In this paper we introduce a fundamentally new concept in the field of wave-propagation in periodic structures. We show that a phenomenal amount of simplification can be achieved by using symmetry arguments. Problems which ordinarily lead to (2n × 2n) determinantal eigenvalue equations, can effectively be reduced to two (n × n) determinantal equations. We state the final result in the form of a factorization theorem and then with the help of a simple problem, we show the superiority of this new result over the traditional methods of solution.
