snompy.pdm.geom_func

pdm.geom_func(z_tip, r_tip, alpha_tip)

Return a complex number that encapsulates various geometric properties of the tip-sample system for bulk point dipole model.

Parameters:

z_tipfloat

Height of the tip above the sample.

r_tipfloat

Radius of curvature of the AFM tip.

alpha_tipcomplex

Polarizability of the conducting sphere used as a model for the AFM tip.

Returns:

f_geomcomplex

A complex number encapsulating geometric properties of the tip- sample system.

Notes

This function implements the equation

\[f = \frac{\alpha_{tip}}{16 \pi (r_{tip} + z_{tip})^3}\]

where \(z_{tip}\) is z_tip, \(r_{tip}\) is r_tip, and \(\alpha_{tip}\) is alpha_tip. This is adapted from equation (14) of reference [1].

References

[1]

A. Cvitkovic, N. Ocelic, and R. Hillenbrand, “Analytical model for quantitative prediction of material contrasts in scattering-type near-field optical microscopy,” Opt. Express, vol. 15, no. 14, p. 8550, 2007, doi: 10.1364/oe.15.008550.