Sellmeier Material Model

The SellmeierMaterial class describes the frequency-dependent refractive index of a dielectric material using the Sellmeier equation. This model is widely used in optical and electromagnetic simulations to accurately account for material dispersion effects.

Overview

The Sellmeier equation expresses the square of the refractive index \(n(\lambda)\) as a function of the wavelength \(\lambda\):

\[n^2(\lambda) = 1 + \sum_{i=1}^{N} \frac{B_i \lambda^2}{\lambda^2 - C_i}\]

Where:

  • \(( B_i )\), \(( C_i )\) are the Sellmeier coefficients.

  • \(( \lambda )\) is the wavelength, typically in micrometers (\(\mu\text{m}\)).

  • \(( n )\) is the refractive index.

This formulation is suitable for modeling transparent materials such as glasses, crystals, and polymers in the visible and near-infrared spectral ranges.

Typical Use Case

The SellmeierMaterial is used in electromagnetic simulations to model how light propagates through dispersive media. You instantiate the material with its Sellmeier coefficients, then use the model to compute refractive index or permittivity as a function of wavelength. Most of the cases this materials will be used in a LayerStack to define the materials of a particular layer.

Examples

Instantiating a Sellmeier Material Object:

from pyOptiShared.Material import SellmeierMaterial

# Example coefficients for BK7 glass
B = [1.03961212, 0.231792344, 1.01046945]
C = [0.00600069867, 0.0200179144, 103.560653]

# Instantiates the Sellmeier Material object
material = SellmeierMaterial("BK7Glass", B, C)
eps = material.eps(0.55)  # Compute permittivity at 550 nm
n = material.index([0.55, 0.65])  # Compute index at 550 nm and 650nm