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. Rev. A 93, 013850 (2016) J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Diffuse vs. Ballistic Optics
Non-Reciprocal Behavior
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016) Martin Wegener
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/c0 =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 -Introduction - Experiments & Applications localized diffusive ballistic - Limitations - Diffuse Optics -Introduction - Experiments & Applications - Limitations 1 〈cos 〉
Martin Wegener C.M. Soukoulis ed., “… and Light Localization in the 21st Century”, Springer (2001)
The regime of light propagation depends on the electromagnetism mechanics thermodynamics transport mean free path length electrostatics fluid mechanics particle diffusion
⋅ 0 ⋅ Φ 0 ⋅ 0
absorptive diffusive ballistic magnetostatics linear elasticity heat conduction 3 / ⋅ 0 ⋅ 0 ⋅ 0
Schrödinger eq. electric conduction 1 〈cos 〉 ⋅ 0 ⋅ 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.
Multiple Layers → Two Layers The regime of light propagation depends on the transport mean free path length
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 -Introduction - Experiments & Applications /2 - Limitations - Diffuse Optics -Introduction - Experiments & Applications - Limitations 5 1.25 ⇒ 4.6 2.6 @ 0 4
Martin Wegener see review: G.W. Milton, “The Theory of Composites”, Cambridge Univ. Press (2002)
air water-paint reference
- Ballistic Optics -Introduction
- Experiments & Applications cloak obstacle - Limitations
- Diffuse Optics -Introduction - Experiments & Applications - Limitations
Martin Wegener
Invisible for Diffuse Light air water-paint reference btcecloak obstacle
R. Schittny et al., Science 345, 427 (2014)
Experimental Setup air water-paint reference btcecloak obstacle
L =6.0 cm, 2R1 = 3.2 cm, 2R2 =4.0cm
Solid-State Realization?
Martin Wegener 7.5% diffusive transmittance relative to undoped PDMS cuboid, D2/D0 =3.9=1.5×2.6
Recipe 1. Ceramic Accuflect® B6 [1] for core, @ L=3mm: > 99% Lambertian diffusive reflectance for wavelengths > 650nm 2. Polydimethylsiloxan (PDMS) doped
with high-quality TiO2 nanoparticles [2] for shell and surrounding, 125nm radius 3. To reduce doping concentrations, hence
increase transmittance, use R2 /R1=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, D2/D0 =3.9=1.5×2.6
Samples
Lx =15cm, Ly =8cm, Lz =3cm, R1 =0.8cm, R2 =1.2cm R. Schittny et al., Opt. Lett. 40, 4202 (2015)
Large Transmission Diffusion
Martin Wegener OSRAM Orbeos OLED module
OLED Wallpaper
2cm 2cm 2cm
metal wires All-solid-state cloak With core absorption 98% core reflectance, 9 D2/D0 = 3.9 =1.52.6 10 incident rays
R. Schittny et al., Laser Photon. Rev. 10, 382 (2016) F. Mayer et al., Adv. Opt. Mater. 4, 740 (2016)
- Ballistic Optics -Introduction - Experiments & Applications Applications - Limitations
- Diffuse Optics -Introduction - Experiments & Applications - Limitations
Martin Wegener Martin Wegener
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 780 nm, coherence length >60m, no polarizer
Reference Partial Coherence
cloak
reference
rear side illumination, laser wavelength 780 nm, 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
, d d d with
1 1 , exp 2 i d
rear side illumination, laser wavelength 780 nm, coherence length >60m, no polarizer C.A. Thompson et al., Appl. Opt. 36, 3726 (1997)
The speckle contrast depends on the spectrum of light and the path-length distribution as
- Ballistic Optics , d d -Introduction - Experiments & Applications d - Limitations with - Diffuse Optics -Introduction - Experiments & Applications 1 1 - Limitations , exp 2 i d
A. Niemeyer et al., Opt. Lett., submitted (2017) Martin Wegener
Partial Coherence
cloak
reference
polarizer in front of camera, illumination with small spot, detection at sample center
- Ballistic Optics -Introduction - Experiments & Applications - Limitations
- Diffuse Optics -Introduction - Experiments & Applications - Limitations
Martin Wegener