Dependence of transient dynamics in a class-C laser upon variation of inversion with time
J. T. Malos, D. Y. Tang, and N. R. Heckenberg
Physics Department, University of Queensland, Queensland 4072, Australia
Received 2 December 1996
The transient statistics of a gain-switched coherently pumped class-C laser displays a linear correlation
between the first passage time and subsequent peak intensity. Measurements are reported showing a positive or
negative sign of this linear correlation, controlled through the switching time and the laser detuning. Further
measurements of the small-signal laser gain combined with calculations involving a three-level laser model
indicate that this sign fundamentally depends upon the way the laser inversion varies during the gain switching,
despite the added dynamics of the laser polarization in the class-C laser. S1050-29479707112-6
PACS numbers: 42.55.Ah, 42.50.Lc, 42.60.Mi, 42.60.Rn
INTRODUCTION
There has been extensive study of the statistical nature of
transient dynamics of a laser that result from controlled
changes in laser parameters 1–4. In most studies, the para-
metric changes involve increasing the laser pumping gain
switching or losses ( Q switching over time scales that are
either fast or slow compared to the response time of the
particular system 5,6. The time taken for the laser intensity
to build up to a macroscopically observable level after a
parameter switch is referred to as the first passage time, or
FPT. The statistical fluctuations observed in the transient dy-
namics of lasers for repeated sweeps of the control parameter
have been identified as macroscopic fluctuations resulting
from quantum noise 7–10. Specifically, statistical fluctua-
tions are observed in the FPT and these reflect the quantum
statistics in laser variables such as the field and population
inversion, at the time of parametric switch.
The FPT statistics, such as mean FPT and standard devia-
tion, are primarily sensitive to statistical events taking place
during the initial linear amplification of the intensity. When
the intensity grows to an observable level, saturation effects
become significant. This is also referred to as the nonlinear
amplification regime. During this time, the character of the
resulting intensity transient response depends on the dynam-
ics of the laser variables as determined by their characteristic
time scales 11,12. In studies to date, lasers of classes A and
B have been studied 5,13 wherein the statistics of the FPT
are observed to be correlated to characteristics of the laser
transient.
One such correlation is that between the FPT and the
subsequent peak intensity obtained. Recent work 6 has
clearly demonstrated for the class-B laser that the sign of the
slope of the linear correlation is determined by the switching
mechanism. If the laser is gain switched, the gain may still
be increasing at the time of first passage, depending upon the
system relaxation speed and the speed of switching. In such
a case the peak intensity obtained is therefore greater for
longer FPT leading to a positive correlation. In the case of
loss switching, the gain is already present when the losses
are swept. Fluctuations upon the gain from one switch to the
next e.g., due to modulation on the pumping mechanism
results in either an earlier FPT and larger peak intensity
when the gain is larger than average or conversely a longer
FPT and smaller peak intensity when the gain is smaller.
This results in a negative correlation.
In this paper we report experimental observations of fluc-
tuations in the FPT of a class-C laser when the laser is gain
switched. This is novel on two counts. First, the laser gain in
the class-C laser is determined by the polarization and not
simply by the inversion, as in classes A and B, for which the
polarization relaxation is fast compared to the inversion. It is
conceivable, therefore, that the linear correlation mecha-
nisms discussed above are complicated by the polarization.
Second, although the laser is solely gain switched we ob-
serve both positive and negative linear correlation between
the FPT and the subsequent peak intensity. This is in contrast
to the generalized behavior reported in 6, wherein gain and
loss switching mechanisms are contrasted. We can control
the slope of the linear correlation via the laser detuning and
also by whether the pump is switched on quickly or swept
slowly relative to the time scale of the laser transient dynam-
ics.
The two-level Lorenz-Haken model 14previously used
to describe the observed dynamics of the laser we use
15,16 adequately accounts for the observed positive slope
of the correlation between FPT and subsequent peak inten-
sity when the pump parameter is slowly swept. In this case,
the form of both the small-signal laser polarization and in-
version with time is essentially the same as that of the pump
intensity. This is consistent with similar results discussed by
6 for the class-B laser. With a slow sweep of the pump, the
peak intensity is greater for FPT events that occur later, giv-
ing rise to a correlation with positive slope.
For the case of quick switching, both positive and nega-
tive slopes are observed for near-resonant and off-resonant
tuning of the laser, respectively. Small-signal gain measure-
ments for the quickly switched pump demonstrate that the
form of the small-signal gain differs significantly from that
of the pump. There is an overshoot in the gain that is con-
sistent with undamped coherence between the pumping lev-
els. A simplified three-level laser model exhibits this effect
and also shows both positive and negative slopes with near-
resonant and off-resonant tuning of the laser, respectively, as
PHYSICAL REVIEW A JANUARY 1998 VOLUME 57, NUMBER 1
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