Microwave lens design using two-dimensional 12-folded quasi-photonic crystals A. Rostami* a, b, c , H. Alipour Banaei a , A. Haddadpour a and F. Janabi-Sharifi d a Photonics and Nanocrystal Research Lab. (PNRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz 51664, Iran b School of Engineering Emerging Technologies, University of Tabriz, Tabriz, Iran c Center of Excellence for Mechatronics, University of Tabriz, Tabriz 51664, Iran d Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada ABSTRACT Two-dimensional quasi-photonic crystal as microwave focusing element is studied. The proposed structure is a random square-triangle tiling system with 12-fold symmetry and, hence, 12-fold symmetry quasi crystal. For this structure, finite difference time domain for illustration of focusing of the electromagnetic wave is used and results show that with suitable selection of crystal structure output signal is exactly the same as input one. The effective index of considered structure is near to -1. This situation is useful for small spatial dispersion that is necessary for focusing. Keywords: Quasi-Photonic Crystal, Negative Refraction, FDTD, Optical Lenses. 1. INTRODUCTION One of the appealing properties of materials with negative refractive index is their ability to focus light, microwave, and ultrasound. Conventional lenses are convex and have a converging affect on light rays. The focusing resolution of conventional lenses is limited by incident light wavelength. A light beam cannot focus to a spot with a diameter smaller than half of the wavelength. In 1967, Veselago showed theoretically that a convex lens made of a negative index material would be diverging and that a concave lens made of negative index material would be converging light. As we said the possibility to observe the negative refraction in photonic crystal and to focus light by means of a slab of photonic crystal is inevitable [1-10]. In this paper, we study the existence of these phenomena in details for some photonic quasi crystals. The 12-fold symmetric quasi crystal consists of number of dielectric cylindrical pillars organized in a Styrofoam template. The pillars are surrounded by air. Considered quasi crystal for some frequencies behaves 12-fold photonic quasi crystal (PQC) slab in many respect as a slab made from a homogeneous effective medium with an effective refractive index of approximately -1 and thus operates as a negative refractive index lens. Thus, quasi crystal sample has a negative refractive index close to -1 and is only weakly dependant on the wave propagation direction in a rather wide range of incidence angles. This all-angle negative refraction feature for PQC can make it serve as a superlens [11-18]. An enormous amount of applications based on electromagnetic field theory are proposed and realized. However, the situations for which analytical solutions can propose for the Maxwell equations are rare. With advance of computer technology and numerical methods, complex electromagnetic systems can be modeled and simulated to investigate the behavior of the propagating electromagnetic waves. Typically, for a photonic crystal the electromagnetic wave exist in a certain frequency range and/or with a certain polarization cannot propagate along certain directions in the crystal. This forbidden frequency range is called a stopgap. If the propagation of the electromagnetic wave for any crystalline direction and any polarization is forbidden, for a certain frequency range, then this forbidden frequency range is named forbidden, for a certain frequency range, then this forbidden frequency range is named a photonic band gap [19-22]. *rostami@tabrizu.ac.ir ; phone 98 411 339 3724; fax 98 411 339 3724 Optomechatronic Technologies 2008, Otani, Bellouard, Wen, Hodko, Katagiri, Kassegne, Kofman, Kaneko, Perez, Coquin, Kaynak, Cho, Fukuda, Yi, Janabi-Sharifi, Eds., Proc. of SPIE Vol. 7266, 726617 • © 2008 SPIE • CCC code: 0277-786X/08/$18 • doi: 10.1117/12.804421 Proc. of SPIE Vol. 7266 726617-1 2008 SPIE Digital Library -- Subscriber Archive Copy