PDielec.Materials

Materials DataBase

An interface to the spreadsheet which holds materials data

Module Contents

Classes

Constant	A class representing a material with constant scalar permittivity, inheriting from the Material class.
DrudeLorentz	A subclass representing a material with a Lorentz-Drude model permittivity.
External	A class for representing materials with externally specified permittivity.
FPSQ	Class representing a material with a FPSQ model for permittivity.
Material	A class for representing materials with properties like name, density, permittivity, and unit cell.
MaterialsDataBase	A class for managing a database of materials' properties.
Sellmeier	A class to define materials using the Sellmeier model for permittivity.
Tabulated	A class for materials with tabulated permittivities.

class PDielec.Materials.Constant(name, permittivity=None, density=None, cell=None)

Bases: Material

A class representing a material with constant scalar permittivity, inheriting from the Material class.

Attributes

typestr

The type of material, set to ‘Constant permittivity’.

Methods

Inherits methods from the Material class.

class PDielec.Materials.DrudeLorentz(name, epsinf, omegas, strengths, gammas, density=None, cell=None)

Bases: Material

A subclass representing a material with a Lorentz-Drude model permittivity.

Parameters

namestr

The name of the material.

epsinfarray_like

Epsilon infinity, either a 3x3 list or a 3x3 array representing the static dielectric constant.

omegaslist

The transverse optical (TO) frequencies.

strengthslist

The oscillator strengths for each resonance.

gammaslist

The damping (or broadening) factors for each resonance.

densityfloat, optional

The density of the material in grams per milliliter (g/ml). Default is None.

cellunitCell, optional

The unit cell of the material. Default is None.

Notes

The Drude-Lorentz model is used to calculate the permittivity of the material by considering the contributions from both free electrons (Drude) and bound electrons (Lorentz). This class requires specifying the infinite frequency dielectric constant (epsinf), the transverse optical frequencies (omegas), the oscillator strengths (strengths), and the damping factors (gammas) for each resonance in the material.

Examples

>>> drude_lorentz_material = DrudeLorentz("Gold", [[1, 0, 0], [0, 1, 0], [0, 0, 1]],
...                                       [0.5, 1.0], [1.0, 2.0], [0.2, 0.1],
...                                       density=19.3)
This represents a Drude-Lorentz material with the name "Gold", an isotropic epsilon infinity,
two resonances with specified frequencies, strengths, and damping factors, and
a density of 19.3 g/ml.

class PDielec.Materials.External(name, permittivityObject=None, density=None, cell=None)

Bases: Material

A class for representing materials with externally specified permittivity.

This class inherits from the Material class and is used to define materials where the permittivity is specified externally, rather than calculated or predefined. Permittivity can be a complex value indicating both the real and imaginary parts.

class PDielec.Materials.FPSQ(name, epsinf, omega_tos, gamma_tos, omega_los, gamma_los, density=None, cell=None)

Bases: Material

Class representing a material with a FPSQ model for permittivity.

Parameters

namestr

The name of the material.

epsinfarray_like

Epsilon infinity (eps0), either a 3x3 list or a 3x3 array representing the dielectric constant at infinite frequency.

omega_toslist

The transverse optical (TO) frequencies.

gamma_toslist

The TO absorption widths.

omega_loslist

The longitudinal optical (LO) frequencies.

gamma_loslist

The LO absorption widths.

densityfloat, optional

The density of the material in grams per milliliter (g/ml).

cellunitCell, optional

The unit cell of the material.

Notes

The FPSQ (fitted phonon simple quantum) model is used to describe the permittivity of the material. This model is based on the harmonic oscillator model and describes the permittivity as a function of frequency.

class PDielec.Materials.Material(name, density=None, permittivityObject=None, cell=None)

A class for representing materials with properties like name, density, permittivity, and unit cell.

The Material class also contains the permittivity object for the material. The permittivity object is an instance of DielectricFunction or one its children. The permittivity object is responsible for calculating the permittivity at the given frequency. The subclasses which inherit from the Material class are: Constant, External, DrudeLorentz, FPSQ, Sellmeier, and Tabulated. Each subclass has an initialisation routine which instantiates the permittivity object of the appropriate type for the material. The relationship between the Material subclass and the DielectricFunction subclass of the permittivity object is shown below.

