2.6     Dielectric Dispersive

Dielectric dispersive is a dispersive dielectric medium. QuickWave allows for considering single-, dual-, and triple-pole dispersive media. For this medium type:

Mu = m_r [dimensionless] – relative magnetic permeability,

Sigma = s [S/m] - electric conductivity,

and

SigmaM = s_m/(k)⁴ [W/m] - magnetic loss 

are defined analogously as for dielectric isotropic. Its complex relative permittivity (including series losses) can be given by an arbitrarily weighted composition of Debye, Drude or Lorentz dispersion model with user-specified parameters:

Drude:            e_r(w) = eps_inf  +  (2p f_p)² / (j w 2p v_c  - w²)

Debye:            e_r(w) = eps_inf  + (eps_s - eps_inf) / (1 + j w tau)

Lorentz:          e_r(w) = eps_inf  + (eps_s - eps_inf) (2p f_p)² / ((2p f_p)²  + j w 2p v_c - w²)

where:

eps_inf  [dimensionless] - relative permittivity at infinite frequency,

eps_s [dimensionless] - static relative permittivity,

tau [ns] - relaxation time,

v_c [GHz] - inverse of the relaxation time (collision frequency),

f_p [GHz] - pole frequency (plasma frequency),

amp [dimensionless] - weight coefficient of the corresponding dispersive pole (relevant for dual- and triple-pole dispersive medium models only)

For Debye and Lorentz, eps_s < eps_inf is not allowed, and eps_s = eps_inf causes that the medium is considered as dielectric isotropic with frequency-independent permittivity eps_inf and conductivity Sigma.

For Drude and Lorentz, f_p =0 causes that the medium is considered as dielectric isotropic with frequency-independent permittivity eps_inf and conductivity Sigma.

For Debye, tau=0 causes that the medium is considered as dielectric isotropic with frequency-independent permittivity eps_s and conductivity Sigma.

There are also limits on the admissible level of losses with respect to the FDTD time step Δt. For Debye, the requirement is:

                                                           tau > 0.5 Δt;

for Drude and Lorentz:

                                                           (2p v_c)^-1 > 0.5 Δt.