The Material Class¶

This class defines the optical parameters for a given material. The optical parameters are defined via the complex refractive index or equivalently the complex permittivity. As a shorthand, we will refer to the real part of the refractive index as n, the imaginary part as k and the complex refractive index as nk. Similarly, the shorthand for permittivity is eps_r, eps_i and eps

There are multiple ways to initalise this class. Typically the objects of this class will be generated using the catalogue.

It can also be initalised in the following ways,

using the path to a file
using a constant value for n, nk, eps_r or eps.
using tabulated data for n, nk or eps
using a predefined model

Apart from the file path, these different definitions can be mixed and matched. For example a model or tabulated data for n, while taking a constant value for k.

A material is full defined when either both the real and imaginary parts of the refractive index or permittivity are defined, or alternatively a complex value for either refractive index or permittivity is defined.

Once a material has been fully defined, the refractive index or permittivity can be evaluated on a given spectrum. The spectrum can be wavelength, frequency, angular frequency or energy. For more information see Spectrum

import numpy as np
from dispersion import Material, Spectrum
mat = Material(fixed_n = 1.5) # k will be set = 0
spm = Spectrum( np.arange(380, 750, 10 ),
               spectrum_type= 'Wavelength',
               unit = 'nanometer')
nk_values = mat.get_nk_data(spm)
eps = mat.get_permittivity(spm)

Interpolation¶

If tabulated data is used to initalise the MaterialData, it will be automatically interpolated. The order of interpolation can be set by passing interp_order as a keyword to the MaterialData constructor. The order must be an integer. The default value is 1 (linear interpolation).

Extrapolation¶

Data can be extrapolated outside of the range in which it is defined. This should be done with great care, as extrapolated values may not even be qualitatively correct. However in circumstances where the material dispersion is very low, it may be practical to extrapolate the close to the spectrum of known values. Note that since the real and imaginary parts are extrapolated separately they must be independent of one another. Therefore, the material must be defined via separate real and imaginary parts, rather than via a complex value.

Extrapolation is achieved as follows,

new_spectrum = Spectrum(800., spectrum_type='Wavelength', unit='nm')
mat.extrapolate(new_spectrum, spline_order=2)

Due to extrapolation using splines, the results can vary greatly depending on the spline order used. For this reason it is recommended to verify the results of extrapolation before using the results for further calculations.

Removing Absorption¶

Sometimes it is useful to remove the absorption by setting the imaginary part of material data to a constant zero value. This can be achieved by,

mat.remove_absorption()

Note that this is only valid for data which have independent real and imaginary parts.

Full API¶

holds the complex refactive index or permittivity data

material_data implements the Material class which can hold different representations of spectral data (e.g. refractive index or permittivity). The data is in the form of either a constant value, tabulated data or a model. These different representations can be combined e.g. model for n (real part of refractive index) and constant value for k (imaginary part of refractive index)

Functions¶

_check_table_shape: validate that a numpy array has a given shape

Classes¶

Material: processes and interfaces refractive index data.

class material.Bruggeman(spectrum, material1, material2, filling_fraction)¶

Methods

`create_effective_data`(self)	this must be implemented in a subclass
`dataset_to_dict`(self)	generate a file_data type dictionary from this object
`extrapolate`(self, new_spectrum[, spline_order])	extrpolates the material data
`get_maximum_valid_range`(self)	find maximum spectral range that spans real and imaginary data.
`get_nk_data`(self, spectrum[, spectrum_type, …])	return complex refractive index for a given input spectrum.
`get_permittivity`(self, spectrum_values[, …])	return complex permittivity for a given input spectrum.
`get_sample_spectrum`(self)	spectrum which covers the maximum valid range of the material data
`plot_nk_data`(self, **kwargs)	plots the real and imaginary part of the refractive index
`plot_permittivity`(self, **kwargs)	plots the real and imaginary part of the permittivity
`print_comment`(self)	print material comment
`print_reference`(self)	print material reference
`remove_absorption`(self)	sets loss (k or epsi) to constant zero value
`utf8_to_ascii`(string)	converts a string from utf8 to ascii

add_dtype_suffix
collapse_datasets
prepare_file_dict

create_effective_data(self)¶: this must be implemented in a subclass

class material.EffectiveMedium(spectrum, material1, material2, filling_fraction)¶

