Biomedical Engineering Reference
In-Depth Information
directions perpendicular to the helix axis. This is different from
conventional wave plates with a certain thickness of birefringent
crystals that can only operate in a narrow frequency range
[3, 24].
Helical structures are useful for optical activity [24, 25, 43],
broad-band antenna [21, 22], and traveling wave tube [33-35, 42].
Helicesarepotentbuildingblocksformetamaterials[11,12,32]and
itisknownthatchiralitycanleadtoanegativerefractiveindex[5,7,
27, 28, 32, 44]. In addition, an analytical model for helicoidal spirals
[2] predicted the elliptical polarization of eigenstates and bandgap
along the directions orthogonal to the spiral axis. Polarization gaps
were demonstrated in a gold helix metamaterial in the THz regime
[12]. However, the underlying physics of such kind of helicoidal
metamaterials is still under exploration. In the following, we will
present a band theory for the helix array by combining multiple
scattering theory (MST) [6, 29] with the semi-analytical solution for
a single helix [42]. We will also review some experimental results
that directly demonstrate the negative refraction in the helical
systems and we will review the wave propagation along directions
perpendicular to the helix axis [51].
We will then switch gear to dielectric PCs and show that robust
transport of light can be achieved using chiral defect modes. The
robusttransportofelectronsinquantumHallsystemsiswellknown
[19, 40, 53]. In such systems, electrons in the chiral edge states
propagate in one direction and the transport is robust against
backscattering from impurities. Recently, chiral edge states have
been predicted [1, 13, 45] and experimentally realized [9, 39,
46] in magneto-optical PCs with a large external magnetic field.
These one-way states rely on breaking time-reversal symmetry. On
the contrary, a new class of topological states has been found in
topologicalinsulators[4,10,14,16,18]thatpossessestime-reversal
symmetry. Robust transport in the form of counter-propagating
currents carrying spin-up or spin-down electrons come as a
consequence of Kramer degeneracy and strong spin-orbit coupling.
These topologically protected electronic states do not require an
applied magnetic field. However, both Kramers' degeneracy and
spin-orbit coupling are specific to electronic systems; it is not
