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Abstract and Figures

Microlasers with a twist Structured light, in the form of helical wavefronts, provides an additional degree of freedom to encode information for optical communications. Creating light beams with the desired amount of optical angular momentum, or twist, has usually been achieved with bulk optic devices. Miao et al. demonstrate a possible route for an integrated optics approach in which a twisted-light source with a controlled amount of optical angular momentum is generated internally to the designed device structure. These microlasers could find application in telecommunication and information technologies to increase the rate of information transmission. Science , this issue p. 464
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Orbital angular
momentum microlaser
Pei Miao,
*Zhifeng Zhang,
*Jingbo Sun,
*Wiktor Walasik,
Stefano Longhi,
Natalia M. Litchinitser,
Liang Feng
Structured light provides an additional degree of freedom for modern optics and practical
applications. The effective generation of orbital angular momentum (OAM) lasing, especially
at a micro- and nanoscale, could address the growing demand for information capacity.
By exploiting the emerging non-Hermitian photonics design at an exceptional point, we
demonstrate a microring laser producing a single-mode OAM vortex lasing with the ability
to precisely define the topological charge of the OAM mode.The polarization associated
with OAM lasing can be further manipulated on demand, creating a radially polarized vortex
emission. Our OAM microlaser could find applications in the next generation of integrated
optoelectronic devices for optical communications in both quantum and classical regimes.
Light typically consists of a stream of linearly
polarized photons, traveling in a straight
line and carrying a linear momentum. How-
ever, it was recognized that beyond the
linear momentum, circularly polarized light
carries angular momentum (1). The angular mo-
mentum associated with the polarization degree
of freedom, or spin angular momentum (SAM),
the SAM, it was also demonstrated that a light
beam can carry orbital angular momentum (OAM)
(2). Such beams possess helical phase fronts so
that the Poynting vector within the beam is
twisted with respect to the principal axis. This
fundamental discovery of an OAM opened a new
branch of optical physics, facilitating studies rang-
ingfromrotaryphotondrag(3), angular uncer-
tainty relationships (4), and rotational frequency
shifts (5), to spin-orbital coupling (6). The OAM
degree of freedom has enabled technological ad-
vances, for example, edge-enhanced microscopy
(7). Moreover, in contrast to the SAM that can
take only two values, the OAM is unbounded.
OAM beams are thus being considered as poten-
tial candidates for encoding information in both
quantum and classical systems. The combined
use of spin and orbital angular momenta is
expected to enable the implementation of entirely
new high-speed secure optical communication
and quantum teleportation systems in a multi-
dimensional space (8), satisfying the exponen-
tially growing demand worldwide for network
To date, most of the light sources only produce
relatively simple light beams with spatially hom-
ogeneous polarization and planar wavefront. Gen-
eration of the complex OAM beams usually relies
on either bulk devices, such as spiral phase plates,
spatial light modulators, and computer-generated
holograms (1), or recently developed planar op-
tical components, including phase modulation
based metasurfaces (914), q-plates (15), and silicon
resonators (16). Although the science of the OAM
light beams on the micro- and nanoscale is still
in its early days, it is likely to advance our
knowledge of light interaction with conventional
and artificial atoms (e.g., quantum dots) pro-
vided that the OAM beam is focused to sub-
wavelength dimensions (17), facilitating on-chip
functionalities for micromanipulation and micro-
fluidics. Nevertheless, it remains a grand chal-
lenge to integrate the existing approaches for
OAM microlasers on-a-chip. For an ultimate min-
iaturized optical communication platform, there
is a necessity of independent micro- and nano-
scalelasersources(18) emitting complex vector
beams carrying the OAM information.
One approach to creating an OAM laser (19)
is based on combining a conventional bulk laser
with additional phase-front shaping components.
