Metamaterials Aos Al-waidh Photonics in Engineering Research Group General Engineering Research Institute Liverpool John Moores University E-mail: A.M.Al-Waidh@2009.ljmu.ac.uk

Outlines Introduction to metamaterials Classification of materials Photonic Crystal Realisation of Metamaterials Unit Cell Size Metamaterial Application Cloaking Conclusions

Introduction To Metamaterials Metamaterials are periodic or quasi-periodic, sub-wavelength metal structures. The electro-magnetic material properties are derived from its structure rather than inheriting them directly from its material composition. He showed that an open ring (C shape) which axis is in the propagation direction could provide a negative permeability . In the same paper, he showed that a periodic array of wires and ring could endow with negative index. The analogy is as follows: Natural materials are made of atoms, which are dipoles. These dipoles modify the light velocity by a factor n (the refractive index). The ring and wire units play the role of atomic dipoles; wire acts as a ferroelectric atom, while the ring acts as an inductor L and the open section as a capacitor C. So the whole ring can be considered as a LC circuit. When the electromagnetic field passes through the ring, an induced current is created and the generated field is perpendicular to the magnetic field of the light. There is a magnetic resonance so the permeability is negative, and the index is negative too. empty glass regular water, n = 1.3 “negative” water, n = -1.3 Based on definition of J.Pendry 2000

Introduction To Metamaterials This term is particularly used when the resulting material has properties that are not found in naturally formed substances as indicated by the prefix “meta”. Negative refraction index Positive refraction index

Is This Refraction Possible? Yes as a backward wave Is This Refraction Possible? Expected refractions 1 ENERGY Air Material like glass PHASE VELOCITY Metamaterial The concept of “Left Handedness” or “Double negative nature” of metamaterials was originally discussed by Veselago way back in 1968 . He put forth the theory that the direction of phase of an EM wave would be opposite to that of the energy flow in a medium that exhibits negative permittivity and permeability simultaneously. He suggested that in such materials the electric filed E, the magnetic field H and the wave vector K form a left handed set of vectors which is why they are termed as “Left-Handed materials”. Because of the lack of any experimental evidence this theory remained as a mere prediction, until recently when Pendry et.al proposed an artificial material consisting of an array of split-ring resonators (SRRs) and thin wires. 2

Classification of materials OR μ 1 (+, +) (−, +) Positive Phase Forward Waves Propagating Standard optical materials Evanescent Metals (UV – Optical) 1 n<1 ε Propagating Metamaterials Evanescent Natural magnetic materials (up to GHz) A medium with the permittivity greater than zero and permeability less than zero (ε > 0, μ < 0) will be designated a mu-negative (MNG) medium. In certain frequency regimes some gyrotropic materials exhibit this characteristic. A medium with both permittivity and permeability less than zero (ε < 0, μ < 0) will be designated a DNG medium or left-handed media (LHM). Negative Phase Backward Waves (−, −) (+, −)

Classification of materials μ POSITIVE REFRACTION ABSORPTION (ENG) ε < 0, μ > 0 Plasma (DPS) Dielectrics ε (DNG) ε < 0, μ < 0 Not found in nature (MNG) ε > 0, μ < 0 Gyrotropic A medium with both permittivity and permeability greater than zero (ε > 0, μ > 0) will be designated a double-positive (DPS) medium. Most naturally occurring media fall under this designation. A medium with permittivity less than zero and permeability greater than zero (ε < 0,μ > 0) will be designated an epsilon-negative (ENG) medium NEGATIVE REFRACTION!! ABSORPTION

Classification of materials ENG DPS Cloak DNG MNG

Realisation of Metamaterials Negative ε Thin metallic wires are arranged periodically Effective permittivity takes negative values below plasma frequency Negative μ An array of split-ring resonators (SRRs) are arranged periodically

Realisation of Metamaterials Embedding a metal split-ring and a metal rod creates left-handedness Realisation of Metamaterials ISRR Hx Ey IROD Magnetic resonance (Negative μ) Electric resonance (Negative ε) y x z

Photonic Crystal Another example of composite material with negative refraction index is the photonic crystal: Photonic crystals may behave as if they possess a negative refractive effect without actually having a negative refractive index. Additionally, e and μ are not defined for photonic crystals as they are not homogeneous systems at their operational wavelength.

