Cavity Calculator

(A simple optical cavity simulation written in Processing)

Jamie Dougherty

International student exchange

The applet below represents a numerical model of the light power in a two-mirror optical cavity as a function of the cavity parameters. The cavity being modeled consists of one flat mirror and one spherical mirror. With the sliders and text fields you can control the reflectivities of each mirror, the radius of curvature of the second mirror, and the resonance condition of the cavity (the value of delta x).

This applet has been built with Processing and makes use of the G4P (GUI for Processing) library.
Download the source code here:

The image at the lower left of the applet is a diagram of the cavity. It consists of a laser, two mirrors (in this case, one flat and one with a variable radius of curvature) with variable reflectivites, a beamsplitter with two photodetectors, and a photodetector for the light transmitted through the second mirror. Note that there are three sliders and accompanying text fields overlaying the cavity image. The bottom left slider controls the reflectivity of the first mirror, while the bottom right slider controls the reflectivity of the second (rightmost) mirror. These reflectivities can range from 0.00 to 0.99, as one cannot have a mirror with a reflectivity of 1.00. The slider above these controls the curvature (i.e. the inverse of the `radius of curvature) of the second mirror, and will commonly be referred to as the ’RoC slider.’

The main output of the calculator is the graph above this image showing the logarithm of the cavity’s internal power as a function of the microscopic tuning of the second mirror. The logarithm of the internal power is plotted for three different transverse modes: the fundamental mode (TEM00) is shown in red, a first order mode (TEM10) is given in green and a second-order mode (TEM20) is shown in blue. Experimentally the internal power of a cavity can often not be measured directly (e.g. not by the shown photodiodes) but must be computed from the reflected and transmitted light. However, in a numerical simulation this light power can be accessed directly.

The microscopic tuning of the second mirror determined the resonance condition of the cavity. The tuning is measured in degrees, where 360 degrees refer to a displacement of the second mirror by one wavelength (which is one micrometer in our example).

Finally, the meter on the bottom right of the calculator below the text box shows how much light power that is leaving through the second mirror (i.e. is transmitted by the cavity and reaches the rightmost photodetector). This power is computed for one resonance condition at a time, which is determined by the delta-x slider. When all light is transmitted the meter should indicate a value of 1, when only one mode is fully transmitted the meter should show a value of about 0.33.