Material subclass	DielectricFunction subclass
Constant	Constant
External	This class is passed a permittivity object which has been defined externally
DrudeLorentz	DrudeLorentz
FPSQ	FPSQ
Sellmeier	Sellmeier
Tabulated	TabulateScalar Tabulate3 Tabulate3 Tabulate6

Parameters

namestr

The name of the material.

densityfloat, optional

The density of the material. If not provided and a cell is given, it will be calculated based on the cell.

permittivityObjectDielectricFunction, optional

An object representing the dielectric function of the material. This is intended to be passed by classes that inherit from Material, and it should contain methods for calculating scalar/tensor permittivity. (see DielectricFunction and its sub-classes)

cellUnitCell, optional

An object representing the unit cell of the material. If provided without a density, the density will be calculated from this cell. (See UnitCell)

Attributes

densityfloat

The density of the material, which may be calculated based on the cell if not provided initially.

cellCell or None

The unit cell of the material if provided.

namestr

The name of the material.

typestr

A string indicating the type of the object. Defaults to ‘Base Class’ for the base Material class.

permittivityObjectDielectricFunction or None

An object to handle the permittivity calculations for the material.

Methods

getName()

Returns the name of the material.

getInformation()

Returns information about the material, including its type and, if applicable, its permittivity frequency range.

getSigmas()

If the material has a lorentzian dielectric this routine returns the sigma parameters

setSigmas()

If the material has a lorentzian dielectric this routine sets the sigma parameters

getFrequencies()

If the material has a lorentzian dielectric this routine returns the frequencies

setFrequencies()

If the material has a lorentzian dielectric this routine sets the frequencies

getOscillatorStrengths()

If the material has a lorentzian dielectric this routine returns the oscillator strengths

setOscillatorStrengths()

If the material has a lorentzian dielectric this routine sets the oscillator strengths

print()

Prints information about the material, such as its name, density, type, and permittivity details.

isScalar()

Checks and returns True if the material’s permittivity is scalar.

isTensor()

Checks and returns True if the material’s permittivity is tensor.

getPermittivityObject()

Returns the permittivityObject of the material.

getPermittivityFunction()

Returns the permittivity function from the permittivityObject.

getDensity()

Returns the density of the material.

setCell(cell)

Sets the cell of the material and updates the density if it was initially None.

getCell()

Returns the cell of the material.

setDensity(value)

Sets the density of the material.

setEpsilonInfinity(eps)

Sets the epsilon infinity of the material

setPermittivityObject(permittivityObject)

Sets the permittivityObject for the material.

getCell()

Return the cell

Parameters

None

Returns

self.cell

getDensity()

Return the density

Parameters

None

Returns

self.density

getFrequencies()

Gets the frequencies for a Lorentzian permittivity

Parameters

None

Returns

1d array of floats

Returns the frequencies for a Lorentzian function in cm-1

getInformation()

Returns information about the material.

Parameters

None

Returns

str

A description of the material.

getName()

Get the name attribute of the object.

Parameters

None

Returns

str

The name attribute of the object.

getOscillatorStrengths()

Gets the oscillator strengths for a Lorentzian permittivity

The oscillator strength of each transition is a 3x3 matrix

Parameters

None

Returns

list of 3x3 array of floats

Returns the oscillator strengths for a Lorentzian permittivity function in cm-1

getPermittivityFunction()

Returns the permittivity function.

Parameters

None

Returns

permittivityObjectFunction

Return the permittivity object function

getPermittivityObject()

Returns the permittivity object.

Parameters

None

Returns

permittivityObject

Return the permittivity object (dielectric function object)

getSigmas()

Gets the sigma parameters for a Lorentzian permittivity

Parameters

None

Returns

1d array of floats

Returns the sigma parameters for a Lorentz permittivity function in cm-1

isScalar()

Returns true if the material returns a scalar permittivity.

Parameters

None

Returns

bool

True if the material returns a scalar permittivity, False otherwise.

isTensor()

Returns true if the material returns a tensor permittivity.

Parameters

None

Returns

bool

True if the material returns a tensor permittivity, False otherwise.

print()

Print information about the material.

