The Electromagnetic Waves, Beam Envelopes Interface
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.
The physics interface can be used efficiently for unidirectional and bidirectional propagation of electromagnetic beams. However, for optical scattering phenomena, where the field is scattered into many different directions, the Electromagnetic Waves, Frequency Domain interface is better suited.
With this physics interface the electric field is factored into a product of a slowly varying envelope function (slowly on the scale of a wavelength) and a rapidly varying phase function. The phase function is a priori prescribed, so the physics interface solves the time-harmonic wave equation for the slowly varying envelope function.
The physics interface supports the study types Frequency domain, Wavelength Domain, Eigenfrequency, and Boundary Mode Analysis. The frequency and wavelength domain study types are used for source driven simulations for a single frequency or wavelength or a sequence of frequencies or wavelengths. The Eigenfrequency study type is used to find resonance frequencies and their associated eigenmodes in cavity problems.
When this physics interface is added, these default nodes are also added to the Model BuilderWave 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.
Settings
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.
Components
This section is available for 2D and 2D axisymmetric models.
Select the Electric field components solved forThree-component vector (the default), Out-of-plane vector, or In-plane vector. Select:
Three-component vector to solve using a full three-component vector for the electric field envelope(s) E1 (and E2).
Out-of-plane vector to solve for the electric field envelope vector component perpendicular to the modeling plane, assuming that there is no electric field in the plane.
In-plane vector to solve for the electric field envelope vector components in the modeling plane assuming that there is no electric field perpendicular to the plane.
Wave Vectors
Select the Number of directionsBidirectional (the default) or Unidirectional.
Select the Type of phase specificationWave 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 φ1 (SI unit: rad) and, if Bidirectional is selected, for Phase, second wave φ2 (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 exp(-jφ1(r)) 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 φ1(r), 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 exp(-jφ2(r)) are the electric field envelope and the prescribed phase function for the second wave. When specifying User defined phases, φ1 and φ2, 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.
In the COMSOL Multiphysics Reference Manual see Table 2-3 for links to common sections and Table 2-4 to common feature nodes. You can also search for information: press F1 to open the Help window or Ctrl+F1 to open the Documentation window.
For 2D and 3D, the default value for k1 (or φ1) represents a wave vector pointing in the x-direction.
The default value for k2 represents the wave vector for a plane wave reflected from a plane normal to the x-direction. Thus, the x-component is negated, whereas the other components are the same as for wave vector of the incident wave.
The default value for the User defined phase for the second wave, φ2, represents a wave propagating in the opposite direction to the first wave.
For 2D axisymmetry, the default value for k1 (or φ1) represents a wave vector pointing in the z-direction, whereas k2 (or φ2) represents a wave propagating in the opposite direction to the first wave.
For an example using the User defined Type of phase specification, see Gaussian Beam Incident at the Brewster Angle: Application Library path Wave_Optics_Module/Optical_Scattering/brewster_interface.
User defined wave vector specification
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).
The default values for the wave vectors are the gradients of the corresponding phases defined in the Wave Vector settings. These values will be correct for most cases. However, they will be wrong for Perfectly Matched Layer domains. There, it is better to explicitly specify the wave vector. For example, if the wave solution is expected to approximate a plane wave in vacuum (or air), it would be better to enter the vacuum wave number ewbe.k0 in the appropriate component field.
Port Sweep Settings
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.
Physics-controlled mesh
Select the Enable check box to use a physics-controlled mesh for the electromagnetic problem. When Enable is selected, choose the Mesh typeSwept 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, etc, 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.
If no input features are defined, for instance for an eigenfrequency simulation, the longitudinal direction is assumed to be the longest direction of the geometry and the transverse plane is orthogonal to the longitudinal direction.
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.
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.
For an example using the Physics-controlled mesh with a Swept mesh, see Directional Coupler: Application Library path Wave_Optics_Module/Waveguides_and_Couplers/directional_coupler.
For an example using the Physics-controlled mesh with a Triangular mesh, see Gaussian Beam Incident at the Brewster Angle: Application Library path Wave_Optics_Module/Optical_Scattering/brewster_interface
Dependent Variables
The dependent variables (field variables) are for the:
Electric field envelope, first wave E1 and its components (in the Electric field envelope components, first wave fields).
Electric field envelope, second wave E2 and its components (in the Electric field envelope components, second wave fields). The second wave is applicable if the Wave Vectors are bidirectional.
The name can be changed but the names of fields and dependent variables must be unique within a model.
Discretization