Methods

`create_effective_data`(self)	this must be implemented in a subclass
`dataset_to_dict`(self)	generate a file_data type dictionary from this object
`extrapolate`(self, new_spectrum[, spline_order])	extrpolates the material data
`get_maximum_valid_range`(self)	find maximum spectral range that spans real and imaginary data.
`get_nk_data`(self, spectrum[, spectrum_type, …])	return complex refractive index for a given input spectrum.
`get_permittivity`(self, spectrum_values[, …])	return complex permittivity for a given input spectrum.
`get_sample_spectrum`(self)	spectrum which covers the maximum valid range of the material data
`plot_nk_data`(self, **kwargs)	plots the real and imaginary part of the refractive index
`plot_permittivity`(self, **kwargs)	plots the real and imaginary part of the permittivity
`print_comment`(self)	print material comment
`print_reference`(self)	print material reference
`remove_absorption`(self)	sets loss (k or epsi) to constant zero value
`utf8_to_ascii`(string)	converts a string from utf8 to ascii

add_dtype_suffix
collapse_datasets
prepare_file_dict

create_effective_data(self)¶: this must be implemented in a subclass

class material.Material(**kwargs)¶

Class for processing refractive index and permittivity data

Parameters:

file_path: str: file path from which to load data
fixed_n: float: fixed real part of refractive index
fixed_nk: complex: fixed complex refractive index
fixed_eps_r: float: fixed real part of permittivity
fixed_eps: complex: fixed complex permittivity
tabulated_n: Nx2 array: table of real part of refractive index to interpolate
tabulated_nk: Nx3 array: table of real and imaginary refractive index values to interpolate
tabulated_eps: Nx3 array: table of real and imaginary permittivity values to interpolate
model_kw: dict: model parameters
spectrum_type: str: sets the default spectrum type
unit: str: sets the default unit
meta_data: dict: contains the meta data for the material
data: dict: holds one or two SpectralData objects to describe the data
options: dict: holds options for the material object
defaults: dict: default values for spectrum data

Warning

the parameters file_path, fixed_n, fixed_nk, fixed_eps_r, fixed_eps, tabulated_n, tabulated_nk, tabulated_eps and model_kw are mututally exclusive.

Methods

`dataset_to_dict`(self)	generate a file_data type dictionary from this object
`extrapolate`(self, new_spectrum[, spline_order])	extrpolates the material data
`get_maximum_valid_range`(self)	find maximum spectral range that spans real and imaginary data.
`get_nk_data`(self, spectrum[, spectrum_type, …])	return complex refractive index for a given input spectrum.
`get_permittivity`(self, spectrum_values[, …])	return complex permittivity for a given input spectrum.
`get_sample_spectrum`(self)	spectrum which covers the maximum valid range of the material data
`plot_nk_data`(self, **kwargs)	plots the real and imaginary part of the refractive index
`plot_permittivity`(self, **kwargs)	plots the real and imaginary part of the permittivity
`print_comment`(self)	print material comment
`print_reference`(self)	print material reference
`remove_absorption`(self)	sets loss (k or epsi) to constant zero value
`utf8_to_ascii`(string)	converts a string from utf8 to ascii

add_dtype_suffix
collapse_datasets
prepare_file_dict

dataset_to_dict(self)¶

generate a file_data type dictionary from this object

Parameters:	material_data: dict keys: name, real, imag, complex
Returns:	dict a list of dicts that has a format suitable for writing to file

extrapolate(self, new_spectrum, spline_order=2)¶

extrpolates the material data

extrapolates the material data to cover the range defined by the spectrum new_spectrum. if new_spectrum has only one element, the data will be extrapolated from the relevant end of its valid range up to the value given by new_spectrum. spline_order defines the order of the spline used for extrapolation. The results of the extrapolation depend heavily on the order chosen, so please check the end result to make sure it make physical sense.

