Abstract
The properties of two-dimensional (2D) photonic crystals (PCs) composed of germanium (Ge) are discussed. We investigate polarization-dependent photonic band diagrams (transverse electric and transverse magnetic polarizations), gap maps, surface plots, contour maps, etc. for 2D PCs with Ge rods in air and vice versa for two different lattices geometries, namely hexagonal and honeycomb lattices. The obtained graphs for the four possible combinations are presented in this paper. All the graphs depict clear photonic band gaps. The conditions for the largest TE and TM band gaps are described. The honeycomb lattice of Ge rods in air background offers a large complete photonic band gap Δω/ωm greater than 8% (for rod radius of r = 0.2 μm). Using these data, new Ge based photonic devices can be fabricated to confine, control and manipulate light in a more useful way.
Highlights
Photonic crystals are one of the most talked of topics of the modern world of science and engineering
We considered Ge rods inserted into air background as well as air holes drilled in Ge background
We observed that Transverse electric (TE) modes have advantage in photonic crystal structures composed of Ge rods in air background whereas Transverse magnetic (TM) modes are favoured in photonic crystal structures composed of air holes in Ge background
Summary
Photonic crystals are one of the most talked of topics of the modern world of science and engineering. Photonic crystals are novel type of optical media with periodic variation of the refractive index, with a period comparable to the wavelength of light [1] [2] They control the propagation properties of light photons in the same way as the natural crystals modify the properties of electrons in solid state physics [3] [4]. The determination of the eigenfunctions in a PC is similar to the calculation of the particle wave functions in solid-state This similarity is used to obtain photonic band diagram or photonic band structure [1] [5] [6]. For this reason, photonic band gap calculations for two-dimensional photonic crystals have been the subject of considerable attention nowadays [9]-[14]. Photonic band gap data are provided for each and every combination
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