Long-wavelength limit (homogenization) for two-dimensional photonic crystals

Metafluid with anisotropic dynamic mass

“…In practice, the inversion of the matrix and sum over G and ′ G require numerical calculation with finite number of reciprocal lattice vectors, i.e., with finite number of plane waves. It was shown that the sums over G and ′ G converge rapidly with number of the plane waves [29], therefore numerical calculation of the sum is not a time consuming procedure at all. For unit cells possessing third (or higher) rotational axis of symmetry the dependence on the unit vector n in the right-hand-side disappears, i.e., in the long wavelength limit these periodic structures are isotropic.…”

Homogenization of Maxwell's equations in periodic composites: Boundary effects and dispersion relations

“…Indeed, the derivations of that section contain one dubious step. Namely, the applicability of the Poisson summation formula (14) can be questioned because the variable q is complex. Strictly speaking, the series in the left-hand side of (14) diverges for an infinite lattice.…”

“…where we have used the Poisson summation formula (14). Still, both terms on the right-hand side of (93) are divergent.…”

“…This paper is an attempt to address the above issues for the case of periodic composites; random media are not considered. The framework we develop is based on the Bloch-Floquet expansion, which is a well-known tool in homogenization theory [5,[14][15][16][17][18][19]. However, in several aspects, we go beyond the standard theory.…”

Fourier Factorization in the Plane Wave Expansion Method in Modeling Photonic Crystals

“…The existence of the optical band gap (which is the part of the spectrum for which the wave propagation is not possible) makes photonic crystals broadly interesting from many viewpoints of fundamental research and applications. Recent studies are motivated by promising applications such as purely optical integrated circuits [e.g., by Lin et al (1998), Noda (2006), or Hugonin et al (2007)], artificial metamaterials with high tunability [Datta et al (1993); Genereux et al (2001); Krokhin et al (2002); Reyes et al (2005)], high-sensitivity photonic biosensors [Block et al (2008); Skivesen et al (2007)], or devices based on phenomena not accessible in conventional media [Benisty (2009); Kosaka et al (1998); Krokhin & Reyes (2004)]. It is also necessary for accounting for structural colors of wings of butterflies or beetles, feathers of birds, or iridescent plants [Kinoshita & Yoshioka (2005); Vukusic & Sambles (2003)].…”