A detailed comparison of the original Gerchberg-Saxton and the Yang-Gu algorithms for the reconstruction of model images from two intensity measurements in a nonunitary transform system is presented. The Yang-Gu algorithm is a generalization of the Gerchberg-Saxton algorithm and is effective in solving the general amplitude-phase-retrieval problem in any linear unitary or nonunitary transform system. For a unitary transform system the Yang-Gu algorithm is identical to the Gerchberg-Saxton algorithm. The reconstruction of images from data corrupted with random noise is also investigated. The simulation results show that the Yang-Gu algorithm is relatively insensitive to the presence of noise in data. In all cases studied the Yang-Gu algorithm always resulted in a highly accurate recovered phase.
The photonic-band-gap ͑PBG͒ structure composed of an anisotropic-dielectric sphere in uniform dielectric medium is studied by solving Maxwell's equations using the plane-wave expansion method. In particular, for a uniaxial material with large principal refractive indices and sufficient anisotropy between them, the photonic band structures possess a full band gap in the whole Brillouin zone for a diamond lattice. Furthermore, in the 1/3 partial Brillouin zone where the Bloch wave vector has a dominant component along the extraordinary axis of uniaxial sphere, the photonic band structures are found to exhibit full band gaps for all the other lattices such as face-centered-cubic, body-centered-cubic, and simple-cubic lattices, although a complete band gap does not open in the whole Brillouin zone. The partial band gaps persist at a very low filling fraction of uniaxial sphere. This phenomenon is attributed to the breakdown of the photonic band degeneracy at high-symmetry points of the Brillouin zone by the anisotropy of material dielectricity. The combination of such an anisotropic PBG structure with the self-arrangement technique of colloidal crystal may provide a possible way to fabricate the three-dimensional photonic crystal in visible and infrared regimes. The application of a strong electric field may bring into alignment the extraordinary axis of uniaxial sphere as this configuration of spheres is most favorable thermodynamically. ͓S0163-1829͑98͒06231-6͔
Decay kinetic properties of a two-level atom near the band edges of photonic crystals (PCs) with absolute gaps are studied based on the Green's function expression for the evolution operator. The local coupling strength between the photons and an atom is evaluated by an exact numerical method. It is found that the decay behavior of an excited atom can be fundamentally changed by the variation of the atomic position: Weisskopf-Wigner and non-Weisskopf-Wigner decay phenomena occur at different atomic positions in the PCs as a result of a significant difference in the local coupling strength. Our finding implies that it is possible to engineer the luminescence spectrum by controlling the atomic position.
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