finesse.gaussian.BeamParam.overlap

static BeamParam.overlap(q1, q2)

Computes the projection from one beam parameter to another to give a measure of the overlap between the two beam parameters. The quantity computed is,

\[\mathcal{O} = \frac{4|\Im{\{q_1\}}\,\Im{\{q_2\}}|}{|q_1^* - q_2|^2}. \]

The return values is \(\mathcal{O} \in [0, 1]\), where 0 implies complete mode mismatch and 1 indicates full mode matching.

This function was provided by Paul Fulda and Antonio Perreca, which came originally from Chris Mueller.

Parameters:

q1BeamParam, complex, array-like

First beam parameter. Note that this can be a numeric or symbolic beam parameter, a complex number or an array of complex values.

q2BeamParam

Second beam parameter. Note that this can be a numeric or symbolic beam parameter, a complex number or an array of complex values.

Returns:

overlapfloat, array-like, Symbol

The overlap between q1 and q2 as defined above.