Lecture 43 : Rectangular Wave Guide and Transverse Magnetic Mode
Transverse field component for TM mode
Substituting for from equation 6.51 and in equations 6.31, 6.32, 6.33 and 6.34 we get the transverse electric and magnetic field components as
---------- (6.52)
---------- (6.53)
---------- (6.54)
---------- (6.55)
The integers and define the order of the mode and the mode is designated as
We can make the following observations regarding mode :
(1)
Similar to that of the parallel plane waveguide the fields exists in the discrete electric and magnetic field pattern called modes of waveguide.
(2)
All field components are sinosoidally in and directions.
(3)
All transverse fields go to zero if either or is zero. In other words, both the indices and have to be non-zero
for existence of the TM mode. That is, and modes can not exist. Consequently, the lowest order
mode which can exist is mode.
Substituting from 6.51 into 6.35, we get what is called the dispersion relation for the mode as
---------- (6.56)
The dispersion relation suggest that the phase constant for the mode is different for different modes (for different values of and ) and is no more proportional to .
Implication of this would be discussed later along with the characteristics of the TE mode.
from equation 
in equations 
define the order of the mode and the mode is designated as 
and 
directions. 
is different for different modes (for different values of 
.
