GUIDED MODES IN PERIODIC SLABS: EXISTENCE AND

For homogeneous lossless three-dimensional periodic slabs of fixed arbitrary geome- try, we characterize guided modes by means of the eigenvalues associated with a variational formula- tion. We treat robust modes, which exist for frequencies and wavevectors that admit no propagating Bragg harmonics and therefore persist under perturbations, as well as nonrobust modes, which can disappear under perturbations due to radiation loss. We prove the nonexistence of guided modes, both robust and nonrobust, in "inverse" structures, for which the celerity inside the slab is less than the celerity of the surrounding medium. The result is contingent upon a restriction on the width of the slab but is otherwise independent of its geometry.