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

Photonic crystals are modern artificially designed periodical systems capable to affect the motion of photons in a similar way that the periodicity of the atomic potential in a semiconductor crystal affects the motion of electrons. The physical properties of light in a photonic crystal resemble those of electrons in atomic crystals, leading to forbidden propagation of electromagnetic modes at certain frequencies, as demonstrated by Yablonovitch (1987), Ho et al. (1990), Joannopoulos et al. (1995; 1997), etc. 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)].