Metamaterials

1. 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

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

3. 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. empty glass regular water, n = 1.3 “negative” water, n = -1.3 Based on definition of J.Pendry 2000

4. 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”. Positive refraction index Negative refraction index

5. Yes as a backward wave Expected refractions Is This Refraction Possible? 1 ENERGY Air Material like glass PHASE VELOCITY Metamaterial 2

6. 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) Negative Phase Backward Waves (−, −) (+, −)

7. 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 ABSORPTION NEGATIVE REFRACTION!!

8. Classification of materials DPS ENG Cloak DNG MNG

9. 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

10. y x z 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)

11. 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.

12.  vs. a /a 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

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

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

15. a w schematics of the elementary cell. w a Unit Cell Size • 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. d

16. a w schematics of the elementary cell. w a Unit Cell Size • 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) d

17. a w schematics of the elementary cell. w a Unit Cell Size 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 d

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

19. a w schematics of the elementary cell. w a Unit Cell Size • 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. d

20. 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 Perfect Lens

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

22. No tricks No Cloaking device Its not that simple

23. Cloaking device Another approach Retro-reflective Projection Technology, Optical Camouflage virtual invisibility

24. Cloaking device What we are locking for ? True invisibility

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

26. Hole in space Constant x: Constant y: Forbidden: y y’ Purely geometrical distortion of space: No material yet x’ x

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

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

29. A 3D Possibility LIGHT SOURCE OBJECT LIGHT RAYS METAMATERIAL

30. 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)

31. Thanks for your attention.