Photonic Crystals: Towards Nanoscale Photonic Devices by Jean-Michel Lourtioz, Henri Benisty, Vincent Berger,

By Jean-Michel Lourtioz, Henri Benisty, Vincent Berger, Jean-Michel Gerard, Daniel Maystre, Alexei Tchelnokov, Pierre de Fornel, Dominique Pagnoux

Like the periodical crystalline capability in solid-state crystals determines their houses for the conduction of electrons, the periodical structuring of photonic crystals ends up in envisioning the opportunity of reaching a keep watch over of the photon flux in dielectric and steel fabrics. using photonic crystals as a cage for storing, filtering or guiding mild on the wavelength scale hence paves easy methods to the realisation of optical and optoelectronic units with final houses and dimensions. this could give a contribution towards assembly the calls for for a better miniaturisation that the processing of an ever expanding variety of facts requires.Photonic Crystals intends to supply scholars and researchers from various fields with the theoretical history wanted for modelling photonic crystals and their optical houses, whereas even as providing the massive number of units, from optics to microwaves, the place photonic crystals have discovered functions. As such, it goals at construction bridges among optics, electromagnetism and solid-state physics. This booklet used to be written through six experts of nanophotonics, and used to be coordinated via Jean-Michel Lourtioz, head of the Institut d'Electronique Fondamentale in Orsay and coordinator of the French learn community in Nanophotonics.

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Extra info for Photonic Crystals: Towards Nanoscale Photonic Devices

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In other terms, it suffices to consider the variation of k within the Brillouin zone for representing the entire set of the dispersion curves of the photonic crystal. The range over which k is considered can be further reduced by using the symmetries of the crystal, as is illustrated in the different examples represented in Fig. 4. In the one-dimensional case, the crystal displays an obvious symmetry with respect to the origin. Thus, if a wave of vector k and frequency co is found to be a solution to the master equation, the counterpropagating wave with the same frequency and vector - k will also be a solution to this equation.

Further, when all the layers of the stacks have the same optical thickness, the band gaps even come to disappear at the even harmonic frequencies 2a;, 4a;.... This can be explained from the fact that, at the harmonics 2a;, 4a;, 6a;, each layer constitutes an optical resonator with length >^/2, \, 3>^/2, ... where stationary waves might be contained. It is quite obvious in this case that the existence of stationary waves is incompatible with the existence of a photonic band gap. The behaviour of Bragg reflectors can be explained in a more traditional way in terms of a construction of multiple interferences inside the periodic stack of layers.

Ky, increases and they may even vanish for a certain value of the incidence angle. In order to fully understand the influence exerted by the polarisation of the field, it should be borne in mind first that the reflection coefficient at each interface, or Fresnel coefficient, comes to depend on the polarisation as soon as the incidence is not normal (Born 1965). Further, the variation of the distribution of the displacement vector depending on the polarisation of the field should also be considered here.

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