Calculate optical response from multilayer thin film. This is a python3 implementation similar to Passler2017 and Vorwerk2018 (see reference).

The semi-infinite thin film is described by a Carteasian coordinate where the origin sits at the medium/film surface defining xy plane. The unit vector pointing to substrate from the medium is +z. The incident plane is xz and the incident light is defined by theta, the angle between its wavevector k and +z. The polarization of incident light is defined by sigma, the angle between its projection on xy plane and +x.

Assuming the medium is isotropic, the inputs for calculating optical response from aformentioned system are:

• theta: in radians, the incident angle
• sigma: in radians, the polarization angle
• thickness_list: in nm, the thickness for each layer
• eps_medium: real number, the relative dielectric constant of isotropic medium
• w_list: a list of frequencies in eV
• eps_list: a list of 3x3 matrices, the dielectric tensors for each layer at certain w
• mu: real number, the magnetic permeability of isotropic medium.

Additionally,

• Euler_alpha, Euler_beta, Euler_gamma: in radians, the Euler angles used to convert eps_list to current Cartesians.

1. you need numpy.

2. prepare input epsilon files:

   The code reads eps_list and w_list from 2 table-like files containing either the imaginary or the real part of epsilon. Both of them have the format:

   # w  xx  xy  xz  yx  yy  yz  zx  zy  zz

   so one needs to make sure the 2 inputs share the identical 1st column.

   For VASP users, there is a script vasp_eps.sh here can be used to extract the 2 input files from vasprun.xml.

3. see test.py for usage

As pointed out in the erratum of Passler2017, total transmittance cannot be calculated directly from the transmission coefficients unless the substrate is vacuum. It seems this restriction is ignored in Vorwerk2018.

Berreman1971: Berreman, Dwight W. "Optics in stratified and anisotropic media: 4× 4-matrix formulation." Josa 62.4 (1972): 502-510.

Yeh1979: Yeh, Pochi. "Optics of anisotropic layered media: a new 4× 4 matrix algebra." Surface Science 96.1-3 (1980): 41-53.

Xu2000: Xu, W., L. T. Wood, and T. D. Golding. "Optical degeneracies in anisotropic layered media: treatment of singularities in a 4× 4 matrix formalism." Physical Review B 61.3 (2000): 1740.

Passler2017: Passler, Nikolai Christian, and Alexander Paarmann. "Generalized 4× 4 matrix formalism for light propagation in anisotropic stratified media: study of surface phonon polaritons in polar dielectric heterostructures." JOSA B 34.10 (2017): 2128-2139.

Vorwerk2018: Vorwerk, Christian, Caterina Cocchi, and Claudia Draxl. "LayerOptics: Microscopic modeling of optical coefficients in layered materials." Computer Physics Communications 201 (2016): 119-125.