The Electromagnetic Waves, Frequency Domain Interface
The Electromagnetic Waves, Frequency Domain (emw) interface () is used to solve for time-harmonic electromagnetic field distributions. It is found under the Radio Frequency branch () when adding a physics interface,
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, Eigenfrequency, Mode Analysis, and Boundary Mode Analysis study types. The Frequency Domain study type is used for source driven simulations for a single frequency or a sequence of frequencies. The Eigenfrequency study type is used to find resonance frequencies and their associated eigenmodes in resonant cavities.
This physics interface solves the time-harmonic wave equation for the electric field.
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 Mode analysis study type is applicable only for 2D and 2D axisymmetric cross sections of waveguides and transmission lines where it is used to find allowed propagating modes. Boundary mode analysis is used for the same purpose in 2D, 2D axisymmetry, and 3D and applies to boundaries representing waveguide ports.
Physics-Controlled Mesh
The physics-controlled mesh is controlled from the Settings window for the Mesh node (if the Sequence type is Physics-controlled mesh). 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 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, 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 the Use check box is selected for the physics interface, in the section for the physics interface below the table, 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 the 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.
The maximum mesh element size in dielectric media is equal to the maximum mesh element size in vacuum divided by the square root of the product of the relative permittivity and permeability.
When Refine conductive edges is selected, the exterior edges of conductive boundaries, configured by perfect electric conductors, transition boundary, or layered transition boundary conditions, are meshed with a user-specified size. Adjust Angular tolerance (SI unit: rad) to include not only edges on flat surfaces but also curved surfaces. Choose Size type — Relative or User defined. For the option Relative, the mesh size on the selected edges is defined relative to the default maximum mesh size. On the other hand, when the option User defined is selected, the mesh size is set by user-defined value in the Size input field (SI unit: m).
In the COMSOL Multiphysics Reference Manual see the Physics-Controlled Mesh section for more information about how to define the physics-controlled mesh.
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 emw.
Formulation
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:
Table 4-1: Background wave type based on component dimension
Component
Background wave type
2D
User defined (default), Gaussian beam
2D Axisymmetric
User defined (default), Circularly polarized plane wave
3D
User defined (default), Gaussian beam, Linearly polarized plane wave
User Defined
Enter the component expressions for the Background electric field Eb (SI unit: V/m). The entered expressions must be differentiable.
Notice that expressions including coupling operators are not differentiable and cannot be used as background fields.
Gaussian Beam
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 (emw) 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 the Helmholtz equation, the plane wave expansion of the electric field is also a solution to the Helmholtz equation. Thus, this option can be used also for tightly focused Gaussian beams.
If the beam spot radius is smaller than the wavelength, evanescent plane waves need to be included in the expansion. The evanescent waves decay exponentially in the propagation direction, why it only makes sense to model such tightly focused beams if the focal plane coincides with the input boundary. If the focal plane is located inside the modeled domain, the field can be dominated by the exponentially decaying evanescent waves. Those waves can have a very high field strength before the focal plane even though they only provide a small contribution to the field at the focal plane.
For Plane wave expansion select Wave vector distribution type — Automatic (the default) or User defined. For Automatic also check Allow evanescent waves, to include evanescent waves in the plane wave expansion. 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))))/emw.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 vectors that will be included per transverse dimension. So for 3D the total number of wave vectors will be Nk·Nk.
Evanescent waves are included in the plane wave expansion if the Maximum transverse wave number kt,max is larger that the specified Wave number k. When the Wave vector distribution type is set to Automatic, evanescent waves are included in the expansion if the Allow evanescent waves check box is selected.
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.
The number of plane waves included in the expansion can be quite large, especially for 3D. For instance, using the default settings, 2·13·13 = 338 plane waves will be included (the factor 2 accounts for the two possible polarizations for each wave vector). Thus, initializing the plane-wave expansion for the Gaussian beam background field can take some time in 3D.
For more information about the Gaussian beam theory, see Gaussian Beams as Background Fields and Input Fields.
Define the Gaussian beam background field using the parameters below:
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Select a Beam orientation: Along the x-axis (the default), Along the y-axis, or for 3D components, Along the z-axis.
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Enter a Beam radius w0 (SI unit: m). The default is 20π/emw.k0 m (10 vacuum wavelengths).
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Enter a Focal plane along the axis p0 (SI unit: m). The default is 0 m.
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Select an Input quantity: Electric field amplitude (the default) or Power.
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Enter the component expressions for the Transverse background electric field amplitude, Gaussian beam ETbg0 (SI unit: V/m) if the Input quantity is Electric field amplitude. Notice that this is the transverse Gaussian beam amplitude in the focal plane. When the Gaussian beam type is set to Paraxial approximation the background field is always orthogonal (transverse) to Beam orientation. However, when the Gaussian beam type is set to Plane wave expansion, the background field amplitude can also have a component in the propagation direction. Specify here only the field amplitude components that are orthogonal to the propagation direction. COMSOL computes automatically the component in the propagation direction, if needed.
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If the Input quantity is set to Power, enter the Input power (SI unit: W in 2D axisymmetry and 3D and W/m in 2D) and the component expressions for the Non-normalized transverse electric field amplitude, Gaussian beam ETbg0 (SI unit: V/m).
