Experiments on Optical Invisibility Cloaking...Experiments on Optical Invisibility Cloaking Martin Wegener - Karlsruhe Institute of Technology (KIT), Germany - Institut für Angewandte

Experiments on

Optical Invisibility CloakingMartin Wegener

- 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

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



Martin Wegener



→

→

Martin Wegener

magnetostatics linear elasticity heat conduction

⋅ 0

all from conservation laws; stationary case, locally isotropic media, E=0 in Schrödinger eq.

⋅ 0

electrostatics fluid mechanics particle diffusion

⋅ Φ 0

electromagnetism mechanics thermodynamics

⋅ 0

⋅ 0

Schrödinger eq. electric conduction

⋅ 0

⋅ 0⋅ 0

Performing a general 3D coordinate transformation

on, e.g.,

leads to a new material distribution via the Jacobian

∙ 0

M. Kadic et al., Rep. Prog. Phys. 76, 126501 (2013)

→ , , ; 1, 2, 3

′ 1

det

Martin Wegener



3D Carpet Cloak

2D Carpet Cloak

T. Ergin et al., Science 328, 337 (2010)

3D Carpet Cloak

scheme not to scale, actual NA=1.4, Tolga Ergin

3D Direct Laser Writing (DLW)

3D STED-DLW Lithography

J. Fischer and M. Wegener, Laser Photon. Rev. 7, 22 (2013)

J. Fischer et al., Opt. Lett. 36, 2059 (2011)

Electron Micrograph

crystal: woodpilerod spacing: 350 nm

bump width: 6 μmbump height: 0.5 μm

cloak height: 5 μmcloak width: 50 μm

Au thickness: 100 nm

DLW power: 10 mWSTED power: 50 mWduty cycle: 3%; 4 kHz

mode: HDRscale bar: 10 μm

Ray-tracing approach: T. Ergin et al., Opt. Express 18, 20535 (2010)

Direct Comparison

ExperimentTheory

Dark-Field Mode

ExperimentTheory

30-degree tilt of sample along bump axis

Woodpile with a=350 nm


Image @ 900 nm


Image @ 850 nm


Image @ 800 nm


Image @ 750 nm


Image @ 700 nm


Image @ 675 nm


Image @ 650 nm


Image @ 625 nm


Image @ 600 nm


Image @ 575 nm


Martin Wegener

Invisibility for rays ≠ invisibility for waves(e.g., “360° sphere“, non-Euclidean cloak)

J.C. Halimeh and M. Wegener, Opt. Express 20, 63 (2012)

The “Invisible Sphere”

U. Leonhardt and T. Tyc, Science 323, 110 (2009)

Non-Euclidean Cloak

Tolga Ergin

Tolga Ergin

Tolga Ergin

carpet cloak @ 700-nm wavelength

Experimental Raw Data


Resulting Phase Images

Control from Other Side


Cross Sections

T. Ergin et al., Phys. Rev. Lett. 107, 173901 (2011)

M.F. Schumann et al., Optica 2, 850 (2015)

Applications

Invisible Contacts?

image source: SITEC GmbH, centrotherm website

An Early Patent

C. Vogeli and P. Nath, US Patent 5110370 (1992); A. Meulenberg, J. Energy 1, 151 (1977)

Light Harvesting Strings (LHS)

J. Schneider et al., Prog. Photovolt: Res. Appl. 22, 830 (2014)

light-beam-induced current

→

→

silicon wafer

metal contact

silicon wafer

metal contact

For example, the Schwarz-Christoffel transformation maps a half-space onto a polygon, leading to

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

; 1

Samuel Wiesendanger

Invisible Contacts

refr

act

ive

ind

ex

n

Si

air

n = n(x,y,z)

x-position (µm)

y-po

sitio

n (µ

m)

contact

i =1

i =2

i =3 @

“Dip-in” Mode

not to scale; T. Bückmann et al., Adv. Mater. 24, 2710 (2012)

Experimental Results

429 woodpile layers, a=0.8μm rod spacing, λ=1.6μm wavelength

M.F. Schumann et al., Optica 2, 850 (2015)

Solar Cell: Phase Irrelevant

For normal incidence of rays, a region of width 2R1can be avoided using the 1D transformation

analogous to Pendry’s transformation of a point to a circle/sphere; timing is ignored

→ ′ ; 0

0

2

2′

This leads to the deflection and the inclination angle

which can be realized by a free-form surface

inclination angle is solution of a nonlinear differential equation, y(0) is free parameter

0 tan d

01 1 2

tan′

⇒ asinsin

made in shell-writing mode

Electron Micrograph

20 μm

Optical Characterization

λ=1.3μm wavelength, normal incidence

Mass Fabrication?

Martin F. Schumann

Contacts are Invisible

imprinted via master on high-end Si solar cell (FZ Jülich), collaboration with U. Paetzold’s group

uncloakedcloaked

1mm

Si solar cell

700

nm

Ag

Solar Simulator

M.F. Schumann et al., submitted (2017)

angle of incidence (degrees)solar cell voltage (V)

–cu

rren

tden

sity

(mA

/cm

2)

rela

tive

impr

ovem

ent(

%)

Martin Wegener



Will an ideal invisibility cloak still work if it movesrelative to the laboratory frame at relativistic speed?

Martin Wegener


J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)

′

′

,

; /

Γ′Γ


Opinion #1: Yes

Electromagnetically, an ideal invisibility cloak is equivalent to vacuum. Moving vacuum is like non-moving vacuum.

Martin Wegener


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, 024008 (2011)


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.

Martin Wegener


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].

[1] F. Monticone and A. Alu, Phys. Rev. X 3, 041005 (2013)


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.

