PropagatingMode¶
Type:  section 

Appearance:  simple 
Excludes:  ResonanceMode, Scattering 
This section specifies a propagating mode problem. This type of problem is also called waveguide problem.
The angular frequency is a fixed parameter of the problem and one defines the vacuum wavelength and kvector by
where is the speed of light in the vacuum.
A waveguide geometry is characterized by a special axis, the waveguide or longitudinal direction, with a dimension much larger than the cross section diameter and measuring a huge number of wavelengths . The waveguide is then modeled as infinitely prolonged. On a macroscopic scale the waveguide axis need not to be straight. JCMsolve
can take bending effects into account, c.f., parameter AxisPositionX. Furthermore, the waveguide geometry is allowed to be twisted along the waveguide axis (parameter Twist, see also [1]).
In the following we only discuss the straight waveguide with a longitudinal axis along the direction. The coordinate system is chosen such that the geometry exhibits an invariance in the direction, that is, the permittivity tensor and the permeability tensor do not depend on the longitudinal direction .
It is the aim to find propagating modes which solve Maxwell equations in sourcefree media and which depend harmonically on , in the sense that
where is the propagation constant and denotes the crosssection coordinates .
Introducing the operator
The time harmonic Maxwell’s equations of second order, see parent section, now read as
with analogue equations for the magnetic field.
The dependency on the coordinate has disappeared and the problem is posed on the crosssection only.
The above eigenmode equation has the structure of an eigenvalue problem: One seeks pairs of the propagating constant and the field distribution.
Traditionally, the eigenvalue is not given as the propagation constant but in the form of an effective refractive index
Bibliography
[1] 
