Emmanuel Centeno

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.

Graded photonic crystals

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.

Multiplexing and demultiplexing with photonic crystals

We investigate the propagation of electromagnetic waves in two-dimensional doped photonic crystals. We numerically demonstrate how photonic crystals may be used to multiplex and demultiplex optical signals. By inserting three different kinds of defect, we are able to design three distinct waveguides inside the same structure. Two waveguides geometrically separate, in two paths, the optical signal for two frequency ranges. The third waveguide mixes the waves in order to multiplex both frequency ranges. The demultiplexing is performed by executing the same operations but in the opposite order.

Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect

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 10GHz. 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.

Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals.

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.

Superprism effect in bidimensional rectangular photonic crystals

In this letter, we show that photonic crystals with geometries of lower symmetry, such as the rectangular geometry, are uniquely suited for applications involving the superprism effect. The extra degree of freedom provided by the anisotropy of the unit cell allows more freedom in searching for suitable iso-frequency curves. Also, the appearance of multiple orders of diffraction allows more than one incident plane wave to couple to the same Bloch mode. This extra degree of freedom is decisive when trying to optimize the transmission. We illustrate these ideas on a particular rectangular configuration which ensures a strong angular superprism effect, a well collimated transmitted beam, and power transmissions of up to 80%.

Second-harmonic emission in two-dimensional photonic crystals

A second-harmonic superprism effect in 2D photonic crystals is demonstrated numerically. A full control of the second-harmonic emission is achieved by tailoring the photonic dispersion curves. This effect is demonstrated by using a multiple scattering method generalized to the second-harmonic generation. We show that small angular variations or a wavelength tuning of the fundamental field induce large shifts of the second-harmonic emission (∼90°).

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.

Discontinuous wavelength super-refraction in photonic crystal superprism

Experimental results on wavelength-dependent angular dispersion in InGaAsP triangular lattice planar photonic crystals are presented. An abrupt variation of the angular dispersion is observed for TM-polarized waves whose frequencies are comprised between those of the fourth and sixth allowed bands. According to the crystal period, the measured angle of refraction is found to either decrease or increase by 30 degrees within a wavelength range smaller than 30 nm. Experimental results are reproduced well from 2D finite difference time domain calculations. The observed phenomena are interpreted from the coupling of the incident light to different modes of the photonic crystal that travel with different group velocities and propagate in different directions within the crystal. Mode dispersion curves and mode patterns are calculated along with isofrequency curves to support this explanation. The observed discontinuous wavelength super-refraction opens a new approach to the application of superprisms.

Ultimate resolution of indefinite metamaterial flat lenses

We show that any metallo-dielectric multilayer with a hyperbolic dispersion relation can actually be characterized by a complex effective index. This refractive index, extracted from the complex Bloch band diagram, can be directly linked to the super-resolution of a flat lens made of this so- called indefinite metamaterials. This allows for a systematic optimization of the lens design, leading to structures that are outperforming state-of-art flat lenses. We show that, even when fully taking absorption into account, our design provides super-resolved images for visible light up to a distance of one wavelength from the lens edge.