Optical Spring
(A Processing program to show the effect of an optical spring)
Alexandre Brieussel
2010
This Processing sketch illustrates the so-called `optical spring', a
particular coupling between a mechanical oscillator and a light
field. You can play with the parameters of the system and see how
the laser field between the two mirrors couples the mechanical
motion of these.
Light that sent to a mirror can be seen as tons of little specks hitting
the surface of mirror. Each of those specks has a momentum. And when they
are absorbed or reflected by the mirror, they transfer momentum to the
mirror. We obtain a force, a so-called radiation pressure force, which
we can employ to build an optical spring.
Light can also be described in the wave picture. If the length between
two mirrors is an integer of two times the light wave length, these waves
interfere constructively and you can obtain a power enhancement inside the
cavity. We call this system a resonant
Fabry Perot interferometer.
The applet above shows a case in which you need both features (particle
and wave) of light to understand what is happening. The graph on the lower
left shows the resonant enhancement of the light power inside the cavity,
with the little box indicating the exact distance between the mirrors as
develops in time. You can adjust the laser power, laser frequency and
the average cavity length buttons to see what happens.
When you increase the power in the cavity, you increase the force acting
on the mirrors, and the mirrors are pushed away from each other. Imagine
that the mirrors are not moving and that the length between the mirrors
correspond to a position on the right hand slope of the resonance peak.
If the mirrors would now move a little bit further apart, as a result the
power inside the cavity would decrease. Since the mirrors are suspended as
pendulums, they would tend come back to their
original position. If the mirrors are moving closer, the power in the cavity
increases, and hence the radiation force increases. For little small movements,
the system behaves exactly as if the two mirrors were connected by a spring.
Just that this spring is not made of metal, but of photons.
http://www.physics.gla.ac.uk/igr/index.php?L1=members&L2=member&name=shild
Now if you excite the right hand mirror at one frequency, the other one will
follow. And if excitation frequency is close to the resonance frequency of
the spring, the left mirror, which has a smaller weight, will move with a
much larger amplitude.
The applet was programmed during a summer project at the
University of Glasgow, UK.
See also our other Processing examples.