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# From unconventional to extreme to functional materials.

Plenary lecture of the XIV SBPMat Meeting, given by Prof. Nader Engheta (University of Pennsylvania) on September 28, 2015, in Rio de Janeiro (Brazil).

Plenary lecture of the XIV SBPMat Meeting, given by Prof. Nader Engheta (University of Pennsylvania) on September 28, 2015, in Rio de Janeiro (Brazil).

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### From unconventional to extreme to functional materials.

1. 1. From Unconventional to Extreme to Functional Materials September 28, 2015 Nader Engheta University of Pennsylvania Philadelphia, PA, USA
2. 2. 17 Equations that Changed the World Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012
3. 3. 17 Equations that Changed the World Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012 Pythagoras’s Theorem a2 +b2 = c2 Pythagoras 530 BC Logarithms log(xy) = log(x)+log(y) Neper, 1610 Calculus df dt = lim f (t + h)− f (t) h |h→0 Newton, 1668 Law of Gravity F = G m1 m2 r2 Newton, 1687 Wave Equation ∂2 u ∂t2 = v2 ∂2 u ∂x2 D’Alambert, 1746
4. 4. 17 Equations that Changed the World Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012 Euler’s Formula for Polyhedra V − E + F = 2 Euler 1751 Normal Distributions Φ(x) = 1 2πσ e − (x−µ)2 2σ 2 Gauss 1810 Fourier Transform F(ω) = f (x)e−2πixω dx −∞ +∞ ∫ Fourier 1822 Navier-Stokes Eq Navier & Stokes, 1845ρ ∂v ∂t + v⋅∇v \$ % & ' ( ) = −∇p+ ∇⋅T + f Square Root of -1 Euler, 1750i2 = −1
5. 5. 17 Equations that Changed the World Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012 Maxwell Equations ∇⋅ D = ρ ∇⋅ B = 0 ∇× E = − ∂B ∂t ∇× H = J + ∂D ∂t Maxwell 1865 2nd law of thermodynamic dS ≥ 0 Boltzmann 1874 Relativity E = mc2 Einstein, 1905 Schrodinger’s Eq. i ∂Ψ ∂t = HΨ Schrodinger 1927 Information Theory Shannon, 1949H = −∑ p(x)log p(x)
6. 6. 17 Equations that Changed the World Ian Stewart, “In Pursuit of the Unknown, 17 Equations that Changed the World”, 2012 Chaos Theory xt+1 = kxt (1− xt ) R. May 1975 Black-Scholes Eq. 1 2 σ 2 S2 ∂2 V ∂S2 + rS ∂V ∂S + ∂V ∂t − rV = 0 Black + Scholes 1990
7. 7. James Clerk Maxwell’s Manuscript Display in Royal Society, London, UK
8. 8. James Clerk Maxwell’s Manuscript Display in Royal Society, London, UK
9. 9. James Clerk Maxwell’s Manuscript Display in Royal Society, London, UK
10. 10. Light-Matter Interaction ε µ (2) ,....χ (3) χ ξ  σ
11. 11. “Natural” Materials
12. 12. “Artificially” Engineered Materials ● Particulate Composite Materials , ,h h r h rn ε µ= , ,c c r c rn ε µ= ● Composition ● Alignment ● Arrangement ● Density ● Host Medium ● Geometry/Shape
13. 13. Metamaterials Samples (2000-2015) Smith, Schultz group (2000) Boeing group Capasso group (2011) Wegener group (2009) Zhang group (2008) Atwater group (2007) Engheta group (2012)Giessen group (2008)
14. 14. Metamaterial Applications (2000-2015) Cloaking Superlens & Hyperlens Ultrathin Cavities ES AntennasTransformation Optics ENZ & MNZ Metasurfaces Metatronics
15. 15. Going to the “Extreme” in Metamaterials
16. 16. “Extreme” in Dimensionality
17. 17. From 3D Metamaterials to 2D Metasurfaces Shalaev & Boltasseva groups (2012)Capasso group (2011) Alu group (2012) Brongersma & Hasman groups (2014) Maci group (2014) Brenner group (2014)
