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TOPOLOGICAL PHOTONICS
Come to light
Topological concepts have been demonstrated in microwave photonic systems but laser-written waveguides show
the way to topological physics for light at optical frequencies.
Alexander B. Khanikaev
R
ecent developments in condensedmatter physics have significantly
expanded the family of topological
states of matter. As they can exhibit a range
of unique phenomena, such as protected
modes and unusual transport properties,
these developments have also been of
interest to those working in classical physics,
such as acoustic, mechanical or photonic
systems. And although a number of these
topological states have been successfully
emulated in photonics1, the complexity of
earlier designs2,3 has somewhat restricted
their application to certain frequencies.
Writing in Nature Physics­, Jiho Noh and
colleagues4 now report the observation
of type-II Weyl points and Fermi arc-like
surface states for light in the optical domain.
The topological concepts transferred
from condensed matter into photonic
systems provide new versatile ways to
control and manipulate electromagnetic
fields1. Most of the functionalities that have
been demonstrated are two-dimensional
(2D), however, and so attention has
shifted towards three-dimensional (3D)
systems, where a variety of new topological
properties have been predicted. The work
by Noh et al. marks an important step in
this direction by emulating Weyl points,
which constitute the simplest possible
topologically nontrivial band structure in
three dimensions.
Weyl fermions are massless spin-1/2
particles that have not been observed
in nature, but can arise in the form of
quasiparticle excitations5. The band structure
of Weyl materials exhibits conical valence
and conduction bands that touch at a single
Weyl point, which carries a topological
charge. Weyl points are surprisingly robust
with respect to perturbations, which,
whether global or local, can only shift the
Weyl point and not lift the degeneracy
between the bands, implying that the conical
dispersion will persist.
Such materials also have exotic
topological excitations on the surface, with
a dispersion referred to as a Fermi arc due
to its distinct shape. Such arcs interconnect
a pair of Weyl points of opposite charges
a
b
Type-II Weyl point and
arc-shaped dispersion
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Topologically nontrivial and trivial
2D projections of 3D bulk and surface states
Figure 1 | Type-II Weyl points and Fermi arcs. a, Schematic of a type-II Weyl point and surface state with
arc-shaped dispersion. b, Schematic of topological and trivial 2D projection of Weyl dispersion and arc
observed in an array of helical waveguides.
in reciprocal space. To realize the optical
equivalent of Weyl points and Fermi arcs,
Noh et al. exploited a platform that has
already been proven to be extremely versatile
and fruitful for topological photonics in the
context of Floquet topological insulators6.
The system comprises a periodic
array of optical waveguides, fabricated by
direct laser writing inside a glass slab. The
hopping between different waveguides can
be controlled by tuning their separation.
A helical shape provides an additional
modulation in the z-direction, making the
structure truly three-dimensional.
The resultant structure represents a
square binary array of helical waveguides,
with their geometrical parameters
tuned to exhibit a special class of type-II
Weyl dispersion (Fig. 1a) in the nearinfrared domain. When compared to the
conventional type-I Weyl points1, the type-II
points appear due to the touching of bands
that have an additional slope in one of the
directions, so that the constant frequency
contours have conical, as opposed to pointlike, shape. Nonetheless, the type-II Weyl
points appear to be as protected as their
type-I cousins.
The Weyl dispersion engineered by
Noh et al. could be probed by coupling
an optical field to the system and imaging
lateral field distributions along the xy-cuts
of the structure near the frequency of one
of the Weyl points. Unfortunately, direct
reconstruction of the band structure the
way it is done in condensed matter with
photoemission tools is not available for 3D
photonic structures. Therefore, to confirm
topological properties the authors had
to look for signatures of the type-II Weyl
dispersion in the 2D field profiles.
It appears that the presence of type-II
Weyl points significantly modifies the
diffraction pattern of light, rendering it
conical in shape. Even more exciting is
that, in addition to this bulk signature,
the Weyl dispersion is expected to
give rise to the emergence of optical
surface states — photonic analogues of
topological excitations forming the arcshaped dispersion connecting two Weyl
points (Fig. 1a).
The 2D geometry of the measured
field maps makes it natural to think of 2D
projections of the 3D system in hand. In
which case, this system appears to map
precisely onto the 2D topological state
described by the massive Dirac Hamiltonian,
with an effective gauge field induced by
the helicity of the waveguides6. Thus,
the mapping establishes an interesting
and intimate connection between the
distinct topological phases in two and
three dimensions.
NATURE PHYSICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephysics
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news & views
In the projected picture (Fig. 1b), the
trivial 2D states would appear as cuts
through the regions of the Weyl system
without Fermi arcs. In contrast, if the cut
is made through the region with Fermi
arcs, these surface states would manifest
themselves as edge states, corresponding to
the topologically nontrivial case in the 2D
system. By fabricating samples corresponding
to different regimes, Noh et al. provided
direct evidence that the arcs originated at
Weyl points.
The observation of Weyl points and the
associated surface states at optical frequencies
is an important advance for two reasons.
First, it shows that these exotic systems
can be emulated in the optical domain,
2
which offers the opportunity to probe other
complex physical systems in photonic crystals
and metamaterials. Second, it brings the
concept of topological photonics one step
closer to practical applications in optics.
The properties unique to this class of
system can now be exploited to the full
extent, controlling light not only classically,
but also in quantum regimes. The synthetic
gauge fields produced by Weyl charges
open a new opportunity for engineering
and controlling entangled states of photons,
and may become indispensable for
quantum computing.
❒
Alexander B. Khanikaev is in the Department of
Electrical Engineering, Grove School of Engineering,
City College of New York, New York, New York
10031, USA, and the Graduate Center of the City
University of New York, New York,
New York 10016, USA.
e-mail: [email protected]
References
1. Lu, L., Joannopoulos, J. D. & Soljačić, M. Nat. Phys.
12, 626–629 (2016).
2. Lu, L. et al. Science 349, 622–624 (2015).
3. Chen, W.-J., Xiao, M. & Chan, C. T. Nat. Commun.
7, 13038 (2016).
4. Noh, J. et al. Nat. Phys.
http://dx.doi.org/10.1038/nphys4072 (2017).
5. Hasan, M. Z., Xu, S.-Y., Belopolski, I. & Huang, S.-M.
Ann. Rev. Condens. Matter Phys. 8, 289–309 (2017).
6. Rechtsman, M. C. et al. Nature 496, 196–200 (2013).
Published online: 8 May 2017
NATURE PHYSICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephysics
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