snompy.fdm.geom_func_multi

fdm.geom_func_multi(z_tip, d_image, r_tip, L_tip, g_factor)

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

Parameters:

z_tipfloat

Height of the tip above the sample.

d_imagefloat

Depth of an image charge induced below the upper surface of a stack of interfaces.

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

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

where \(z_{tip}\) is z_tip, \(d_{Q_j'}\) is d_image, \(r_{tip}\) is r_tip, \(L_{tip}\) is L_tip, and \(g\) is g_factor. This is given as equation (11) 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.