Encyclopedia Of Nanoscience And Nanotechnology Inorganic

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Extra resources for Encyclopedia Of Nanoscience And Nanotechnology Inorganic Nanotubes Structure, Synthesis, And Properties

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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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