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Metasurface Hologram Invisibility - ppt

Carlo Andrea Gonano's PhD thesis, titled 'A Perspective on Metasurfaces, Circuits, Holograms and Invisibility,' presents an exploration of electromagnetic metamaterials, specifically focusing on metasurfaces and their applications. The thesis includes foundational concepts, boundary conditions for Maxwell's equations, and discusses advanced topics such as scattering, holography, and invisibility cloaks. The work was submitted to Politecnico di Milano in January 2016 and highlights the design and control of electromagnetic fields using tailored metamaterial structures.

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PhD candidate: Carlo Andrea Gonano Supervisor: Prof. Riccardo Enrico Zich PhD Thesis, 28th cycle, Electrical Engineering, Politecnico di Milano, Italy A PERSPECTIVE ON METASURFACES, CIRCUITS, HOLOGRAMS AND INVISIBILITY 26th January 2016
2PhD thesis - Gonano Carlo Andrea This work was presented on 26 January 2016 for the final examination of a PhD course. Some slides have been modified or cut and the videos are currently not available. Further versions of this presentation could be published online in a next future. https://www.researchgate.net/profile/Carlo_Gonano https://polimi.academia.edu/CarloAndreaGonano Full work: Carlo Andrea Gonano, A perspective on metasurfaces, circuits, holograms and invisibility, PhD Thesis, Politecnico di Milano, 2015. The PhD thesis first-version will be soon available at the online institutional archive “POLITesi”, Politecnico di Milano, Italy. https://www.politesi.polimi.it/handle/10589/32801/advanced-search?locale=en The author retains all the rights. Milan, 6 february 2016. Notes for the reader
3PhD thesis - Gonano Carlo Andrea 1. Introduction on meta-materials and meta-surface 2. Boundary Conditions for Maxwell’s eq.s 8. Conclusions 9. Question time 3. Space Time BC 4. Radiated Plane Waves 5. Scattering and circuits 6. Holographic screen 7. Invisibility cloak Summary
4PhD thesis - Gonano Carlo Andrea 1- Introduction
5PhD thesis - Gonano Carlo Andrea Introduction on MTMs (I) • Artificial bulk material • Sub-wavelength unit cell : D x << l0 • Designed to exhibit specific properties Metamaterial definition: THIS PHD THESIS IS ABOUT METAMATERIALS…. • Properties are due to MTM’s microscopic structure, rather than to its chemical composition That is quite a general definition!
6PhD thesis - Gonano Carlo Andrea Introduction on MTMs (II) • At microscopic level, a MTM is composed by unit cells • At macroscopic level, a MTM looks homogeneous • Many kinds of metamaterials: • Acoustic • Elastic • ElectroMagnetic • Thermal • etc… Here we focus on ElectroMagnetic MTMs, specially on metasurfaces Example of DNG metamaterial’s structure by David R. Smith [1]
7PhD thesis - Gonano Carlo Andrea ElectroMagnetic MTMs • EM metamaterials can be tailored to exhibit desired permittivity e(w) and permeability m(w) e-m MTM classification • Negative refraction • Superluminal propagation • Cloaking devices DNG super-lens [1] ENZ-MNZ shell cloaking device [2] Paradoxical effects can arise or be achieved! • Etc…
8PhD thesis - Gonano Carlo Andrea Metasurfaces Metasurface: In this thesis we deal with a special class of MTM 2D metamaterial made by a single layer of unit cells Simulation of beam-redirection by M. Selvanagayam et al. [4] Many applications for antennas: • More simply, an artificial thin screen • Flat high-gain antennas • Beam-steering Spiral Leaky-wave antenna at 17 GHz by S. Maci et al. [3] • Reflect and trasmit- arrays • One-way transparent sheets • Etc…
