KEYWORDS: Photonic crystals, Line width roughness, Metamaterials, Light wave propagation, Geometrical optics, Near field scanning optical microscopy, Dielectrics, Near field optics, Radio propagation, Crystals
The transition between the long-wavelength and the short-wavelength regimes of light propagation in all-dielectric
metamaterials is experimentally probed using a hyperspectral near-field scanning microscope technique. Our
measurements lead to an invariant quantity “λ/n” of only 1.78 times the dielectric lattice period as the criterion for the possible application of homogenization theories.
The dispersive properties of planar photonic crystals (PhCs) have been envisaged for years. In particular, the superprism
effect has been considered to obtain a strong influence of input beam conditions (e.g. wavelength or input angle) on the
light group velocity direction, enabling the design and fabrication of on-chip infra-red spectrometers and integrated
optical demultiplexers. We extend here the properties of PhCs to the study of graded photonic crystals (GPhCs) made of
a two-dimensional chirp of lattice parameters and show that GPhCs enable solving several drawbacks of dispersive PhCs
like the beam divergence issues or the need of long preconditioning regions to precompensate beam diffraction effects.
The proposed approach is applied to a square lattice air-hole PhC with a gradual filling factor that was fabricated using ebeam
lithography and ICP etching techniques. A nearly-constant 0.25μm/nm spatial dispersion is demonstrated for a
60μm square GPhC structure in the 1470-1600nm spectral range without noticeable spatial or spectral spreading.
Moreover, contrary to PhC superprism structures, a linear dispersion is obtained in the considered wavelength range.
We report an analytic approach to describe all-dielectric graded periodical media (namely graded photonic crystals)
operating in the homogeneous regime. Beneath this condition, the method is based on the equations of Hamiltonian
optics and provides an analytical expression of the two-dimensional refraction index needed to make light follow
prescribed paths. It is applied to a proof-of-concept structure (light 90° bend), which behaviour is investigated by
considering a two-dimensional planar silicon on insulator slab waveguide drilled by a sub-wavelength air-hole lattice
with a gradual filling factor corresponding to the required optical index map. The electromagnetic properties of the
considered structure are then verified using Finite Difference Time Domain simulation. As a whole, the proposed method
is an alternative solution to conformal space coordinate transforms applied to all-dielectric photonic metamaterials and
could help the design of new structures in forthcoming works.
Experimental results on light bending effect in a non-homogenizable graded photonic crystals operating at optical
wavelengths are presented. A square lattice photonic crystal made with a two-dimensional chirp of the air-hole filling
factor is exploited to produce this bending effect in a near bandgap frequency range. Experimental results are in good
agreement with the prediction that had been performed using the equations of Hamiltonian optics and Finite-Difference
Time-Domain simulations. This experimental demonstration performed in one particular configuration opens
opportunities for light manipulation using a combination of unusual dispersive phenomena in PhCs and additional
degrees of freedom brought by a generalized two-dimensional chirp of PhCs lattice parameters. This approach is also an
alternative solution to the use of photonic metamaterials combining dielectric and metallic materials with sub-wavelength
unit cells.
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