Mode Analysis and Boundary Mode Analysis
In mode analysis and boundary mode analysis, COMSOL Multiphysics solves for the propagation constant. The time-harmonic representation is almost the same as for the eigenfrequency analysis, except for a known propagation in the out-of-plane direction:
The spatial parameter, α = −λ, can have a real part and an imaginary part. For mode analysis, the propagation constant, β, is equal to the imaginary part, while the real part, δz, represents the damping along the propagation direction. Thus,
,
where λ is the eigenvalue.
In 2D axisymmetry, the complex propagation constant is given by
,
where rave is the average radius of curvature for the geometry.
For boundary mode analysis, the propagation constant, β, is complex,
.
Variables Influenced by Mode Analysis
The following table lists the variables that are influenced by the mode analysis:
Name
Expression
Can be Complex
Description
beta
imag(alpha)
No
Propagation constant
dampz
real(alpha)
No
Attenuation constant
dampzdB
20*log10(exp(1))*dampz
No
Attenuation per meter in dB
neff
-j*alpha/k0
Yes
Effective mode index
In the table above, alpha=-lambda, lambda is the eigenvalue, and k0 is the vacuum wave number.
Variables Influenced by Boundary Mode Analysis
The table below lists the variables that are influenced by the boundary-mode analysis:
Name
Expression
Can be Complex
Description
beta_i
j*lambda
Yes
Propagation constant
neff_i
beta_i/k0
Yes
Effective mode index
The name suffix indicates that the variables are defined for the port labeled i.
For an example of Mode Analysis, see the model Step-Index Fiber Bend: Application Library path Wave_Optics_Module/Waveguides/step_index_fiber_bend.
For an example of Boundary Mode Analysis, see the model Directional Coupler: Application Library path Wave_Optics_Module/Couplers_Filters_and_Mirrors/directional_coupler.
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For a list of the studies available by physics interface, see The Wave Optics Module Physics Interface Guide
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Studies and Solvers in the COMSOL Multiphysics Reference Manual