18. 18. Ultimate Metasurface Thinnest Metamaterials http://math.ucr.edu/home/baez/graphene.jpg A. Vakil and N. Engheta, Science, 2011
19. 19. One-Atom-Thick Optical Devices ,Region 1: 0g iσ > ,Region 2: 0g iσ < 150c meVµ = 65c meVµ = mc =0.15eV mc =0.065eV A. Vakil and N. Engheta, Science, 2011
20. 20. Experimental Verification of Mid IR Surface Wave on Graphene Basov group, Nature (2012) Koppens, Hillenbrand and Garcia de Abajo, Nature (2012)
21. 21. Graphene-coated dielectric waveguide: Hybrid Graphene-Dielectric Systems A. Davoyan and N. Engheta, submitted under review 2D 3D “Meta-Tube”
22. 22. Squeezing THz energy into Nanoscale WG Ez 2D taper 3D taper A. Davoyan and N. Engheta, submitted under review
23. 23. Information Processing at the Extreme
24. 24. “Modular Blocks” in electronics L C R
25. 25. “Building Blocks” in Optics? Optics Waveguide Lens Mirror from: D. Prather's group
26. 26. “Lumped” Circuit Elements in Nanophotonics? L C R Nano-Optics ? ? ? ? ? Radio Frequency (RF) electronics
27. 27. Optical Metatronics: Materials Become Circuits Engheta, Physics Worlds, 23(9), 31 (2010) Engheta, Science, 317, 1698 (2007) Engheta, Salandrino, Alu, Phys. Rev. Lett, (2005) Sun, Edwards, Alu, Engheta, Nature Materials (2012) Electronics a λ<< ( )Re 0ε > C ( )Re 0ε < E H L ( )Im 0ε ≠ E H E H Metatronics R
28. 28. Optical Metatronics for Information Processing? f x, y,z;t( ) Metastructures g x, y,z;t( )
29. 29. Analogy between Electronics and Photonics Input(y) Output(y) R R C C CL L L C Input (t) Output (t)
30. 30. Equivalent C and L 60 nm CSiO2 18 2 10C F− ≈ × 633 nmλ = ( )Re 0ε < L Ag 15 7 10L H− ≈ ×
31. 31. First Metatronic Circuit in mid IR Y. Sun, B. Edwards, A. Alu, and N. Engheta, Nature Materials, March 2012 “empty circle”: Experimental data “Thick line”: Circuit theory “Thin line” : Full wave simulation Magenta: w ~ 75 nm, g ~ 75 nm Royal blue: w ~ 125 nm, g ~ 75 nm Red: w ~ 225 nm, g ~ 75 nm 800 1000 1200 30 40 50 60 70 80 90 14 13 12 11 10 9 8 Transmittance(%) 800 1000 1200 30 40 50 60 70 80 90 14 13 12 11 10 9 8 800 1000 1200 14 13 12 11 10 9 8 λ ( µm ) ν ( cm -1 ) 800 1000 1200 14 13 12 11 10 9 8 λ ( µm ) ν ( cm -1 ) 800 1000 1200 30 40 50 60 70 80 90 14 13 12 11 10 9 8 800 1000 1200 30 40 50 60 70 80 90 14 13 12 11 10 9 8 Transmittance(%) ParallelSeries 325nm250nm175nm
32. 32. TCO NIR Metatronic Circuits Experimental Results Caglayan, Hong, Edwards, Kagan, Engheta, Phys. Rev. Lett. 111, 073904 (2013)
33. 33. “Stereo-Circuits” Different “Circuits” for Different “Views” Alu and Engheta, New Journal of Physics, 2009 EH L C E H L C Salandrino, Alu, Engheta, JOSA B, Part 1, 2007 Alu, Salandrino, Engheta, JOSA B, Part 2, 2007
34. 34. Integrated Metatronic Circuits (IMC) Inspired by the work of Jack Kilby (1959) Integrated Metatronic Circuits F. Abbasi and N. Engheta, Optics Express, 2014 http://www.cedmagic.com/history/integrated-circuit-1958.html
35. 35. Metatronic Filter Design Y. Li, I. Liberal and N. Engheta, work in progress F. Abbasi and N. Engheta, Optics Express, 2014
36. 36. Thinnest Possible Circuits? 0iIf σ > Inductor L 0iIf σ < Capacitor C A. Vakil and N. Engheta
37. 37. Metamaterial Processors L C R Tr a λ<< ( )Re 0ε > ( )Re 0ε < ( )Im 0ε ≠ Metatronics R R C C CL L L C Electronic Processor
