Determination of Complex Refractive Index using Prism composed of Absorbing Medium

TL;DR

This paper develops two methods to determine the complex refractive index of absorbing media using optical path differences in a prism, extending beyond Snell's law which fails for absorbing materials.

Contribution

It provides an exact solution to Maxwell's equations for light in absorbing media and introduces novel methods to determine complex refractive indices from optical path differences.

Findings

Methods accurately determine complex refractive index from deviation angles.

Refractive index obtained is independent of prism's apex angle.

Significant optical path differences near perfect reflection areas.

Abstract

In light refraction between two transparent media, Snell's law describes the relationship between the incident angle and refraction angle. The refractive index is usually determined from Snell's law using the minimum deviation angle through a prism. A medium that partially absorbs light has complex permittivity (or permeability), and its refractive index has an imaginary part. Because of the imaginary part, Snell's law does not hold for light-absorbing media. Accordingly, other methods is required to determine the complex value of the refractive index in a light-absorbing medium. The exact solution of Maxwell's equations was obtained for light passing through a prism composed of a light-absorbing medium. Thereby the optical path was determined. The difference of optical paths between light-absorbing medium and transparent medium was calculated numerically. The difference is very large in the neighborhood of perfect reflection area of transparent medium. We found two methods to determine the complex value of the refractive index using the optical path. Both methods analyzed the solutions in detail for two specific incident angles. The deviation angles corresponding to the two incident angles determined the complex value of the prism's refractive index. The obtained refractive index is independent of the apex angle of the prism.