Despite being straightforward, this approach re-
lies on rather different device technologies and
material platforms, and therefore it is not easily
scalable and integratable. On the contrary, here
we integrate the advantages of semiconductor
microlasers with the pronounced changes in light
propagation at the exceptional point to realize a
fundamentally new, compact, active OAM source
on a complementary metal-oxide-semiconductor
(CMOS) compatible platform. We consider a mic-
roring cavity that supports whispering gallery
modes (WGMs). These modes circulate inside
of the mirror symmetry of a ring cavity, clockwise
and counterclockwise eigen-WGMs can be simul-
taneously excited, and their carried OAMs con-
sequently cancel each other. This is evidenced by
the quantized phase, taking values of either 0 or
p, azimuthally distributed in the ring, which re-
sults from the interference between two counter-
propagating WGMs (fig. S1) (20). To observe the
OAM of an individual WGM, it is essential to
464 29 JULY 2016 VOL 353 ISSUE 6298 SCIENCE
Department of Electrical Engineering, The State University
of New York at Buffalo, Buffalo, NY 14260, USA.
Dipartimento di Fisica, Politecnico di Milano and Istituto di
Fotonica e Nanotecnologie del Consiglio Nazionale delle
Ricerche, Piazza L. da Vinci 32, Milano I-20133, Italy.
*These authors contributed equally to this work. Corresponding
author. Email: (L.F.); (N.M.L.)
Fig. 1. Design of OAM microlaser. (A) Schematic of the OAM microlaser on an InP substrate.The diam-
eter of the microring resonator is 9 mm, the width is 1.1 mm, and the height is 1.5 mm(500nmofInGaAsP
and 1 mm of InP). Thirteen-nanometer Ge single-layer and 5-nm Cr/11-nm Ge bilayer structures are
periodically arranged in the azimuthal direction on top of the InGaAsP/InP microring, mimicking real index
and gain/loss parts of an EP modulation at n¼n¼0:01 to support unidirectional powe r circulati on. The
designed azimuthal order is N¼56 at the resonant wavelength of 1472 nm. Equidistant sidewall scatters
with a total number of M¼57 are introduced to couple the lasing emission upward, creating an OAM vortex
emission with a helical wavefront. Its topological charge is defined by l¼NM¼1. (B) Simulated phase
distribution of emitted light. A spiral phase map for an OAM charge-one vortex is clearly demonstrated.
on July 29, 2016 from
introduce a mechanism of robust selection of
either clockwise or counterclockwise mode. In
conventional bulk optics, unidirectional ring lasers
have been demonstrated by implementing a non-
reciprocal isolator in the light path. The optical
isolator breaks the reciprocity between counter-
propagating waves, facilitating the desired uni-
directional flow. This approach, however, is not
feasible at the micro- and nanoscale, as the reali-
zation of micrometer-sized isolators is extremely
To overcome this fundamental limitation, we
realize the unidirectional power circulation by
introducing complex refractive-index modulations
to form an exceptional point (EP) (Fig. 1A). Driven
by non-Hermiticity (i.e., gain and loss in optics)
(21,22), an EP occurs when multiple eigenstates
coalesce into one (2326). In our device, EP ope-
ration is essential to obtaining OAM laser emis-
sion (20). The microring laser resonator is designed
with 500-nm-thick InGaAsP multiple quantum
wells on an InP substrate. The complex refractive-
index grating is achieved by placing on top of
InGaAsP along the azimuthal direction (q)pe-
riodically alternate single-layer Ge and bilayer
Cr/Ge structures, corresponding to the refrac-
tive index (n) and gain/loss (n) in the cavity,
infor 2pp=N<q<2ppþ1
nfor 2ppþ3
where Ndenotes the azimuthal number of the
targeted WGM and ptakes integer values from
the set {0, N1}. An EP is obtained when the
amplitudes of index and gain/loss gratings are
set equal (i.e., n¼n). At EP, the Fourier trans-
form of the complex refractive-index modulation
is one-sided, yielding one-way distributed feedback
(2729) and robust unidirectional laser emission
above threshold, as shown by a detailed semicon-
ductor rate equation analysis (20). As a result,
the counterclockwise WGM unidirectionally cir-
culates in the cavity carrying large OAM through
the azimuthally continuous phase evolution (figs.
