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 Pendulum. 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

kat = finesse.Model()
    # 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)

    # 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 the xaxis anyway. Next, the sgen command is used to inject a signal at the model’s signal frequency into the Laser’s amp port, which causes a small amplitude modulation to be generated.

Output plots

out = kat.run()

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 xd detector here essentially probes the shape of this transfer function, a single pole at 10 Hz with a Q factor of 1000.

See also

For further reading, [16] gives a brief but fairly detailed introduction to radiation pressure effects in the context of gravitational wave detectors.