Parameters

None

Returns

None

setCell(cell)

Set the unit cell

Parameters

cell : a unit cell

Returns

None

setDensity(value)

Set the density

Parameters

value : float

Returns

None

setFrequencies(frequencies)

Sets the frequencies for a Lorentzian permittivity

Parameters

frequencies1D array of floats

The frequencies for a Drude-Lorentzian permittivity in cm-1

Returns

None

setOscillatorStrengths(strengths)

Sets the oscillator strengths for a Lorentzian permittivity

Parameters

strengthsa 3x3 array of floats for each frequency

The oscillator strengths for a Lorentzian permittivity function in cm-1

Returns

None

setPermittivityObject(permittivityObject)

Set the permittivity object.

Parameters

permittivityObject : a permittivity object (dielectric function object)

Returns

None

setSigmas(sigmas)

Sets the sigma parameters for a Lorentzian permittivity

Parameters

sigmas1D array of floats

The sigma parameters for a Lorentzian permittivity function in cm-1

Returns

None

class PDielec.Materials.MaterialsDataBase(filename, debug=False)

A class for managing a database of materials’ properties.

This database is initialized from an Excel spreadsheet which contains various material properties including names, densities, refractive indices, and permittivities, among others. Additional functionalities include validation checks, retrieval of sheet names, material information, and specific data based on the property of interest (e.g., constant permittivity, tabulated refractive index). The getMaterial() method returns a material with a dielectric function of the appropriate type. There are routines which read (process) the data stored for the following dielectric functions:

• constant refractive index

• constant permittivity

• tabulated refractive index (may be 1, 3 or 6 parameters for isotropic, uniaxial or anisotropic)

• tabulated permittivity (may be 1, 3 or 6 parameters for isotropic, uniaxial or anisotropic)

• Lorentz-Drude

• FPSQ (Four parameters semi-quantum model)

• Sellmeier

Further information can be found in the following classes and their sub-classes:

• Material

• DielectricFunction

Parameters

filenamestr

The filename of the spreadsheet/database.

debugbool, optional

Set to true for additional debugging information

Attributes

filenamestr

The path to the Excel spreadsheet containing materials data.

sheetNameslist

A list of strings representing the names of the sheets within the Excel spreadsheet.

debugbool, optional

A flag indicating whether debugging information should be printed. Default is False.

Methods

__init__(filename, debug=False)

Initializes the MaterialsDataBase class with a given Excel spreadsheet and a debug flag.

getFileName()

Returns the filename of the Excel spreadsheet being used as the database.

valid()

Checks if the spreadsheet is a valid materials database based on certain criteria.

getSheetNames()

Retrieves a sorted list of sheet names within the spreadsheet, including additional predefined names.

getMaterial(sheet)

Returns a material object based on the data in a given sheet of the Excel spreadsheet.

readConstantRefractiveIndex(sheet, worksheet, density)

Reads constant refractive index data for a given material from the spreadsheet.

readConstantPermittivity(sheet, worksheet, density)

Reads constant permittivity data for a given material from the spreadsheet.

readTabulatedRefractiveIndex(sheet, worksheet, density)

Reads tabulated refractive index data for a given material from the spreadsheet.

readTabulatedPermittivity(sheet, worksheet, density)

Reads tabulated permittivity data for a given material from the spreadsheet.

readLorentzDrude(sheet, worksheet, density, unitCell)

Reads Drude-Lorentz model parameters for a given material from the spreadsheet.

readFPSQ(sheet, worksheet, density, unitCell)

Reads FPSQ model parameters for a given material from the spreadsheet.

readSellmeier(sheet, worksheet, density, unitCell)

Reads Sellmeier model parameters for a given material from the spreadsheet.

getFileName()

Return the filename

Parameters

None

Returns

str

The filename.

getMaterial(sheet)

Return a material object based on the data in sheet (an excel sheet).

If one of the following is requested: air, vacuum, ptfe, ldpe, mdpe, kbr, nujol, then the material is created even if it is not in the database.

Parameters

sheetExcel sheet

The excel sheet containing the material data.

Returns

Material object

The material object created from the excel sheet data.

getSheetNames()

Returns a list of the sheetnames in the database.

As well as the sheets in the database, there are some default materials which will be added to the list of materials and which are provided internally by this module.

Parameters

None

Returns

list

A list of the sheet names present in the database.

readConstantPermittivity(sheet, worksheet, density)

Read constant permittivity data from the spreadsheet.

