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 power in solid-state crystals determines their houses for the conduction of electrons, the periodical structuring of photonic crystals results in envisioning the opportunity of attaining a regulate of the photon flux in dielectric and metal fabrics. using photonic crystals as a cage for storing, filtering or guiding mild on the wavelength scale therefore paves the best way to the realisation of optical and optoelectronic units with final homes 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 calls for. Photonic Crystals intends to supply scholars and researchers from various fields with the theoretical heritage wanted for modelling photonic crystals and their optical homes, whereas even as proposing the massive number of units, from optics to microwaves, the place photonic crystals have discovered functions. As such, it goals at development bridges among optics, electromagnetism and solid-state physics. This booklet used to be written via six experts of nanophotonics, and was once coordinated via Jean-Michel Lourtioz, head of the Institut d'?lectronique Fondamentale in Orsay and coordinator of the French examine community in Nanophotonics.

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55 (-'41%). 4 f. \/ \/ ^^ ^ CO CD C D > \A \ / \ / \ / \/ \/ \ r=\/\/\/ {I4\iit\i/N O E, field Intensity Fig. 6. Evolutions of the transverse electric field (left) and of the optical intensity (right) along the one-dimensional photonic crystal for frequencies located at the edges of the valence band (middle) and conduction band (bottom) respectively. -^, expressed by Eqs. 53b respectively, for each of the frequencies given by Eq. 54. e at the edge of the valence band, plus sign in Eq. 54), the application of Eqs.

5. For instance, the two lines ^0 (^) and ^-1 (^) intersect at the edge of the zone k = n/a^ for the frequency 60o= Kc/{a^j£^). This specific band diagram is also referred to as the free-photon diagram in order to point to the fact that it corresponds to the case of an homogeneous material in the absence of any loss, reflection or diffraction. Let us now assume a proper sinusoidal modulation (s^ ^ 0), but with only a moderate amplitude {E^ < Sm)- The second and third terms in Eq. 51 may be regarded as perturbative terms.

7. Band diagrams of two one-dimensional photonic crystals in the form of two multilayer films consisting of periodically alternating layers with different widths dj and J2 and different permittivities s^ and £2. In both cases, the permittivities of the layers are equal to s^ = 13 and £2=1 respectively. 7a 32 1 Models for Infinite Crystals 1 2 ^ w 3 Z)~]7 , ^ 4 5 \ ^— \ — \ ^ 7 ,7 1 w 6 7 , i, 7— 7— —^ ^ 7 7 7 W ^ i^ ^ \ \ 1 7 ^J J Fig. 8. Construction of multiple interferences in the Bragg reflector Nevertheless, contrary to the structure exhibiting a permittivity with a sinusoidal modulation, Bragg multilayers might present band gaps with different widths at the fundamental and at the different harmonic frequencies a>, 2 a;, 3a>, 4co...

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