Some wondrous optical technology can result from depositing coatings less than a few micrometers thick on glass, plastic, and other surfaces. These coatings are used to enhance the reflectivity of astronomical mirrors or diminish the reflections from visual displays and lenses; they can improve the efficiency of window glass and solar cells.
FreeSnell computes these effects for parallel layers of dielectric and conductive materials.
I couldn't find a free implementation of thin-film optical calculations I needed for a project. So I rolled my own.
The first versions were based on webpages [NCSU] and [Nave], but differences in signs and conventions of the complex index of refraction caused havoc with metallic layers. [Sernelius] has a comprehensive treatment with signs consistent from start to finish. The current version is based on that.
The properties of granular films are taken from [Heavens] discussion of Maxwell Garnett theory. [Granfilm] computes properties of granular films with great sophistication, but appears to require a PhD in physics in order to use it.
Optics is wavelength based; so this package is also. These routines work out the complex voltages in the forward and reverse directions to find the transmitted and reflected amplitudes. This works only for intensities where the layers act linearly (superposition).
Each layer 0:n has an index of refraction and height. Because the P and S polarizations are independent, they are calculated separately. The square of the absolute value of computed field values expressing power ratios are the returned quantities.
The effects of coatings on light are determined by Snell's law and Fresnel's equations, which model the light's electric and magnetic fields.
Taking the Laplace-transform of the differential equations relating the fields at the surface of each parallel layer of materials yields algebraic equations relating the indexes-of-refraction and the (complex) attenuation and phase as functions of wavelength.
These algebraic equations can be organized into products of 2x2 matrices and 2-vectors. The 2-vectors represent the Laplace transforms of the forward and reverse radiation. Each interface between adjacent materials corresponds to a 2x2 matrix.
The product of the chain of 2x2 matrices produces a single 2x2 matrix expressing the transmittance and reflectance of the layered stack as a whole, solving the system of equations.
This method is not unique to thin-film optics; it is essentially the same as the 2-port method for analysis of linear electrical circuits.
Because these optical systems are passive and linear, the attenuation of radiation passing through in one direction must be the same as the attenuation of radiation passing through in the opposite direction.
Radiation that is not transmitted through the stack must be either absorbed or reflected. The absorption at the top is not necessarily the same as the absorption at the bottom.
Rays impinging on the stack with non-normal incidence will leave the stack with non-normal incidence; the angles being identical if the indexes of refraction of the top and bottom materials are identical.
Rays impinging on the stack with non-normal incidence have different attenuation and reflectance depending on the polarization of the impinging radiation. FreeSnell computes outcomes for both polarizations; and can report these separately or averaged.