All-dielectric rod-type metamaterials at optical frequencies.

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, Phys. Rev. Lett. 98, 157403 (2007)10.1103/PhysRevLett.98.157403]. A scaling analysis shows that this effect holds at optical frequencies and can be obtained by using rods made, for example, of silicon.

Homogenization of negative-index composite metamaterials: a two-step approach.

We present a two-step homogenization method for composite metamaterials. First, each layer of wires or resonators is homogenized as a slab with negative permittivity or permeability, respectively. Second, the single negative stack which results is homogenized to form the effective medium. Comparing the predictions of the first and second step can serve as a gauge of the homogeneity of the composite. We thus take a gradual approach to homogenization, asking not whether, but to what extent a composite metamaterial approaches the sought after effective medium. Our two-step approach can also capture phenomena which otherwise may be wrongly attributed to effective medium behavior. We illustrate by qualitatively reproducing and reinterpreting a set of experimental data from the literature.

Equifrequency surfaces in a two-dimensional GaN-based photonic crystal.

We established the angular conditions that maintain the quasi-phase matching conditions for enhanced second-harmonic generation. To do that, we investigated the equifrequency surfaces of the resonant Bloch modes of a two-dimensional periodic, hole-array photonic crystal etched into a GaN/sapphire epitaxial structure. The equifrequency surfaces exhibit remarkable shapes, in contrast to the simpler surfaces of a one-dimensional structure. The observed anisotropy agrees well with the surfaces calculated by a scattering matrix method. The equifrequency surfaces at fundamental and second-harmonic frequencies provide the values of polar and azimuthal angles that maintain quasi-phase matching conditions for enhanced second-harmonic generation over an extended tuning range. The predicted values for quasi phase-matching conditions show that frequency tuning for the two-dimensional case covers an about two times larger fractional bandwidth relative to the one-dimensional case.

Diffraction of light from thin-film polymethylmethacrylate opaline photonic crystals.

Photonic crystals in the form of large area thin films consisting of closely packed polymethylmethacrylate beads were sedimented on glass substrates. The high ordering of the opaline films made it possible to observe a number of fine features in the optical diffraction, including Fabry-Perot oscillations of the reflectivity and branching of the angular dispersion of the Bragg resonances with increase of the angle of incidence of the light beam. Results of calculations of the photonic band structure and simulations of the reflectance spectra agree well with experimental observations.