snompy.pdm.eff_pol_n_taylor

pdm.eff_pol_n_taylor(sample, A_tip, n, z_tip=None, r_tip=None, eps_tip=None, alpha_tip=None, n_trapz=None, n_tayl=None)

Return the effective probe-sample polarizability using the point dipole model, demodulated at harmonics of the tapping frequency, using a Taylor series representation of the bulk PDM.

Note

This function primarily exists to check the validity of the Taylor approximation to eff_pol_n which is used by other functions. For best performance it is recommended to use eff_pol_n.

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.

A_tipfloat

The tapping amplitude of the AFM tip.

nint

The harmonic of the AFM tip tapping frequency at which to demodulate.

z_tipfloat

Height of the tip above the sample.

r_tipfloat

Radius of curvature of the AFM tip.

eps_tipcomplex

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

alpha_tipcomplex

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

n_trapzint

The number of intervals used by snompy.demodulate.demod() for the trapezium-method integration.

n_taylint

Maximum power index for the Taylor series in beta.

Returns:

alpha_effcomplex

Effective polarizability of the tip and sample, demodulated at n.

See also

eff_pol_n

The non-Taylor series version of this function.

snompy.demodulate.demod

The function used here for demodulation.

Notes

This function is valid only for reflection coefficients, beta, with magnitudes less than around 1. For a more generally applicable function use eff_pol_n()

This function implements \(\alpha_{eff, n} = \sum_{j=0}^{J} a_j \beta^j\), where \(\beta\) is beta, \(j\) is the index of the Taylor series, \(J\) is n_tayl and \(a_j\) is the Taylor coefficient, implemented here as taylor_coef().