Multiple-line directional couplers

The problem of many directionally coupled parallel waveguides is considered for circular and flat configurations. The case of a finite number of continuously and uniformly coupled lines is solved by the application of normal modes. This case is extended to an infinite number of lines, and a Bessel function solution is obtained. A comparison of solutions for finite and infinite sets of coupled lines indicates that the Bessel functions are sufficiently accurate for most practical systems. Discrete coupling is considered, and it is shown that, although ideal matching of all the normal modes is not in general possible, the multiple-line directional coupler is nevertheless a feasible component.