Interfaces and thin films

PyOptik provides Fresnel interface calculations and a coherent characteristic- matrix solver for isotropic multilayer coatings. Refractive indices may be constant complex numbers or wavelength-dependent PyOptik material models.

Single interfaces

fresnel_coefficients returns electric-field amplitude coefficients and power fractions for s or p polarization. Angles may be Pint/TypedUnit angle quantities; bare angles are interpreted as radians.

from TypedUnit import ureg
from PyOptik import fresnel_coefficients

result = fresnel_coefficients(
    incident_index=1.0,
    transmitted_index=1.5,
    angle=45 * ureg.degree,
    polarization="p",
)

print(result.reflection_amplitude)
print(result.transmission_amplitude)
print(result.reflectance)
print(result.transmittance)
print(result.transmitted_angle.to(ureg.degree))

For a dispersive material, provide the evaluation wavelength:

glass = catalog.get("specs/SCHOTT-optical/N-BK7").load()
result = fresnel_coefficients(
    1.0,
    glass,
    wavelength=550 * ureg.nanometer,
    polarization="s",
)

Characteristic angles

brewster_angle returns the p-polarized zero-reflection angle, while critical_angle returns the onset of total internal reflection.

from PyOptik import brewster_angle, critical_angle

brewster = brewster_angle(1.0, 1.5).to(ureg.degree)
critical = critical_angle(1.5, 1.0).to(ureg.degree)

These helpers require positive, scalar, lossless indices. A critical angle exists only when the incident index is greater than the transmitted index.

Coherent multilayers

Use ThinFilmLayer for each film, ordered from the incident medium toward the substrate. A (material, thickness) tuple is accepted as shorthand.

import numpy
from PyOptik import ThinFilmLayer, thin_film_stack

design_wavelength = 600 * ureg.nanometer
substrate_index = 1.5
coating_index = numpy.sqrt(substrate_index)

coating = ThinFilmLayer(
    material=coating_index,
    thickness=design_wavelength / (4 * coating_index),
)
wavelengths = numpy.linspace(450, 750, 301) * ureg.nanometer
result = thin_film_stack(
    wavelengths,
    [coating],
    incident_index=1.0,
    substrate_index=substrate_index,
    angle=0 * ureg.degree,
    polarization="s",
)

# Arrays aligned with ``wavelengths``.
reflectance = result.reflectance
transmittance = result.transmittance
absorptance = result.absorptance

Materials in any layer or bounding medium are evaluated independently at every wavelength. Positive extinction coefficient k follows PyOptik’s n + i k convention and contributes positive absorptance.

Model limits

The solver assumes plane waves, homogeneous isotropic non-magnetic layers, parallel interfaces, and full coherence throughout the stack. It does not yet include incoherent propagation through thick substrates, graded or anisotropic layers, surface roughness, scattering, fluorescence, or partial coherence. Power coefficients are evaluated from the normal optical flux. Numerical round-off can produce absorptance extremely close to zero for lossless stacks.