Experiments on Optical Invisibility Cloaking

Transcription

1 Experiments on Optical Invisibility Cloaking - Karlsruhe Institute of Technology (KIT), Germany - Institut für Angewandte Physik (AP), KIT, Germany - Institut für Nanotechnologie (INT), KIT, Germany - Karlsruhe School of Optics & Photonics (KSOP), KIT, Germany - Nanoscribe GmbH, Eggenstein-Leopoldshafen, Germany - Ballistic Optics Workshop Novel Optical Materials, Minneapolis (USA), March 13-17, Ballistic Optics - Ballistic Optics

2 - Ballistic Optics electromagnetism mechanics thermodynamics 3D Carpet Cloak electrostatics fluid mechanics particle diffusion 0 Φ 0 0 magnetostatics linear elasticity heat conduction Schrödinger eq. electric conduction 0 0 all from conservation laws; stationary case, locally isotropic media, E=0 in Schrödinger eq. Performing a general 3D coordinate transformation 2D Carpet Cloak,, ; 1,2,3 on, e.g., 0 leads to a new material distribution via the Jacobian 1 det M. Kadic et al., Rep. Prog. Phys. 76, (2013)

3 3D Carpet Cloak Electron Micrograph crystal: woodpile rod spacing: 350 nm bump width: 6 μm bump height: 0.5 μm cloak height: 5 μm cloak width: 50 μm Au thickness: 100 nm DLW power: 10 mw STED power: 50 mw duty cycle: 3%; 4 khz mode: HDR scale bar: 10 μm T. Ergin et al., Science 328, 337 (2010) 3D Direct Laser Writing (DLW) Direct Comparison Theory Experiment scheme not to scale, actual NA=1.4, Tolga Ergin Ray-tracing approach: T. Ergin et al., Opt. Express 18, (2010) 3D STED-DLW Lithography Dark-Field Mode Theory Experiment J. Fischer and M. Wegener, Laser Photon. Rev. 7, 22 (2013) 30-degree tilt of sample along bump axis

4 Woodpile with a=350 nm 800 nm 900 nm 750 nm 850 nm 700 nm

5 675 nm 600 nm 650 nm 575 nm 625 nm Invisibility for rays invisibility for waves (e.g., 360 sphere, non-euclidean cloak)

6 The Invisible Sphere J.C. Halimeh and M. Wegener, Opt. Express 20, 63 (2012) Tolga Ergin Non-Euclidean Cloak U. Leonhardt and T. Tyc, Science 323, 110 (2009) Tolga Ergin Experimental Raw Data Tolga Ergin carpet 700-nm wavelength

7 Resulting Phase Images Applications carpet 700-nm wavelength M.F. Schumann et al., Optica 2, 850 (2015) Control from Other Side Invisible Contacts? carpet 700-nm wavelength image source: SITEC GmbH, centrotherm website Cross Sections An Early Patent T. Ergin et al., Phys. Rev. Lett. 107, (2011) C. Vogeli and P. Nath, US Patent (1992); A. Meulenberg, J. Energy 1, 151 (1977)

8 Light Harvesting Strings (LHS) light-beam-induced current J. Schneider et al., Prog. Photovolt: Res. Appl. 22, 830 (2014) metal contact silicon wafer metal contact silicon wafer

9 For example, the Schwarz-Christoffel transformation maps a half-space onto a polygon, leading to Experimental Results ; 1 The distribution is infinitely extended and contains zeroes and singularities, all of which we truncate. We use n 0 =1.5, m=3, and two maps back to back. Samuel Wiesendanger 429 woodpile layers, a =0.8μm rod spacing, λ=1.6μm wavelength Invisible Contacts air n = n(x,y,z) y-position (µm) i =1 i =2 i refractive index n Solar Cell: Phase Irrelevant contact Si x-position (µm) Samuel Wiesendanger M.F. Schumann et al., Optica 2, 850 (2015) Dip-in Mode For normal incidence of rays, a region of width 2R 1 can be avoided using the 1D transformation ; not to scale; T. Bückmann et al., Adv. Mater. 24, 2710 (2012) analogous to Pendry s transformation of a point to a circle/sphere; timing is ignored