9PhD thesis - Gonano Carlo Andrea Metasurfaces • The sources of the EM fields are electric charges and currents OK, BUT WHAT IS OUR TASK? • Control the EM fields using metasurfaces (screens) • In general, a field is generated by some sources How can we control fields? 1. Assign the desired behaviour (input- output fields) 2. Determine the required sources 3. Project the screen’s constitutive elements (e.g. circuits) • Thus, try to control the sources! BASIC DESIGN PROCEDURE:
10PhD thesis - Gonano Carlo Andrea 2- Boundary Conditions for Maxwell’s equations
11PhD thesis - Gonano Carlo Andrea Maxwell’s equations       -  t B E BT    0          t E c JB E e e T    2 0 0 0 1 / m e ( )     --    Ec t A AB A    2 0 0   A t TA         -   -   e eA A JA t A c tc   0 2 2 2 2 0 0 2 2 2 2 0 1 1 m m  “Classic” Maxwell’s eq.s in terms of E and B Maxwell’s eq.s in terms of EM potentials A and A For our purpose it’s better to rewrite them Wave eq.s Lorentz Gauge Faraday set
12PhD thesis - Gonano Carlo Andrea The advantages of EM potentials J.C. Maxwell P.A.M. Dirac, “Is there an aether?”, Nature, vol. 168, pp. 906–907, 1951 • J.C. Maxwell originally (1865) wrote his equations in terms of “Electromagnetic momentum”, that is vector potential A “It is natural to regard it [A] as the velocity of some real physical thing. Thus with the new theory of electrodynamics we are rather forced to have an aether” • Easy analogy with mechanics and fluid-dynamics • Usefulness in Relativity and need in Quantum Mechanics P.A.M. Dirac • Aharonov-Bohm effect (1959): EM potentials are not a mere math. construction Why should we use the EM potentials instead of E and H? • Numerical stability: no low-frequency catastrophe
13PhD thesis - Gonano Carlo Andrea Boundary Conditions for EM potentials (I) BCs FOR SCALAR POTENTIAL 21 12 0 n xx AA e           -   -  m ( ) 21120 nd AAe  - m surface charges surface dipole • In order to control the discontinuities for scalar potential and its gradient across a surface you need charges and dipoles:
14PhD thesis - Gonano Carlo Andrea Boundary Conditions for EM potentials (II) 21 12 ,0 n x A x A J es               -   -m ( ) 21120 nAADe  -m surface currents surface doublets • In order to control the discontinuities for vector potential and its gradient across a surface you need currents and doublets: BCs FOR VECTOR POTENTIAL
15PhD thesis - Gonano Carlo Andrea Boundary Conditions for E and B • The BCs for the Maxwell’s Eq.s in terms of E and B are: NOT ALL THE DISCONTINUTIES ARE ALLOWED… ( ) ( )    - - es e T JBBn EEn ,01221 01221 /   m e ( ) ( )   - - 0 0 1221 1221   EEn BBnT discontinuity for En discontinuity for “Bt”
16PhD thesis - Gonano Carlo Andrea Limits for the classic BCs • Need of magnetic currents for Et discontinuities The BCs written in terms of E and B have many limits: • Need of magnetic monopoles for Bn discontinuities • Fail to describe static phenomena, like the Volta Effect. • E and B can get infinite values on the boundary ( ) msJEEn ,1221  -- ( ) m T BBn - 1221  Till now, neither magnetic currents nor monopoles have ever been observed
17PhD thesis - Gonano Carlo Andrea 3- Space -Time Boundary Conditions
18PhD thesis - Gonano Carlo Andrea Space-Time Surf. Equivalence • The Extended Huygens’ principle can be applied also to space- time domains and fields     dSd vnv m  m     - dSyyd nxx )()()( ffff     mm  )- mm   yxN (1 Theorem for space-time Surface Equivalence • Theorem for space-time gradient and normals (vector case): • Green’s function for Wave eq.:
19PhD thesis - Gonano Carlo Andrea Space-Time (N+1)-normals 0m mdxn 1m mnn domain “at rest” “moving” domain time-like (N+1)-normal 1-m mnn space-like (N+1)-normal ACTUALLY “UNITARY” AND PERPENDICULAR TO SPACE-TIME BOUNDARY…