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Enter a Wave number k (SI unit: rad/m). The default is emw.k0 rad/m. The wave number must evaluate to a value that is the same for all the domains the scattered field is applied to. Setting the Wave number k to a positive value, means that the wave is propagating in the positive x-, y-, or z-axis direction, whereas setting the Wave number k to a negative value means that the wave is propagating in the negative x-, y-, or z-axis direction.
Linearly Polarized Plane Wave
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 compare with Figure 4-1 below.
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Enter an Electric field amplitude E0 (SI unit: V/m). The default is 1 V/m.
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Enter a Roll angle (SI unit: rad), which is a right-handed rotation with respect to the +x direction. The default is 0 rad, corresponding to polarization along the +z direction.
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Enter a Pitch angle (SI unit: rad), which is a right-handed rotation with respect to the +y direction. The default is 0 rad, corresponding to the initial direction of propagation pointing in the +x direction.
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Enter a Yaw angle (SI unit: rad), which is a right-handed rotation with respect to the +z direction.
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Enter a Wave number k (SI unit: rad/m). The default is emw.k0 rad/m. The wave number must evaluate to a value that is the same for the domains the scattered field is applied to.
Figure 4-1: Schematic of the directions for the wave vector k, the electric field E0, and the roll, pitch and yaw rotations. The top image represents an initial wave propagating in the x direction with a polarization along the z direction.
Circularly Polarized Plane Wave
The background wave is defined as
,
where
,
m is the azimuthal mode number (+1 or -1) varying depending on the Circular polarization type and Direction of propagation settings, and and are the unit vectors in the r and ϕ directions, respectively.
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Select the Circular polarization type — Right handed or Left handed.
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Select the Direction of propagation — +z or -z.
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Enter an Electric field amplitude E0 (SI unit: V/m). The default is 1 V/m.
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Enter an Wave number k (SI unit: rad/m). The default is emw.k0 rad/m.
Components
This section is available for 2D and 2D axisymmetric components.
Select the Electric field components solved for — Three-component vector, Out-of-plane vector, or In-plane vector. Select:
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Three-component vector (the default) to solve using a full three-component vector for the electric field E.
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Out-of-plane vector to solve for the electric field vector component perpendicular to the modeling plane, assuming that there is no electric field in the plane.
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In-plane vector to solve for the electric field vector components in the modeling plane assuming that there is no electric field perpendicular to the plane.
Out-of-Plane Wave Number
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.
Analysis Methodology
From the Methodology options list, select one of three solver configurations: Robust, Intermediate, or Fast (the default).
The settings of each methodology option are found in Solver Configurations and the subsidiary nodes.
Port Sweep Settings
Select the Use manual port sweep check box to enable the port sweep. When selected, this invokes a parametric sweep over the ports in addition to the frequency sweep already added. The generated lumped parameters are in the form of an S-parameter matrix.
For Use manual 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. This process can be automated by clicking the Configure Sweep Settings button. The Configure Sweep Settings button helps add a necessary port sweep parameter and a Parametric Sweep study step in the last study node. If there is already a Parametric Sweep study step, the sweep settings are adjusted for the port sweep.
In the COMSOL Multiphysics Reference Manual see the Frequency Domain Source Sweep section for a discussion of how to use the Frequency Domain Source Sweep study type to perform efficient port sweeps.
Select Export Touchstone file and the S-parameters are subject to Touchstone file export. Click Browse to locate the file, or enter a file name and path. Select an Parameter format (value pair): Magnitude angle, Magnitude (dB) angle, or Real imaginary.
Enter a Reference impedance for Touchstone file export Zref (SI unit: Ω) that is used only for the header in the exported Touchstone file. The default is 50 Ω.
It is also possible to export Touchstone files during postprocessing under the Results node. In the COMSOL Multiphysics Reference Manual, see the Touchstone section for more information on how to export Touchstone files as a postprocessing step.
Port Options
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
The electric field on port boundaries is expanded as
,
where E, r, Einc, Si, Ei, αi, n, r0 are, respectively, the electric field on the port boundary, the position vector, the incident electric field, the expansion coefficient (or S-parameter), the mode field, the propagation constant for the mode, the normal vector, and a position on the port boundary.
Select the Use constraint-free ports check box to calculate the expansion coefficients as overlap integrals
,
where Pi, S, and Hi are the mode power, the port boundary area, and the magnetic mode field, respectively.
In the default port formulation, when the Use constraint-free port check box is disabled (the default setting), the expansion coefficients (or S-parameters) are calculated by adding a scalar dependent variable for each coefficient and then adding a constraint to enforce the series expansion above.
Dependent Variables
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.
Discretization
Select the shape order for the Electric field dependent variable — 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.
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Domain, Boundary, Edge, Point, and Pair Nodes for the Electromagnetic Waves, Frequency Domain Interface
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Theory for the Electromagnetic Waves Interfaces
H-Bend Waveguide 3D: Application Library path RF_Module/Transmission_Lines_and_Waveguides/h_bend_waveguide_3d demonstrates how to set up a port sweep.