Brendel–Bormann oscillator model

The Brendel–Bormann (BB) oscillator model is a mathematical formula for the frequency dependence of the complex-valued relative dielectric permittivity, also known as the dielectric function. The model has been used to fit the complex refractive index of materials with absorption lineshapes exhibiting non-Lorentzian broadening, such as metals and amorphous insulators, 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, although, it was first used by A. M. Efimov and V. N. Khitrov (1979) to characterize the optical constants of glasses; it was also enhanced by A. M. Efimov and E. G. Makarova in 1983. Around that time, several other research groups independently discovered the model.

The physical validity and causality of the BB model are debated in the physics literature. J. Orosco and C. F. M. Coimbra reported that the model does not satisfy Kramers–Kronig relations, due to a singularity at zero frequency, and non-Hermiticity. These claims inspired the authors to develop an elaborate causal correction to the BB model. The claims were later contested by S. Nordebo and M. Štumpf, who proved the analyticity of the model on the basis of Jordan's lemma and attributed the observed non-Hermiticity to the incorrect choice of branch cut in the complex square root.