1/2] are the transversal wave numbers of the semiconductor and dielectric layers, respectively; the Bloch wave number [bar.
However, the possibility of SW existence on the interfaces between the entire multilayer periodic structure and surrounding half-spaces can be considered only when the Bloch wave number is imaginary.
a complex Bloch wave number should exist in both the PBGs and passbands.
As will be seen later, in the CPBS, both the real and the imaginary parts of the Bloch wave vector can exist in the pass band or the stop band.
In this equation K is the Bloch wave
vector that takes the values of the reduced Brillouin zone, 0 [less than or equal to] K [less than or equal to] [pi] / a; ([m.
The Bloch wave
vector K can be determined by the half trace of the translational matrix in Eq.
The PBG structure in a PC can also be investigated by directly plotting the dispersion relation K vs [lambda], where K is the Bloch wave
This features resemble those appearing in the band structure associated to two-dimensional photonic crystals where the dispersion relation depends on a Bloch wave
vector with two components.
In sections on acoustic waves in sonic crystals, elastic waves in phononic crystals, and wave phenomena in phononic crystals, he considers such topics as scalar waves in periodic media, sonic crystals, phononic crystals for surface and plate waves, coupling acoustic and elastic waves in phononic crystals, evanescent Bloch waves
, and spatial and temporal dispersion.
R])] and d and [beta] are a length of the unit cell and a phase constant for Bloch waves
Theory of dynamic scattering and phase contrast formation is now well developed for multislice and Bloch waves
Among his topics are from classical bodies to microscopic particles, electrons in crystals and Bloch waves
in crystals, the tight-binding model and embedded-atom potentials, transition metals, high-temperature creep, and modeling kinetic processes.