Wave Equation, Electric is the main feature node for this physics interface. The governing equation can be written in the form

for the time-harmonic and eigenfrequency problems. The wave number of free space k0 is defined as

where c0 is the speed of light in vacuum.

In 2D the electric field varies with the out-of-plane wave number kz as

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.

In 2D axisymmetry, the electric field varies with the azimuthal mode number m as

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.

Select an Electric displacement field model — Relative permittivity, Refractive index (the default), Loss tangent, loss angle, Loss tangent, dissipation factor, Dielectric loss, Drude-Lorentz dispersion model, Debye dispersion model, or Sellmeier dispersion model.

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 a zero conductivity.

When Loss tangent, dissipation factor is selected, the default Relative permittivity (real part) ε′ and Loss tangent, dissipation factor tanδ 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 tanδ, enter a value to specify a dissipation for dielectric losses. This assumes a 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.

For the Drude-Lorentz dispersion model select User defined (default) or From material for Relative permittivity, high frequency ε∞ (dimensionless). 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.

In the table, enter values or expressions in the columns for the Oscillator strength, Resonance frequency (rad/s), and Damping in time (rad/s).

The Debye dispersion model is given by

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.

For the Debye dispersion model select User defined (default) or From material for Relative permittivity, high frequency ε∞ (dimensionless). For User defined select Isotropic, Diagonal, Symmetric, or Full and enter a value or expression in the field or matrix.

In the table, enter values or expressions in the columns for the Relative permittivity contribution and Relaxation time (s).

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 (m2).

Select the Constitutive relation — Relative permeability (the default) or Magnetic losses.

By default, the Electrical conductivity σ (SI unit: S/m) uses values From material.