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Experiments on Optical Invisibility Cloaking Experiments on - Ballistic Optics -Introduction Optical Invisibility Cloaking - Experiments & Applications - Limitations Martin Wegener - Diffuse Optics - Karlsruhe Institute of Technology (KIT), Germany -Introduction - Institut für Angewandte Physik (AP), KIT, Germany - Institut für Nanotechnologie (INT), KIT, Germany - Experiments & Applications - Karlsruhe School of Optics & Photonics (KSOP), KIT, Germany - Limitations - Nanoscribe GmbH, Eggenstein-Leopoldshafen, Germany Workshop “Novel Optical Materials”, Minneapolis (USA), March 13-17, 2017 Martin Wegener - Ballistic Optics -Introduction - Experiments & Applications - Limitations - Diffuse Optics -Introduction - Experiments & Applications - Limitations → Martin Wegener - Ballistic Optics -Introduction - Experiments & Applications - Limitations - Diffuse Optics -Introduction - Experiments & Applications - Limitations → Martin Wegener - Ballistic Optics -Introduction - Experiments & Applications - Limitations - Diffuse Optics -Introduction - Experiments & Applications - Limitations Martin Wegener Martin Wegener 3D Carpet Cloak electromagnetism mechanics thermodynamics electrostatics fluid mechanics particle diffusion ⋅ 0 ⋅ Φ 0 ⋅ 0 magnetostatics linear elasticity heat conduction ⋅ 0 ⋅ 0 ⋅ 0 Schrödinger eq. electric conduction ⋅ 0 ⋅ 0 all from conservation laws; stationary case, locally isotropic media, E=0 in Schrödinger eq. 2D Carpet Cloak Performing a general 3D coordinate transformation → ,, ; 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, 126501 (2013) 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) J. Fischer et al., Opt. Lett. 36, 2059 (2011) 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, 20535 (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 Woodpile with a=350 nm Image @ 800 nm J. Fischer et al., Opt. Lett. 36, 2059 (2011) J. Fischer et al., Opt. Lett. 36, 2059 (2011) Image @ 900 nm Image @ 750 nm J. Fischer et al., Opt. Lett. 36, 2059 (2011) J. Fischer et al., Opt. Lett. 36, 2059 (2011) Image @ 850 nm Image @ 700 nm J. Fischer et al., Opt. Lett. 36, 2059 (2011) J. Fischer et al., Opt. Lett. 36, 2059 (2011) Image @ 675 nm Image @ 600 nm J. Fischer et al., Opt. Lett. 36, 2059 (2011) J. Fischer et al., Opt. Lett. 36, 2059 (2011) Image @ 650 nm Image @ 575 nm J. Fischer et al., Opt. Lett. 36, 2059 (2011) J. Fischer et al., Opt. Lett. 36, 2059 (2011) Image @ 625 nm Invisibility for rays ≠ invisibility for waves (e.g., “360° sphere“, non-Euclidean cloak) J. Fischer et al., Opt. Lett. 36, 2059 (2011) Martin Wegener 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 cloak @ 700-nm wavelength Resulting Phase Images Applications carpet cloak @ 700-nm wavelength M.F. Schumann et al., Optica 2, 850 (2015) Control from Other Side Invisible Contacts? carpet cloak @ 700-nm wavelength image source: SITEC GmbH, centrotherm website Cross Sections An Early Patent T. Ergin et al., Phys. Rev. Lett. 107, 173901 (2011) C. Vogeli and P. Nath, US Patent 5110370 (1992); A. Meulenberg, J. Energy 1, 151 (1977) 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 Experimental Results For example, the Schwarz-Christoffel transformation maps a half-space onto a polygon, leading to ; 1 The distribution is infinitely extended and contains zeroes and singularities, all of which we truncate. We use n0=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) n i =1 Solar Cell: Phase Irrelevant i =2 -position (µm) -position y i =3 @ refractive index 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 2R1 can be avoided using the 1D transformation →′ ; 0 0 2 ′ 2 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 Mass Fabrication? This leads to the deflection and the inclination angle ′ sin tan ⇒ asin which can be realized by a free-form surface 0 tan d 0 1 1 2 inclination angle is solution of a nonlinear differential equation, y(0) is free parameter Martin F. Schumann Electron Micrograph Contacts are Invisible cloaked uncloaked 20 μm Si solar cell 700 nm Ag 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 ) 2 relative improvement (%) – current density (mA/cm solar cell voltage (V) angle of incidence (degrees) λ=1.3μm wavelength, normal incidence M.F. Schumann et al., submitted (2017) Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? - Ballistic Optics -Introduction - Experiments & Applications - Limitations Opinion #1: Yes - Diffuse Optics Electromagnetically, an ideal invisibility cloak is -Introduction equivalent to vacuum. Moving vacuum is like - Experiments & Applications non-moving vacuum. - Limitations Martin Wegener Martin Wegener Will an ideal invisibility cloak still work if it moves Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? 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. Martin Wegener [1] R.T. Thompson et al., J. Opt. 13, 024008 (2011) Will an ideal invisibility cloak still work if it moves Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? 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. ; / J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) Martin Wegener Will an ideal invisibility cloak still work if it moves relative to the laboratory frame at relativistic speed? Opinion #4: No Mathematical Description 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]. [1] F. Monticone and A. Alu, Phys. Rev. X 3, 041005 (2013) J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) Will an ideal invisibility cloak still work if it moves In the co-moving frame (primed), the known linear relative to the laboratory frame at relativistic speed? transformation [1] of a line to a cylinder leads to the tensor components (in cylinder coordinates) ′ ′ , ,′ , , 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. at the cloak operation frequency. We choose [2] and / 2 Martin Wegener [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 This distribution is mapped onto a distribution of relative to the laboratory frame at relativistic speed? eigenfrequencies of two Lorentz oscillators [1] ′ , ′ 1 , , Ω, ′ Ω, ′ Opinion #6: It depends. Ω, , , 10, 1, 10 Still, in most cases, cloaking will not work. However, Ω, in (infinitely many) special cases, cloaking does work, but it becomes non-reciprocal. Hamiltonian ray tracing [2] in the co-moving frame uses ′ , ′ ′, ′ ′ , J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) [1] just one resonance is not sufficient; [2] D. Schurig et al., Opt. Express 14, 9794 (2006) Speed v/c0=0 The Lorentz transformation (in 2D space) from the laboratory frame to the co-moving frame reads 0 / / 0 ⋅ ′ 001 ′ with the Lorentz factor ′ 1 ,, 1 Martin Wegener J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) Speed v/c0=0.001 Within the laboratory frame, the frequency of light will change if the direction of light changes. 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 1 0 ′ 1 corresponding to inelastic light scattering. Martin Wegener J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) Speed v/c0=0.01 Numerical Results ′ ′ J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) Speed v/c0=0.1 Speed v/c0=0.4 ′ ′ ′ ′ J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) Speed v/c0=0.2 Speed v/c0=0.5 ′ ′ ′ ′ J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) Speed v/c0=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. J.C. Halimeh et al., Phys.
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