English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider conditions under which photonic crystals (PCs) can be homogenizedin the higher photonic bands and, in particular, near the $\Gamma$-point. Byhomogenization we mean introducing some effective local parameters$\epsilon_{\rm eff}$ and $\mu_{\rm eff}$ that describe reflection, refractionand propagation of electromagnetic waves in the PC adequately. The parameters$\epsilon_{\rm eff}$ and $\mu_{\rm eff}$ can be associated with a hypotheticalhomogeneous effective medium. In particular, if the PC is homogenizable, thedispersion relations and isofrequency lines in the effective medium and in thePC should coincide to some level of approximation. We can view this requirementas a necessary condition of homogenizability. In the vicinity of a$\Gamma$-point, real isofrequency lines of two-dimensional PCs can be close tomathematical circles, just like in the case of isotropic homogeneous materials.Thus, one may be tempted to conclude that introduction of an effective mediumis possible and, at least, the necessary condition of homogenizability holds inthis case. We, however, show that this conclusion is incorrect: complexdispersion points must be included into consideration even in the case ofstrictly non-absorbing materials. By analyzing the complex dispersion relationsand the corresponding isofrequency lines, we have found that two-dimensionalPCs with $C_4$ and $C_6$ symmetries are not homogenizable in the higherphotonic bands. We also draw a distinction between spurious $\Gamma$-pointfrequencies that are due to Brillouin-zone folding of Bloch bands and "true"$\Gamma$-point frequencies that are due to multiple scattering. Understandingof the physically different phenomena that lead to the appearance of spuriousand "true" $\Gamma$-point frequencies is important for the theory ofhomogenization.

Can photonic crystals be homogenized in higher bands?