Parameters:	new_spectrum: Spectrum the values to exrapolate to spline_order: int the order of spline to use for interpolation -> extrpolation
Raises:	NotImplementedError if the material is defined as via a complex value

get_maximum_valid_range(self)¶

find maximum spectral range that spans real and imaginary data.

Checks both real and imaginary parts of spectral data and finds the maximum spectral range which is valid for both parts.

Returns:	2x1 np.array the maximum valid range

get_nk_data(self, spectrum, spectrum_type='wavelength', unit='meter')¶

return complex refractive index for a given input spectrum.

Parameters:	spectrum: np.array or Spectrum the spectral values to evaluate spectrum_type: str {‘wavelength’, ‘frequency’, ‘energy’} type of spectrum unit: str {‘meter’, ‘nanometer’, ‘micrometer’, ‘hertz’, ‘electronvolt’} unit of spectrum (must match spectrum type)
Returns:	np.complex128 the complex n/k values (if input spectrum has size == 1) np.array with np.complex128 dtype the complex n/k values (if input spectrum has size > 1)

get_permittivity(self, spectrum_values, spectrum_type='wavelength', unit='meter')¶

return complex permittivity for a given input spectrum.

Parameters:	spectrum: np.array or Spectrum the spectral values to evaluate spectrum_type: str {‘wavelength’, ‘frequency’, ‘energy’} type of spectrum unit: str {‘meter’, ‘nanometer’, ‘micrometer’, ‘hertz’, ‘electronvolt’} unit of spectrum (must match spectrum type)
Returns:	np.complex128 the complex permittivity values (if input spectrum has size == 1) np.array with np.complex128 dtype the complex permittivity values (if input spectrum has size > 1)

get_sample_spectrum(self)¶: spectrum which covers the maximum valid range of the material data

plot_nk_data(self, **kwargs)¶: plots the real and imaginary part of the refractive index

plot_permittivity(self, **kwargs)¶: plots the real and imaginary part of the permittivity

print_comment(self)¶: print material comment

print_reference(self)¶: print material reference

remove_absorption(self)¶: sets loss (k or epsi) to constant zero value

Warning

has no effect if the material is defined as via complex data instead of separate real and imaginary parts.

static utf8_to_ascii(string)¶: converts a string from utf8 to ascii

class material.MaxwellGarnett(spectrum, material1, material2, filling_fraction)¶

Methods

`create_effective_data`(self)	this must be implemented in a subclass
`dataset_to_dict`(self)	generate a file_data type dictionary from this object
`extrapolate`(self, new_spectrum[, spline_order])	extrpolates the material data
`get_maximum_valid_range`(self)	find maximum spectral range that spans real and imaginary data.
`get_nk_data`(self, spectrum[, spectrum_type, …])	return complex refractive index for a given input spectrum.
`get_permittivity`(self, spectrum_values[, …])	return complex permittivity for a given input spectrum.
`get_sample_spectrum`(self)	spectrum which covers the maximum valid range of the material data
`plot_nk_data`(self, **kwargs)	plots the real and imaginary part of the refractive index
`plot_permittivity`(self, **kwargs)	plots the real and imaginary part of the permittivity
`print_comment`(self)	print material comment
`print_reference`(self)	print material reference
`remove_absorption`(self)	sets loss (k or epsi) to constant zero value
`utf8_to_ascii`(string)	converts a string from utf8 to ascii

add_dtype_suffix
collapse_datasets
prepare_file_dict

create_effective_data(self)¶: this must be implemented in a subclass