 vs. a /a 0 1  a <<<    a a >>  Effective medium 0 1  a <<<    a a >>  Effective medium description using Maxwell equations with µ and  Example: Metamaterials Properties determined by diffraction and Interference Example: Photonics crystals Properties described using geometrical optic and ray tracing Example: Lens system Shadows

The right hand rule Not this one If then is a right set of vectors:

The left hand rule ! Not this one If then is a left set of vectors:

Unit Cell Size a w schematics of the elementary cell. d A simple calculation can be carried out to verify the UV laser capability to create the required size. Mostly the open ring resonator can be considered as an LC circuit where the capacitance can described by the usual textbook formula.

Unit Cell Size a w schematics of the elementary cell. d For a large capacitor with the separation between the plates is small compared to the dimensions of the plates, to ensure a uniform distribution of the field over plate’s area: C ∝ plate area/distance And the inductance by the formula for a coil with N windings: L ∝ coil area/length (for N = 1)

Unit Cell Size a w schematics of the elementary cell. d For simplicity, we can consider the width of the metal is equal to the distance between the capacitor plates (a) C = oc ad/a where: c = the effective permittivity of the material in between the plates and d= the metal thickness L = o w2/d where: W= width = length of the coil

Unit Cell Size d LC-resonance frequency: LC = 1/ = Where c = w schematics of the elementary cell. d LC-resonance frequency: LC = 1/ = Where c = And the LC-resonance wavelength LC =

Unit Cell Size For relevant parameters c ≈ 3.5 w schematics of the elementary cell. d For relevant parameters c ≈ 3.5 this yield LC ≈ 10 ×w. Thus, for microwave wavelength of  ≈ 10 mm, the linear dimension of the coil would need to be on the order of w = 1 mm, implying minimum feature sizes around 200.

Metamaterial Application Negative phase velocity, reversal of Doppler Effect and Backward Cerenkov radiation are interesting novel physical properties emerging from left-handed metamaterials phenomena. The Doppler effect, named after Christian Andreas Doppler, is the apparent change in frequency or wavelength of a wave that is perceived by an observer moving relative to the source of the waves. Cherenkov radiation (also spelled Cerenkov or sometimes Čerenkov) is electromagnetic radiation emitted when a charged particle passes through an insulator at a speed greater than that of light in the medium. The Perfect Lens

Metamaterial Application Cloaking device Is it real, how? Can I borrow your cloak to get my PhD ?

Cloaking device Its not that simple No tricks No

Cloaking device Retro-reflective Projection Technology, Optical Camouflage Another approach virtual invisibility The cloak is made of rrt materials First a digital camera captured the seen behind the person wearing the cloak then Hi tech approaches that use cameras and projectors

Cloaking device What we are locking for ? True invisibility If we can control light to bend backward or around the object and not reflect back to our eye, they will appear invisible

creating a new material The idea is to create a region We need to manipulate space To be realised by creating a new material The idea is to create a region that is inaccessible 25

Hole in space y’ y x x’ Purely geometrical distortion of space: Constant x: Constant y: Forbidden: Purely geometrical distortion of space: No material yet Use transformation optics. In this method we consider space, represented here by a Cartesian coordinate system, and mathematically create a hole in the fabric of space, and distort the coordinate system. The pink circle now represents our cloaked region which is invisible because the space that the light travels in has been deformed, and therefore no light can be scattered from it. The simple mathematical calculation that has been performed is then applied to Maxwell's equations. In order to retain the invariance of Maxwell’s equations, the properties of the transform are subsumed into a new form of spatially dependent permittivity and permeability, which now give the same cloaking effect as creating the hole in space. x x’

Transformation of a region Preserve form of Maxwell’s equations Realisation Transformation of a region Preserve form of Maxwell’s equations Predict form of permittivity and permeability to use in the original frame for cloaking

Fill the original empty space with this material The cloak Fill the original empty space with this material Now we have a cloaking device

A 3D Possibility LIGHT SOURCE OBJECT LIGHT RAYS METAMATERIAL

Conclusions Meta-materials have been shown to have remarkable applications LHM s and negative e materials can be used to overcome diffraction limit and construct a super-lens A super-lens enables ultra-deep sub-surface imaging Very new field, lots of work to do (theory and experiments)

Thanks for your attention.