20PhD thesis - Gonano Carlo Andrea Relativistic notation for Maxwell’s eq.s mm  m JA 0    -  mmm m m AAF A 0        A c A A  0m (N+1)-potential        e e J c J  0m (N+1)-current         -  BcE cE F T 0 0 / /0   m EM tensor
21PhD thesis - Gonano Carlo Andrea Charges and currents in Space-Time mm vQI e 0,
22PhD thesis - Gonano Carlo Andrea Dipoles and doublets in Space-Time • Relativistic net doublet: ( ) mmm 21,1,2, 2 1 xIIDnet D-
23PhD thesis - Gonano Carlo Andrea Relativistic BC for EM fields ( ) mmm m 21,1,2,0 nAAD --( ) 21,1,2,,0  mmm m nAAJ s - What is it useful for? • Scattering for moving bodies (e.g. RADARs) • Echo-Doppler systems (e.g. telemeters) • Study of plasmas (e.g. MHD numerical simulations ) • Relativistic Quantum Mechanics This form is analogous to the one found for space BCs! (N+1)-current doublet tensor
24PhD thesis - Gonano Carlo Andrea 4- Radiated plane waves
25PhD thesis - Gonano Carlo Andrea Planar radiating screen • Once we know the sources, we calculate the radiated fields Radiated electric and magnetic fields xki ss T t eJJ  D  0 xki es n T enDJ k iA   D       - 1 210001 1 2 1 m xki es n T enDJ k iA   D        2 210002 1 2 1 m Sources Radiated vector potential 111 0 1 1 Akk k IsE        -- xki ee T t eDD  D  0 222 0 2 1 Akk k IsE        --  11 0 1 1 AkiH   m  22 0 2 1 AkiH   m
26PhD thesis - Gonano Carlo Andrea Radiated plane waves
27PhD thesis - Gonano Carlo Andrea Symmetric radiating screen 0;//;60.0 0  etst DkJkk  xki T eA  D1 10 xki T eA  D2 20 (video)
28PhD thesis - Gonano Carlo Andrea Anti-symmetric radiating screen test knDJkk  //;0;60.0 210  xki T eA  D1 10 xki T eA  D2 20 (video)
29PhD thesis - Gonano Carlo Andrea Leaky plane waves
30PhD thesis - Gonano Carlo Andrea Symmetric leaky wave 0;//;02.1 0  etst DkJkk  xki T eA  D1 10 xki T eA  D2 20 (video)
31PhD thesis - Gonano Carlo Andrea Anti-symmetric leaky wave test knDJkk  //;0;02.1 210  xki T eA  D1 10 xki T eA  D2 20 (video)
32PhD thesis - Gonano Carlo Andrea 5- Scattering and circuits
33PhD thesis - Gonano Carlo Andrea Finite circuit screen HOW IS THE SCREEN MADE? • The BCs for EM potentials tell us the screen should have 2 layers • Small finite width: D x < l0 /(2p) • Circuits are often used to model or project MTMs • We have to assign the desired behaviour for the metasurfaces • Need to define scattering properties • Need to determine the constitutive elements (e.g. impedances)
34PhD thesis - Gonano Carlo Andrea Scattering theory VERY BRIEF SUMMARY… EJ Y tr,0intr EEE  S J-Eirr irrZ • Assign the desired scattering (input-output): • Derive the radiation law from the BCs: • Need to determine the control law: Thus we have a constitutive relation • …after some calculi: 1 0 ))(( - -- SISSYZirr • Y can be interpreted as an “admittance” matrix material or circuit
35PhD thesis - Gonano Carlo Andrea Circuit model Thin screen with assigned e and m                    D D H E i H E r r 0 0 210 21 0 0 e m   • Constitutive relations for thin screen: • Boundary Conditions:                      D D       -       H E i H E D J ec s 0 0 210 21 0 01 101 0    100 D xk • Circuit variables EyV D ( ) zJII D 12 ( ) eD x z II D D - 212 z yx L D DD  00 m y zx C D DD  00 e ( ) ( ) ( ) ( )   --  122 1 12 21122 1 IIZVV IIZVV M E circuit relation
36PhD thesis - Gonano Carlo Andrea Circuit screen (I) • Solution for a symmetric 2-layer screen: symmetric component0 1 1 1 sC Z r E -  e 0 r 1 LsZ r M m m -  MZ 2 1 MZ 2 1 EZ anti-symmetric component Circuit unit cell Important: active elements, like negative capacitors and inductors, are required for some values of e and m WHICH IMPEDANCES SHOULD BE INSTALLED ON THE SCREEN?
