Experiments on Optical Invisibility Cloaking...Experiments on Optical Invisibility Cloaking Martin Wegener - Karlsruhe Institute of Technology (KIT), Germany - Institut für Angewandte
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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
Will an ideal invisibility cloak still work if it movesrelative to the laboratory frame at relativistic speed?
Martin Wegener
Will an ideal invisibility cloak still work if it movesrelative to the laboratory frame at relativistic speed?
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
′
′
,
; /
Γ′Γ
Will an ideal invisibility cloak still work if it movesrelative to the laboratory frame at relativistic speed?
Opinion #1: Yes
Electromagnetically, an ideal invisibility cloak is equivalent to vacuum. Moving vacuum is like non-moving vacuum.
Martin Wegener
Will an ideal invisibility cloak still work if it movesrelative 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, 024008 (2011)
Will an ideal invisibility cloak still work if it movesrelative to the laboratory frame at relativistic speed?
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
Will an ideal invisibility cloak still work if it movesrelative 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].
[1] F. Monticone and A. Alu, Phys. Rev. X 3, 041005 (2013)
Will an ideal invisibility cloak still work if it movesrelative 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.
Martin Wegener
Will an ideal invisibility cloak still work if it movesrelative to the laboratory frame at relativistic speed?
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.
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
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
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Numerical Results
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Speed v/c0=0
′
′
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Speed v/c0=0.001
′
′
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Speed v/c0=0.01
′
′
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Speed v/c0=0.1
′
′
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Speed v/c0=0.2
′
′
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Speed v/c0=0.3
′
′
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
Speed v/c0=0.4
′
′
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
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.
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)
J.C. Halimeh et al., Phys. Rev. A 93, 013850 (2016)