Linear Cavity Calculator

What does this calculate?

This is a simple calculator for linear optical resonators (cavities), i.e. for an optical system that looks like this:

If this doesn't look familiar to you, you probably won't need this calculator.
You will need to provide some basic optical and geometric properties of the cavity:

• Power reflectivity (or transmission) of the two mirrors,
• Radii of curvature (RoC) of the mirrors,
• The separation between the two mirrors (assumed to be air, with index of refraction = 1),
• The operating wavelength.

From these inputs, the calculator will do some heavy thinking and then come up with these results:

• the FSR (free spectral range), i.e. the frequency separation between two successive cavity resonances,
• the finesse and the spectral linewidth of each resonance, given as FWHM (full width at half maximum) and cavity pole (half width at half maximum),
• the power-buildup inside the cavity,
• the transmitted and reflected power on resonance, in percent of the incident power,
• the cavity g-factor product, this product must be between 0 and 1 for a stable cavity, i.e. a cavity that supports a TEM₀₀ fundamental mode.

The above results are always calculated, even if the cavity is unstable. This is done for convenience: one can quickly play around with e.g. the mirror reflectivities to find a suitable finesse value, without caring about suitable RoCs. Of course, to also see those values in an experiment one would first of all have to make the cavity stable.
For a stable cavity, the following additional parameters will be calculated:

• the round-trip Gouy phase, which is the additional phase accumulated by a Gaussian beam, compared to a plane wave
,
• the mode spacing (in frequency space) between successive higher-order mode orders, e.g. how far the TEM₀₁ is separated from the TEM₀₀ mode,
• the beam waist, the 1/e² radius of the fundamental mode at its smallest point,
• the waist position, relative to mirror M₁, where positive values are towards M₂,
• the spot sizes (1/e² radius) of the fundamental mode on the two mirrors,
• a mode spectrum showing the resonance locations of the first 20 higher-order modes; this can be used to quickly check for mode degeneracy, i.e. when two modes of different mode order coincide^†.

Note that the calculation assumes that all modes of Nth order (TEM_mn where m+n=N) are degenerate. This is usually a good approximation as long as there is rotational symmetry within the cavity, e.g. the mirrors are non-astigmatic.

^†The height and intensity of the lines just serve to visually distinguish them and should not be mistaken for a representation of the actual mode content.

What do I need to run it?

Just a recent version of one of the standard web browsers (Chrome, Safari, Firefox, Edge, Opera, etc.). It should even run fine on your mobile phone! To keep things simple (for me, mostly...), I used some code techniques that were introduced only recently (as of 2016), so if you're stuck with an older web browser for some reason, it's highly likely that this calculator won't work for you, sorry.
The calculation runs entirely inside your browser, so apart from loading this webpage once, it does not need any internet connection. Oh, and if you disable JavaScript, then this won't work at all.

What if I get wrong results?

Whoops :-( Would you please file a bug report detailing the parameters you used and what went wrong?