Brendel-Bormann oscillator model. The real (blue dashed line) and imaginary (orange solid line) components of relative permittivity are plotted for a single oscillator model with parameters = 500 cm, = 0.25 cm, = 0.05 cm, and = 0.25 cm.
The Brendel–Bormann oscillator model is a mathematical formula for the frequency dependence of the complex-valued
relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit to the complex
refractive index of materials with absorption lineshapes exhibiting
non-Lorentzian broadening, such as metals[1] and amorphous insulators,[2][3][4][5] across broad spectral ranges, typically near-
ultraviolet,
visible, and
infrared frequencies. The
dispersion relation bears the names of R. Brendel and D. Bormann, who derived the model in 1992,[2] despite first being applied to optical constants in the literature by Andrei M. Efimov and E. G. Makarova in 1983.[6][7][8] Around that time, several other researchers also independently discovered the model.[3][4][5] The Brendel-Bormann oscillator model is aphysical because it does not satisfy the
Kramers–Kronig relations. The model is non-causal, due to a singularity at zero frequency, and
non-Hermitian. These drawbacks inspired J. Orosco and C. F. M. Coimbra to develop a similar, causal oscillator model.[9][10]
Mathematical formulation
The general form of an oscillator model is given by[2]
where
is the relative permittivity,
is the value of the relative permittivity at infinite frequency,
^Efimov, Andrei M.; Makarova, E. G. (1983). "[Vitreous state and the dispersion theory]". Proc. Seventh All-Union Conf. on Vitreous State (in Russian). pp. 165–71.
^Efimov, Andrei M.; Makarova, E. G. (1985). "[Dispersion equation for the complex equation constant of vitreous solids and dispersion analysis of their reflection spectra]". Fiz. Khim. Stekla [The Soviet Journal of Glass Physics and Chemistry] (in Russian). 11 (4): 385–401.
Brendel-Bormann oscillator model. The real (blue dashed line) and imaginary (orange solid line) components of relative permittivity are plotted for a single oscillator model with parameters = 500 cm, = 0.25 cm, = 0.05 cm, and = 0.25 cm.
The Brendel–Bormann oscillator model is a mathematical formula for the frequency dependence of the complex-valued
relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit to the complex
refractive index of materials with absorption lineshapes exhibiting
non-Lorentzian broadening, such as metals[1] and amorphous insulators,[2][3][4][5] across broad spectral ranges, typically near-
ultraviolet,
visible, and
infrared frequencies. The
dispersion relation bears the names of R. Brendel and D. Bormann, who derived the model in 1992,[2] despite first being applied to optical constants in the literature by Andrei M. Efimov and E. G. Makarova in 1983.[6][7][8] Around that time, several other researchers also independently discovered the model.[3][4][5] The Brendel-Bormann oscillator model is aphysical because it does not satisfy the
Kramers–Kronig relations. The model is non-causal, due to a singularity at zero frequency, and
non-Hermitian. These drawbacks inspired J. Orosco and C. F. M. Coimbra to develop a similar, causal oscillator model.[9][10]
Mathematical formulation
The general form of an oscillator model is given by[2]
where
is the relative permittivity,
is the value of the relative permittivity at infinite frequency,
^Efimov, Andrei M.; Makarova, E. G. (1983). "[Vitreous state and the dispersion theory]". Proc. Seventh All-Union Conf. on Vitreous State (in Russian). pp. 165–71.
^Efimov, Andrei M.; Makarova, E. G. (1985). "[Dispersion equation for the complex equation constant of vitreous solids and dispersion analysis of their reflection spectra]". Fiz. Khim. Stekla [The Soviet Journal of Glass Physics and Chemistry] (in Russian). 11 (4): 385–401.