Materials

Material models and dispersive media in WiTwin Maxwell

Overview #

WiTwin Maxwell extends the base witwin.core.Material with dispersive pole models, anisotropic tensors, and convenience constructors.

import witwin.maxwell as mw
 
# Simple dielectric
mat = mw.Material(eps_r=12.0)
 
# Conductive material
mat = mw.Material(eps_r=4.0, sigma_e=0.01)
 
# Dispersive Drude metal
mat = mw.Material.drude(eps_inf=1.0, plasma_frequency=2.0e15, gamma=1.0e13)

Material #

Constructor #

Parameter	Type	Default	Description
`eps_r`	`float`	`1.0`	Relative permittivity
`mu_r`	`float`	`1.0`	Relative permeability
`sigma_e`	`float`	`0.0`	Electrical conductivity. Must be >= 0
`name`	`str \| None`	`None`	Optional material name
`debye_poles`	`tuple[DebyePole]`	`()`	Electric Debye dispersion poles
`drude_poles`	`tuple[DrudePole]`	`()`	Electric Drude dispersion poles
`lorentz_poles`	`tuple[LorentzPole]`	`()`	Electric Lorentz dispersion poles
`mu_debye_poles`	`tuple[DebyePole]`	`()`	Magnetic Debye dispersion poles
`mu_drude_poles`	`tuple[DrudePole]`	`()`	Magnetic Drude dispersion poles
`mu_lorentz_poles`	`tuple[LorentzPole]`	`()`	Magnetic Lorentz dispersion poles
`epsilon_tensor`	`DiagonalTensor3 \| None`	`None`	Anisotropic permittivity tensor
`mu_tensor`	`DiagonalTensor3 \| None`	`None`	Anisotropic permeability tensor
`sigma_e_tensor`	`DiagonalTensor3 \| None`	`None`	Anisotropic conductivity tensor

Convenience Constructors #

# Debye dispersive medium
mw.Material.debye(eps_inf=2.0, delta_eps=1.5, tau=1.0e-12)
 
# Drude metal
mw.Material.drude(eps_inf=1.0, plasma_frequency=2.0e15, gamma=1.0e13)
 
# Lorentz resonant medium
mw.Material.lorentz(eps_inf=1.0, delta_eps=2.0, resonance_frequency=1.0e12, gamma=1.0e10)

Properties #

Property	Description
`material.is_dispersive`	`True` if any dispersion poles are set
`material.is_electric_dispersive`	`True` if electric poles are set
`material.is_magnetic_dispersive`	`True` if magnetic poles are set
`material.is_anisotropic`	`True` if any tensor is set
`material.is_nonlinear`	`True` if `kerr_chi3` is set

Methods #

material.relative_permittivity(frequency) — Returns complex permittivity at the given frequency in Hz including all dispersion poles and conductivity.

material.relative_permeability(frequency) — Returns complex permeability at the given frequency in Hz.

Dispersive Pole Models #

DebyePole #

A first-order relaxation pole for modeling dielectric relaxation.

mw.DebyePole(delta_eps=1.5, tau=1.0e-12)

Parameter	Description
`delta_eps`	Permittivity change. Must be >= 0
`tau`	Relaxation time in seconds. Must be > 0

DrudePole #

A free-electron pole for modeling metals and plasmas.

mw.DrudePole(plasma_frequency=2.0e15, gamma=1.0e13)

Parameter	Description
`plasma_frequency`	Plasma frequency in Hz. Must be > 0
`gamma`	Collision rate in Hz. Must be >= 0

LorentzPole #

A second-order resonant pole for modeling phonon resonances and bound electrons.

mw.LorentzPole(delta_eps=2.0, resonance_frequency=1.0e12, gamma=1.0e10)

Parameter	Description
`delta_eps`	Permittivity change at resonance. Must be >= 0
`resonance_frequency`	Resonance frequency in Hz. Must be > 0
`gamma`	Damping rate in Hz. Must be >= 0

Anisotropic Tensors #

Use DiagonalTensor3 for axis-aligned anisotropic materials:

mat = mw.Material(
    epsilon_tensor=mw.DiagonalTensor3(xx=4.0, yy=4.0, zz=2.0),
)

Parameter	Description
`xx`	Tensor component along x
`yy`	Tensor component along y
`zz`	Tensor component along z

Note

Full Tensor3x3 off-diagonal support is not yet implemented. Use DiagonalTensor3 for anisotropic materials.

Next Steps #

Simulation — run the simulation
First simulation tutorial — end-to-end example