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BELL SYSTEM TECHNICAL JOURNAL 



the velocity of the wave is high, and the field extends far in the y direction 

 and becomes higher at high frequencies, where the velocity is low and the 

 field falls off rapidly. 



We will next consider a symmetrical array of two opposed sets of slots 

 (Fig. 4.3) similar to that shown in Fig. 4.1. Two modes of propagation will 

 be of interest. In one the field is symmetrical about the axis of physical 

 symmetry, and in the other the fields at positions of physical symmetry are 

 equal and opposite. 



In writing the equations, we need consider only half of the circuit. It is 

 convenient to take the z axis along the boundary, as shown in Fig. 4.4. 



^Ly///////////// 



Fig. 4.3 — A double finned structure which will support a transverse mode (no longi- 

 tudinal electric field on axis) and a longitudinal mode (no transverse electric field on axis). 



Fig. 4.4 — The coordinates used in connection with the circuit of Fig. 4.3. 



This puts the axis of symmetry at }' = +^, and the slots extend from y — 

 to y = —h. 



For negative values of y, (4.9), (4.10), (4.12) hold. 



Let us first consider the case in which the fields above are opposite to the 

 fields below. This also corresponds to waves in a series of slots opposite a con- 

 ducting plane, as shown in Fig. 4.5. In this case the appropriate form of the 

 magnetic field above the boundary is 



_ cosh y{d - y) jp, 



iix — -tJO \ 3 ^ 



cosh 7a 

 From Maxwell's ecjuations we then find 



/3 





cosh 7((/ - y) ^^jp, 

 cosh yd 



(4.21) 



(4.22) 



