Robust Photonic Band Gap from Tunable Scatterers

Abstract

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...

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