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 check box.
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) or FEAST. See Eigenvalue for more information.
From the Mode search method list, select a search method:
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Manual (the default), to specify some search criteria manually. See Manual Mode Search Settings below.
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Region, to define a mode search region in a complex plane. See Mode Search Region Settings below.
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All (filled matrix), to search for all modes. This option is only applicable for small mode analysis problems. See All (Filled Matrix) Settings below.
Manual Mode Search Settings
Use the Desired number of modes field to specify the number of modes you want the solver to return (default: 1).
From the Unit list, choose a suitable unit (default rad/m).
In the Search for modes around field, you can specify a value or expression around which the eigenvalue solver should look for solutions to the eigenvalue equation (default: 1).
Use the Mode search method around shift list to control how the eigenvalue solver searches for modes around the specified shift value:
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Select Closest in absolute value (the default value) to search for modes that are closest to the shift value when measuring the distance as an absolute value.
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Select Larger real part to search for modes with a larger real part than the shift value.
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Select Smaller real part to search for modes with a smaller real part than the shift value.
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Select Larger imaginary part to search for modes with a larger imaginary part than the shift value.
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Select Smaller imaginary part to search for modes with a smaller imaginary part than the shift value.
From the Use real symmetric eigenvalue solver list, choose Automatic (the default) or Off. If you chose Automatic, you can select the Real symmetric eigenvalue consistency check check box to check for positive definiteness.
Mode Search Region Settings
Use the Approximate number of modes field to specify the approximate number of modes you want the solver to return (default: 20).
In the Maximum number of modes field, you can specify a maximum number of modes to limit the eigenvalue solver’s search for additional modes (default: 200).
The Perform consistency check check box is selected by default to increase confidence that the solver finds all modes in the search region.
Under Search region, you define the size of the search region for modes as a rectangle in the complex plane by specifying the Smallest real part, Largest real part, Smallest imaginary part, and Largest imaginary part in the respective text fields. The search region also works as an interval method if the Smallest imaginary part and Largest imaginary part are equal; the eigenvalue solver then only considers the real axis and vice versa.
From the Use real symmetric eigenvalue solver list, choose Automatic (the default) or Off. If you chose Automatic, you can select the Real symmetric eigenvalue consistency check check box to check for positive definiteness.
All (Filled Matrix) Settings
To specify a shift to use in the modes computation, select the Shift used in the modes computation check box and then enter a shift (in rad/m) in the associated text field.
In the Maximum matrix size field, enter an upper limit on the matrix size (default: 200).
From the Unit list, choose a suitable unit (default rad/m).
Values of Linearization Point
Use the settings under Values of linearization point 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).
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 check box, 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.