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We got into this game because in studying
nonlinear optical processes and noise
we were working with things that happen very fast, on a timescale of
10-15s.
Basically, electrons in an atom or molecule oscillate up and down once every
10-15s or so, and generate light waves with the same period. In
a nonlinear optical process the light might have a somewhat different period
but not very different - it's still damn fast!
When things happen that fast you can't see directly the effect of external
noise on dynamical changes. There is no detector fast enough to "see" the
electric field in a light wave oscillating up and down.
You can only measure the intensity averaged over maybe 10-11s, and
that corresponds to a pretty fast detector too.
In order to get around this limitation of not being able to follow the
dynamics directly we decided to switch to a system with slower dynamics.
The laser! A laser has fast dynamics as well as slow. The fast is just
the oscillation of electrons at optical frequencies that gives the laser
light. The slow dynamics is a movement of stored energy back and forth
between the laser medium and the electromagnetic field (the light)
confined between the mirrors of the laser.
If you just look at the total intensity of the laser output beam you can
pretty much ignore the optical frequency oscillation and just concentrate
on the slower dynamics.
What timescale these slow dynamics have depends very much on the type of
laser and the details of its design. In some lasers, such as the common
HeNe laser, the atomic physics of the gaseous medium actually washes out
the slow dynamics pretty much completely. In other lasers such as
CO2 or neodymium, the dynamics is fairly slow - it has a
timescale of around about 1 microsecond. In diode lasers it's about
1ns. That is slow!
If you change
the conditions of the laser suddenly, it will oscillate about
its new operating point for a bit. The oscillations will die down over
about 10-6s as the laser settles down to its new operating point.
It's called a relaxation oscillation.
So what's so interesting about that? Well if you keep perturbing
the laser at the right frequency, you can keep the oscillations going.
Furthermore they are nonlinear which means that they start to alter
themselves as they get stronger. This leads to all the usual nonlinear
phenomena that you may have heard of: bifurcations, limit cycles, chaos ...
...and then you can start to study what happens when the nonlinear
relaxation oscillator is perturbed by noise that is deliberately brought
into the system.
So why do that? The hope is that such work can tell
us something about how general systems interact with their environments.
General systems are typically nonlinear, and typically complex. But the
environment is, almost by definition really, much bigger and more complex.
So all of the myriad little interactions that the environment has with the
system cannot be tracked individually - statistical methods must be used.
What this boils down to is that the influence of the environment is pretty
much random. Noise is random too, so you can mimic, or model, the
effect of the enviroment by perturbing the system with noise.
This talk of system and enviroment is pretty abstract. What's a
concrete example? The common interpretation of the word "environment" is
that which is all around us and enables us to exist as a species, or a
society, or a civilisation ... What the environment actually comprises
depends a bit on which of these you're talking about!
All a bit vague
really!
But to look for an example away from lasers and physics, consider
a lizard basking on a rock in the sun. As an organism
it's a complex nonlinear system. The environment is this case is the
immediate surroundings of the lizard; trees, rocks, air and so on. The sun
is part of it's enviroment; so is the cloud which temporarily blocks the
sun; the wind is also. The sum total of all of these influences on the
lizard is really rather random, though there is a certain degree of
predictability - the sun will set after all. This system, the lizard,
is vastly more complex than those that we are tackling, but, Hey!, you've
got to begin somwhere.
So what are we up to at the moment? Well it turned out that the lasers
we had for this study were a bit more complex that we'd bargained on!
They were multimode, meaning that they put out light which had
several components, each with a slightly different wavelength. Each
of these components is called a mode, a longitudinal mode to be
specific.
(There are also
transverse modes. )
This then led us to consider
and the detailed dynamics of
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diode lasers, (Section 4) taking into account their multimode
nature and some of the complications of semiconductor physics.
In this work we have produced results which indicate that the
effect of noisy excitation of an oscillator array is different from
single frequency exitation. The relative contributions of the
individual oscillators in the array to the collective modes of the
array seems to be different in each case.
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