I am wondering about the logic why TEM mode cannot propagate in rectangular waveguides.
A TEM mode has the electric field and the magnetic field normal to the direction of propagation. There is no component of either in the direction of propagation. Hollow rectangular waveguide has metal walls where the parallel component of the electric field has to be zero. Because there are four walls, both the x and the y component have to be zero at some point on the walls, (x and y, if z is the direction of propagation). Unless there is no power, the electric field has to be non-zero somewhere in the guide. In order for it to change across the guide cross-section, from zero parallel component at the edges to not zero somewhere else, Maxwell's equations demand that there must be a component of the electric or magnetic field in the direction of propagation., because if there is curl in the electric field the magnetic field along the axis of curl has to change with time (so can't be zero). If the x component of electric field changes from something in the middle of the guide to nothing at the edge then the curl of the electric field points in the direction of propagation and so there is magnetic field along the direction of propagation and it is not TEM.
In fact, no TEM-mode can propagate within any waveguide with simply-connected cross section and metallic mantle.
Unfortunately, I can give as reference only an old paper written in German:
E. Ledinegg. Annalen der Physik (5) vol.41, pp. 537-566, in particular 562/3.
See also: F. Brognis asnd Ch. H. Papas in :
Encyclopedia of Physics, Springer, vol. 16, p. 294 and
eqs.4.14, 4.15 on p.292. which must hold simultaneously with both gammas = 0.
B. Schnizer is correct. My arguments for a rectangular waveguide hold for any simply connected cross-section and metallic mantle, which means a hole in a piece of metal without a second conductor in it (or with no loops round a conductor).
Dear Researcher Lee Beomseok ,
These two attached articles, published in journals, and their references will help you better understand the electromagnetic phenomena involved in this propagation.
Boundary conditions on metallic surface will answer your doubt to main propagation.
Sir Malcolm White,
If there has to be any field component along the direction of propagation then how TEM wave propagates in free space? As last I have studied in the Transmission line two concentric coaxial conductors were required to produce TEM wave where the inner conductor was made positive (DC) with respect to the outer one, I am facing difficulty to realise the situation with displacement current (time varying electric field) and magnetic field, and how they behave jointly in free space and in any other medium ?
I will be grateful if you help me to understand this.
Thank you.
Bishal Keshari
I said that in a simply connected waveguide there has to be a field component along the direction of propagation. In free space, where there are no walls, or in a coaxial transmission line, for instance, there does not need to be a field component in the direction of propagation. Displacement current just behaves like current. In free space it is at right angles to the direction of the wave, just as the current in an electric dipole is at right angles to the direction of the strongest wave it radiates. No power is radiated in the direction of the current that is in an electric dipole.
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