# Making a mirror move through radiation pressure

## (An optics simulation with Finesse) The following shows a simple example for a Finesse simulation of a radiation pressure effect, including the text input file, a brief explanation and the resulting plot.

## The input file

```%------------------------------------------------------------------------
% Finesse input file to plot the mirror motion due to radiation pressure
% Daniel Brown 21.03.2014
%------------------------------------------------------------------------

# optical setup: laser, space and mirror:
l l1 1 0 n1
s s1 1 n1 n2
m m1 1 0 0 n2 n3

# define transfer function with pole at 10Hz and Q factor 1000
tf pendulum 1 0 p 10 1000
# apply transfer function to mirror as force->motion
attr m1 mass 1 zmech pendulum

# measuring the mirror longitudinal motion
xd m1_z m1 z

# generate amplitude modulation at the laser
fsig sig1 l1 amp 1 0

xaxis sig1 f log 1 100 400
yaxis log abs:deg```

## The optical layout

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 so that it acts like a free mass. The 'xd' detector is then used to plot the transfer function from laser amplitude fluctuations to the mirror's longitudinal motion.

## Output graphs

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 this transfer function, a single pole at 10 Hz with a Q factor of 1000.

Finesse simulation result: the traces show the amplitude of the mirror longitudinal motion (amplitude in meters and phase in degrees).