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2D photonic crystal waveguide
Let us consider planar photonic waveguide manufactured in a 2D hexagonal PhC designed for the purpose of the third telecommunication window [43]. Left figure shows geometry of the considered PhC waveguide manufactured in 200 nm thick Si wafer (n = 3.26) with air cladding. In principle, photonic crystal lattice (a = 390 nm) surrounding waveguide region is composed of the air holes of radius r = 107 nm. TE polarization (electric field parallel to the wafer plane) exhibits a photonic bandgap (PBG) inside the PhC region around 1.4mm wavelength. Line defect operating as a PhC waveguide is about 6 mm wide and 10 mm long. Due to symmetry of the excited mode and structure, we can reduce the size of the model imposing electric symmetry in the middle of the waveguide width.
Left figure shows calculated transmission coefficient in the 1.1  - 1.8 mm wavelength range. We can notice that the passband is mainly between 1.2 and 1.45 mm, corresponding to the PBG of the applied PhC.
Transmission coefficient spectrum (power scaling)
Envelope of the magnetic field (in the logarithmic scale) at f = 207579 GHz (l = 1.44 mm). It can be seen that the field is concentrated near the waveguide region and only a few PhC rows are needed to guide the light properly.
2D photonic crystal waveguide bend
Another example depicts a unique advantage of PhC waveguide very difficult to obtain in waveguiding structures with strict boundary conditions. We consider a sharp 900 bend hollowed in a 2D PhC composed of GaAs rods of radius r = 104 nm distributed with lattice constant a = 580 nm [12]. Spectrum of a transmitted signal is set in the third telecommunication window at l = 1550 nm. Proper design of the corner neighbourhood allows us to optimise transmission efficiency.
Scattering parameters obtained around frequency of our interest f = 193414 GHz (l = 1550 nm). It can be noticed that the transmission coefficient is about |S21| = -0.09 dB providing ~98% of injected energy to the output.
Envelope of the Poynting vector calculated at frequency f = 193414 GHz (l = 1550 nm) clearly indicates that energy is very well concentrated in a waveguiding defect penetrating interior of PhC only a little.
2D photonic crystal lens
This example shows application of an all-angle negative refraction effect obtained using PhC slab. We leave theoretical consideration how to design such structure and focus on a specific application, namely PhC slab that operates like a focusing lens. However, unlike typical optical lenses it is of the orders of magnitude smaller and, most of all, flat. Thus, it is much easier to be manufactured and due to a compact shape it can be used as a casing element. The left figure presents about 60 mm thick dielectric slab (er = 12) with air holes of radius r = 3.5 mm arranged in a lattice with constant a = 10 mm [39]. It has been tuned in a manner to manifest its specific behaviour at f = 5.846 GHz. Nevertheless, it should be strongly emphasized that since geometry of PhC is scalable we can observe the same phenomenon in any frequency range providing that we properly rescale scenario maintaining electric properties unchanged. Besides, unlike spherical lens, since an optical axis does not appear in PhC lens there is no issue of source misalignment.
To exemplify focusing effect we put a TE polarized point source in close vicinity of the PhC slab and the left figure shows a snapshot of the Poynting vector obtained in this scenario. What is meaningful, we observe a real point image of the excitation source on the opposite side of the slab.
Snapshot of the Poynting vector in a logarithmic scale obtained in the PhC_lens1.pro at f = 5.846 GHz.
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