Manipulating the transparency and other optical properties of metamaterials by applying a magnetic field Yakov M. Strelniker a,Ã , David J. Bergman b , Yafit Fleger a , Michael Rosenbluh a , Anna O. Voznesenskaya c , Alexey P. Vinogradov d , Andrey N. Lagarkov d a Department of Physics, Bar-Ilan University, IL-52900 Ramat-Gan, Israel b Raymond and Beverly Sackler School of Physics and Astronomy, Faculty of Exact Sciences, Tel Aviv University, IL-69978 Tel Aviv, Israel c St. Petersburg State University of Information Technologies, Mechanics and Optics, St. Petersburg 197101, Russia d Institute for Theoretical and Applied Electromagnetics, Moscow 125412 Izhorskaya 13, Russia article info Keywords: Magneto-optics Metamaterials Composite materials Extraordinary light transmission Plasmonics Raman plasmon enhancement abstract The light transmission through metallic films with different types of nano-structures was studied both theoretically and experimentally. It is shown that the positions of the surface plasmon resonances depend on nano-structural details. Those can be changed from sample to sample or in given sample by applying an external dc electric or magnetic field. The dependence of transmission spectrum on the shape of holes (inclusions) and external fields can be used for manipulation of the light transmission, as well as the polarization of the transmitted light and other optical properties, by external field. Two complementary situations are considered: a metal film with dielectric holes and a dielectric film with metallic islands. A new analytical asymptotic approach for calculation of the optical properties of such plasmonic systems is developed. & 2010 Elsevier B.V. All rights reserved. Within the past two decades, progress in nanotechnology has allowed researchers to create complex metal-dielectric structures (called metamaterials) in which the presence of the surface plasmons plays a crucial role. After the pioneering articles of Ebbesen [1], Veselago [2], Pendry [3], and others [4,5], the field of plasmonics experiences its second birth with tremendous applications in many branches of science and industry. In particular much interest is attracted to the basic research of the extraordinary light transmission (ELT) through a periodic array of sub-wavelength holes [1] and of the Raman plasmon enhancement [5]. We discuss some phenomena which can be used for manip- ulating the transmission of light through thin metal (with dielectric inclusions) and dielectric (with metal inclusions) films by applying an external magnetic field. The ELT through a metal film perforated by a periodic array of sub-wavelength holes [1] is widely believed to result from the coupling of light to plasmons [6] on the surface of the patterned metal film. Continuing this idea, the effect of an applied static magnetic field on the ELT has been discussed [7–11]. It was shown there that the applied static magnetic field shifts the surface plasmon resonance and the ELT peaks. Quite recently our predictions were verified experimentally [12]. Now the influence of a magnetic field on the ELT is under intensive study [13]. Let us consider a geometry which corresponds to ELT [1]:a metal film with a square array of identical perpendicular elliptical holes. A monochromatic light beam of angular frequency o impinges upon this film along the perpendicular axis y, with linear polarization in the x, z-plane (see Fig. 1). Following Refs. [7–11,14] we can treat the holes as dielectric inclusions embedded in a conducting host [8,15]. If the holes form a periodic lattice, as in experiments, this description is suitable, provided the lattice constant d is much smaller than the wavelength l, i.e., when the film is homogeneous on the scale of the local electromagnetic wavelength and/or local skin depth. (In the opposite case l od some other approximations can be applied [16].) In our approach, the local electric potential f ðaÞ ðrÞ is then the solution of the following partial differential equation: r  ^ e F  rf ðaÞ ¼ r  y I d ^ e  rf ðaÞ ; ð1Þ with the boundary condition f ðaÞ ¼ r a . Here r a is the a- component of r, ^ e I and ^ e F are the electrical permittivity tensors of the inclusions and the host (film), respectively, d ^ e  ^ e F  ^ e I , and y I ðrÞ is the characteristic function describing the location and the shape of the inclusions (y I ¼ 1 inside the inclusions and y I ¼ 0 outside of them) [8,15,17,18]. The host with anisotropic permittivity tensor ^ e M can be transformed to an isotropic ^ e 0 M by the following rescaling ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physb Physica B 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.01.008 Ã Corresponding author. E-mail address: strelnik@mail.biu.ac.il (Y.M. Strelniker). Please cite this article as: Y.M. Strelniker, et al., Physica B (2010), doi:10.1016/j.physb.2010.01.008 Physica B ] (]]]]) ]]]–]]]