Parameters

sheetstr

The worksheet name.

worksheetworksheet

The worksheet instance.

densityfloat

The density of the material.

Returns

None

readConstantRefractiveIndex(sheet, worksheet, density)

Read constant refractive index from the spreadsheet.

Parameters

sheetstr

The worksheet name.

worksheetworksheet

The worksheet.

densityfloat

The density of the material.

Returns

None

readFPSQ(sheet, worksheet, density, unitCell)

Read FPSQ data from the spreadsheet.

Parameters

sheetstr

The worksheet name.

worksheetworksheet

The actual worksheet object.

densityfloat

The density of the material.

unitCellobject

The unit cell.

Returns

None

readLorentzDrude(sheet, worksheet, density, unitCell)

Read Drude-Lorentz data from the spreadsheet.

Parameters

sheetstr

The worksheet name.

worksheetworksheet

The worksheet.

densityfloat

The density of the material.

unitCellobject

The unit cell.

Returns

None

readSellmeier(sheet, worksheet, density, unitCell)

Read Sellmeier data from the spreadsheet.

Parameters

sheetstr

The worksheet name.

worksheetworksheet

The worksheet.

densityfloat

The density of the material.

unitCellobject

The unit cell.

Returns

None

readTabulatedPermittivity(sheet, worksheet, density)

Read tabulated permittivity data from the spreadsheet.

Parameters

sheetstr

The worksheet name.

worksheetworksheet

The worksheet.

densityfloat

The density of the material.

Returns

None

readTabulatedRefractiveIndex(sheet, worksheet, density)

Read tabulated refractive index data from the spreadsheet.

Parameters

sheetstr

The worksheet name.

worksheetworksheet

The worksheet.

densityfloat

The density of the material.

Returns

None

valid()

Test to see if the spreadsheet is a valid materials database.

Parameters

None

Returns

bool

True if the spreadshee is ‘valid’

Notes

None

class PDielec.Materials.Sellmeier(name, Bs, Cs, density=None, cell=None)

Bases: Material

A class to define materials using the Sellmeier model for permittivity.

Parameters

namestr

The name of the material.

Bslist or array_like

The B parameters (coefficients) in the Sellmeier equation.

Cslist or array_like

The C parameters (coefficients) in the Sellmeier equation.

densityfloat, optional

The density of the material in g/ml. Default is None.

cellunitCell, optional

The unit cell of the material. Default is None.

Attributes

typestr

The type of the material, which is ‘Sellmeier’ for instances of this class.

Methods

__init__(self, name, Bs, Cs, density=None, cell=None)

Initializes a Sellmeier material with specified parameters.

class PDielec.Materials.Tabulated(name, vs_cm1=None, permittivities=None, density=None, cell=None)

Bases: Material

A class for materials with tabulated permittivities.

Parameters

namestr

The name of the material.

vs_cm1list or None, optional

The list of tabulated frequencies in cm-1. Defaults to None.

permittivitiesarray-like or None, optional

The permittivities, either as a single vector (n,) or a tensor (3,n) or (6,n) for more complex materials. Defaults to None.

densityfloat or None, optional

The density of the material in g/ml. Defaults to None.

cellunitCell or None, optional

The unit cell of the material. Defaults to None.

Notes

• This class is designed to handle materials with a constant permittivity as well as those requiring more complex permittivity tensors.

• The permittivity can be defined using either a scalar for simple materials or tensors for materials that require a support matrix.

• The constructor converts the input lists of frequencies (vs_cm1) and permittivities into numpy arrays, and then generates the appropriate permittivity object depending on the complexity of the material’s permittivities.

Examples

>>> material1 = Tabulated("Quartz", vs_cm1=[500, 1000, 1500], permittivities=[2.1, 2.3, 2.5], density=2.65)
>>> material2 = Tabulated("Synthetic", vs_cm1=[200, 400, 600], permittivities=[[2.1, 2.3, 2.5], [2.4, 2.6, 2.8], [3.0, 3.2, 3.4]], density=1.5)

setEpsilonInfinity(eps)

Sets the value of epsilon infinity for the material

Parameters

epsfloat or 3x3 np array

The epsilon infinity tensor. If a single float then an isotropic 3x3 np array is created

Returns

None