snompy.pdm.eff_pol_n#
- pdm.eff_pol_n(sample, A_tip, n, z_tip=None, n_trapz=None, **kwargs)#
Return the effective probe-sample polarizability, demodulated at higher harmonics, using the bulk point dipole model.
- Parameters:
- sample
snompy.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.
- n_trapzint
The number of intervals used by
snompy.demodulate.demod()for the trapezium-method integration.- **kwargsdict, optional
Extra keyword arguments are passed to
eff_pol().
- sample
- Returns:
- alpha_effcomplex
Effective polarizability of the tip and sample, demodulated at n.
See also
snompy.fdm.eff_pol_nThe finite dipole model equivalent of this function.
eff_polThe unmodulated/demodulated version of this function.
snompy.demodulate.demodThe function used here for demodulation.
Notes
This function implements \(\alpha_{eff, n} = \hat{F_n}(\alpha_{eff})\), where \(\hat{F_n}(\alpha_{eff})\) is the \(n^{th}\) Fourier coefficient of the effective polarizability of the tip and sample, \(\alpha_{eff}\), as described in reference [1]. The function \(\alpha_{eff}\) is implemented here as
eff_pol().If eps_tip is specified it is used to calculate alpha_tip according to
\[\alpha_{tip} = 4 \pi r_{tip}^3 \frac{\varepsilon_{tip} - 1}{\varepsilon_{tip} + 2}\]where \(\alpha_{tip}\) is alpha_tip, \(r_{tip}\) is r_tip and \(\varepsilon_{tip}\) is eps_tip, which is given as equation (3.1) in reference [2].
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.
[2]F. Keilmann and R. Hillenbrand, “Near-field microscopy by elastic light scattering from a tip,” Philos. Trans. R. Soc. London. Ser. A Math. Phys. Eng. Sci., vol. 362, no. 1817, pp. 787–805, Apr. 2004, doi: 10.1098/rsta.2003.1347.