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

Calculates the WS phase space overlap.

This overlap function is computed by,

\[O(W,S) = \frac{4}{W^2 W_P^2} \frac{1}{\left(\frac{1}{W^2} + \frac{1}{W_p^2}\right)^2 + \frac{k^2}{4}\left(S - S_P\right)^2},\]


The equation above was derived from the work in [2].

where \(W\) and \(S\) are the beam size and defocus, respectively, of a gaussian beam propagated to the same plane as the primary mode (which has \(W_p\), \(S_p\)).


W : number, array-like

Beam size of mode [metres].

S : number, array-like

Defocus of mode [1/metres].

Wp : number, array-like

Beam size of primary mode [metres].

Sp : number, array-like

Defocus of primary mode [1/metres].

wavelength : float, optional

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


O : number, array-like

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