finesse.gaussian.ws_overlap

finesse.gaussian.ws_overlap(W, S, Wp, Sp, wavelength=None)[source]

Calculates the WS phase space overlap.

This overlap function is computed by,

O(W,S)=4W2WP21(1W2+1Wp2)2+k24(SSP)2,O(W,S) = \frac{4}{W^2 W_P^2} \frac{1}{\left(\frac{1}{W^2} + \frac{1}{W_p^2}\right)^2 + \frac{k^2}{4}\left(S - S_P\right)^2},

Note

The equation above was derived from the work in [34].

where WW and SS are the beam size and defocus, respectively, of a gaussian beam propagated to the same plane as the primary mode (which has WpW_p, SpS_p).

Parameters
Wnumber, array-like

Beam size of mode [metres].

Snumber, array-like

Defocus of mode [1/metres].

Wpnumber, array-like

Beam size of primary mode [metres].

Spnumber, array-like

Defocus of primary mode [1/metres].

wavelengthfloat, optional

Wavelength of the beam. Defaults to the value in the loaded config file.

Returns
Onumber, array-like

The overlap between the mode (W,S)(W,S) and the primary mode (Wp,Sp)(W_p,S_p).