38. 38. Metamaterials that Do Math A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
39. 39. Input OutputGRIN(+) n1 metasurface Δ GRIN(+) w/2-w/2 n1 w/2-w/2 d Metamaterials that Do Math A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014 F. Monticone, N. Mohammadi Estakhri, A. Alù, PRL (2013)
40. 40. Metamaterial as Differentiator 0 1 -­‐5λ Width 5λ Re(Sim.)(x1.4) Im(Sim.)(x1.4) 1 0 -1 -5λ 5λ Derivative (MS) A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
41. 41. Metamaterial as 2nd Differentiator -­‐0.5 0.0 0.5 -­‐5λ Width 5λ Re(Sim.)(x3.8) Im(Sim.)(x3.8) 1 0 -1 -5λ 5λ Derivative (MS) εms y( )/εo = µms y( )/ µo = i2 λo / 2πΔ( )" # \$ %ln −iW / 2y( )( ) A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
42. 42. Metamaterial as Integrator -­‐4 -­‐2 0 -­‐5λ Width 5λ Re(Sim.)(x8.5) Im(Sim.)(x8.5) 1 0 -1 -5λ 5λ Derivative (MS) εms y( )/εo = µms y( )/ µo = i λo / 2πΔ( )" # \$ %ln iy / d( ) εms y( )/εo = µms y( )/ µo = − λo / 4Δ( )# \$ % &sign y / d( ) A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
43. 43. Metamaterial as Convolver -­‐3 0 3 -­‐5λ Width 5λ Re(Sim.)(x14) Im(Sim.)(x14) 1 0 -1 -5λ 5λ Derivative (MS) εms y( )/εo = µms y( )/ µo = i λo / 2πΔ( )" # \$ %ln i / sinc Wk y / 2s2 ( )( )" #& \$ %' A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
44. 44. Engineering Kernels Using MTM g(y) = f (y')G(y − y')dy'∫ A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014
45. 45. Metamaterial as “Edge Detector” A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, N. Engheta, Science, 343, Jan 2014 Photo: Tod Grubbs
46. 46. Metamaterial “Eq. Solvers”? Metamaterial Eq. Solver Metamaterial as a “solving” machine? ( ) ( ) df x af x dx = ( ) ( ) ( )k u x f u du af x− =∫ Informatic Metamaterials( )f x ( )df x dx
47. 47. “Extreme” Parameters and “Extreme” in Cavity Resonators
48. 48. ωn ω'n ≠ωn Conventional High-Q Cavity
49. 49. Which Material? ?
50. 50. Epsilon-and-Mu-Near-Zero (EMNZ) Materials
51. 51. How do we make such EMNZ structures?
52. 52. ENZ Structures ( )Re 0ε ≅ ITO kz =ω µ0 ε0 εr − 1 ω2 µo εo π a ! " # \$ % & 2 a z x y Bi1.5Sb0.5Te1.8Se1.2 Zheludev Group
53. 53. How do we make an EMNZ structure? M. Silveirinha and N. Engheta Physical Review B, 75, 075119 (2007) ENZ εi >1 µeff = µo Acell Ah,cell + 2πR2 J1 ki R( ) ki RJ0 ki R( ) ! " # # \$ % & & A. Mahmoud and N. Engheta, Nature Communications, Dec 2014 CT Chan’s group Nature Materials, 10, 582-585 (2011)
54. 54. 2D EMNZ Cavity I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
55. 55. 2D EMNZ Cavity I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
56. 56. 3D EMNZ Cavity εp PEC ENZ H Field E Field I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
57. 57. 3D EMNZ Cavity (A) (B) (C) ωres /ωp I. Liberal, A. Mahmoud and N. Engheta, Manuscript submitted, under review
58. 58. EMNZ in Quantum Electrodynamics Superradiance? Subradiance? Long-Range Collective States of Multi-emitters? Long-Range Entanglement? Cavity QED?
59. 59. Summary Metamaterials can perform processing, functionality at the compact scale Metamaterials can play important roles in quantum electrodynamics Sculpting waves using extreme scenarios can play interesting roles Metatronic Processing Quantum MTM One-Atom-Thick Optical Devices !
60. 60. Thank you very much