snompy.fdm.refl_coef_qs_from_eff_pol

fdm.refl_coef_qs_from_eff_pol(alpha_eff, z_tip=None, r_tip=None, L_tip=None, g_factor=None, d_Q0=None, d_Q1=None)

Return the quasistatic reflection coefficient corresponding to a particular effective polarizability using the finite dipole model.

Parameters:

alpha_effcomplex

Effective polarizability of the tip and sample.

z_tipfloat

Height of the tip above the sample.

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.

d_Q0float

Depth of an induced charge 0 within the tip. Specified in units of the tip radius.

d_Q1float

Depth of an induced charge 1 within the tip. Specified in units of the tip radius.

Returns:

betacomplex, masked array

Quasistatic reflection coefficient of the interface.

See also

eff_pol

The inverse of this function.

refl_coef_qs_from_eff_pol_n

The demodulated equivalent of this function.

Notes

This function implements the equation

\[\beta = \frac {2 (\alpha_{eff} - 1)} {f_0 + 2 f_1 (\alpha_{eff} - 1)}\]

where \(\alpha_{eff}\) is alpha_eff, and \(f_j\) is a function encapsulating the FDM geometry, taken from reference [1]. Here it is given by geom_func(), with arguments z_tip, d_Q0 or d_Q1 (for \(f_0\) or \(f_1\)), r_tip, L_tip, and g_factor

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.