Geometry & light:! the science of invisibility!! Ulf Leonhardt"! SCNU & Weizmann Institute!
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1 " Geometry & light:! the science of invisibility!! Ulf Leonhardt"! SCNU & Weizmann Institute!!
2 Geometry and Light!
3 Review on transformation REVIEW ARTICLE optics! PUBLISHED ONLINE: 23 APRIL 2010 DOI: /NMAT2743 Transformation optics and metamaterials Huanyang Chen 1 *, C. T. Chan 2 and Ping Sheng 2 Underpinned by the advent of metamaterials, transformation optics offers great versatility for controlling electromagnetic waves to create materials with specially designed properties. Here we review the potential of transformation optics to create functionalities in which the optical properties can be designed almost at will. This approach can be used to engineer various optical illusion effects, such as the invisibility cloak. A CHAPTER 2 Transformation Optics and the Geometry of Light Ulf Leonhardt* and Thomas G. Philbin
4 Arabia!
5 Ilusions!
6 Mirage!
7 Fermat s Principle - the principle of the shortest optical path! s = n dl
8 Leonhardt 2002: Invisibility cloak?!
9 Nachman s Theorem: invisibility is impossible!
10 Invisibility: Invisible Man versus Invisible Woman! transparency! curved space!
11 Fermat s Principle - the principle of the shortest optical path! s = n dl
12 Maxwell s electromagnetism and Einstein s general relativity! The covariant free-space Maxwell equations are equivalent to electromagnetism in a material medium (Tamm, 1924; Plebanski, 1960).
13 Refraction in ordinary medium!
14 Refraction in ordinary medium: virtual image depends on viewpoint!
15 Transformation medium!
16 Transformation medium: definite virtual image!
17 Transformation medium! Virtual space! Physical space!
18 Transformation medium! Virtual space! Physical space!
19 [Leonhardt, Science 312, 1777 (2006)] Conformal! Virtual space! Physical space!
20 [Pendry, Schurig and Smith, Science 312, 1780 (2006)] Transformation! Virtual space! Physical space!
21 Maxwell s electromagnetism and Einstein s general relativity! The covariant free-space Maxwell equations are equivalent to electromagnetism in a material medium (Tamm, 1924; Plebanski, 1960).
22 Patent office!
23 Cloaking device for electromagnetic microwaves!
24 Transformation optics! [Greenleaf, Lassas and Uhlmann, Math. Res. Lett. 10, 685 (2003) electrostatics;! Leonhardt, Science 312, 1777 (2006) conformal transformations;! Pendry, Schurig and Smith, Science 312, 1780 (2006) spatial transformations;! Leonhardt and Philbin, NJP 8, 247 (2006)] space-time & negative refraction]!
25 Challenge: Broadband invisibility! Problems: * anomalous dispersion, * infinite speed of light at inner lining [Leonhardt and Philbin, New J. Phys. 8, 247 (2006)]. Ideas from Non-Euclidean Geometry
26 Optical deformation aka carpet cloaking: from fugu to flatfish!
![3D and optical implementation! [Science 328, 337 (2010)]! Three-Dimensional Invisibility Cloak at Optical Wavelengths Tolga Ergin, 1,2 * Nicolas Stenger, 1,2 * Patrice Brenner, 2 John B.](/docs-images/80/81389303/images/27-0.jpg "Pendry, 3 Martin Wegener 1,2,4 We have designed and realized a three-dimensional invisibility-cloaking structure operating at optical wavelengths based on transformation optics.")
27 3D and optical implementation! [Science 328, 337 (2010)]! Three-Dimensional Invisibility Cloak at Optical Wavelengths Tolga Ergin, 1,2 * Nicolas Stenger, 1,2 * Patrice Brenner, 2 John B. Pendry, 3 Martin Wegener 1,2,4 We have designed and realized a three-dimensional invisibility-cloaking structure operating at optical wavelengths based on transformation optics. Our blueprint uses a woodpile photonic crystal with a tailored polymer filling fraction to hide a bump in a gold reflector. We fabricated structures and controls by direct laser writing and characterized them by simultaneous high numerical-aperture, far-field optical microscopy and spectroscopy. A cloaking operation with a large bandwidth of unpolarized light from 1.4 to 2.7 micrometers in wavelength is demonstrated for viewing angles up to 60.
28 To invisibility and beyond! [Leonhardt, Nature 471, 292 (2011)]
29 Pendry s paper!
30 The resolution limit of imaging, established around 1870! Ernst&Abbe& Carl&Zeiss& O0o&Scho0&
31 Photolithography!
32 Microscopy!
33 Pendry s paper!
34 Negative refraction and perfect lens! ε = µ = g g 00 g ij ε = µ =1 ε = µ = 1 ε = µ =1 Xiang Zhang et Berkeley! [Leonhardt and Philbin, New J. Phys. 8, 247 (2006)]
35 Controversy on perfect imaging with negative refraction!
36 Poor man s perfect lens [Science. 308, 534 (2005)]!
37 Problems of negative refraction: dispersion and hence dissipation!
38 Invisibility: Invisible Man versus Invisible Woman! transparency! curved space!
39 Cloaking at a distance! [Lai, Chen, Zhang and Chan, Phys. Rev. Lett. 102, (2009)] Invisible slab! Invisible sphere!
40 The Invisible Man - cloaking at a distance! [Lai, Chen, Zhang and Chan, Phys. Rev. Lett. 102, (2009)]
41 Section Perfect imaging!
42 Maxwell and Luneburg!
43 Conformal maps!
44 Maxwell s fish eye makes a perfect lens" Maxwell 1854! Luneburg 1944: Stereographic projection!
45 Perfect imaging without negative refraction! [Leonhardt, New J. Phys. 11, (2009)] n 2n0 = 2 Index contrast: factor of 2! 1+ r / r 2 0
46 Controversy! Nature 480, (1 December 2011)!
47 Feynman s objection to the diffraction limit! Maxwell s equations are time-reversible!! But you have to inverse the source, too.!!
48 Perfect imaging with positive refraction for microwaves! [Ma, Sahebdivan, Ong, Tyc, Leonhardt, NJP 13, (2011)] ]
49 Space-time transformations: moving media! Constitutive equations of electromagnetism in a space-time geometry: Moving media
50 Space-time cloaking! Experiment: M. Fridman et al., Nature 481, (2012)!
51 Artificial black holes!
52 Ligh in 1D moving fluids! Light in 1D moving media!
53 Artificial event horizons! Piotr Pieranski!
54 Hawking radiation of black holes!
55 Moving fluids and pulse in fibre! [Philbin et al., Science 319, 1367 (2008)]
56 Fibre-optical black holes!
57 General relativity in electrical engineering! [Leonhardt and Philbin, New J. Phys. 8, 247 (2006)]
58 Einwell and Maxstein!
59 Geometry and Light!
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