.. _materials:


Materials
---------

The materials are characterized by refractive index, which is a square root (complex valued) of macroscopic dielectric function.
Generally, this should be the spectral function, i. e. 

.. math::

    n_c(\lambda) = n(\lambda) + i \cdot k(\lambda) = \sqrt{ \epsilon_1(\omega) + i \cdot \epsilon_2(\omega) }

so that

.. math::

    n = \sqrt{(|\epsilon|+\epsilon_1)/2} \\
    k = \sqrt{(|\epsilon|-\epsilon_1)/2}


with :math:`\hbar \omega = 2 \pi \hbar c / \lambda`.


Constant Material
^^^^^^^^^^^^^^^^^

The material with constant refreactive index can be specified as first constructor argument (`file_name`)::

    >>> from mstm_studio.mstm_spectrum import Material
    >>> mat_glass = Material('1.5')
    >>> mat_glass.get_n(500)
    array(1.5)

Complex value can be supplied too::

    >>> mat_lossy = Material('3+1j')
    >>> mat_lossy.get_n(500)
    array(3.)
    >>> mat_lossy.get_k(500)
    array(1.)

Also the predifned names can be used: `air`, `water`, `glass`.

Loading from file
^^^^^^^^^^^^^^^^^

The tabular data on refractive index is convinient to store in file.
The header of the file required to have special labels: ``lambda	n	k``. The example file "etaGold.txt" can be found in directory "nk" of source distribution.

Assuming the file "etaGold.txt" is in the same directory where script is running, it can be loaded with

.. literalinclude:: load_gold.py
   :lines: 3-5

Resulted plot

.. image:: loaded_gold.png

.. Note:: The extending database of refractive indeces of materials <https://refractiveindex.info/>.




Material from numpy array
^^^^^^^^^^^^^^^^^^^^^^^^^

Material data can be specified directly by numpy (complex) array by passing `nk` or `eps`.
Next examples shows loading of Drude-like dielectric function:

.. literalinclude:: drude_gold.py
   :lines: 1-12


Material class members
^^^^^^^^^^^^^^^^^^^^^^

.. autoclass:: mstm_studio.mstm_spectrum.Material
   :members:
   


Analytical formula for AuAg
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Silver, gold and thier alloy materials can be specified using analytical expression proposed in the study [Rioux2014]_.
Example for Au:Ag = 1:2 alloy:

.. literalinclude:: mat_au1ag2.py
   :lines: 1-5

Resulted plot

.. image:: mat_au1ag2.png


.. autoclass:: mstm_studio.alloy_AuAg.AlloyAuAg
   :members:


.. [Rioux2014] D. Rioux, S. Vallières, S. Besner, P. Muñoz, E. Mazur, and M. Meunier, "An Analytic Model for the Dielectric Function of Au, Ag, and their Alloys" Adv. Opt. Mater. (2014) *2* 176-182 <http://dx.doi.org/10.1002/adom.201300457>