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.

Radiation losses occurring in photonic crystals etched into planar waveguides are analyzed using a first-order perturbation approximation. Assuming the incoherent scattering limit, the model indicates that losses diminish as the cladding index approaches the core index. A simple scheme is devised to include these losses into purely two-dimensional calculations by using an imaginary index. Such calculations are shown to agree with corresponding experimental transmission through near-infrared photonic crystals, reproducing the contrasting behavior of the “dielectric” and “air” band edges.

Abstract-We describe experiments on a quasi-two-dimensional (2-D) optical system consisting of a triangular array of air cylinders etched through a laser-like Ga(Al)As waveguiding heterostructure. Such a configuration is shown to yield results very well approximated by the infinite 2-D photonic crystal (PC). We first present a set of measurements of the optical properties (transmission, reflection, and diffraction) of slabs of these photonic crystals, including the case of in-plane Fabry-Perot cavities formed between two such crystals. The measurement method makes use of the guided photoluminescence of embedded quantum wells or InAs quantum dots to generate an internal probe beam. Out-of-plane scattering losses are evaluated by various means. In a second part, in-plane micrometer-sized photonic boxes bounded by circular trenches or by two-dimensional photonic crystal are probed by exciting spontaneous emission inside them. The high quality factors observed in such photon boxes demonstrate the excellent photon confinement attainable in these systems and allow to access the detail of the modal structure. Last, some perspectives for applications are offered.

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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.

We present quantitative measurements of the interaction between a guided optical wave and a two-dimensional photonic crystal using spontaneous emission of the material as an internal point source. This is the first analysis at near-infrared wavelengths where transmission, reflection, and inplane diffraction are quantified at the same time. Low transmission coincides with high reflection or in-plane diffraction, indicating that the light remains guided upon interaction. Also, good qualitative agreement is found with a two-dimensional simulation based on the transfer matrix method. [S0031-9007(97)04591-2]

Defectless two-dimensional photonic crystal structures have been fabricated by drilling holes in a thin multi-quantum-well InP-based heterostructure transferred onto a silicon host wafer. Extremely low group velocity modes, which correspond to the predicted photonic valence band edge, have been observed for different filling factors. Under pulsed optical pumping, room temperature laser operation around 1.5 μm has been achieved on these structures with a threshold in the milliwatt range.

Single-line photonic-crystal waveguides are investigated. Photoluminescence experiments and three-dimensional calculation are performed and allow a clear identification of the guided modes. The propagation properties of the latter (group velocity, losses) are extracted from photoluminescence spectra obtained on closed waveguides which act as linear cavities.