Optical Properties Of Nanometer-Scale Structures

TL;DR

This paper investigates how optical properties of nanometer-scale layers depend on thickness, revealing dimension resonance effects, and derives formulas considering absorption and conductivity, explaining phenomena like luminescence and unusual refraction behaviors.

Contribution

It introduces new formulas for optical parameters of thin layers accounting for absorption and conductivity, and explains dimension resonance and light reemission in nanostructures.

Findings

Optical parameters depend strongly on layer thickness.

Dimension resonance occurs at specific thicknesses, enhancing luminescence.

Unusual refraction behaviors are observed in high-conductivity materials.

Abstract

Two approaches (micro- and macro- investigations) are used to determine the dimension dependences of the optical parameters of the nanometer-scale layers of materials. It is shown that both an index of refraction and coefficient of absorption depend strongly on the thickness of the layer. In this region of thicknesses, the dimension resonance occurs, where an index of refraction has a maximum and a coefficient of absorption has a minimum. The numerical calculation of the optical parameters of some materials (Ag, Al, Fe, Ge, Si, Se, Te) have been carried out with the use of the experimental data of reflection and transparency of thin layers, obtained in a series of works, and with our formulas for the wave amplitudes and the laws of refractions. The analogues of the Fresnel formulas and the Snell law have been derived from the Maxwell boundary conditions where the absorption and conductivity of media were taken into account. The use of our formulas for the wave amplitudes leads to the fulfillment of the conservation law of energy both for the TE- and TM- polarizations of light. The reemission of light is possible for the thicknesses, which is equal to the wavelength of light in a medium, divisible by integer: $\frac{2{\pi}d_{res}}{2}={\lambda}_m{\cdot}m=\frac{{\lambda}_0}{n}{\cdot}m$, where m=1,2,3... The visible luminescence of the porous silicon, silicon whiskers and other nanometer-scale structures can be explained by their emission in the case of dimension resonance because in this region of thicknesses, layers have a big negative coefficient of absorption and little - of a damping. It is also shown that in the case of the TM-polarization, in a material with a high conductivity, light refracts in a "wrong" direction (at all positive optical parameters) due to a surface current. In the case of the TE-polarization, light refracts only in a "right" direction.