By Olivier Vanbésien, Emmanuel Centeno
This e-book indicates how dispersion engineering in dimensional dielectric photonic crystals promises new results for the correct regulate of sunshine propagation for built-in nanophotonics.
Dispersion engineering in normal and graded photonic crystals to advertise anomalous refraction results is studied from the options to experimental demonstration through nanofabrication concerns. Self collimation, extremely and adverse refraction, moment harmonic new release, mirage and invisibility results which result in an extraordinary keep watch over of sunshine propagation on the (sub-)wavelength scale for the sector of built-in nanophotonics are specified and commented upon.
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Extra info for Dispersion Engineering for Integrated Nanophotonics
As proven by Lombardet and co-authors, this strategy has to be extended for PhCs. Finally, a Bloch wave can be decomposed into a set of waves each of which carry a part of the energy. Far from the band gap edge, a Bloch mode can be assimilated to a unique plane wave whose wavevector and group velocity have to be researched in the unfolded band diagram. 13. Band diagram of a 1D periodic homogeneous medium presenting a positive refraction index. The bold lines represent the unfolded dispersion relation.
For the second 26 Dispersion Engineering for Integrated Nanophotonics dispersion band, negative refraction is finally explained by the negative curvature of the EFC at point B. This conclusion enables us to generalize the concept of the curvature index that drives the beam shaping operation in PhCs. 14. EFCs of the second band. The light gray (blue in color version) and dark gray (red in color version) areas correspond to the 1st and 2nd Brillouin zones respectively. The black arrows are the group velocities at points A and B.
In such a case, we fiind n = -1 annd z = 1. Thee negative vallue found forr n, when extractin ng the square root r of the prooduct εµ, presserves causalitty of phenomeena when ε and µ are simultanneously negattive (some au uthors have named n such a material “anti-vaccuum”). 1. 1, a slab of such material acts as a double focusing lens for an incident point source. Using Snell–Descartes’ law, the ray tracing shows two ideal spots: one within the lens, the second behind the lens. Let us mention that using an incident harmonic wave decomposition in terms of propagating and evanescent components, each component is perfectly restituted in the image: propagating components since no reflection occurs at lens interfaces (z = 1 everywhere) and evanescent components since they are amplified in the lens of the same magnitude that they are vanishing in air.