S2 and S3) (20).
The OAM associated with the unidirectional
power flow is extracted upward into free space
by introducing sidewall modulations periodically
arranged along the microring perimeter (16). The
azimuthal phase dependence of the targeted uni-
directional Nth WGM is given by φ¼Nq.The
sidewall modulations coherently scatter light,
with the phase continuously varying in azimuthal
direction, defined by the locations of the scatters
(Fig. 1A, inset). For Mequidistant scatters, the
locations of the scatters are given by qs¼2ps=M,
where sf0;M1g, resulting in the extracted
phase qs¼2psN =Mthat carries OAM. Because
modulo 2p,wecansubtract2psfrom each of the
extracted phases and derive
Equation 2 shows that the extracted phase
increases linearly from 0 to 2pðNMÞ,thereby
creating a vortex beam with topological charge
of the vortex laser emission from our OAM mic-
rolaser, where N¼56 and M¼57. The phase of
SCIENCE 29 JULY 2016 VOL 353 ISSUE 6298 465
Fig. 3. Characterization of OAM lasing. (A) Evolution of the light emission spectrum from PL, to ASE, and
to lasing at 1474 nm, as the peak power density of pump light was increased from 0.63, to 0.68, to 2.19 GW m
respectively. (B) Input-output laser curve, showing a lasing threshold of ~1 GW m
.(C) Far-field intensity
distribution of the laser emission exhibiting a doughnut-shaped profile, where the central dark core is due
to the phase singularity at the center of the OAM vortex radiation. (D) Off-center self-interference of the
OAM lasing radiation, showing two inverted forks (marked with arrows) located at two phase singularities.
Originating from the superposition of central helical and outer quasiplanar phases intrinsically associated
with OAM, the double-fork pattern confirms the OAM vortex nature of the laser radiation.
Fig. 2. Scanning electronmicroscope images of OAM microlaser.The OAM microlaser was fabricated
on the InGaAsP/InP platform. Alternating Cr/Ge bilayer and Ge single-layer structures were periodically
implemented in the azimuthal direction on top of the microring, presenting, respectively, the gain/loss
and index modulations required for unidirectional power circulation.
on July 29, 2016 from
the electric field changes by 2pupon one full
circle around the center of the vortex. The phase
is continuous everywhere except for the center
of the emission path, presenting a topological
phase singularity point at the beam axis. The
topological charge of the vortex emission can
be viewed as the number of twists done by the
wavefront in one wavelength, exhibiting OAM
lasing of charge l¼1.
The OAM microlaser with the EP modula-
tion by periodically arranged Ge and Cr/Ge (Fig.
2) was fabricated by means of overlay electron
beam lithography (20). The unidirectional power
flow oscillating in the cavity eliminates the un-
desired spatial hole-burning effect that would
be created by the interference pattern of two
counterpropagating WGMs. The preferential
gain saturation in the antinodes of the interfer-
ence pattern would cause spatial gain inhomo-
geneity, leading to a decrease in the laser slope
efficiency, multilongitudinal mode operation,
and unstable laser emission. In our OAM mic-
rolaser, unidirectional power flow forced at the
EP modulation (fig. S3) (20) enables efficient and
stable single-mode lasing with a sideband sup-
pression ratio of ~40 dB (Fig. 3A). In the tran-
sition from broadband photoluminescence (PL),
to amplified spontaneous emission (ASE), and
finally to lasing (Fig. 3, A and B), the emission
peak stabilized at the same resonant wavelength,
demonstrating the avoidance of multimode osci-
llation typically existing in a microring cavity.
The OAM characteristics, such as the vortex
nature and the phase singularity, were charac-
terized by analyzing the spatial intensity profile
of lasing emission and its self-interference (fig.
