.. _sellmeier-material:

Sellmeier Material Model
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The :class:`SellmeierMaterial <pyOptiShared.Material.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
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The Sellmeier equation expresses the square of the refractive index :math:`n(\lambda)` as a function of the wavelength :math:`\lambda`:

.. math::

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

Where:

- :math:`( B_i )`, :math:`( C_i )` are the Sellmeier coefficients.
- :math:`( \lambda )` is the wavelength, typically in micrometers (:math:`\mu\text{m}`).
- :math:`( 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
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The :class:`SellmeierMaterial <pyOptiShared.Material.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 :class:`LayerStack` to 
define the materials of a particular layer.

Examples
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**Instantiating a Sellmeier Material Object:**

.. code-block:: python

    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