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Transformation optics (TO)

The science of invsiiblity is enabled by taking a transformation approach on Maxwell's equation. We are interested to see how different kinds of coordinate transformations, polarization transformations can be used as the driving mechanism to manipulate light. These transformations essentially make the dispersion surfaces becomes either inhomogeneous or unconventional in their shapes


Artificial boundary appraoch
A metasurface can be treated as an effective boundary condition, which can be written down as a few parameters. A pair of such can be used to do control guided light.
Maxwell's fish eye and bending: J. Opt. 18, 044015 (2016)
Asymmetric transmission: Nat. Commn 4, 2561 (2013)
External cloak and designer cavities: ACS Photonics 5, 1749 (2018)

2D gauge transformation
An abstract rotation between TE and TM modes behaves like the U(1) gauge transformation in Schrodinger equation. The gauge field corresponds to a splitting of dispersion surfaces. A non-trivial gauge field generates pseudo-magnetic field for cyclotron motion of photon, AB effect and one-way edge states.
Phys. Rev. Lett. 114, 103902 (2015)
A cylindrical cloak and TO with asymmetric functions.
Phys. Rev. B 95, 075157 (2017) (Editor's suggestion)
Roadmap with other scientists in transformation optics:
J. Opt. 20, 063001 (2018)


Field transformation
A pure gauge for the polarization transformation (abstract rotation between TE&TM) can be used for changing impedance and polarization signature.
Example, changing PEC to a PMC with metamaterial
Phys. Rev. Lett. 111, 033901 (2013) (Editor's suggestion)
Wide angle waveplate:
Appl. Phys. Lett. 107, 241106 (2015)
Related experiment from Hao: Sci. Rep. 5, 17532 (2015)

Photonic crystal approach
Photonic crystals, although without effective medium description, can be used manipulate light based on a gardient profile of dispersion surfaces, either elliptical or square-like.
Opt. Exp. 19, 16821 (2011)

Carpet Cloak
Hiding under a carpet is much feasible at optical frequencies than hiding in the middle of air due to a less singular coordiante transformation.
Theory: Phys. Rev. Lett. 101, 203901 (2008) (Editor's suggestion)
Experiment: Nature Materials 8, 568 (2009)
Acoustics: New J. Phys. 10, 115032 (2008)

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