Convergent power series for fields in positive or negative high-contrast periodic media
We obtain convergent power series representations for Bloch waves in periodic highcontrast media. The material coefficient in the inclusions can be positive or negative. The small expansion parameter is the ratio of period cell width to wavelength, and the coefficient functions are solutions of the cell problems arising from formal asymptotic expansion. In the case of positive coefficient, the dispersion relation has an infinite sequence of branches, each represented by a convergent even power series whose leading term is a branch of the dispersion relation for the homogenized medium. In the negative case, there is a single branch. © Taylor & Francis Group, LLC.
Publication Source (Journal or Book title)
Communications in Partial Differential Equations
Fortes, S., Lipton, R., & Shipman, S. (2011). Convergent power series for fields in positive or negative high-contrast periodic media. Communications in Partial Differential Equations, 36 (6), 1016-1043. https://doi.org/10.1080/03605302.2010.531860