37PhD thesis - Gonano Carlo Andrea Circuit screen (II) ( ) ( )21122 1 IIZVV E  ( ) ( )122 1 12 IIZVV M -- symmetric anti-symmetric
38PhD thesis - Gonano Carlo Andrea Bulk screen • Screens or bulk MTMs are composed by assembled unit cells 3D anisotropic impedance star 3D anisotropic impedance octahedron
39PhD thesis - Gonano Carlo Andrea 6- Holographic screen
40PhD thesis - Gonano Carlo Andrea Holographic metasurface Ray model Wave model • Huygens’ principle: equivalent surface source distribution MAPPING A 3D FIELD ON A 2D SURFACE • Basic surf. sources for EM fields: currents J and doublets De
41PhD thesis - Gonano Carlo Andrea Holographic pixel • Subwavelength pixels : • Visible spectrum: l0 = 380 - 750 nm )2/(0 plDy nm40Dy • Holographic image (30 cm x 40cm): nanopixel NEED TO COMPRESS THE INFORMATION! !nanopixels105,7 13  TeraBytes!900• Excessive amount of data! • Assign spatial, chromatic and angular resolutions angular resolution N=9 • In fact, a pixel can look different depending on the viewpoint IDEA: pixel phased array
42PhD thesis - Gonano Carlo Andrea Macropixel: phased array • Pixel radiated fields 21 0 0- nD c s E eIRR    JnH IRR  -21  xki t eJyxJ  D  0),( xki ee t eDyxD  D  0,),( Compressing the information… • Spatial res: 1 mm? • Phased array sources • Angular res. N : 28 kx, 28 ky • Chromatic res.: 12 Byte/macropixel • Holographic image (30 cm x 40cm): GigaBytes120
43PhD thesis - Gonano Carlo Andrea 7- Invisibility cloak
44PhD thesis - Gonano Carlo Andrea Invisibility in popular culture FROM MYTHS AND MAGIC TO SCIENCE FICTION
45PhD thesis - Gonano Carlo Andrea Transparency and light deflection HOW CAN WE MAKE AN OBJECT INVISIBLE? • Two main techniques (and their combinations): optical transparency light deflection • Conditions required for a cloaking device: • No reflection and no refraction • No shading (no absorption) • No emission unperturbed outer light field
46PhD thesis - Gonano Carlo Andrea Invisibility by transparency • The light interacts with the cloaked object, passing through it • The object has the same impedance and refractive index of the surrounding medium: ;0  0cc  • Pirex bottle filled with and merged in glycerin      0 47.1 mmm GLYPIR GLYPIR nn Classic experiment:      GLYPIR GLYPIR cc 
47PhD thesis - Gonano Carlo Andrea Scattering cancellation (I) • Achieving bulk transparency by scattering cancellation • The cloaking shell produces a destructive interference • Opposite dipole oscillation: • Problem: this technique works well just if you know in advance the scattering properties of the cloaked object      0 0 21 21 mm pp  • In some cases negative e2 and/or m2 could be mandatory  ENG, MNG or DNG metamaterials! • Need to cancel higher-order terms (e.g.: quadrupole moments) 0,0  me
Andrea Alù 48PhD thesis - Gonano Carlo Andrea Scattering cancellation (II) • That technique has been deeply investigated by the groups of Nader Engheta and Andrea Alù Nader Engheta Francesco Monticone[5] [5] [6]
49PhD thesis - Gonano Carlo Andrea Invisibility by light bending SUPERLUMINAL PROPAGATION 2 2 1 12 2 )( r Rr RR R rr - -  me • Method based on Transformation Optics technique • Exact calculus of the shell material properties • Light is deflected around the cloaked object: no interaction Cloaking device by J.B. Pendry [2] • Light should travel faster inside the shell... 0 1 c k v  me w  • Need for active ENZ, MNZ metamaterials. 10  me Very difficult to achieve for a broadband optical cloak!
