pyetalon

PyEtalon is a Python library to analyse the multilayer interference of thin films in the context of etalons.

It provides an easy interface to calculate the phase shift of a known multilayer stack. Also, it allows fitting of the multilayer stack parameters to measured peak data of an etalon.

PyEtalon makes heavy use of PyIndexRepo, a python library to access the refractive index data from RefractiveIndex.info. See the documentation of PyIndexRepo for more information on how to access the refractive index data.

User guide

Background

The free spectral range (FSR) of an etalon is the distance between two adjacent transmission peaks. For an ideal etalon, it is given by the following equation:

$FSR_{\nu}= \Delta \nu = \frac{c}{2nL\cdot \cos(\theta)}$

where $c$ is the speed of light in vacuum, $n$ is the refractive index of the medium between the plates, $\theta$ is the angle of incidence, and $L$ is the distance between the plates.

In wavelength, the FSR is given by:

$FSR_{\lambda} = \Delta \lambda = \frac{\lambda^2}{2nL \cos(\theta)}$

where $\lambda$ is the wavelength of light in vacuum.

Similarly, the absolute peak wavelength of the etalon is given by:

$\lambda = \frac{2nL \cos(\theta)}{m}$

where $m$ is the order of the interference peak.

All equations above are only valid for an ideal etalon. In reality, upon reflection on the etalon mirrors, the light undergoes a phase shift. This phase shift is given by the Fresnel equations and depends on the refractive index of the materials involved. As a consequence, both, the FSR and the absolute peak wavelength are modified by the phase shift. It is most intuitive to think of the phase shift as a change in the effective optical path length or mirror separation $L$.

The peak wavelength is then given by:

$\lambda = \frac{2nL \cos(\theta)+ \lambda \frac{\Phi_{\lambda}}{\pi}}{m}$

Example

Let's walk through the simulation of a simple etalon with a single layer of 30nm of silver on a glass substrate. The etalon is illuminated with a plane wave at normal incidence.

The wavelength dependent refractive indices of the three materials are represented by a Material object, which can be created from a tabulated data set or a formula or by querying the refractive index database.

To calculate optical properties of an etalon, create an Etalon object and use the provided helper functions.

import numpy as np

from pyetalon.etalon import Etalon
from pyetalon.plotting import plot_fsr
from pyindexrepo import RefractiveIndexLibrary, Material, TabulatedIndexData, FormulaIndexData
from pyindexrepo.dispersion_formulas import formula_2


# Create vacuum 'material' by using a tabulated data set
Vacuum = Material(TabulatedIndexData([.1, 10.000], [1.0, 1.0]))
# Create the substrate material by using the Sellmeier formula and vendor data for Suprasil
Suprasil = Material(FormulaIndexData(formula_2, [0., 6.72472034E-01, 4.50684530E-03, 4.31646851E-01, 1.33090179E-02, 8.85914296E-01, 9.67375952E+01], .185, 2.326), None)
# Create the silver material by querying the refractive index database, selecting the Ciesielski data set for thin films
db = RefractiveIndexLibrary()
Silver = db.get_material('main', 'Ag', 'Ciesielski')


# Create an etalon object
silver_etalon = Etalon(
    [Vacuum, Silver, Suprasil],                     # specify the layer materials
    ["Vacuum", "Silver", "Substrate"],              # specify the layer names
    [-np.inf, 30., np.inf],                         # specify the layer thicknesses
    [0, 1, 2],                                      # specify the layer order/indices
    wavelength=np.linspace(500, 1100, 5000),        # specify the wavelength range
    d_spacer=5E-3,                                  # specify the spacer thickness in meters
    aoi=.0,                                         # specify the angle of incidence in degrees
    identifier='Silver 30nm'                        # specify the identifier of the etalon
)