1 Scientific RepoRts | 7:41869 | DOI: 10.1038/srep41869 www.nature.com/scientificreports Magnetic Fano resonances by design in symmetry broken tHz meta-foils Jianfeng Wu 1,2 , Herbert o. Moser 3 , Rujiang Li 4,5,6 , Yihao Yang 4,5,6 , Liqiao Jing 4,5,6 , Hongsheng Chen 4,5,6 & Mark B. H. Breese 7 Magnetic Fano resonances in there-dimensional symmetry broken meta-foils at tHz frequencies are theoretically and experimentally studied. sharp Fano resonances occur due to the interference between diferent resonances and can be designed by choosing geometric parameters of the meta-foil. At the Fano resonances, the meta-foil supports antisymmetric modes, whereas, at the main resonance, only a symmetric mode exists. the meta-foil is left-handed at the Fano resonances and shows sharp peaks of the real part of the refractive index in transmission with small efective losses opening a way to very sensitive high-speed sensing of dielectric changes in the surrounding media and of mechanical confguration. Fano resonance is a fundamental interference phenomenon exhibited by various diferent oscillating systems encountered in many felds including quantum physics 1 , classical electromagnetism 2 , and acoustics 3 . It is char- acterized by a peculiar asymmetric profle. Its physical origin is the superposition of a specifc narrow band resonance peak on a broad band resonance peak, which leads to constructive interference on the low-frequency side and to destructive interference on the high-frequency side. Over the past years, Fano-type resonances in metamaterials were extensively studied 4–12 . Tey were exclusively electrically excited in two-dimensional (2D) metamaterials while, for three-dimensional (3D) metamaterials in the THz range, it was considered a challenge to demonstrate Fano resonances 6 . Here, we show that the meta-foil can meet this challenge owing to its fully three-dimensional structure, the magnetic excitation and the highly efcient direct galvanic coupling between resonators. Moreover, the meta-foil ofers the inclusion of multiple Fano resonances in one specifc meta-foil depending on design. Meta-foils are three-dimensional double-negative metamaterials transmitting electromagnetic waves at characteristic resonance frequencies. Tey originate from S-string metamaterials, frst introduced in the GHz 13 domain and later extended to THz frequencies 14 . When such THz S-strings are transversally connected to each other at selected locations 15,16 , free-standing all-metal thin-layer space grids are formed. Being locally stif, yet globally fexible, they can wrap around objects like foils. Te meta-foil is unique among fexible metamaterials 17 as it is all-metal and free-standing. So, the absence of any supporting or embedding dielectric material enables the meta-foil to withstand high temperatures only limited by the melting point of the structural metal, which avoids slowing down of resonance frequencies by dielectric capacitive load, and results in excellent resistance to moisture, chemicals, and ionizing radiation. Meanwhile, a great many of diferent structures and applications of meta-foils were presented 18–22 . Te geometry of meta-foils lends itself not only to varying resonance peaks by design, but also to create a wealth of resonances in one meta-foil by either introducing diferent cell sizes 19 or by altering the sequence of interconnecting lines or by combining both. Te infuence of the sequence of interconnecting lines is the topic 1 Department of Physics, National University of Singapore, 2 Science Drive 3, 117542 Singapore. 2 Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, 117576 Singapore. 3 Karlsruhe Institute of Technology (KIT), Institute of Microstructure Technology (IMT), Postfach 3640, 76021 Karlsruhe, Germany. 4 State Key Laboratory of Modern Optical instrumentation, Zhejiang University, Hangzhou 310027, China. 5 the innovative institute of electromagnetic information and electronic integration, college of Information Science & Electronic Engineering, Zhejiang University, Hangzhou 310027, China. 6 the electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027, China. 7 Singapore Synchrotron Light Source (SSLS), National University of Singapore, 5 Research Link, 117603 Singapore. Correspondence and requests for materials should be addressed to J.W. (email: elewujf@nus.edu.sg) Received: 05 October 2016 accepted: 29 December 2016 Published: 02 February 2017 opeN