S4) (20). In the far field, we observed the inten-
sity of lasing emission spatially distributed in a
doughnut shape with a dark core in the center
(Fig. 3C). The observed dark center is due to
the topological phase singularity at the beam
axis where the phase becomes discontinuous,
as predicted in Fig. 1B. The presence of the OAM
was then validated by the self-interference of two
doughnut-shaped beams split from the same
lasing emission. In each doughnut beam, be-
cause of its OAM, optical phase varies more
markedly with a helical phase front close to the
central singularity area, whereas the outer dough-
nut area is of a relatively uniform quasiplanar
phase front. At the observation plane, we inten-
tionally created a horizontal offset between two
doughnut beams, so that the dark center of one
beam overlapped with the bright doughnut area
of the other, and vice versa. The resulting in-
terference patterns between the helical and
quasiplanar phase fronts revealed two inverted
forks (Fig. 3D), as the quasiplanar and helical
phases were reversed at the centers of two
doughnuts. For both of them, the single fringe
split into two at the fork dislocation, evidently
confirming that the radiation from our OAM
laser was an optical vortex of topological charge
The polarization properties of the demonstra-
ted OAM microlaser can be designed on demand.
In particular, radially polarized beams, charac-
terized by a nonuniform spatial distribution of
their polarization vector, have enabled unique
functionalities, such as highspatial resolution
microscopy by their sharp focusing (30). Although
the conventional schemes require external op-
tical components, such as geometric phasebased
diffraction elements (9), radially polarized beams
can be directly produced from our OAM micro-
laser. In a microring cavity, the resonant mode
can be designed to be either quasitransverse
magnetic (TM) or quasitransverse electric (TE).
The radially polarized component of the quasi-
TM mode is tightly confined at the microring
perimeter and sensitive to sidewall modulations,
facilitating the outcoupling of this mode from the
laser (fig. S5) (20). Therefore, in our microring
cavity, the dominant oscillating mode is designed
to be a quasi-TM mode, and its scattering by the
sidewall modulation results in the radially polar-
ized OAM lasing. In experiments, the polarization
state of the OAM lasing was validated. After trans-
mission through a linear polarizer, the doughnut
profile splits into two lobes aligned along the
orientation of the polarizer (Fig. 4). The two
lobes remained parallel to the polarization axis
regardless of the rotation of the polarizer, man-
ifesting pure radially polarized OAM lasing.
Additionally, in contrast to linearly polarized
OAM modes that are not compatible with op-
tical fibers, fibers can support radially polar-
ized OAM eigenmodes.
We have demonstrated a microring OAM laser
producing an optical vortex beam with an on-
demand topological charge and vector polariza-
index and gain/loss modulations at an EP, which
breaks the mirror symmetry in the lasing gen-
eration dynamics and facilitates the unidirec-
tional power oscillation. Finally, OAM vector
laser beams might offer novel degrees of freedom
for the next generation of optical communica-
tions in both classical and quantum regimes.
1. A. M. Yao, M. J. Padgett, Adv. Opt. Photonics 3, 161
2. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman,
Phys. Rev. A 45,81858189 (1992).
3. S. Franke-Arnold, G. Gibson, R. W. Boyd, M. J. Padgett, Science
333,6567 (2011).
4. S. Franke-Arnold et al., New J. Phys. 6, 103 (2004).
5. J. Courtial, D. Robertson, K. Dholakia, L. Allen, M. Padgett,
Phys. Rev. Lett. 81, 48284830 (1998).
6. Q. Guo, W. Gao, J. Chen, Y. Liu, S. Zhang, Phys. Rev. Lett. 115,
067402 (2015).
7. C. Maurer, A. Jesacher, S. Bernet, M. Ritsch-Marte, Laser
Photonics Rev. 5,81101 (2011).
8. N. Bozinovic et al., Science 340, 15451548 (2013).
9. Z. Bomzon, G. Biener, V. Kleiner, E. Hasman, Opt. Lett. 27,
11411143 (2002).
10. N. Yu et al., Science 334, 333337 (2011).
11. D. Lin, P. Fan, E. Hasman, M. L. Brongersma, Science 345,
298302 (2014).
