According to the definition of displacement current: Jd=dD/dt (integral), which requires that there is an electric field in the propagation direction. Obviously, this conclusion contradicts the definition of TEM wave (there is neither electric field nor magnetic field in the propagation direction), so rectangular waveguide cannot propagate TEM wave. It can only propagate te (transverse electric field) or TM (transverse magnetic field) waves.
The electromagnetic waves in the waveguide are various linear combinations of TMmn mode and TEmn mode,
M and n are subscripts.
Physical meaning of m, n: m is the number of semi-periods changing in the x direction,
N is the number of half periods that vary along the y direction.
As you can see, m and n are integers. Based on Maxwell's equation and the boundary conditions of electromagnetic waves on the waveguide
Rectangular waveguide can support an infinite number of TM wave modes and te wave modes, and each mode corresponds to an integer m, n.
However, the waveguide is a high-pass filter. Only when the operating frequency of each mode wave is higher than the cutoff frequency can the mode wave propagate in the waveguide. In other words, the wavelength of the mode should be less than the cutoff wavelength of the mode propagation.
Different mode waves (m, n are different) have different cutoff wavelengths.
The cutoff wavelengths of different m and n corresponding to rectangular waveguides are:
λc = 2/{[(m/a)^2+(n/b)^2]^( 1/2)}
Where a is the width of the rectangular waveguide and b is the height of the rectangular waveguide.
For example, when the cutoff wavelengths of two modes TMmn and TEmn are equal, it means that the possibility of these two modes appearing in rectangular waveguide is the same, which is called degeneracy.
It can be seen that for rectangular waveguides, as long as M and N of TMmn and TNmn are equal, their cutoff wavelengths (or cutoff frequencies) are equal. At this time, these two TM and TN modules are degenerate modules. ?