Observation of Localized Electromagnetic Waves in Three-Dimensional Networks Of Waveguides

Abstract

We have directly observed the Anderson localized wave functions in three dimensions in a new class of photonic band gap systems. Such systems are networks made of one-dimensional waveguides. By adopting a simple scattering geometry in a unit cell, we are able to obtain large photonic band gaps. In the presence of defects or randomness, we have systematically studied the structures of transmission and the localized wave functions inside a gap. The effects due to absorption are investigated. Excellent quantitative agreements between theory and experiments have been obtained. [S0031-9007(98) PACS numbers: 41.20.Jb In the past decade, the localization of classical waves in random media has been under intensive studies [1]. Unlike electrons, the localization of classical waves is purely a result of multiple scatterings in a random environment and free from the complications arising from interaction effects. However, due to the Rayleigh scattering at low frequencies, it is more difficult to localize classical waves than to localize electrons. In 3D, waves can be localized only in certain windows in the intermediate frequency range with a minimum dielectric contrast [2]. It has been suggested that waves are more easily localized inside a gap or pseudogap of a photonic band gap (PBG) material [3]. The PBG material in its own right is of great interest and has important implications in both fundamental science and technological applications [4]. The localization of electromagnetic waves has been observed in 1D and 2D PBG materials [5,6]. For 3D systems, efforts have been focused only on wave localization in random media. The effects arising from wave localization have been reported in microwave experiments [7]. Nevertheless, a direct interpretation of localization was complicated by the presence of large absorption. Very recently, direct evidence of light localization has been reported in strong scattering media of semiconductor powders based on the size dependence of the transmission coefficient [8]. These important developments lead us to question if one can directly observe Anderson localized wave functions in 3D. For this purpose, like earlier investigations in 2D [6], we need to investigate the strongly localized states inside the gap of a PBG system, where the localization length is short. In addition, a direct measurement of the 3D wave function should be allowed in such systems.To meet these two requirements, we propose a new class of PBG systems here. Such systems are networks connected by segments of 1D waveguides [9]. There are two important advantages in such systems. First, strong scattering can be easily introduced in a unit cell to produce large full gaps in any dimension. Thus, unlike usual PBG systems, our systems do not require a material with a large dielectric constant. Second, the wave function at each node is physically accessible so that 3D localized wave functions can be probed.In our study, the coaxial cable was adopted as the 1D waveguide. The 3D network considered was in a diamond structure...

Photonic band structure of Sierpinski waveguide networks

“…With these four generations, we have already seen the main characteristics of wave transport in SNs. In order to make our results ready for experimental comparison 9 we have considered the dissipation effect by including the absorption length and the additional dissipation The frequency range of interest here is 0-500 MHz. To examine the accuracy of our numerical calculations, we check at every intermediate stage of the calculation so that the criterion TϩRϭ1 is satisfied to very high accuracy.…”

“…To simulate the experiment conditions 9 we need to incorporate an additional dissipation due to connectors into the theoretical calculation. For this purpose we add a constant ␥ to the terms zl i j , i.e., we replace zl i j by zl i j ϩ␥.…”

“…Since we have adopted two realistic parameters used in Ref. 9 for dissipation, all the results obtained here should also represent experimental measurements in a quantitative way. This paper is organized as follows.…”

“…Direct evidence of light localization has also been reported in strongly scattering media of semiconductor powders based on the size dependence of the transmission coefficient. 8 Very recently Zhang et al 9 have proposed a class of PBG systems that are networks connected by segments of 1D waveguides. By introducing randomness into such systems, they have directly observed the Anderson localized wave functions inside the photonic band gap, despite the presence of dissipation.…”

The photonic band structures of body-centred-tetragonal crystals composed of ionic or metal spheres

“…This has been so since Yablonovitch et al [1][2][3] showed that an absolute band gap prohibits the spontaneous emission of light and therefore such photonic crystals can be used to study a wide range of physical problems such as those of light localization [4][5], optical polarizers, optical filters, and micro-cavity lasers [6,7]; they also have broad potential commercial applications.…”