# Michelson Interferometer

## (A Processing program for visualising interference)

Charlotte Bond

summer project
2009

The applet below illustrates the interference of optical waves in a Michelson interferometer. You can change the length of one interferometer arm and observe how the light power in the two interferometer output changes. You can also play with the reflectivity of the beam splitter or the mirrors to understand their effect on the interference. If you want to know how light fields are reflected or transmitted at an optical surface, have a look at my other applet: Reflection!

This applet has been built with Processing and makes use of the G4P (GUI for Processing) library.

In this sketch the light is depicted as waves. Using the tick box `play waves continuously' you can choose to have static or travelling waves. The amplitude of the waves represent the light power in the respective beam. The input beam (black, coming in from the left) is split by the beam-splitter into two beams (up and right) which then move through the interferometer arms, are reflected by the so-called end mirrors and then recombine at the beam-splitter. This creates in general to output beams: one travelling to the left and one down. By changing the length of one interferometer arm the amount of power can be moved between the two output beams.

The sliders can be used to change several parameters of the interferometer:
• Length of second arm – This controls the position of the second mirror
• Reflectivity: beam-splitter – This controls the power reflectivity of the beam-splitter
• Reflectivity: first mirror – This controls the power reflectivity of the first mirror
• Reflectivity: second mirror – This controls thepower reflectivity of the second

In gravitational wave detectors the Michelson interferometer is typically used at the so-called `dark fringe', i.e. a setup in which no light leaves the interferometer `downwards'. This can be achieved with a microscopic arm length difference of 0.25 wavelength. Try to set the Michelson above to the dark fringe yourself.

You can also find out what happens, e.g. to the dark fringe, when you change the reflectvity of the end mirrors. And of course it's worth investigating the extreme settings just to see what happens: when you set the beam-slitter reflectivity to 0 or to 1, what do you expect to see?