10 This leads to the deflection and the inclination angle Mass Fabrication? tan asin sin which can be realized by a free-form surface 0 tan d inclination angle is solution of a nonlinear differential equation, y(0) is free parameter Martin F. Schumann Electron Micrograph Contacts are Invisible 20 μm cloaked uncloaked 700nm Ag Si solar cell 1mm made in shell-writing mode imprinted via master on high-end Si solar cell (FZ Jülich), collaboration with U. Paetzold s group Optical Characterization Solar Simulator current density (ma/cm 2 ) relative improvement (%) solar cell voltage (V) angle of incidence (degrees) λ=1.3μm wavelength, normal incidence M.F. Schumann et al., submitted (2017)

11 Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? - Ballistic Optics Opinion #1: Yes Electromagnetically, an ideal invisibility cloak is equivalent to vacuum. Moving vacuum is like non-moving vacuum. Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? Opinion #2: No Seen from the laboratory frame, the moving cloak turns into a bi-anisotropic material distribution [1]. This mixes electric and magnetic responses in a very complicated manner. [1] R.T. Thompson et al., J. Opt. 13, (2011) Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? Γ, Γ Opinion #3: Yes Can Lorentz transform back and forth between laboratory frame and co-moving frame. Seen from the co-moving frame, the cloak works perfectly. ; /

12 Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? Opinion #4: No Seen from the co-moving frame, the cloak is not the same, because the frequency of light changes due to the relativistic Doppler effect and because relativity implies that even an ideal cloak must be dispersive [1]. Mathematical Description [1] F. Monticone and A. Alu, Phys. Rev. X 3, (2013) Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? Opinion #5: Yes The Doppler effect can be pre-compensated such that the frequency in the co-moving frame is equal to the cloak operation frequency. In the co-moving frame (primed), the known linear transformation [1] of a line to a cylinder leads to the tensor components (in cylinder coordinates),,,,, at the cloak operation frequency. We choose [2] and, / 2 [1] J. B. Pendry et al., Science 312, 1780 (2006); [2] PEC at inner boundary Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? This distribution is mapped onto a distribution of eigenfrequencies of two Lorentz oscillators [1], 1 Ω,,, Ω, Opinion #6: It depends. Still, in most cases, cloaking will not work. However, in (infinitely many) special cases, cloaking does work, but it becomes non-reciprocal. Ω, Ω, 10,, 1,, 10 Hamiltonian ray tracing [2] in the co-moving frame uses,,, [1] just one resonance is not sufficient; [2] D. Schurig et al., Opt. Express 14, 9794 (2006)

13 The Lorentz transformation (in 2D space) from the laboratory frame to the co-moving frame reads Speed v/c 0 =0 / / with the Lorentz factor 1 1,, Within the laboratory frame, the frequency of light will change if the direction of light changes. Speed v/c 0 =0.001 For example, for light impinging along the positive x-direction and emerging in the xy-plane, one gets the relative frequency shift Δ Δ cos corresponding to inelastic light scattering. Speed v/c 0 =0.01 Numerical Results

14 Speed v/c 0 =0.1 Speed v/c 0 =0.4 Speed v/c 0 =0.2 Speed v/c 0 =0.5 Speed v/c 0 =0.3 Can the Doppler frequency shift be pre-compensated? Yes, it can under the condition Together with the vacuum dispersion relation of light the wave vectors obeying this condition lie on a cone.

