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,
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.
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.
|
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
|
|
In the COMSOL Multiphysics Reference Manual see the Physics-Controlled Mesh section for more information about how to define the physics-controlled mesh.
|
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:
•
|
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.
|
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.
|
In the COMSOL Multiphysics Reference Manual see Table 2-4 for links to common sections and Table 2-5 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 ) 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 reversed, 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, , 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.
|
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.
•
|
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.
|
Select the shape order for the Electric field envelopes dependent variables —
Linear,
Quadratic (the default), or
Cubic. For more information about the
Discretization section, see
Settings for the Discretization Sections in the
COMSOL Multiphysics Reference Manual.