slmsuite.holography.analysis.fitfunctions.lorentzian

lorentzian(x, x0, a, c, Q)

For fitting a resonance. There are many ways to describe a Lorentzian. Commonly, a full-width-half-maximum definition is used. Here, with roots in photonic crystal cavities, we use a form defined using the quality factor \(Q\) of the resonance.

\[y(x) = c + \frac{a}{1 + \left[\frac{x - x_0}{x_0/2Q}\right]^2}.\]

Parameters:

• x (numpy.ndarray) – Points to fit upon.

• x0 (float) – Center wavelength.

• a (float) – Amplitude.

• c (float) – Constant offset.

• Q (float) – Quality factor.

Returns:

y – Lorentzian fit evaluated at all x.

Return type:

numpy.ndarray