Photon dispersion

The Bragg equation for a fee crystal as assumed in the photonic crystal based on polystyrene nanoparticles [154] is expressed in Eq. (82). The spacing between (111) planes in the fee crystal is related to dm. The effective refractive index ( eff) was obtained by considering the long-wavelength limit of the photon-dispersion relation co(k), Eq. (83), where c is the speed of light. 

Photodiode array (PDA) A detector that works by detecting photons dispersed in space one photodiode per geometrical location. 

The most informative probe to extract the detailed hydride s band structure is a beam of particles with energy and momentum comparable to that of the band electrons. The obvious choice, the low energy electron beam, is not applicable in the condensed matter bulk properties studies, because its shallow penetration. Other choices, such as the photon beam emission and absorption spectroscopy, can provide information either about the electron s energy or about the electron s momentum, but not for both at the same time, because the photon dispersion relation is generally quite different from that of the band electrons. This is not however the case in Compton spectroscopy, where the spectra of incoherently scattered radiation are more informative because the probing "particle" has energy... 

Photonic dispersion relation of QD photonic crystals, (a) Primitive cubic lattice, (b) Face-centered cubic lattice... 

The dispersion relationship w(q) for a QD dimer fee lattice is presented in O Fig. 23-6. The lattice is denoted by its lattice constant a, which is set to be 0.95flBragg (which is 116 nm for GaAs), where ciBragg = cnlw n. The lossy type-1 QDs hw = 1.5 eV) occupy the normal fee lattice sites, while the excited type-11 QDs hw2 = 1.503 eV) are displaced by t = ajlyU/2, a 12). hwn = 5 meV. Here we observe the modification of the photonic band structure of the QD dimer system by pumping one type of the QDs (type-11 QDs), which evolves from the one of only type-1 QDs c f = 0, i.e., at their ground exciton state) when type-11 QDs are transparent [ c2p = 0.5, O Fig. 23-6c] to the compound system [ c2p = 1.0, O Fig. 23-6a]. We can observe modified but stUl characteristic features of the photonic dispersions of individual type-1 and type-11 QDs in their separate photonic crystal formats in the compound system, see O Fig- 23-4. More specifically, the resonance features of type-I QDs around (w - (Oi)l(on = 0.3 in O Fig. 23-6d become compressed by the radiative interaction between type-I QDs and type-II QDs, and they are also shifted down to around 0.18 in O Fig. 23-6a. 

By varying c2p from 0.0 to 1.0 we find that the solutions of O Eq. 23.66 are symmetric with respect to c2 and 1 - c2 when ci = 0. Thus, O Fig. 23-6a represents also the photonic dispersion of the QD dimer system when both type-I and type-II QDs are all initially at their ground exciton states, that is, cip = c2p = 0. Thus the modification of the exciton state (from ground state to excited state) in one type of QDs in the dimer system does not affect the feature of the dispersion structure. 

Fu, Y., Willander, M., Ivchenko, E. L. (2000). Photonic dispersions of semiconductor-quantum-dot-array-based photonic crystals in primitive and face-centered cubic lattices. Superlattices and Microstructures, 27, 255-264. 

Patterson and Lynn [6] have reported a lattice dynamical study of the host lattice CsjSiFg based on neutron scattering, Raman, and infrared absorption measurements. Dispersion relations for phonons with energies less than 160 cm have been determined along three symmetry directions by coherent inelastic neutron scattering experiments. In Fig. 7 the photon dispersion results for Cs2SiFg are shown [6] in which the experimental data are represented by circles. The solid lines correspond to dispersion curves calculated with a rigid-ion, lattice dynamical model. 

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