TABLE OF CONTENTS Like as the waves make towards the pebbled shore So do our minutes hasten to their end, Each changing place with that which goes before, In sequent toil all forward to contend.
William Shakespeare
Waves always behave in a similar way, whether they are longitudinal or transverse, elastic or electric. Scientists of last century always kept this idea in mind. This general philosophy of wave propagation, forgotten for a time, has been strongly revived in the last decade
L. Brillouin (1946)
Since Newton deduced the formula for the speed of sound using a one-dimensional lattice model, wave propagation in periodic structures has been a topic of study by physicists. In the 19th century Kelvin et al. investigated the problem of dispersion of light also using a one-dimensional mechanical lattice model. At the beginning of the 20th century engineers considered a periodic structure composed of LC circuits, developed a theory of filters for electric waves and proposed such important concepts as the cut-off frequency, pass band and forbidden band. The behavior of electrons and lattice vibrations in periodic structures form the basis of solid state physics. In recent years, the study of classical waves, including electromagnetic and elastic waves, in periodic materials has expanded the domain...
