The Electromagnetic Waves, Frequency Domain (ewfd) interface (), found under the Wave Optics branch () when adding a physics interface, is used to solve for time-harmonic electromagnetic field distributions.

For this physics interface, the maximum mesh element size should be limited to a fraction of the wavelength. The domain size that can be simulated thus scales with the amount of available computer memory and the wavelength. The physics interface supports the Frequency Domain, Wavelength Domain, Eigenfrequency, Mode Analysis, and Boundary Mode Analysis study types. The Frequency Domain and Wavelength Domain study types are used for source driven simulations for a single frequency/wavelength or a sequence of frequencies/wavelengths. The Eigenfrequency study type is used to find resonance frequencies and their associated eigenmodes in resonant cavities.

When this physics interface is added, these default nodes are also added to the Model Builder — Wave Equation, Electric, Perfect Electric Conductor, and Initial Values. Then, from the Physics toolbar, add other nodes that implement, for example, boundary conditions. You can also right-click Electromagnetic Waves, Frequency Domain to select physics features from the context menu.

The Label is the default physics interface name.

The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.

The default Name (for the first physics interface in the model) is ewfd.

From the Formulation list, select whether to solve for the Full field (the default) or the Scattered field.

For Scattered field select a Background wave type according to the following table:

Enter the component expressions for the Background electric field Eb (SI unit: V/m). The entered expressions must be differentiable.

For Gaussian beam select the Gaussian beam type — Paraxial approximation (the default) or Plane wave expansion.

When selecting Paraxial approximation, the Gaussian beam background field is a solution to the paraxial wave equation, which is an approximation to the Helmholtz equation solved for by the Electromagnetic Waves, Frequency Domain (ewfd) interface. The approximation is valid for Gaussian beams that have a beam radius that is much larger than the wavelength. Since the paraxial Gaussian beam background field is an approximation to the Helmholtz equation, for tightly focused beams, you can get a nonzero scattered field solution, even if you do not have any scatterers. The option Plane wave expansion means that the electric field for the Gaussian beam is approximated by an expansion of the electric field into a number of plane waves. Since each plane wave is a solution to Helmholtz equation, the plane wave expansion of the electric field is also a solution to Helmholtz equation. Thus, this option can be used also for tightly focused Gaussian beams. The limitation though is that only propagating (not evanescent) plane waves are considered in the expansion.

For Plane wave expansion select Wave vector distribution type — Automatic (the default) or User defined. For User defined also enter values for the Wave vector count Nk (the default value is 13) and Maximum transverse wave number kt,max (SI unit: rad/m, default value is (2*(sqrt(2*log(10))))/ewfd.w0). Use an odd number for the Wave vector count Nk to make sure that a wave vector pointing in the main propagation direction is included in the plane-wave expansion. The Wave vector count Nk specifies the number of wave vector that will be included per transverse dimension. So for 3D the total number of wave vectors will be Nk*Nk. The value for the Maximum transverse wave number kt,max should not be larger than the value for the Wave number k, as only propagating waves will be including in the plane wave expansion.

A plane wave expansion with a finite number of plane waves included will make the field periodic in the plane orthogonal to the main propagation direction. If the separation between the transverse wave vector components, given by 2kt,max/(Nk-1), is too small, replicas of the Gaussian beam background field can appear. To avoid that, increase the value for the Wave vector count Nk.

For more information about the Gaussian beam theory, see Gaussian Beams as Background Fields.

The initial background wave is predefined as E0 = exp(−jkxx)z. This field is transformed by three successive rotations along the roll, pitch, and yaw angles, in that order. For a graphic representation of the initial background field and the definition of the three rotations, c.f. Figure 3-1 below.

and m is azimuthal mode number (+1 or -1) varying depending on the Circular polarization type and Direction of propagation settings.

Select the Electric field components solved for — Three-component vector, Out-of-plane vector, or In-plane vector. Select:

This section is available for 2D and 2D axisymmetric components, when solving for Three-component vector or In-plane vector.

For 2D components, assign a wave vector component to the Out-of-plane wave number field. For 2D axisymmetric components, assign an integer constant or an integer parameter expression to the Azimuthal mode number field.

Select the Enable check box to use a physics-controlled mesh for the electromagnetic problem. When selected, this invokes a parameter for the maximum mesh element size in free space. The physics-controlled mesh automatically scales the maximum mesh element size as the wavelength changes in different dielectric and magnetic regions. If the model is configured by any periodic conditions, identical meshes are generated on each pair of periodic boundaries. Perfectly matched layers are built with a structured mesh, specifically, a swept mesh in 3D and a mapped mesh in 2D.

When Enable is selected, choose one of the four options for the Maximum mesh element size control parameter — From study (the default), User defined, Frequency, or Wavelength. When From study is selected, 1/5 of the vacuum wavelength from the highest frequency defined in study step is used for the maximum mesh element size. For the option User defined, enter a suitable Maximum element size in free space. For example, 1/5 of the vacuum wavelength or smaller. When Frequency is selected, enter the highest frequency intended to be used during the simulation. The maximum mesh element size in free space is 1/5 of the vacuum wavelength for the entered frequency. For the Wavelength option, enter the smallest vacuum wavelength intended to be used during the simulation. The maximum mesh element size in free space is 1/5 of the entered wavelength.

When Resolve wave in lossy media is selected, the outer boundaries of lossy media domains are meshed with a maximum mesh element size in free space given by the minimum value of half a skin depth and 1/5 of the vacuum wavelength.

Select the Activate port sweep check box to switch on the port sweep. When selected, this invokes a parametric sweep over the ports in addition to the automatically generated frequency/wavelength sweep. The generated lumped parameters are in the form of an S-parameter matrix.

For Activate port sweep enter a Sweep parameter name to assign a specific name to the parameter that controls the port number solved for during the sweep. Before making the port sweep, the parameter must also have been added to the list of parameters in the Parameters section of the Parameters node under the Global Definitions node.

For this physics interface, the S-parameters are subject to Touchstone file export. Click Browse to locate the file, or enter a file name and path. Select an Output format: Magnitude angle, Magnitude (dB) angle, or Real imaginary.

Enter a Reference impedance, Touchstone file export Zref (SI unit: Ω). The default is 50 Ω.

The dependent variables (field variables) are for the Electric field E and its components (in the Electric field components fields). The name can be changed but the names of fields and dependent variables must be unique within a model.