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 (also called xd) is then used to plot the transfer function from laser amplitude fluctuations to the mirror’s longitudinal motion. See for example Modelling transfer functions and Calculating general transfer functions for discussions on how transfer functions are used in Finesse.

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
    """
)

<finesse.model.Model at 0x7833b1fb9d30>

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

# Sweep the frequency of the amplitude modulation
out = kat.run("xaxis(fsig.f, log, 1, 100, 400)")
out.plot(log=True);

../../_images/radiation_pressure_1_0.svg

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.