50PhD thesis - Gonano Carlo Andrea Cloaking device (Pendry’s concept) initial configuration transformed domain (video)
51PhD thesis - Gonano Carlo Andrea The MTM cloak experiment - 2006 • Cilindrical MTM cloak at 8-12 GHz (microwave region, l0 = 3 cm) David Schurig John B. Pendry David R. Smith [7]
52PhD thesis - Gonano Carlo Andrea Tachi’s technique • Developed by S. Tachi’s group (2003) • Retro-reflection projection technique • Problem: it works just for few viewpoints... • Not a metasurface • Easier to realize [8]
53PhD thesis - Gonano Carlo Andrea Various camouflage techiques... Well,they have some limits...
54PhD thesis - Gonano Carlo Andrea Invisibility metasurface LET’S START FROM THE DESIRED FINAL RESULT 1. Zero scattering 2. Internal shielding 3. Broadband 4. Arbitrary geometry 5. Small thickness • Now we desire to project an invisibility metasurface or screen Required properties: • Unperturbed external incident fields • Darkness inside the cloaked region (hyp: the body does not radiate)        inc inc BB EE 22 22       0 0 1 1 B E  Mathematical conditions on EM fields
55PhD thesis - Gonano Carlo Andrea BCs for invisibility What material is the screen made of? • Use the Boundary Conditions                - -           2100 0 021 2 21 0 nH E i i nD J t ec s t        100 D xk • Calculate the constitutive relations • Thin screen hypothesis:                    t t t t H E iBc D     000 1 01 1020  e • Very strange relation: the E field induces vortices De, while the H field induces currents J Tellegen material? Usually in Nature the opposite happens!
56PhD thesis - Gonano Carlo Andrea Absorber, waveguide and emitter The screen is made by a non-reciprocal material • The inner side is different from the outer one • It can behave as a perfect absorber, waveguide or emitter (!) • Amazing, but that’s consistent with the calculated scattering matrix S: absorbing wave-guiding emitting                    -   - 2 1 2221 1211 2 1 E E SS SS E E        -  0 0 lim 1 G G S G intr EE S
57PhD thesis - Gonano Carlo Andrea Invisibility circuit screen Deriving a circuit model... • From scattering to circuit constitutive relation:                    2 1 2 1 0 00 I I ZV V ( )04 1 0 00 2 4 1 0 // 1 CsL CLs sL Z - -  • Need for active non-Foster elements • Non-symmetric unit cell (as expected) • Intrinsically unstable! • Other configurations are possible
58PhD thesis - Gonano Carlo Andrea Technical difficulties OK, BUT CAN IT ACTUALLY BE CONSTRUCTED? Unfortunately, there are many serious difficulties • In my personal opinion, the answer is “no”... at least for now. • Need for nanoscale unit cells: )2/(0 plDy nm40Dy • Need for active nano-elements for broadband cloaking • Extremely high “switching” frequency: • Probable high costs for the production of a single metasurface 2 m1 cells!1025.6 14  THz7904000 f However, those are just technological and economical limits, not physical ones We cannot exclude that someday they will be overcome
59PhD thesis - Gonano Carlo Andrea WHAT HAS BEEN DONE: • Study of the metamaterial topic Conclusions • Boundary Conditions with EM potentials • Theorems for Space-time Boundary Conditions • Scattering and circuit model for a metasurface • Test for a plane infinite radiating screen INVESTIGATED APPLICATIONS: • Holographic television (3D dynamical images) • Invisibility cloak • Screen with assigned permittivity e and permeability m
60PhD thesis - Gonano Carlo Andrea THANKS FOR THE ATTENTION. ANY QUESTION? That’s all, in brief…
• The cross fertilization of sciences • Ancient metamaterials • Multi-screen system • Bulk MTM simulation 61PhD thesis - Gonano Carlo Andrea • Extended Huygens’ principle • Magnetic monopoles and currents • About invisibility • References Extra details
62PhD thesis - Gonano Carlo Andrea The whole thesis is 224 pages long, it contains over 80 figures and 1000 equations. DISCLAIMER: THIS PRESENTATION IS JUST A SUMMARY
