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.

We present a concept of graded photonic crystals used to enhance the control of light propagation. Gradual modifications of the lattice periodicity make it possible to bend the light at the micrometer scale. This effect is tailored by parametric studies of the isofrequency curves. As a demonstration, we propose a two-dimensional graded photonic crystal that could provide frequency-selective tunable bending.

We present a study of graded photonic crystals presenting a mirage effect. This light bending is understood through parametric studies of the isofrequency curves. We derive a model based on the effective index computation and on the Eikonal equation in order to demonstrate that photonic mirages originate from the same physical principles as atmospheric mirages. A graded photonic crystal presenting a superbending effect is proposed for designing a bent waveguide

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We demonstrate a mesoscopic self-collimation effect in photonic crystal superlattices consisting of a periodic set of all-positive index 2D photonic crystal and homogeneous layers. We develop an electromagnetic theory showing that diffraction-free beams are observed when the curvature of the optical dispersion relation is properly compensated for. This approach allows us to combine slow-light regime together with self-collimation in photonic crystal superlattices presenting an extremely low filling ratio in air.

We report the experimental demonstration of a beam curvature in graded photonic crystals via a spectacular mirage effect. A two-dimensional structure of metallic rods is constructed to produce this effect in the microwave domain near 10 GHz. Experimental results are in excellent agreement with theoretical predictions, thus, proving the versatility of graded photonic crystals in view of their integration in future photonic circuits. (C) 2008 American Institute of Physics

We provide a numerical tool to quantitatively study the impact of nonlocality arising from free electrons in metals on the optical properties of metallo-dielectric multilayers. We found that scattering matrices are particularly well suited to take into account the electron response through the application of the hydrodynamic model. Though effects due to nonlocality are, in general, quite small, they, nevertheless, can be important for very thin (typically below 10 nm) metallic layers, as in those used in structures characterized by exotic dispersion curves. Such structures include those with a negative refractive index, hyperbolic metamaterials, and near-zero index materials. Higher wave vectors mean larger nonlocal effects, so that it is not surprising that subwavelength imaging capabilities of hyperbolic metamaterials are found to be sensitive to nonlocal effects. We find in all cases that the inclusion of nonlocal effects leads to at least a 5% higher transmission through the considered structure.

In order to determine the angular geometry that satisfies quasi-phase matching conditions for enhanced second-harmonic generation (SHG), the equi-frequency surfaces of the resonant photonic modes (that lie above the light line) of a one-dimensional GaN photonic crystal have been experimentally and theoretically studied as a function of frequency, angle of incidence, and azimuthal direction. Enhancement of the SHG has been observed when the angular configuration satisfies the quasi-phase matching conditions, i.e., when both the fundamental and second-harmonic fields coincide with resonant modes of the photonic crystal. The SHG enhancement achieved to the double resonance was 5000 times with respect to the unpatterned GaN layer. A smaller, but still substantially enhanced SHG level was also observed when the fundamental field is coupled into a resonant mode, while the second-harmonic field is not