PHOTONIC CRYSTALS

NEGATIVE REFRACTION AND FOCUSING OF ELECTROMAGNETIC WAVES

BY METALLODIELECTRIC PHOTONIC CRYSTALS

  Photonic crystals are to photons as semiconductors to electrons. Semiconductor crystals greatly modify the flow of electrons and the density of states   for electrons. Similary, photonic crystals dramatically modify the dispersion properties of photons. This dramatic modification of the propagation of   photons by photonic crystals have inspired many exciting scientific research activities in the past two decades. These scientific studies have revealed   many novel phenomena. One particular phenomenon of great excitement in recent years is the negative refraction effect. This effect is observed for   frequency ranges at which the wave vector of the incident waves and the group velocity of the transmitted waves fell into the opposite sides of the   interface normal. As a result, for such frequency ranges photonic crystal behaves as if the index of refraction is negative.

  In order to make use of the negative refraction effect in certain applications such as focusing of electromagnetic waves, one usually requires negative   indices of refraction over a wide range of angles. To obtain negative indices of refraction over a wide range of angles is still a major challenge for   photonic crystal based structures, especially for metallic photonic crystals. Due to the very large dielectric constants of metals (especially in microwave   region), the bands that exhibit negative refraction for metallic photonic crystals occur at higher frequencies when compared to the dielectric photonic   crystals with the same lattice parameters. As a result, it is difficult to obtain negative refraction of electromagnetic waves for large incidence angles by   using metallic photonic crystals.

  We proposed the use of metallodielectric photonic crystals in order to obtain negative refraction for large incidence angles. The metallodielectric   photonic crystal that we used in our experiments and calculations is a square lattice of metallic and dielectric rods. The basis of the crystal consists of a   metallic and a dielectric rod placed along the diagonal of the square unit cell. Cylindrical alumina rods with a radius of 1.55 mm are used for the dielectric   rods and in the frequency range of interest the dielectric constant of alumina is 9.61. Metallic rods have a radius of 1.5 mm. The band structure of the   metalloielectric photonic crystal over the first Brillouin zone shows one may observe the negative refraction effect between 9.2 GHz and 10.2 GHz.

Figure 1: Equal-frequency contours (solid curves) are shown for the metallodielectric photonic crystal. Crystal orientation is shown by the dashed line. Dotted circle represents the free-space equalfrequency contour at 9.5 GHz. Frequencies are shown in gigahertz. Long dashed arrowwith black color represents the free-space wave vector whereas the short black arrow represents the free-space group velocity. Long dashed arrow with white color represents the wave vector of the refracted waves in the photonic crystal. Small white colored arrow indicates the direction of the group velocity inside photonic crystal.

In order to theoretically demonstrate the negative refraction of electromagnetic waves by the metallodielectric photonic crystal, we calculated the electric field intensities for electromagnetic waves of different incident angles.

Figure 2: Calculated electric field intensity distributions for incidence angles of 15 degrees.

Figure 3: Calculated electric field intensity distributions for incidence angles of 45 degrees.

  We experimentally dmeonstrated the negative refraction effect by measuring the electric field intensities on the output side of the photonic crystal over   an area of 40x15 cm2 area. The measurements were carried out by using a precision X-Y stage with steps of 2.5 mm. Our measurement setup consists   of a HP-8510C vector network analyzer and a Velmex precision XY positioner. The measurement results for an incidence angle of 25° are shown in the   below figure. Figure 6 (a) shows the electric field intensity for 9 GHz. Note that at 9 GHz the incident electromagnetic waves are positively refracted by   the metallodielectric photonic crystal. On the other hand, Fig. 6 (b) shows the electric field intensities for 9.7 GHz. Figure 6 (b) clearly demonstrates that   the electromagnetic waves are negatively refracted at 9.7 GHz when they are incident by 25° on the metallodielectric photonic crystal.

Figure 4: Experimental setup.

Figure 5: a) Electric field intensity for 9 GHz. b) Electric field intensity for 9.7 GHz. Incidence angle is 25 degrees.

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