Boundary Mode Analysis
The Boundary Mode Analysis () study and study step are used to compute the propagation constants or wave numbers as well as propagating mode shapes, for a given frequency at a port.
As a study, the Boundary Mode Analysis combines a Boundary Mode Analysis study step at a port (boundary) (which can represent, for example, a cross section of a waveguide) with a Frequency Domain study step for the full geometry.
This study is available with the Electromagnetic Waves, Frequency Domain and Microwave Heating interfaces, which both require the RF Module, and the Electromagnetic Waves, Frequency Domain; Electromagnetic Waves, Beam Envelopes; and Laser Heating interfaces, which all require the Wave Optics Module. It is also available for the 3D Solid Mechanics interface, if you have a license for the Structural Mechanics Module, and the 3D Pressure Acoustics, Frequency Domain interface, if you have a license for the Acoustics Module.
The Boundary Mode Analysis study step’s Settings window contains the following sections:
Study Settings
If desired, select the Include geometric nonlinearity checkbox.
Select a method to Transform: Effective mode index (the default), Out-of-plane wave number, or None. For 3D Solid Mechanics and Pressure Acoustics, Frequency Domain, Effective mode index is not available, and Out-of-plane wave number is the default.
Enter a Port name if applicable. The default is 1.
Enter a value or expression for the Mode analysis frequency. The default frequency depends on the physics interfaces in the study.
From the Mode solver list, choose ARPACK (the default), FEAST, or LAPACK (filled matrix). See Eigenvalue for more information.
Values of Linearization Point
Use the settings in this section to specify a linearization point.
From the Settings list, choose Physics controlled (the default) to use linearization point settings controlled by the physics interfaces. Choose User defined to specify the linearization point using the Method list. Select:
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 Initial expression to use the expressions specified on the Initial Values nodes under a specific physics interface as a linearization point.
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 Solution to use a solution as a linearization point.
Use the Study list to specify which solution to use from the available studies. Select:
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 Zero solution to use a linearization point that is identically equal to zero.
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Any other available solution to use it as a linearization point. It can be the current solution in the sequence, or a solution from another sequence, or a solution that was stored with the Solution Store node. You select a stored solution by changing Use to the name of the stored solution. Choose a solution using the Selection list (see Values of Dependent Variables under Common Study Step Settings).
Filtering and Sorting
Filtering
The eigenvalues can be excluded if there is a filter expression that they do not satisfy. In the table below, in the Filter expression (store if true or >0) column, add expressions for the filtering Those expressions can be functions of the eigenvalue lambda or eigenfrequency freq and can be logical expressions such as lambda>10. If desired, add some descriptive text in the Description column for the expressions.
The Store solutions list is always available: Choose All converged solutions (the default) or First Nth for the first Nth solutions. Then specify that number in the Maximum number of stored solutions field (default: 1000).
Sorting
The eigenvalues can be sorted in Ascending (the default) or Descending order depending on the Ordering setting. When the Sorting method is Predefined, you can choose to Sort primarily based on the Real part, Imaginary part, Real part magnitude, Imaginary part magnitude, or Absolute value. The same settings are available for the Sort secondly option, which is used to resolve conflicts. The defaults for eigenvalues are Real part for Sort primarily and Imaginary part magnitude for Sort secondly. For eigenfrequencies, the defaults are Imaginary part for Sort primarily and Imaginary part magnitude for Sort secondly. Also, the Sort based on transformed eigenvalues checkbox is selected by default to take and eigenvalue transformation into account when sorting.
Alternatively, Manual can be chosen for the Sorting method and then an arbitrary number of (ordered) custom sorting priority expressions can be defined in the table that appears. In the Sorting priority expression column, add expressions for the sorting, in order of priority. Those expressions can be functions of the eigenvalue lambda or eigenfrequency freq. For example, you can specify an expression such as abs(freq-1) to sort according to the distance from a given shift (1 in this case). If desired, add some descriptive text in the Description column for the expressions.
The Conjugate-pair consecutive sort checkbox is selected by default to make sure that complex-conjugate eigenpairs appear one after the other, regardless of the sorting rules.
The Boundary Mode Analysis study step stores the frequency fref and propagation constant βref for which it was run. For a TE, TM, or TEM mode, the propagation constant β for an arbitrary frequency f is given by
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In addition, for TE, TM, and TEM modes, the mode field shape is independent of the frequency. Thus, when making a frequency sweep including only TE, TM, and TEM modes, the Boundary Mode Analysis study steps can be done for just one frequency, with the propagation constants obtained from the expression above for the other frequencies. For waveguides consisting of multiple dielectric materials, like optical fibers, where there are no TE, TM, or, TEM modes, the Boundary Mode Analysis steps must be recomputed for each frequency.
The Include geometric nonlinearity checkbox, Mesh Selection, and Study Extensions are described in Common Study Step Settings. There is also detailed information in the Physics and Variables Selection and Values of Dependent Variables sections.
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With the RF Module, see Polarized Circular Ports, Application Library path RF_Module/Tutorials/polarized_circular_ports.
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With the Wave Optics Module, see Dielectric Slab Waveguide, Application Library path Wave_Optics_Module/Verification_Examples/dielectric_slab_waveguide.