Martin Wegener


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.



Mathematical Description

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

[1] J. B. Pendry et al., Science 312, 1780 (2006); [2] PEC at inner boundary

′ , , ′ ,′

,

′ ,′′, ′

/ 2

This distribution is mapped onto a distribution of eigenfrequencies of two Lorentz oscillators [1]

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)

′ , ′ 1 ,

Ω , ′,

Ω , ′

Ω ,

Ω ,10, , 1, , 10

′ , ′ ′ , ′ ′ ,

The Lorentz transformation (in 2D space) from thelaboratory frame to the co-moving frame reads

with the Lorentz factor

Martin Wegener

1

1, ,

/

′

00

0 0 1⋅

/

Within the laboratory frame, the frequency of lightwill 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

corresponding to inelastic light scattering.

Martin Wegener

Δ1cos 1 0

Δ


Numerical Results


Speed v/c0=0

′

′


Speed v/c0=0.001

′

′


Speed v/c0=0.01

′

′


Speed v/c0=0.1

′

′


Speed v/c0=0.2

′

′


Speed v/c0=0.3

′

′


Speed v/c0=0.4

′

′


Speed v/c0=0.5

′

′

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.



Non-Reciprocal Behavior

v/c0=0.1

Non-Reciprocal Cloaking

′

′

Martin Wegener



Diffuse vs. Ballistic Optics

Martin Wegener

In a medium containing random scatterers, photons have a finite scattering mean free path length

A. Ishimaru, “Wave Propagation and Scattering in Random Media”, Academic Press (1978)

density of scattering centers

scattering cross section

1

The regime of light propagation depends on thetransport mean free path length

ballisticdiffusivediffusive

C.M. Soukoulis ed., “… and Light Localization in the 21st Century”, Springer (2001)

localized

1 ⟨cos ⟩



absorption limit for l from finite photon lifetime and αL=1

absorptive

3 /

1 ⟨cos ⟩


13


J. Crank, “The Mathematics of Diffusion”, Oxford Sci. Publ. (1956)

3 /

absorptive

Martin Wegener



magnetostatics linear elasticity heat conduction

⋅ 0

all from conservation laws; stationary case, locally isotropic media, E=0 in Schrödinger eq.

⋅ 0

electrostatics fluid mechanics particle diffusion

⋅ Φ 0

electromagnetism mechanics thermodynamics

⋅ 0

⋅ 0

Schrödinger eq. electric conduction

⋅ 0

⋅ 0⋅ 0

Multiple Layers → Two Layers

E.H. Kerner, Proc. Phys. Soc. B 69, 802 (1956)

“core-shell“

see review: G.W. Milton, “The Theory of Composites”, Cambridge Univ. Press (2002)

Thin Cloak Shells Feasible

cylinders spheres

/2

54

1.25 ⇒ 4.6 2.6 @ 054

1.25 ⇒ 4.6 2.6 @ 0

Martin Wegener



Invisible for Diffuse Light

R. Schittny et al., Science 345, 427 (2014)

Experimental Setup

L=6.0cm, 2R1 =3.2cm, 2R2 =4.0cm

water-paint

referenceobstacle

cloak

air

water-paint

referenceobstacle

cloak

air

water-paint

referenceobstacle

cloak

air

Martin Wegener

Solid-State Realization?

[1] Accuratus Corporation (USA); [2] DuPont R700 (Germany), thanks to Georg Maret’s group

1. Ceramic Accuflect® B6 [1] for core, @ L=3mm: > 99% Lambertian diffusive reflectance for wavelengths > 650nm

2. Polydimethylsiloxan (PDMS) dopedwith high-quality TiO2 nanoparticles [2] for shell and surrounding, 125nm radius

3. To reduce doping concentrations, henceincrease transmittance, use R2 /R1=1.5

Recipe

Lx=15cm, Ly=8cm, Lz=3cm, R1=0.8cm, R2=1.2cm

Samples

7.5% diffusive transmittance relative to undoped PDMS cuboid, D2/D0=3.9=1.5×2.6

7.5% diffusive transmittance relative to undoped PDMS cuboid, D2/D0=3.9=1.5×2.6

R. Schittny et al., Opt. Lett. 40, 4202 (2015)

Martin Wegener

Large Transmission Diffusion

R. Schittny et al., Laser Photon. Rev. 10, 382 (2016)

98% core reflectance,109 incident rays

2cm 2cm 2cm

All-solid-state cloak With core absorptionD2/D0 = 3.9 =1.52.6

Martin Wegener

Applications

OSRAM Orbeos OLED module

OLED Wallpaper

F. Mayer et al., Adv. Opt. Mater. 4, 740 (2016)

metal wires

Martin Wegener



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

Reference

rear side illumination, laser wavelength 780nm, coherence length >60m, no polarizer

Obstacle


Cloak


Partial Coherence

polarizer in front of camera, illumination with small spot, detection at sample center

reference

cloak

The speckle contrast depends on the spectrum of light and the path-length distribution as

with

C.A. Thompson et al., Appl. Opt. 36, 3726 (1997)

, d d

d

, exp 2 i1 1

d

The speckle contrast depends on the spectrum of light and the path-length distribution as

with

A. Niemeyer et al., Opt. Lett., submitted (2017)

, d d

d

, exp 2 i1 1

d

Partial Coherence

polarizer in front of camera, illumination with small spot, detection at sample center

reference

cloak

Martin Wegener



Martin Wegener



Documents

Experiments on Optical Invisibility Cloaking...Experiments on Optical Invisibility Cloaking Martin Wegener - Karlsruhe Institute of Technology (KIT), Germany - Institut für Angewandte