1. TOROIDAL RESPONSE IN DIELECTRIC METAMATERIALS
Ε. Ν. Εconomou
IESL, FORTH, Dept of Physics, U of Crete
Spetses, June 4, 2015

2. WORK BY A. A. Basharin 1,2, M. Kafesaki 1,3, E. N. Economou 1,4, C. M
WORK BY A. A. Basharin 1,2, M. Kafesaki 1,3, E. N. Economou 1,4, C. M. Soukoulis 1,5, V. A. Fedotov 6, V. Savinov 6, and N. I. Zheludev 6,7
1Institute of Electronic Structure and Laser (IESL), Foundation for Research and Technology Hellas (FORTH), P.O. Box 1385, Heraklion, Crete, Greece 2National Research University “Moscow Power Engineering Institute,” Moscow, Russia 3Department of Materials Science and Technology, University of Crete, Heraklion, Greece 4Department of Physics, University of Crete, Heraklion, Greece 5Ames Laboratory-USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA 6Optoelectronics Research Centre and Centre for Photonic Metamaterials, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom 7Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore , Singapore

3. OUTLINE Toroidal dipole/polypoles Outline of derivation
Metallic MMs with toroidal dipole
Polar dielectric MMs with toroidal dipole
Resonances, results and comments

4. In books of EM the radiation energy per unit time, J, is given in terms of electric and magnetic polypoles:
The dipoles P M
The quadropoles

5. There is though a third type of polypoles: The toroidal
Toroidal dipole
Toroidal dipole:
There is one more term of O(1/c5)

6. Unusual electromagnetic phenomena
High Q-factor
Optical activity & circular dichroism
Negative refraction and backward waves
Generation of waves with gauge irreducible vector potentials with no EM fields
Aharonov-Bohm Effect
The Radiation pattern P=T

7. Toroidal static dipole in nature
Why toroidal dipole?
Correct characterization of toroidal objects
Interaction with electromagnetic fields
Sensitive sensors of toroidal objects
Fundamental interest
Y. B. Zel'dovich, 1958, Parity
I. Naumov, at al., 2004, f-e-n
M. Kläui at al., 2003, f-m-r
Y. F. Popov at al., 1998, m-e
Y. V. Kopaev at al., 2009, t-Cr
L. Ungur at al., 2012, t in mo
A. Ceulemans at al., 1998, ))
A. Karsisiotis at al., 2013
For potentials without fields and Aharonov-Bohm see G. N. Afanasiev and Yu. P. Stepanovsky, J. Phys. A: Math. Gen. 28 (1995)

8. Wave Equation:

9. The charge density ρ(r,t) and the current density j(r,t) can be expanded in terms of a complete orthonormal scalar and vector sets1:
1 See E. E. Radescu and G. Vaman, Phys. Rev. E 65, (2002) and their comments

10. T. Kaelberer et al, Science 330, 1510 (2010)
Yuancheng Fan, et al. , Phys. Rev, B 87, (2013)

11. A. A. Basharin et al. Phys. Rev. X 5, 011036 (2015)

12. Polaritonic (phonon-polariton) materials
Polar crystals (e.g. NaCl) in which incident radiation excites crystal vibrations (acoustic waves) - resonant in the THz regime + + - - - E k
Phonon-polariton modes? Electromagnetic waves coupled to transverse crystal vibrations (phonons)

13. Easily obtained by eutectics self-organization approach
Polaritonic systems
Alkali-halide (2D periodic) systems of rods in a host , e.g.
LiF rods in KCl (6%LiF)
in NaCl (25% LiF)
μm scale systems (lattice const from ~2 to 30 μm)
Easily obtained by eutectics self-organization approach
Coronado et. al., Opt. Express 20, (2012)
Basharin et. al., Phys. Rev. B 87, (2013)
Massaouti et. al., Opt. Lett. 38, 1140 (2013)

14. Polaritonic material permittivity
ωΤ : transverse bulk eigenfrequency
ωL: longitudinal bulk eigenfrequency
For LiTaO3 we have
LiTaO3/LiNbO3- very promising candidates for toroidal dielectric metamaterials in THz due to high permittivity ε ~ 40 and low losses up to half the transverse eigenfrequency.

15. Magnetic moment due to Mie-resonance in high-index dielectric cylinderEz k y x m
j, Ez
A. A. Basharin et al. Phys. Rev. X 5, (2015)
Mie- resonance frequency of the single cylinder when at THz

16. (a)
(b)
(c) Ez
|H| j
-2, ,3
A. A. Basharin et al. Phys. Rev. X 5, (2015); f=1.89 THz

17. A. A. Basharin et al. Phys. Rev. X 5, 011036 (2015)
Normalized power reflected by multipoles, a.u.
A. A. Basharin et al. Phys. Rev. X 5, (2015)

18. Magnetic quadrapole, (a) (b) (c) Ez |H| j -4.4 4.4 0 21.1 -175.2 175.2
A. A. Basharin et al. Phys. Rev. X 5, (2015); f=1.95 THZ

19. Dependence on the angle of incidence
A. A. Basharin et al. Phys. Rev. X 5, (2015); fres. tor. =white bar

20. Cylinders of finite length
(a)
(b)
(c) Ez
|H| j
-2, ,2
A. A. Basharin et al. Phys. Rev. X 5, (2015); at f=1.87 THz

21. TE polarization
A. A. Basharin et al. Phys. Rev. X 5, (2015); f=1.95 THZ

22. CONCLUSIONS
Resonance (approximate eigenmode) in a single cylinder for E//axis y x m
This mode suppresses electric dipole and boosts the magnetic dipole

23. Four coupled modes
One of them is toroidal

24. (a)
(b)
(c) Ez
|H| j
-2, ,3
A. A. Basharin et al. Phys. Rev. X 5, (2015); f=1.89 THz

25. Thank you for your attention