All-Dielectric Rod-Type Metamaterials at Optical Frequencies

Abstract

Light propagation in all-dielectric rod-type metamaterials is studied theoretically. The electric and magnetic dipole moments of the rods are derived analytically in the long-wavelength limit. The effective permittivity and permeability of a square lattice of rods are calculated by homogenizing the corresponding array of dipoles. The role of dipole resonances in the optical properties of the rod array is interpreted. This structure is found to exhibit a true left-handed behavior, confirming previous experiments [L. Peng et al., Phys. Rev. Lett. 98, 157403 (2007)]. A scaling analysis shows that this effect holds at optical frequencies and can be obtained by using rods made, for example, of silicon.

Magnetic and electric coherence in forward- and back-scattered electromagnetic waves by a single dielectric subwavelength sphere

“…These are reminiscences of electric and magnetic whispering gallery modes. On resorting to the theory on magnetodielectric spheres reported in our previous work 25,26,39 , and that on Si and ceramic cylinders 28 , and recalling the scaling ratio l/(na) that maintains the existence of these phenomena in different frequency ranges, we also predict similar observations in conventional semiconductor spheres in the nearinfrared. The rescaling property of our scattering problem, together with the intrinsic interest that our results have in technological applications in the microwave range (electrically small antennas) aimed us to perform our simulations and experiments in the microwave regime (vB3-9 GHz-lB33-100 mm) 15 .…”

“…The ratio l/(na) constitutes a scaling factor that keeps the effects in the angular distribution of scattered intensity derived from the aforementioned interference between the induced electric and magnetic dipoles, (this magnetodielectric behaviour was actually proven for dielectric cylinders, rescaled from those being made of ceramic in the microwave region to those of Si in the near-infrared 28 ). Here we use the same argument for spheres: the similar value of l/(na) in the experiments carried out in this paper should be compared with that of a Si sphere in the near-infrared 25,26 .…”

Achieving anisotropy in metamaterials made of dielectric cylindrical rods

“…For simplicity, we emphasize the ordered case but the composite could be disordered, since the low-frequency macroscopic EM properties of this kind of MM do not rely on band structure phenomena, but the low-lying Mie resonances of the isolated cylinders. 8,10 As discussed in Ref. 8, the displacement current distribution inside the cylinder in the basic two Mie resonance modes would be similar to that of the conductive current in metallic rod and split-ring resonator, thus also supporting effective negative permittivity/permeability of the MM.…”

“…8,9 Recent scaling analysis have also pointed out that LH behaviors at optical frequencies would also be possible by use of rod-type MMs made of silicon. 10 Rod-type dielectric MMs with an isotropic density of rods ͑ordered or disordered͒ will commonly possess an isotropic dispersion in the two dimensions. 8,10 While isotropic dispersion is advantageous in a number of cases, there is however also a strong call for realizing anisotropic MMs for practical applications, as is in general required for a transformation medium.…”

Past achievements and future challenges in the development of three-dimensional photonic metamaterials

“…Thus, it is interesting to ask whether purely dielectric off-resonant hence low-loss constitutive materials might offer effective magnetic and/or negative-index metamaterials properties as well. Similar for the metallic structures, Mie resonances of dielectric particles play a key role 62 to achieve a negative magnetic permeability µ [63][64][65][66][67][68][69] . It is known from Mie resonance theory that the first resonance of a dielectric sphere is a magnetic-dipole mode (the second resonance for a cylinder).…”