2010/07/15 by Santiago P. Fortes, Robert Lipton, Fortes, Santiago P. +3
Computer Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Photonic Crystals and Applications
paper · pdf · doi:10.48550/arxiv.1007.2640
openalex publication_date 2010/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain convergent power series representations for Bloch waves in periodic\nhigh-contrast media. The material coefficient in the inclusions can be positive\nor negative. The small expansion parameter is the ratio of period cell width to\nwavelength, and the coefficient functions are solutions of the cell problems\narising from formal asymptotic expansion. In the case of positive coefficient,\nthe dispersion relation has an infinite sequence of branches, each represented\nby a convergent even power series whose leading term is a branch of the\ndispersion relation for the homogenized medium. In the negative case, there is\na single branch.\n