Quasicrystal structure in metamaterials regime - Presentation.pdf · [5] Rybin et al., Nat....

References[1] Li, Kivshar, Rybin, ACS Photonics (2018)[2] X. Huang et al., Nat. mat. 10, 582–586 (2011).[3] J.-W. Dong et al., PRL 114, 163901 (2015).

Ekaterina E. Maslova1, Mikhail V. Rybin1,2

Quasicrystal structure in metamaterials regime

1Department of Physics and Engineering, ITMO University, St Petersburg 197101, Russia

2Ioffe Institute, St. Petersburg 194021, Russia

[email protected]

Introduction Theory Penrose tilling Transmission Phase transition Conclusion

Typical band diagram for metamaterialsTypical band diagram for photonic crystal

Photonic phase transition

Periodic structures

Quasicrystal structures

Homogeneous mode is observedin the samples, which confirmsthe transition of the quasicrystalstructure to the metamaterialmode.Analyze homogeneous mode, weconstructed phase diagram.

Quasicrystal

Metamaterial

Penrose lattice

Band diagrams are not existingin quasicrystal structures andwe cannot see polaritonicfeature in the metamaterialregime.

Polaritonic feature

Introduction Theory

References[5] Rybin et al., Nat. Comm.(2015)

Photonic phase transition in periodic structures

References[4] Li, Kivshar, Rybin, ACS Photonics (2018)

Polaritonic feature

Ekaterina E. Maslova, Mikhail V. Rybin


Polaritonic feature is a criterion of metamaterials

Typical band diagram for metamaterials

Typical band diagram for photonic crystal

Filling ratio

Die

lect

ric

ind

ex

r/a - scenario

ε - scenario

Phase transition ConclusionPenrose tilling Transmission

Phase diagram “photonic crystal –metamaterial” for a square lattice ofdielectric cylinders. TE polarization. Thedielectric constant ε of variousmaterials is indicated by the horizontallines.

The first way to makemetamaterials is thedecreasing lattice constantand the second one is theincreasing dielectricpermittivity.

Structural factorPenrose tilling generate



Introduction Theory Phase transition ConclusionPenrose tilling Transmission

Penrose lattice

Hexagonal lattice

Square lattice

Real space Reciprocal space

References[6] M. Chodyn et al., Acta Cryst. (2015). A71, 161–168

The projection ofunit cell of a 5Dhypercubic latticeinto 3D space inthe form of anicosahedron.

Penrose tilling

For quasicrystals maxima in the reciprocalspace become very dense including the areaaround the origin. As a result multipole Braggbands appear in the low frequency range.

Projection method toconstruct of one-dimensionalquasicrystals of theFibonacci type.

Transmission spectrum




Transmission spectra for (a) photonic crystal, (b) quasicrystal;metamaterials: (c) periodic structure, (d) quasicrystal structure.

Dependence of minimum of transmission on number of rods. The transportregime in a quasicrystal is not the same as in the periodic structure; therefore,the close arrangement of diffraction maxima does not prohibit the existenceof a metamaterial regime.

Photonic phase transitionHomogeneous mode




Photonic phase diagram for structure withPenrose lattice.

Distribution of field for structures with Penrose latticefor different values of parameter s.(a)-(c) photonic quasicrystals, (g)-(i) metamaterials.

(a)

ε = 12

ε = 50

ε = 100

1. The transport regime in a quasicrystal is not the same as in the periodic structures.2. The appearance of a homogeneous mode confirms the transition of the quasicrystal

structure to the metamaterial regime.3. We constructed phase diagram “quasicrystal - metamaterial”.

[email protected]

Ekaterina E. Maslova1, Mikhail V. Rybin1,2


1Department of Physics and Engineering, ITMO University, St Petersburg 197101, Russia

2Ioffe Institute, St. Petersburg 194021, Russia

[email protected]

Introduction Theory Penrose tilling Transmission Phase transition Conclusion

Quasicrystal structure in metamaterials regime - Presentation.pdf · [5] Rybin et al., Nat....

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