15 Diffuse vs. Ballistic Optics Non-Reciprocal Behavior Non-Reciprocal Cloaking In a medium containing random scatterers, photons have a finite scattering mean free path length 1 density of scattering centers scattering cross section v/c 0 =0.1 A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press (1978) The regime of light propagation depends on the transport mean free path length - Ballistic Optics localized diffusive ballistic 1 cos C.M. Soukoulis ed., and Light Localization in the 21st Century, Springer (2001)

16 The regime of light propagation depends on the transport mean free path length electromagnetism mechanics thermodynamics electrostatics fluid mechanics particle diffusion 0 Φ 0 0 absorptive diffusive ballistic magnetostatics linear elasticity heat conduction 3 / cos Schrödinger eq. 0 electric conduction 0 absorption limit for l from finite photon lifetime and αl=1 all from conservation laws; stationary case, locally isotropic media, E=0 in Schrödinger eq. The regime of light propagation depends on the transport mean free path length Multiple Layers Two Layers absorptive diffusive ballistic 3 / core-shell 1 3 J. Crank, The Mathematics of Diffusion, Oxford Sci. Publ. (1956) E.H. Kerner, Proc. Phys. Soc. B 69, 802 (1956) Thin Cloak Shells Feasible - Ballistic Optics cylinders spheres / see review: G.W. Milton, The Theory of Composites, Cambridge Univ. Press (2002)

17 air water-paint - Ballistic Optics reference obstacle cloak Invisible for Diffuse Light air water-paint reference obstacle cloak R. Schittny et al., Science 345, 427 (2014) Experimental Setup air water-paint reference obstacle cloak L = 6.0 cm, 2R 1 = 3.2 cm, 2R 2 =4.0cm

18 Solid-State Realization? 7.5% diffusive transmittance relative to undoped PDMS cuboid, D 2 /D 0 = 3.9= Recipe 1. Ceramic Accuflect B6 [1] for L=3mm: > 99% Lambertian diffusive reflectance for wavelengths > 650nm 2. Polydimethylsiloxan (PDMS) doped with high-quality TiO 2 nanoparticles [2] for shell and surrounding, 125nm radius 3. To reduce doping concentrations, hence increase transmittance, use R 2 /R 1 =1.5 [1] Accuratus Corporation (USA); [2] DuPont R700 (Germany), thanks to Georg Maret s group 7.5% diffusive transmittance relative to undoped PDMS cuboid, D 2 /D 0 = 3.9= Samples L x =15cm, L y =8cm, L z =3cm, R 1 =0.8cm, R 2 =1.2cm R. Schittny et al., Opt. Lett. 40, 4202 (2015)

19 Large Transmission Diffusion OSRAM Orbeos OLED module OLED Wallpaper 2cm 2cm 2cm All-solid-state cloak With core absorption D 2 /D 0 = 3.9 = % core reflectance, 10 9 incident rays metal wires R. Schittny et al., Laser Photon. Rev. 10, 382 (2016) F. Mayer et al., Adv. Opt. Mater. 4, 740 (2016) Applications - Ballistic Optics

20 Cloak Statistics of fully coherent speckles is universal J.W. Goodman, Speckle phenomena in optics: theory and applications (Roberts & Company Publ., 2007) Analysis using second-order statistics M. Koirala and A. Yamilov, Opt. Lett. 41, 3860 (2016) Andreas Niemeyer; theory: Alexey Yamilov, Missouri S&T, USA rear side illumination, laser wavelength 780nm, coherence length >60m, no polarizer Reference Partial Coherence cloak reference rear side illumination, laser wavelength 780nm, coherence length >60m, no polarizer polarizer in front of camera, illumination with small spot, detection at sample center Obstacle The speckle contrast depends on the spectrum of light and the path-length distribution as with, d d d, exp 2i 1 1 d rear side illumination, laser wavelength 780nm, coherence length >60m, no polarizer C.A. Thompson et al., Appl. Opt. 36, 3726 (1997)

21 The speckle contrast depends on the spectrum of light and the path-length distribution as with, d d d, exp 2i 1 1 d - Ballistic Optics A. Niemeyer et al., Opt. Lett., submitted (2017) Partial Coherence cloak reference polarizer in front of camera, illumination with small spot, detection at sample center - Ballistic Optics