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.
The Boundary Mode Analysis study step’s Settings window contains the following sections:
Study Settings
Select a method to Transform: Effective mode index (the default), Out-of-plane wave number, or None.
Enter a Port name if applicable. The default is 1.
Enter a value or expression for the Mode analysis frequency. The default frequency is 1 GHz.
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.
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).
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.
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.
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.