Journal of Magnetism and Magnetic Materials 300 (2006) 29–32 An experimental study of the properties of magnetoinductive waves in the presence of retardation A. Radkovskaya a , M. Shamonin b , C.J. Stevens c , G. Faulkner c , D.J. Edwards c , E. Shamonina d , L. Solymar e,Ã a Faculty of Physics, M.V. Lomonosov Moscow State University, Vorob’evy Gory, 119992 Moscow, Russia b Department of Electrical Engineering and Information Technology, University of Applied Sciences, Regensburg D-93025, Germany c Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK d Department of Physics, University of Osnabru ¨ ck, Osnabru ¨ ck D-49069, Germany e Department of Electrical and Electronic Engineering, Imperial College, London SW7 2BT, UK Available online 16 November 2005 Abstract Magnetoinductive (MI) waves owe their existence to the magnetic coupling between metamaterial elements. First experiments confirming the existence of MI waves were carried out on capacitively loaded loops and Swiss Rolls about three orders of magnitude smaller than the operating wavelengths (5–15 m) so that the radiation effects did not play any significant role. In the present paper MI waves are studied experimentally on various types of split ring resonators of about 1 cm diameter operating in the microwave region between 1 and 2 GHz. Our results prove that retardation has a significant effect upon the propagation of MI waves. r 2005 Elsevier B.V. All rights reserved. PACS: 41.20.jb; 81.05.zx; 84.30.bv Keywords: Metamaterials; Split ring resonators; Magnetoinductive waves; Retardation 1. Introduction Waves propagating on coupled LC circuits were investigated by Atabekov [1] and Silin and Sazonov [2] in the 1960s as simple examples of periodic filters and slow wave structures, respectively. The properties of these waves were studied in more detail [3–6] four decades later as a by- product of the research on metamaterials. Due to the coupling between the elements they were called magne- toinductive (MI) waves. Applications as waveguides [7,8], delay lines [9], phase shifters [10] and lenses [11] have already been proposed. Experiments confirming the ex- istence of MI waves were conducted in the MHz region on arrays consisting of capacitively coupled loops and of ‘Swiss Rolls’ [5,6]. The aim of the present paper is to extend the detailed experimental studies to a higher frequency region at which the size of the structure can no longer be regarded as small relative to the electromagnetic wavelength. The elements investigated belong to the broader family of split ring resonators (SRRs), introduced by Hardy and Whitehead [12]. They were made popular by Pendry et al. [13] who proved that they can, in a certain frequency range, offer negative effective permeability. 2. The elements We have looked at the properties of two types of elements. SRRs on a dielectric substrate as proposed by Pendry et al. [13], and a more recent realization [14] using short metallic pipes of 5 mm height. The dimensions and resonant frequencies of the five elements investigated are shown in Table 1. They will be referred to as A d , B d , A p , B p and C p . The subscripts d and p stand for dielectric and pipe samples, respectively. Note that A d and A p are doubly split double rings, B d and B p are singly split double rings with the outer ring open and C p is a split single ring. They can be ARTICLE IN PRESS www.elsevier.com/locate/jmmm 0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.10.026 Ã Corresponding author. E-mail address: laszlo.solymar@eng.ox.ac.uk (L. Solymar).