2005 Conference on Lasers and Electro-Optics Europe

Left-handed properties of disordered metamaterialsAlexander A. Zharov 2, Ilya V. Shadrivov', and Yuri S. Kivshar'

'Nonlinear Phvsics Centre, Research School ofPhysical Sciences and Engineering,Australian National University, Canberra ACT 0200, Australia

2Institutefor Phvsics ofMicrostructures, Russian Academy ofSciences, Nizhnv Novgorod 603950, Russia

Recently fabricated composite structures [11 open unique possibilities to study experimentally the fundamental properties ofthe so-called left-handed metamaterials [2]. Specifically, such composite materials are created by arrays of wires and split-ring resonators (SRRs), and they are known to possess a negative real part of the magnetic permeability and negativedielectric permittivity in the microwave range [1]. Such composites demonstrate many unusual properties predictedtheoretically long time ago [2], including negative refraction, inverse light pressure, reverse Vavilov-Cherenkov andDoppler effects, etc. Moreover, many ideas to create such left-handed metamaterials for optical frequencies have recentlybeen suggested, and the experimental demonstrations are expected to be reported soon.

In this work, we study the etTect of weak disorder in the SRR parameters on the magnetic response of the compositestructures and the existence of the frequency domain where the composite material exhibits the specific left-handedproperties such as negative refraction. We show that even relatively small variation of the SRR parameters, which ischaracterized by a characteristic width F of the statistical distribution function, can result in a dramatic decrease of the sizeof the left-handed frequency domain (see Figs. 1 and 2) and, above a certain threshold value r=Fc, disorder can completelysuppress the left-handed properties of the metamaterial. We estimate that approximately 5% variation of the SRR slit sizescan result in complete elimination of the left-handed frequency range.

6

1 ~~~~~~~~~~4

Ac~oAa

o_ _ _ __ _ _ -- I ii

. ._. 9.4 9.6 9.8 1.0 1O. 1 0.4l c r } Frequency (GHz)

Fig. 1. Dependence of the normalized size of the left- Fig. 2. Real part of the effective magnetic permeability as ahanded frequency range on the width of the distribution function of the wave frequency for Fr0.2F, (solid), 1=0.517function F for a disorder of the SRR parameters. (dashed), and r = rc (dotted).We demonstrate that a random variation of the SRR eigenfrequencies is equivalent to some additional losses in the structure,and even for an ideal case of lossless resonators, the composite structure with random variation of the SRR frequencies isexpected to possess effective losses. From the physical point of view, such effective losses resemble the collisionlessLandau damping in plasmas caused by the presence of resonant particles.

In addition, we demonstrate that some premeditative introduction of disorder does not allow increasing the size of the left-handed frequency domain, because for any given SRR density a disorder in the eigenfrequencies results in a decrease of theeffective number of resonators, which contribute into the negative magnetization.

References1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, Phys. Rev. Lett. 84, 4184 (2000).2. V. G. Veselago, Usp. Fiz. Nauk 92, 517 (1967) [Sov. Phys. Usp. 10, 509 (1968)]

0-7803-8974-3/05/$20.00 ©2005 IEEE 568