The Electromagnetic Waves, Beam Envelopes (ewbe) interface (), found under the Wave Optics branch () when adding a physics interface, is used to compute electric and magnetic field distributions for systems and devices where the field amplitude varies slowly on a wavelength scale.

When this physics interface is added, these default nodes are also added to the Model Builder — Wave Equation, Beam Envelopes, 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, Beam Envelopes to select physics features from the context menu.

The physics-controlled mesh is controlled from the Mesh node’s Settings window (if the Sequence type is Physics-controlled mesh). There, in the table in the Physics-Controlled Mesh section, find the physics interface in the Contributor column and select or clear the check box in the Use column on the same table row for enabling (the default) or disabling contributions from the physics interface to the physics-controlled mesh.

When the Use check box for the physics interface is selected, in the section for the physics interface below the table, choose the Mesh type — Swept mesh (default for 3D), Mapped mesh (default for 2D), Tetrahedral mesh (3D), and Triangular mesh (2D).

When a structured Mesh type (either Swept mesh in 3D or Mapped mesh in 2D) is selected, enter values for Number of transverse mesh elements (default is 10) and Number of longitudinal mesh elements (default is 10). The entered Number of transverse mesh elements will be distributed along the longest side of the input boundary. A boundary is identified as an input boundary if there is an active feature, like a Port, a Scattering Boundary Condition, and so on, added to that boundary and the feature defines an incident wave. The mesh will be denser in domains where the refractive index is larger. Similarly, the entered Number of longitudinal mesh elements will be distributed along propagation direction. Also here, the mesh will be denser in domains where the refractive index is larger.

When an unstructured Mesh type (either Tetrahedral mesh in 3D or Triangular mesh in 2D) is selected, enter a value for the Maximum element size in free space. The physics-controlled mesh automatically scales the maximum mesh element size as the material wavelength changes in different dielectric and magnetic regions.

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 ewbe.

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

Select the Number of directions — Bidirectional (the default) or Unidirectional.

Select the Type of phase specification — Wave vector (the default) or User defined.

In the tables, if Wave vector is selected for Type of phase specification, enter values or expressions for the Wave vector, first wave k1 (SI unit: rad/m) and, if Bidirectional is selected, for Wave vector, second wave k2 (SI unit: rad/m).

If User defined is selected for Type of phase specification, enter an expression for Phase, first wave (SI unit: rad) and, if Bidirectional is selected, for Phase, second wave (SI unit: rad).

When Unidirectional is selected, the electric field is expressed as

where E1 is the electric field envelope that is solved for and is the prescribed rapidly varying phase function. When Wave vector is selected for Type of phase specification, the phase is defined as

Notice that the wave vector k1 is assumed to be the same for all domains selected for the physics interface. This also means that the phase will satisfy the condition of being continuous everywhere. If the wave is assumed to bend or there are different materials in the domains, the phase approximation above is not good and it is better to select a User defined Type of phase specification. When specifying the phase expression , it is important that it is continuous everywhere.

The solution for the electric field envelope E1 is as exact as the solution for the total electric field E, as is done for The Electromagnetic Waves, Frequency Domain Interface. The advantage is that the mesh only need to resolve the spatial variation of the field envelope E1 and not the rapid variation of the phase factor. On the other hand, for problems involving reflections and scattering there is a rapid spatial variation also for the field envelope. Then there is a no advantage of using the Unidirectional formulation.

When Bidirectional is selected, the electric field is expressed as

where E2 and are the electric field envelope and the prescribed phase function for the second wave. When specifying User defined phases, and , each phase should be continuous across the boundaries.

The Bidirectional formulation is good to use when there are boundaries reflecting the wave in another direction than that of the incident wave. The direction for the reflected beam is typically in the opposite direction to the incident beam. The boundary conditions at these internal and/or external boundaries couple the electric field envelopes E1 and E2.

Notice, however, that there is no coupling between E1 and E2 within domains, unless weak expressions are explicitly added to the domains in the Model Builder. For more information about how to add weak domain expressions, see Common Physics Interface and Feature Settings and Nodes.

This section is available when the Type of phase specification is set to User defined. Expand the section and enter values or expressions for the Wave vector, first wave k1 (SI unit: rad/m) and, if Bidirectional is selected, for Wave vector, second wave k2 (SI unit: rad/m).

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 or wavelength sweep.

For Activate port sweep enter a Sweep parameter name to assign a specific name to the variable that controls the port number solved for during the sweep.

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

Select an option from the If file exists list — Overwrite (the default) or Create new.

Enter a Reference impedance, Touchstone file export. The default is 50 Ω.

To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.

Select Weak formulation (the default) or Constraint-based from the Port formulation list. For a more detailed discussion of these options, see Port Options in the documentation of The Electromagnetic Waves, Frequency Domain Interface.

Select the Use averaged loss calculation check box to remove cross terms between the two waves, when calculating the electromagnetic loss (and heat source) in the bidirectional formulation. This setting can be useful when the cross terms create a beating field that is not resolved by the mesh. If this spatially fast varying heat source distribution anyhow is washed out by the heat transfer, it can be advantageous to not include the cross terms when calculating the electromagnetic loss (and heat source). If the cross terms are of importance when solving the associated heat transfer problem, use a mesh that is fine enough to resolve the fast spatial variations of the heat source.

Select the shape order for the Electric field envelopes dependent variables — Linear, Linear type 2, Quadratic (the default), Quadratic type 2, Cubic, or Cubic type 2. For more information about the Discretization section, see Settings for the Discretization Sections in the COMSOL Multiphysics Reference Manual.