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.
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.
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-plant, 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.
We show that photonic crystals with ring-shaped holes (RPhCs) exhibit superior properties compared to conventional photonic crystals (PhCs). At low air-fill factors RPhCs can have a larger bandgap ...than conventional PhCs. Moreover, RPhC waveguides with both high group index and small group velocity dispersion can be designed. RPhC waveguides are also more sensitive to external refractive index changes, which is attractive for sensor applications. Finally we set up a procedure to pattern RPhCs in silicon-on-insulator.
We demonstrate InP-based triangular and hexagonal two-dimensional (2-D) planar photonic bandgap (PGB) crystal-based microcavities, positioned on a suspended membrane. Photoluminescence spectra of the ...structure clearly show well-resolved cavity modes, whose structure depends on the cavity shape. Q factors from 200 up to at least 900 are derived.
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.
We design an efficient coupler to transmit light from a strip waveguide into the flatband slow mode of a photonic crystal waveguide with ring-shaped holes. The coupler is a section of a photonic ...crystal waveguide with a higher group velocity, obtained by different ring dimensions. We demonstrate coupling efficiency in excess of 95% over the 8 nm wavelength range where the photonic crystal waveguide exhibits a quasi-constant group velocity
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and observe a more than 12-fold intensity enhancement in the slow-light waveguide. An analysis based on the small Fabry–Pérot resonances in the simulated transmission spectra is used for studying the effect of the coupler length and for evaluating the coupling efficiency in different parts of the coupler. The mode conversion efficiency within the coupler is more than 99.7% over the wavelength range of interest. The parasitic reflectance in the coupler, which depends on the propagation constant mismatch between the slow mode and the coupler mode, is lower than 0.6%.
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