The optical constants of the material are two functions that are used to evaluate the interaction of the material with the electromagnetic field. Despite its name, the optical constants vary across the spectrum and therefore must be measured at each wavelength / energy of the photon. Simple optical models can often accurately reproduce the optical constants of a material in a certain range of wavelengths of light. The use of optical models simplifies obtaining the optical constants, since only a few free parameters need to be determined.

Optical models must satisfy several requirements in order to reproduce the optical constants of materials. Optical constants are two real functions that vary with the wavelength / energy of the photon, such as ε1 and ε2 or n and k, which combine into a complex function, such as ε1 + iε2. The fact that this function is complex is relevant to establish such requirements. This is a complex function of a real variable, for example the energy of the photon. Due to a property as basic as causality, that is, that the response of a material to an electrical stimulus cannot anticipate the appearance of this stimulus, the energy variable can be extended to the complex plane. The function of the optical constants extended to the complex plane must also fulfill the property of being analytical (holomorphic).

Although it is not normally required to know such an extension of the optical constants to complex energy values, in some cases it is useful. An example of this is a procedure developed by Adachi to model the optical constants of materials, such as indirect bandgap semiconductors, among other models and groups of materials.

Adachi modeled these materials with simple but incorporating divergence functions, which Adachi circumvented by phenomenologically adding a positive imaginary part to the energy of the photon. Adachi added this energy term only to the real component of the dielectric function ε1, and not to the imaginary part ε2. Operating like this, you not only obtained the real part of the dielectric function, already with the divergence resolved, but you also obtained the imaginary part. The Adachi procedure for adding flare has the advantage of being very simple to apply.

The procedure has been successful in modeling many materials and groups of materials, although it has been applied phenomenologically, that is, why it works had not been proven.

The article rigorously demonstrates the Adachi procedure. It also establishes the conditions to be able to apply this procedure. Finally, it is shown that the Adachi procedure is equivalent to a convolution procedure of the optical constants with Lorentz oscillators that the same authors had developed in 2018.

The work is a collaboration between the Institute of Optics, the Catholic University of America and NASA Goddard Space Flight Center (CRESST 2)

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