We show theoretically and experimentally that photonic band gaps can be realized using metal or metal-coated spheres as building blocks. Robust photonic gaps exist in any periodic structure built from such spheres when the filling ratio of the spheres exceeds a threshold. The frequency and the size of the gaps depend on the local order rather than on the symmetry or the global long range order. Good agreement between theory and experiment is obtained in the microwave regime. Calculations show that the approach can be scaled up to optical frequencies even in the presence of absorption.PACS numbers: 42.70.Qs Photonic band gap (PBG) is a spectral gap in which electromagnetic waves cannot propagate in any direction [1]. Recently, two promising routes have been discovered that may lead to PBG in the IR͞optical frequencies: (i) microfabrication [2] and (ii) inverse-opal and related techniques [3]. Both methods seek to create some predefined artificial structure with an interconnected array of high dielectrics. Here we propose an alternate route. Instead of emphasizing the structure, we focus on the building blocks. The building blocks we propose are spheres with a dielectric core, a metal coating, and an outer insulating layer. With multiple coatings of variable thicknesses, these coated spheres have continuously tunable scattering cross sections and resonances. In analogy with semiconductor physics, we have designable "photonic atoms" which have continuously tunable properties. Depending on how we assemble these spheres together, we can choose the crystal structure which in turn can be changed by external fields [4]. In this paper, we show by physical argument and by explicit calculation and experimentation that any periodic structure formed from such spheres can exhibit photonic band gaps. This contrasts with the conventional PBG systems where the global symmetry and the structure factors are equally important, which in turn lead to added difficulties in their fabrication.In order to handle the calculation involving spherical scatterers with metallic coating, we developed a band structure code based on the multiple scattering technique (MST) [5]. We checked our results against photonic band structures calculated using the finite-difference time domain (FDTD) method, where the convergence has been carefully monitored [6]. The test case is the photonic band structure of ideal metal spheres arranged in the diamond structure with a filling ratio f 0.31, embedded in a medium with e 2.1. This is a demanding test case since the metal spheres touch at f 0.34. With our code, we obtain a gap͞midgap frequency of 0.56 (with angular momentum up to l 7), which is in excellent agreement with that of FDTD [6]. Our result lies between their finest grid value of 0.53 and the extrapolated value of 0.56. The transmission spectra reported below are computed with the layer-MST formalism of Stefanou-Yannopapas-Modinos [7]. The agreement between the band structure code and the transmission code is excellent.Since metallic elements are invo...
A TiO(2) nanotube layer with a periodic structure is used as a photonic crystal to greatly enhance light harvesting in TiO(2) nanotube-based dye-sensitized solar cells. Such a tube-on-tube structure fabricated by a single-step approach facilitates good physical contact, easy electrolyte infiltration, and efficient charge transport. An increase of over 50% in power conversion efficiency is obtained in comparison to reference cells without a photonic crystal layer (under similar total thickness and dye loading).
We present a unified framework for the first-principles calculation of the frequency dependent shear modulus, static yield stress, and structures of dielectric electrorheological systems. It is shown that a strong (applied field) frequency dependence of the static yield stress, in good quantitative agreement with those measured experimentally, can arise from Debye relaxational effects that are typical of poor insulators. Physical upper bounds on the yield stress and the shear modulus, as well as frequencyinduced structural soft modes, are predicted. [S0031-9007(96) PACS numbers: 61.90.+ d, 41.20.Cv, Electrorheological (ER) fluids are a class of materials whose rheological characteristics are controllable through the application of an electric field. In this work, we consider a particular type of ER fluids, the dielectric electrorheological (DER) systems, defined as colloidal dispersions of dielectric particles in which the electrical response of both the solid and the liquid components is governed by linear electrostatics. Besides being a topic of general theoretical interest in itself, the DER model has been widely invoked to explain the various aspects of the ER phenomenon, such as the mechanism of chain formation [1], the solid structure under an electric field [2], and the widely observed quadratic field dependence of the yield stress [3]. In spite of these successes, however, serious gaps still exist. Among them are the lack of quantitative understanding for the observed (applied electric field) frequency and conductivity dependencies of the yield stress, and the question concerning the upper bounds of ER shear modulus and yield stress. In the absence of a first-principles account for those issues, the gaps in our understanding are the source of much speculation about the basic mechanism of the ER effect and its potential limitation(s).In this Letter, we present a general framework for firstprinciples DER model calculations that is based on the formulation of the problem as one of effective dielectric constant optimization. That is, since the operating frequencies of ER fluids are generally ,104 Hz and the typical particle size and interparticle separation are ,10 22 cm, most ER systems are in the "long-wavelength limit," or the electrostatic limit, by a comfortable margin [4]. Provided the components of the system are governed by linear response, the DER model applies, and the electrostatic free energy density is given by 2´z z E 2 ͞8p, where´z z is the component of the effective dielectric tensor along the field ͑z͒ direction [5], and E Df͞ᐉ is the applied electric field, where Df is the voltage difference and is the length of the sample. The condition of minimum free energy thus directly translates into the maximization of´z z as a function of particle configurations, plus the consideration of configurational entropy for temperature effects. Below we focus only on the case where the electrostatic energy dominates over the temperature effects. Results of our calculations show that the DER model not only ...
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