63PhD thesis - Gonano Carlo Andrea Cross fertilization of the sciences James Clerk Maxwell “In a University we are especially bound to recognize not only the unity of science itself, but the communion of the workers in science. We are too apt to suppose that we are congregated here merely to be within reach of certain appliances of study, such as museums and laboratories, libraries and lecturers, so that each of us may study what he prefers. […]. We cannot, therefore, do better than improve the shining hour in helping forward the cross-fertilization of the sciences” J.C. Maxwell, “The Telephone”, Nature, 15, 1878
64PhD thesis - Gonano Carlo Andrea Ancient optical metamaterials • Stained glasses of the XIIIth century cathedrals Stained glasses in the Saint-Chapelle, Paris Lycurgus cup, VI Century Ag-Au alloy nanoparticle within glass • Roman “Lycurgus cup” (VIth Century) • Different colours are due to metallic nano-inclusions • Controlled massive production Plasmonic resonance!
65PhD thesis - Gonano Carlo Andrea Multi-screen system
66PhD thesis - Gonano Carlo Andrea Active screen – 1 radiating layer • Electric field radiated by 1 current sheet 0,00, 2 1 - SIRR JE   00 0,)( xxki IRRIRR eExE -   Symmetric field Wave amplitude 0 0 c k w  Wavenumber (video)
67PhD thesis - Gonano Carlo Andrea Active screen – 2 radiating layers • Electric field radiated by 2 current sheets Coherent radiation Symmetric Anti - symmetric 2 layers are always sufficient (video)
• Electric field radiated by 10 current sheets Coherent radiation phased array Other config. are possible 68PhD thesis - Gonano Carlo Andrea Active screen – 10 radiating layers (video)
69PhD thesis - Gonano Carlo Andrea Bulk MTM simulations
70PhD thesis - Gonano Carlo Andrea Bulk MTM - dielectric vacuum lossy dielectric vacuum )05.01(2.25 ir e • Slab made of a lossy dielectric. E.g.: glass panel. 1rm Incident wave Relative permittivity Relative permeability Reflected wave Transmitted wave (video)
71PhD thesis - Gonano Carlo Andrea Bulk MTM - metal vacuum metal vacuum ir 05.00e 1rm Relative permittivity Relative permeability • Metallic slab, e.g. silver mirror (non-magnetic) High reflectivity Unmatched, lossy (video)
72PhD thesis - Gonano Carlo Andrea Bulk MTM – ideal DNG 1-re 1-rm Relative permittivity Relative permeability • Ideal Double Negative material BACKWARD PROPAGATION! ,0,0  rr me Perfectly matched, no losses (video)
73PhD thesis - Gonano Carlo Andrea Bulk MTM - superluminal • Epsilon Near Zero (ENZ) material 1)Re(0  re SUPERLUMINAL PHASE VELOCITY )05.01(0.25 ir e 1rm 0 rr em (video)
74PhD thesis - Gonano Carlo Andrea Superluminal Transmission Line • In 2012 the group of S. Hrabar experimented a broadband superluminal propagation • ENZ Trasmission Line with shunted negative capacitors 0c k v  w  0c k vg     w• Superluminal phase and group velocities: Apparently, there is no contradiction with Relativity theory • The signal velocity is not superluminal (really?) [9, 10]
75PhD thesis - Gonano Carlo Andrea Extended Huygens’ principle
76PhD thesis - Gonano Carlo Andrea Fields and sources • Need to calculate the sources associated to field’s discontinuities across the surface or boundary • General relation among field f and its sources J: Jf )(S • We start considering a closed boundary dividing two domains Here the Huygens’ principle could be helpful…
77PhD thesis - Gonano Carlo Andrea Mapping a 3D field on a 2D surface The original configuration of sources J1 inside domain 1 can be replaced by an equivalent boundary distribution J1,d such that field f is unchanged outside and null inside. Extended Huygens’ Principle: THAT IS VALID ALSO FOR STATIC FIELDS! Original source configuration Equivalent boundary sources
78PhD thesis - Gonano Carlo Andrea Huygens’ principle for gravity (I) • The Extended Huygens’ principle can be applied also to static gravity • The mass is the source of the gravity field g homogeneous lumped hollow • Let’s consider three different planets having all the same mass • Spherical symmetry, but different internal “source” distribution Are these distributions equivalent outside?
