No abstract

Abs(raeL An interatomic potential for arbon is developed Ihal is kmed on an empirical tighl-binding approach. The model repmduces aocuraleiy the energyversus-volume diagram of arbon polyiypes and gives a good description of Ihe phonons and elastic mnslanls for carbon in the diamond and graphite structures. To test the transferability of the model to differen1 atomic environments further, w performed moleculardpamics simulations to study the liquid phase and lhe pmpenies of mall arbon micmdus ters. The rerults obtained are in good agreement wilh those obtained from ob bzitio calculations.

It is generally believed that long range periodic order is instrumental in the formation of a photonic band gap. Using a spectral method that scales linearly with the system size, we found that sizable spectral gaps for each polarization in 2D can be found in aperiodic arrangements of dielectrics that resemble quasicrystalline tiling. Since the aperiodic arrangement has many inequivalent sites, the defect properties of these systems are more complex and interesting than conventional photonic band gap systems. [S0031-9007(97)05157-0] PACS numbers: 42.70. Qs, 41.20.Jb, In the past few years, there has been much research activity pertaining to photonic band gap (PBG) material, which has a spectral gap in the electromagnetic (EM) wave spectrum in which EM wave propagation is forbidden in all directions [1,2]. PBG can suppress vacuum fluctuation and spontaneous emission, and can lead to interesting quantum electrodynamics effects [3]. This is also seen as a road map to strong photon localization, itself a fascinating but elusive phenomena [4]. It has potential applications in quantum electronic devices, distributed-feedback mirror, microwave antennae substrate [5], and its unusual optical properties can be exploited to control and guide the propagation of light [6].PBG materials are often viewed as analogs of electronic semiconductors. Only short-range order is necessary for the formation of an electronic band gap. Amorphous semiconductors exist and have band gaps that are comparable in size to those of crystalline semiconductors. However, electrons form bound states and photons do not. Most of the theoretical demonstration of the existence of an electronic band gap without periodicity is based on simplified tight-binding models, which is a reasonable description because electrons can form bound states. While it is now firmly established that a certain periodic arrangement of dielectric structures can support full photonic band gaps in 2D and 3D [2], it is not obvious whether a structure without periodic order can have complete photonic gaps or not. The photonic band gap we know of to date in 2D and 3D is the consequence of periodicity: We can define a Brillouin zone because of the periodicity; and a complete photonic gap is formed when the spectral gaps at the Brillouin zone boundary overlap in all directions. Can there be photonic gaps without periodicity and without a Brillouin zone? This is a fundamental question. Motivated by the known existence of 1D stop bands in superlattices stacked in the Fibonnaci sequence [7], and acoustic spectral gaps in nearest-neighbor coupled tuning fork arrays arranged in a Penrose tiling [8], we seek to show that sizable spectral gaps can exist a in 2D "quasiperiodic" arrangement of dielectrics.The photonic band problem for a perfect photonic crystal can be handled well by band theoretic methods, such as the plane wave method [9], which scales typically like the third power of the size of the system. Here, we use an equation-of-motion method [10] that employs discretization of the ...