Abstract
We present a study on relation between the refraction and rightness effects in photonic crystals applied on a 2D square lattice photonic crystal. The plane wave (the band and equifrequency contour analyses) and FDTD calculations for both TM and TE modes revealed all possible refraction and rightness cases in photonic crystal structures in the first three bands. In particular, we show for the first time, a possibility of the left-handed positive refraction. This means that left-handedness does not necessarily imply negative refraction in photonic crystals.
Highlights
Left-handed materials attracted a lot of attention
The left-handed materials were predicted in the seminal work by Veselago [1] who analyzed a hypothetical meta-material that had both the electrical permittivity ε and the magnetic permeability μ simultaneously negative
The righthanded (RH) negative refraction has already been discussed [8] in the valence band and here we show that the left-handed (LH) negative refraction is possible in the second photonic band (“conduction” band) close to the second gap
Summary
Left-handed materials attracted a lot of attention. These structures can be either realized as so-called meta-materials or photonic crystals. In 1999, Pendry [3] proposed and tested the new meta-materials consisting of conducting loops (split-ring resonators (SRR)) or tubes ('Swiss rolls') Their magnetic permeability μ has a resonance and a narrow frequency range with μ < 0. A prism made of this meta-material showed negative refraction at 10.5 GHz. In contrast to the split rings or 'Swiss roll' structures, photonic crystals (PhC) consist of periodically modulated dielectric or metallic material. The losses can be much smaller in PhCs comparing to LHMs since a non-conducting dielectric material is used Both negative refraction and left-handedness in PhCs were experimentally demonstrated in the microwave range [9,10,11,12,13]. The propagation of EMW across both the ΓM and ΓX interface of the 2D square lattice PhC is investigated
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