Wave Equation, Electric is the main feature node for this physics interface. The governing equation can be written in the form
where c0 is the speed of light in vacuum.
where z is the unit vector in the out-of-plane
z direction.
Notice that the ansatz above just explains how the wave equation is modified when the out-of-plane wave vector component kz is not zero. As an example, for a plane wave with a nonzero out-of-plane wave vector component, the electric field is of course given by
where A is a constant amplitude and
kx,
ky, and
kz are the wave vector components.
When solving the equations as an eigenfrequency problem the eigenvalue is the complex eigenfrequency λ = −jω + δ, where
δ is the damping of the solution. The Q-factor is given from the eigenvalue by the formula
Using the relation εr =
n2, where
n is the refractive index, the equation can alternatively be written
When the equation is written using the refractive index, the assumption is that μr =
1 and
σ = 0 and only the constitutive relations for linear materials are available. When solving for the scattered field the same equations are used but
E = Esc + Ei and
Esc is the dependent variable.
When Relative permittivity is selected, the default
Relative permittivity εr takes values
From material. For
User defined select
Isotropic,
Diagonal,
Symmetric, or
Full and enter values or expressions in the field or matrix.
When Refractive index is selected, the default
Refractive index n and
Refractive index, imaginary part k take the values
From material. To specify the real and imaginary parts of the refractive index and assume a relative permeability of unity and zero conductivity, for one or both of the options, select
User defined then choose
Isotropic,
Diagonal,
Symmetric, or
Full.
Enter values or expressions in the field or matrix.
When Loss tangent, loss angle is selected, the default
Relative permittivity (real part) ε′ and
Loss tangent, loss angle δ take values
From material. For
User defined select
Isotropic,
Diagonal,
Symmetric, or
Full and enter values or expressions in the field or matrix. Then if
User defined is selected for
Loss tangent, loss angle δ, enter a value to specify a loss angle for dielectric losses. This assumes zero conductivity.
When Loss tangent, dissipation factor is selected, the default
Relative permittivity (real part) ε′ and
Loss tangent, dissipation factor tan
δ take values
From material. For
User defined select
Isotropic,
Diagonal,
Symmetric, or
Full and enter values or expressions in the field or matrix. Then if
User defined is selected for
Loss tangent, dissipation factor tan
δ, enter a value to specify a dissipation for dielectric losses. This assumes zero conductivity.
When Dielectric loss is selected, the default
Relative permittivity ε′ and
Relative permittivity (imaginary part) ε″ take values
From material. For
User defined select
Isotropic,
Diagonal,
Symmetric, or
Full and enter values or expressions in the field or matrix.
The Drude-Lorentz dispersion model is defined by the equation
where ε∞ is the high-frequency contribution to the relative permittivity,
ωP is the plasma frequency,
fj is the oscillator strength,
ω0j is the resonance frequency, and
Γj is the damping coefficient.
When Drude-Lorentz dispersion model is selected, the default
Relative permittivity, high frequency ε∞ (dimensionless) takes its value
From material. For
User defined select
Isotropic,
Diagonal,
Symmetric, or
Full and enter a value or expression in the field or matrix.
Enter a Plasma frequency ω∞ (SI unit: rad/s). The default is 0 rad/s.
where ε∞ is the high-frequency contribution to the relative permittivity,
Δεk is the contribution to the relative permittivity, and
τk is the relaxation time.
When Debye dispersion model is selected, the default
Relative permittivity, high frequency ε∞ (dimensionless) takes its value
From material. For
User defined select
Isotropic,
Diagonal,
Symmetric, or
Full and enter a value or expression in the field or matrix.
The Sellmeier dispersion model is often used for characterizing the refractive index of optical glasses. The model is given by
where the coefficients Bk and
Ck determine the dispersion properties.
When Sellmeier dispersion model is selected, in the table, enter values or expressions in the columns for
B and
C (m^2).
By default, the Electrical conductivity σ (SI unit: S/m) uses values
From material.