC
are presented: stabilisation of a chaotic frequency-doubled Nd:YAG laser and manipulation
of spatio-temporal dynamics of a complex Ginzburg-Landau equation.
6.1 Stabilisation of a frequency-doubled Nd:YAG laser
Multiple delay feedback control has been applied very successfully [87,90] to suppress
chaotic intensity fluctuations of a compact frequency-doubled Nd:YAG laser which
are notoriously difficult to avoid (green problem [91,92]). Figure 18(a) shows the
experimental set-up where the laser’s pump current provided by a current source is
modulated by the feedback signal via a bias-T. The laser emits infrared radiation of
wavelength 1064 nm as well as frequency-doubled green laser light with a wavelength
of 532 nm. Both light emissions are separated from each other by a frequency selective
beam splitter. Input signals of the control loop are either the two ac coupled
orthogonally polarised infrared intensities Ĩx and Ĩy or the ac component of the green
intensity ˜ G. Using the infrared signals the pump current modulation for MDFC may
be written as
u(t) = ax Ĩx(t − τx) − bx Ĩx(t) + ay Ĩy(t − τy) − by Ĩy(t) (27)
and with the green laser light intensity
u(t) = ax ˜ G(t − τx) − bx ˜ G(t) + ay ˜ G(t − τy) − by ˜ G(t) . (28)
In both cases, the delay times τx and τy are typically in the range of τx ≈ 0.6 µs and
τy ≈ 2.8 µs. All control parameters ax, bx, ay, by, τx, τy are chosen experimentally
to achieve fixed point stabilisation. Fig. 18(b) shows a successful laser stabilisation
using MDFC. Before the control signal is switched on at t = 0 s intensity fluctuations
are visible which are then damped out by the feedback until the noise level is reached.
In this laser experiment three to four lasing modes were active. This case was also
simulated [90] with an extended (multi mode) laser model describing an inhomogenous
end-pumped YAG crystal.
(a) (b)
current
source
bias
feedback
controller
laser
532 nm
filter
1064 nm
1064 nm
U [mV]
200
100
0
−100
−200
−500 0
t [µs]
500
Figure 18. Suppression of chaotic intensity fluctuations of a frequency doubled Nd:YAG
laser using MDFC as defined in Eq. (27). (a) Experimental setup. (b) Time series showing
the orthogonally polarised ac coupled infrared signals Ĩx (upper trace) and Ĩy (lower trace).
After activation of feedback control at t = 0 the chaotic fluctuations are suppressed.