  Reduced Bloch mode expansion is presented for fast periodic media band
structure calculations. The expansion employs a natural basis composed of a
selected reduced set of Bloch eigenfunctions. The reduced basis is selected
within the irreducible Brillouin zone at high symmetry points determined by the
medium's crystal structure and group theory (and possibly at additional related
points). At each of the reciprocal lattice selection points, a number of Bloch
eigenfunctions are selected up to the frequency range of interest for the band
structure calculations. Since it is common to initially discretize the periodic
unit cell and solution field using some choice of basis, reduced Bloch mode
expansion is practically a secondary expansion that uses a selected set of
Bloch eigenvectors. Such expansion therefore keeps, and builds on, any
favorable attributes a primary expansion approach might exhibit. Being in line
with the well known concept of modal analysis, the proposed approach maintains
accuracy while reducing the computation time by up to two orders of magnitudes
or more depending on the size and extent of the calculations. Results are
presented for phononic, photonic and electronic band structures.
