Two band structures of two 2D metallic photonic crystals made of copper strips set on a dielectric substrate and arranged in a square lattice whose lattice constant a is 12 mm wide. The incident electric field is parallel to the axis of the strips (TM mode). The width of the strips of each photonic crystal is constant. The blue and the red curves correspond to the smallest width and to the greatest width of the used strips, respectively. In the first photonic band, at the normalized frequency (dashed line), the IFC are circular.
Six iso-frequency curves (curves in colour) for increasing filling factor η and that of the vacuum at (black curve), the latter being referred to as the “light cone.” Each of these curves is nearly circular. The outer curve (purple curve) corresponds to , while the corresponding filling factor of the other curves in colour varies from (red curve) to (blue curve). The discretization of the constitutive strips by a square mesh may bring about approximations in the simulations.
Gradient-index lens which behaves as a phase compensator, that is, all the incident parallel rays converge towards the focal point with the same optical path. The index of refraction n(r) is varied symmetrically and perpendicularly to the axis of the lens, from r = 0 (optical axis of the lens) towards the edges. f is the focal length of the lens and d is its thickness.
Picture of the GRIN Photonic Crystal Lens which consists of five layers of PCB. The strips are arranged in a square lattice of side a = 12 mm (inset). Their width w, and consequently the filling factor η, increases from center (w = 0) towards the edges.
Map of the mean value of the square of the electric field ( ) at 9.6 GHz of an incident TM plane wave onto the flat GRIN PC lens of focal length f = 15 cm. The lens consists of a graded photonic crystal made of five layers of copper strips whose width is varying perpendicularly to the direction of propagation. The two vertical green lines delimit the lens.
Profile of the electric field at 9.6 GHz (blue curve) in the focal plane extracted from simulations reported in Fig. 5 . The Full Width at Half Maximum is . Four other profiles at several frequencies are also reported.
Map of the instantaneous electric field Ez at 9.6 GHz issued from a point TM source located at the focal point and illuminating the same GRINPC lens. The emerging phase fronts are plane. The two vertical black lines delimit the lens.
Experimental map of the electric field ( in a.u.) over the output area of the flat GRIN PC lens at 9.6 GHz. The incident plane wave is focused and the focal length is around 15 cm.
Experimental profile of the electric field at 9.6 GHz (blue curve) in the focal plane of the GRIN lens extracted from the reported map in Fig. 8 . The Full Width at Half Maximum (FWHM) is . Four other profiles at several frequencies are also reported.
Experimental map of the instantaneous electric field Ez ( in a.u.) at 9.6 GHz in the output area when the same GRIN PC lens is illuminated by a point TM source located at the focal point (15 cm away from the input interface of the lens). Due to the dimensions of the measurement area, the electric field has been mapped in two steps: firstly, from 0 to 40 cm, secondly from 40 cm to 80 cm. The vertical blue line distinguishes these two steps. The phase fronts emerging from the lens are nearly plane.
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