Example 6 - radiation pressure¶
This example shows a simple example for a Finesse simulation of radiation pressure causing a mirror to move.
The optical configuration¶
The optical layout is very simple, with a laser beam being reflected by a single mirror.
The interesting aspects of this setup are hidden in the details: The laser beam includes
an amplitude modulation ‘signal’ whose frequency we can tune; secondly, the mirror is
suspended on a
MotionDetector is then used to plot the transfer
function from laser amplitude fluctuations to the mirror’s longitudinal motion.
The Finesse model¶
import finesse finesse.configure(plotting=True) kat = finesse.Model() kat.parse( """ # Optical setup: laser, space and mirror: l l1 P=1 s s1 l1.p1 m1.p1 m m1 R=1 T=0 # Define a pendulum for our mirror, with a z-motion resonance at 10Hz # and Q factor of 1000 pendulum sus1 m1.mech mass=1 fz=10 Qz=1000 # Measure the mirror's longitudinal motion xd m1_z m1.mech.z # Set a signal frequency to activate the signal simulation # (needed for radiation pressure effects to be observed) fsig(1) # Generate amplitude modulation at the laser sgen sig l1.amp # Sweep the frequency of the amplitude modulation xaxis(fsig.f, log, 1, 100, 400) """ )
The are also two new commands in this script.
fsig sets the “signal
frequency” of the model; this is the frequency at which effects such as field amplitude
or mirror oscillations are modeled. It is set to 1 Hz, as the frequency will be swept by
xaxis anyway. Next, the
sgen command is used to
inject a signal at the model’s signal frequency into the
amp port, which causes a small amplitude
modulation to be generated.
out = kat.run() out.plot(log=True);
Upon reflection by the mirror the photons reverse their momentum. This momentum transfer
gives rise to a force on the mirror, the so-called ‘radiation-pressure force’. Finesse
assumes a steady state of the optical system, which in this case means that we assume
the static radiation-pressure force to be compensated by another static force, for
example via active control or through gravity. The amplitude modulation signal on the
laser light, however, creates a modulation of the force which we can model and measure
in a steady state. The mechanical transfer function of the mirror determines how the
longitudinal force (as a function of frequency) translates into motion. Thus the
detector here essentially probes the shape of this transfer function, a single pole at
10 Hz with a Q factor of 1000.
For further reading,  gives a brief but fairly detailed introduction to radiation pressure effects in the context of gravitational wave detectors.