Robust topologically protected transport
in photonic crystals at telecommunication
wavelengths
Mikhail I. Shalaev, Wiktor Walasik, Alexander Tsukernik, Yun Xu and Natalia M.
Litchinitser
Nature nanotechnology.14,31-34(2019)
Previous Research
The first photonic analogue of a quantum Hall topological insulator, realized
in the microwave regime using gyromagnetic materials, and a strong
magnetic field to break the time-reversal symmetry
Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić
Nature 461, 772–775 (2009)
Previous Research
non-magnetic quantum Hall topological insulators mimicking time-reversalsymmetry breaking demonstrated at near-infrared frequencies
Honeycomb
lattice
helical waveguides
along z-direction
Band structures for the case of non-helical/helical waveguides
Rechtsman, M. C. et al. Nature 496,196–200 (2013)
Previous Research
photonic analogues of the spin and valley Hall effects that require spatial
symmetry breaking
Bianisotropic
metawaveguide (BMW)
The bianisotropy is
generated by finite
vacuum gap between rods
and one of the metal
plates
Hexagonal
lattice
Ma, T., Khanikaev, A. B., Mousavi, S. H. & Shvets,G.
Phys. Rev. Lett. 114, 127401 (2015)
Previous Research
SOC: spinorbit coupling
QSH
QVH
QH
gyromagnetic
material
Ma, T. & Shvets, G. Phys. Rev. B 95, 165102 (2017)
Breaking of spatial(rotational)
symmetry in QVH-PTI
Design of The Device
• Realization of optical topological insulator that demonstrates valley Hall effect at nearinfrared frequencies
• Demonstration that transmittances are the same for light propagation along a straight
topological interface and one with four sharp turns
Silicon
SiO2
a0 = 423nm
h = 0.639a0
d1 = 0.4a0
d2 = 0.6a0
honeycomb lattice with two inverted
equilateral triangular air holes per unit cell
Optimization of The Design
Results in the opening
of an indirect band
gap when asymmetry
is introduced. The size
is limited by the
frequency of the first
band at the K
point and the second
band at the M point
Smaller
triangle(d=0.5a) with
reduced etched area
introduces lower
propagation losses per
unit length than the
large one
The electron-beam-resist (EB-resist) contrast limits the minimum
allowed distance between the triangles to around 40 nm.
Band Structures
Blue: C6 symmetry with Dirac cones at K and K’
Red: C3 symmetry. A band gap opens.
The Berry curvature Ω is calculated with numerical plane wave expansion(PWE)
method. The Chern number is calculated as below:
C𝑘
.
2𝜋 𝐻𝐵𝑍𝑘
/𝑘′
1
=
Ω 𝑘 𝑑2𝑘 = ± 1/2
/
𝑘′
where the integration is carried over half of the first Brillouin zone around K or K’
points
Simulation of Topologically Protected Edge Waves
ωa0/2π c =
0.263
Observation of TPEWs
Numerical
calculation
Experiment
Results
optical parametric
amplifier
Beam splitter
for the sample with no
edge, the low
transmittance
region(1420–1510 nm)
indicates a band gap.
for the samples with an
interface, high
transmittance in the
band gap region proves
the existence of edge
states
the transmittances of the samples
with straight and trapezoidal
interfaces presented very similar
spectral dependencies. This
confirms that edge state is immune
to scattering at sharp turns.
Conclusions
• Demonstration of a silicon based VPC at
telecommunications wavelengths
• Observation of robust transport of light along a
topological interface with four sharp turns and a straight
interface.
• Confirmed the suppression of backscattering and robust
topological transport