2015/10/31 by Maria V. Perel, Perel, Maria V., Mikhail S. Sidorenko +1
Engineering · Mathematics · Physics and Astronomy · #35Q61 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Photonic Crystals and Applications #math-ph #math.MP #msc:35Q61
paper · pdf · doi:10.48550/arxiv.1511.00115
36 pages
openalex publication_date 2015/10/31 · arxiv created 2016/05/07 · arxiv updated 2016/05/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find solutions of Maxwell equations by the method of two-scale asymptotic expansions. We establish that the principal order of the expansion of a solution dependent on three spatial coordinates is the sum of two differently polarized Floquet-Bloch solutions, each of which is multiplied by a slowly varying envelope function. We derive that the envelope functions satisfy a system of differential equations with constant coefficients. In new variables, it is reduced to a system of two independent equations, both of them are either hyperbolic or elliptic, depending on the type of the stationary point. The envelope functions are independent only in the planar case. Some consequences are discussed.