snompy.fdm.geom_func

fdm.geom_func(z_tip, d_Q, r_tip, L_tip, g_factor)

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

Parameters:

z_tipfloat

Height of the tip above the sample.

d_Qfloat

Depth of an induced charge within the tip. Specified in units of the tip radius.

r_tipfloat

Radius of curvature of the AFM tip.

L_tipfloat

Semi-major axis length of the effective spheroid from the finite dipole model.

g_factorcomplex

A dimensionless approximation relating the magnitude of charge induced in the AFM tip to the magnitude of the nearby charge which induced it. A small imaginary component can be used to account for phase shifts caused by the capacitive interaction of the tip and sample.

Returns:

f_ncomplex

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

Notes

This function implements the equation

\[f_j = \left( g - \frac{r_{tip} + 2 z_{tip} + r_{tip} d_{Q_j}}{2 L_{tip}} \right) \frac{\ln{\left( \frac{4 L_{tip}}{r_{tip} + 4 z_{tip} + 2 r_{tip} d_{Q_j}} \right)}} {\ln{\left(\frac{4 L_{tip}}{r_{tip}}\right)}}\]

where \(z_{tip}\) is z_tip, \(d_{Q_j}\) is d_Q, \(r_{tip}\) is r_tip, \(L_{tip}\) is L_tip, and \(g\) is g_factor. This is given as equation (2) in reference [1].

References

[1]

B. Hauer, A. P. Engelhardt, and T. Taubner, “Quasi-analytical model for scattering infrared near-field microscopy on layered systems,” Opt. Express, vol. 20, no. 12, p. 13173, Jun. 2012, doi: 10.1364/OE.20.013173.