79PhD thesis - Gonano Carlo Andrea Huygens’ principle for gravity (II) • Outside, the three planets generates the same gravity field g(r) homogeneous lumped hollow • The “hollow” planet can be regarded as the equivalent surface source distribution for the other two planets
80PhD thesis - Gonano Carlo Andrea Love and Schelkunoff Surf. Equivalence ( )1221, EEnJ ms  -- ( )1221, HHnJ es  - • In 1901 A.E.H. Love formulated his surface equivalence principle for EM fields • In 1936 S. Schelkunoff extended it, deriving the Boundary Conditions surf. magnetic current surf. electric current Problem: do magnetic currents exists?
81PhD thesis - Gonano Carlo Andrea Magnetic monopoles and currents
82PhD thesis - Gonano Carlo Andrea The magnetic field is not a vector • The magnetic field B is not a “true” vector, but a pseudovector • In fact, it does not respect usual vector reflection rules - C. A. Gonano, and R. E. Zich, “Cross product in N Dimensions - the doublewedge product”, Arxiv, August 2014 • In a wider, ND view, B is a matrix or tensor - C. A. Gonano, Estensione in N-D di prodotto vettore e rotore e loro applicazioni, Master’s thesis, Politecnico di Milano (2011). ijjiij AAB // - For further details, see also:
83PhD thesis - Gonano Carlo Andrea Magnetic monopoles BUT WHAT IS A MAGNETIC MONOPOLE? • Let consider field E: its “monopòles” are the electric charges, isolable and observable • A magnet generates a field B and its poles are called North and South: can they be isolated? • Problem: breaking a magnet you will not obtain two magnetic monopòles, but two magnets! • This difference between fields E and B has be known for a long time… HOWEVER, WHY THE DIVERGENCE OF B SHOULD BE ALWAYS ZERO ?
     m T e T B E  e   0/            -- t E c JB t B JE e m     2 0 0 1 m 84PhD thesis - Gonano Carlo Andrea Dirac’s symmetrisation Symmetrized Maxwell’s Equations In absence of magnetic monopòles and currents we get back the “classic” Maxwell’s eq.s and EM force • In 1931 Paul A. M. Dirac, starting from a quantistic approach, symmetrizes Maxwell’s eq.s adding magnetic monopòles and currents The generalized EM force per unit of volume is:       - EJ c BBJEf mmee  2 00 11  m 
WHY THE DIVERGENCE OF B SHOULD BE ALWAYS ZERO ? • In “A Treatise on Electricity and Magnetism” (1873) J. C. Maxwell reports that experimentally magnetic flux F(B) is always zero across a closed surface • In 1894 Pierre Curie defends the possible existence of “magnetic charge” • In early XIX cent., Gauss and Weber already considered the question • In his “Wirbelbewegung”(1858) H. von Helmholtz calculates the force exterted on a “magnetic particle” by an electric current • In 1931 Paul A. Dirac, starting from a quantistic approach, symmetrizes Maxwell eq.s adding magnetic monopòles and currents 85PhD thesis - Gonano Carlo Andrea Hystory of “magnetic particles” 85PhD thesis - Gonano Carlo Andrea
86PhD thesis - Gonano Carlo Andrea No experimental evidence • In september 2009, Science reported that J. Morris, A. Tennant et al. from the Helmholtz-Zentrum Berlin had detected a quasi-magnetic monopole in spin ice dysprosium titanate (Dy2Ti2O7) • On december 2009 at CERN started the Monopole and Exotics Detector At the LHC (MoEDAL) Nowaday, isolated “magnetic charges” have never been observed, though many experiments have been brought on to detect them A moving magnetic monopole would cause an E field, so it could be detected by measuring the current induced in a conducting ring HOW TO FIND MONOPOLES? However, this would be not sufficient to prove their existence! Magnetic current could be solenoidal!
