Zero-average index metamaterials and photonic crystal superlattices are well known for presenting uncommon
properties such as a new forbidden band for photons and self-collimation effect. In this work, we show how these
two approaches can be combined to finely control beam propagation and we develop a theory that provides a
comprehensive understanding of these phenomenon. We show that the curvature of the dispersion relation plays
a crucial role to cancel light diffraction. This concept leads to the design of PhC superlattices with a very low
filling factor in air and presenting a slow light regime. The frequency selectivity of the self-collimation effect is
in addition shown to be increased by 10 or 50 compared to common 2D photonic crystal devices.
Recent research on second-harmonic generation in left-handed materials has shown a light localization mechanism
that originates from an all-angle phase-matching condition between counter-propagating electromagnetic modes
at fundamental and double frequencies. This phenomenon opens the route for the design of second-harmonic
lenses. In this paper, we recall the essential nonlinear properties needed to generate second harmonic images of
linear objects. We show that this approach enable one to realize SH images of objects placed inside or outside the
nonlinear lens. In the case of an external source, two distinct devices are proposed: a double lens configuration
which enables to image objects between symmetric metamaterial slabs, and a single lens case characterized by
an impedance mismatched interface. The versatility of these SH lenses opens new routes for the second harmonic
imaging technics since they are able to produce SH images from linear objects.
We study the coupling of light between strip and rib waveguides and supercollimating photonic crystals on
silicon-on-insulator substrates. The dispersive properties of the supercollimating photonic crystal are used to
define the design requirements on the excitation waveguide and the boundary of the photonic crystal is optimized
to improve the impedance matching between the two structures. By 3D calculations, we find that rib waveguides
can yield transmission effciencies up to about 96 % and reflections lower than 0.2 % at wavelengths close to
1.55 μm, while insuring single-mode propagation. This work therefore constitutes an important step toward the
integration of supercollimation-based optical circuits on photonic chips.
We demonstrate an isotropic phase matching condition achieved in nonlinear 2D PhCs that suppresses the incident angle
constraint . In addition, we show a backward SH localization effect by combining this unusual all-angle phase
matching and left-handed PhC properties. The SH emission is confined in a small area of dimension close to the pump
wavelength without the introduction of defect lattices. An analytical model is proposed in order to explain this parametric localization mechanism.
In the past few years, self assembly colloidal structures based on opals have received large attention because they offer a
cost-effective way of designing ultra-compact and efficient all-optical devices. In this study, we present various
approaches to design waveguides and cavities in three-dimensional opal-based photonic crystals. Three practical designs
with size suitable to telecommunication technologies at 1.55 μm are presented. First, we show that the creation of a
hexagonal superlattice of defects in a direct monolayer of spheres yields the opening of a photonic band gap below the
light line so that the inclusion of a linear defect in this structure enables the creation of a theoretically lossless
waveguide. We also propose the design of a waveguide in a 2D-3D heterostructure, where a graphite lattice of rods is
sandwiched between two inverse opal claddings. This structure enables single-mode waveguiding with a maximal
bandwidth of 129 nm. Finally, we give the design of a linear cavity, whose quality factor is increased by a factor of 5
when surrounded by an inverse opal.
We propose the fusion of the superprism effect and of the second harmonic generation: small variations of the
fundamental field parameters cause large variations in the direction of the second harmonic emission. Phase matching
conditions with very different propagation directions for the fundamental and the second harmonic fields are achieved
inside 2D PCs. These results are obtained by the use of a multiple scattering method extended to the second harmonic
generation problem. This nonlinear effect could possibly be applied for the design of new directional compact sources or of sensor devices.
We demonstrate the possibility of waveguiding electromagnetic waves in a monolayer of dielectric spheres. While light is confined vertically by index guiding, a triangular superlattice monolayer of spheres was found to exhibit a photonic band gap below the light cone, thereby preventing light from propagating laterally. A gap map of this structure is presented. We propose a possible waveguide configuration that yields two non-degenerate defect modes lying within the photonic band gap. Such a structure may be particularly interesting for coupling light into self-assembled colloidal photonic crystals.
We present the concept of graded photonic crystals (GPC) and show its ability to enhance the control of light propagation. It is shown that gradual modifications of photonic crystal parameters are able to curve the path of light. This light bending which depends on the wavelength and on the incident angle is examined through parametric studies of the iso-frequency curves. We demonstrate that photonic mirages originate from the same physical principles as the usual atmospheric mirages. Two optical components based on two-dimensional GPCs presenting a super bending effect and a large beam shifting are presented.
In this work, 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 this on a particular rectangular configuration which ensures a strong angular superprism effect, a well collimated transmitted beam, and power transmissions of up to 80%. We also study the effect of the incident beam width on the super-prism effect, and propose a possible solution to the problem of beam diffraction at the exit surface.
We describe a scattering matrix formalism used to model optical properties of two dimensional photonic crystals slabs. The determination of the scattering matrix poles allows us to simultaneously calculate the band structure and the corresponding losses of the electromagnetic modes, which contributes then to give a complete physical insight of the intrinsic properties of photonic crystal slabs. Using an in-plane supercell approach, a linear defect is also studied, leading to a complete evaluation of photonic crystal slab waveguides performances.
The second-harmonic field generated has been measured in reflection from the surface of one-dimensional and two-dimensional photonic crystals etched into a GaN layer. A very large second-harmonic enhancement is observed when simultaneously the incident beam at the fundamental frequency w excites a resonant Bloch mode and the second-harmonic field generated is coupled into a resonant Bloch mode at 2w. A smaller, but still substantially enhanced, second-harmonic generation level was also observed when the fundamental field was coupled into a resonant mode, while the second-harmonic field was not. By using calculated and experimental equifrequency surfaces, it is possible to identify the geometrical configurations that will allow quasi-phase matching to be satisfied - and observed experimentally in the available wavelength tuning range of the laser. The extended transparency window of III-nitride wide-bandgap semiconductors, coupled with large non linearities, is an appealing feature pointing towards the control and manipulation of light in photonic structures.
Investigations of polarizations effects in second-harmonic generation of a one-dimensional photonic crystal based on gallium nitride were performed for the fundamental beam incident on the surface of the photonic crystal. The angle of incidence, the azimuthal rotation angle of the photonic crystal, the frequency, and the polarization behaviour for strongly enhanced second-harmonic generation agree well with the identified position and polarization of the resonant Bloch modes. Along the direction, giant enhancements of 7500 times in the second-harmonic conversion have been obtained in the one-dimensional photonic crystal by comparison with the unpatterned GaN layer. The combined role of the resonant coupling of the fundamental field and of the second-harmonic field has been observed as the polarization of the fundamental beam is rotated.