snompy.pdm.eff_pol

pdm.eff_pol(sample, z_tip=None, r_tip=None, eps_tip=None, alpha_tip=None)

Return the effective probe-sample polarizability using the bulk point dipole model.

Parameters:

samplesnompy.sample.Sample

Object representing a layered sample with a semi-infinite substrate and superstrate. Sample must have only one interface for bulk methods.

z_tipfloat

Height of the tip above the sample.

r_tipfloat

Radius of curvature of the AFM tip.

eps_tipcomplex

Dielectric function of the tip. Used to calculate alpha_tip, and ignored if alpha_tip is specified. If both eps_tip and alpha_tip are None, the model sphere is assumed to be perfectly conducting.

alpha_tipcomplex

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

Returns:

alpha_eff_0complex

Effective polarizability of the tip and sample.

See also

snompy.fdm.eff_pol

The finite dipole model (FDM) equivalent of this function.

eff_pol_n

The modulated/demodulated version of this function.

Notes

This function implements the equation

\[\alpha_{eff} = \frac{\alpha_{tip}}{1 - f \beta}\]

where \(\alpha_{eff}\) is alpha_eff, \(\alpha_{tip}\) is alpha_tip, \(\beta\) is beta, and \(f\) is a function encapsulating various geometric properties of the tip-sample system, implemented here as snompy.pdm.geom_func(). This is given as equation (14) in 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.