87PhD thesis - Gonano Carlo Andrea “The invisible man”
88PhD thesis - Gonano Carlo Andrea Invisibility by transparency • The light interacts with the cloaked object, passing through it • The object has the same impedance and refractive index of the surrounding medium: ;0  0cc  • Pirex bottle filled with and merged in glycerin      0 47.1 mmm GLYPIR GLYPIR nn Classic experiment:      GLYPIR GLYPIR cc 
89PhD thesis - Gonano Carlo Andrea “The Invisible Man” by H.G. Wells “You make the glass invisible by putting it into a liquid of nearly the same refractive index; a transparent thing becomes invisible if it is put in any medium of almost the same refractive index. And if you will consider only a second, you will see also that the powder of glass might be made to vanish in air, if its refractive index could be made the same as that of air; for then there would be no refraction or reflection as the light passed from glass to air.” • The same principle was well explained by H.G. Wells in his novel “The Invisible Man” (1897): • Problem: the human body is made by many different tissues and it is not optically homogeneous... ;0  0cc 
90PhD thesis - Gonano Carlo Andrea Invisibility metasurface LET’S START FROM THE DESIRED FINAL RESULT 1. Zero scattering 2. Internal shielding 3. Broadband 4. Arbitrary geometry 5. Small thickness • Now we desire to project an invisibility metasurface or screen Required properties: • Unperturbed external incident fields • Darkness inside the cloaked region (hypothesis: the body does not radiate)        inc inc BB EE 22 22       0 0 1 1 B E  Mathematical conditions on EM fields
91PhD thesis - Gonano Carlo Andrea Internal shielding • The cloaked object could emit some radiation • Need for an internal screen in order to confine radiation inside • Common metallic mirror • A perfect internal shielding is probably impossible because of the black-body radiation • The external and the internal screen must not interact through EM field • …however, at T = 20°C the emitted visible light is very low and thus it can be neglected
92PhD thesis - Gonano Carlo Andrea [1] - J. B. Pendry, “Negative refraction,” Contemporary Physics, vol. 45, no. 3, pp. 191–202, 2004. [2] - J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science, vol. 312, no. 5781, pp. 1780–1782, 2006. [3] – S. Maci et al. "Metasurfing: Addressing waves on impenetrable metasurfaces." Antennas and Wireless Propagation Letters, IEEE ,10 pp. 1499-1502, 2011. [4] - M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Optics express, vol. 21, no. 12, pp. 14 409–14 429, 2013. [5] - A. Alù and N. Engheta, “Multifrequency optical invisibility cloak with layered plasmonic shells,” Physical review letters, vol. 100, no. 11, p. 113901, 2008. [6]- P.-Y. Chen, C. Argyropoulos, and A. Alù, “Broadening the cloaking bandwidth with non-Foster metasurfaces,” Physical review letters, vol. 111, no. 23, p. 233001, 2013. [7] - D. Schurig et al., “Metamaterial electromagnetic cloak at microwave frequencies,” Science, vol. 314, no. 5801, pp. 977–980, 2006. [8] - S. Tachi, “Telexistence and retro-reflective projection technology (RPT),” in Proceedings of the 5th Virtual Reality International Conference (VRIC2003) pp, vol. 69, 2003, pp. 1–69 [9] - S. Hrabar et al., “Negative capacitor paves the way to ultra-broadband metamaterials,” Applied physics letters, vol. 99, no. 25, p. 254103, 2011. [10] - S. Hrabar at al., “Ultra-broadband simultaneous superluminal phase and group velocities in non-Foster epsilon-near-zero metamaterial,” Applied physics letters, vol. 102, no. 5, p. 054108, 2013. References