12. K. E. Chong et al., Nano Lett. 15, 53695374 (2015).
13. M. I. Sha laev et al., Nano Lett. 15,62616266 (2015).
14. G. Kn öner et al., Opt. Express 15, 55215530 (2007).
15. E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, E. Santamato,
Appl. Phys. Lett. 94, 231124 (2009).
16. X. Cai et al., Science 338,363366 (2012).
17. R. W. Heeres, V. Zwiller, Nano Lett. 14, 45984601
18. M. A. Noginov et al., Nature 460, 11101112 (2009).
19. D. Naidoo et al., Nat. Photonics 10, 327332 (2016).
20. Materials and methods are available as supplementary
materials on Science Online.
21. K. G. Makris, R. El-Ganainy, D. N. Christodoulides,
Z. H. Musslimani, Phys. Rev. Lett. 100, 103904
22. C. E. Rüter et al., Nat. Phys. 6, 192195 (2010).
23. J. Wiersig, S. W. Kim, M. Hentschel, Phys. Rev. A 78, 053809
24. B. Peng et al., Nat. Phys. 10, 394398 (2014).
25. H. Schomerus, Phys. Rev. Lett. 104, 233601 (2010).
26. M. Brandstetter et al., Nat. Commun. 5, 4034 (2014).
27. Z. Lin et al., Phys. Rev. Lett. 106, 213901 (2011).
28. A. Regensburger et al., Nature 488, 167171 (2012).
29. L. Feng et al., Nat. Mater. 12, 108113 (2013).
30. R. Dorn, S. Quabis, G. Leuchs, Phys. Rev. Lett. 91, 233901
466 29 JULY 2016 VOL 353 ISSUE 6298 SCIENCE
Fig. 4. Polarization state of OAM lasing. Measured intensity distributions of the OAM lasing radiation passing through a linear polarizer with different polar-
ization orientations indicated by arrows: (A)0°,(B)90°,(C) 45°, and (D)45°. The two-lobe structure rotated with the rotation of the polarizer in the same fashion,
confirming radially polarized OAM lasing.
on July 29, 2016 from
We acknowledge funding from the U.S. Army Research Office
Award (W911NF-15-1-0152) that enabled the design, modeling, and
topological char ge characterization of the EP-based OAM laser,
Department of Energy Award (DE-SC0014485) that was used to perform
the analysis and characterization of the spectral properties of OAM lasing,
and National Science Foundation Award (DMR-1506884) that facilitated
the fabrication of the device and optimization of the EP modulation.
Supplementary Text
Figs. S1 to S5
References (3134)
10 April 2016; accepted 30 June 2016
Nanostructured transition metal
dichalcogenide electrocatalysts for
reduction in ionic liquid
Mohammad Asadi,
Kibum Kim,
*Cong Liu,
*Aditya Venkata Addepalli,
Pedram Abbasi,
Poya Yasaei,
Patrick Phillips,
Amirhossein Behranginia,
José M. Cerrato,
Richard Haasch,
Peter Zapol,
Bijandra Kumar,
Robert F. Klie,
Jeremiah Abiade,
Larry A. Curtiss,
Amin Salehi-Khojin
Conversion of carbon dioxide (CO
) into fuels is an attractive solution to many energy and
environmental challenges. However, the chemical inertness of CO
renders many
electrochemical and photochemical conversion processes inefficient. We report a transition
metal dichalcogenide nanoarchitecture for catalytic electrochemical CO
conversion to carbon
monoxide (CO) in an ionic liquid.We found that tungsten diselenide nanoflakes show a current
density of 18.95 milliamperes per square centimeter, CO faradaic efficiency of 24%, and CO
formation turnover frequency of 0.28 per second at a low overpotential of 54 millivolts. We also
applied this catalyst in a light-harvesting artificial leaf platform that concurrently oxidized water
in the absence of any external potential.
Electrochemical or photochemical reduction
of carbon dioxide (CO
) could in principle
conveniently recycle the greenhouse gas back
into fuels (16). However, existing catalysts
are too inefficient in practice (711): Either
weak binding interactions between the reaction
overpotentials, or slow electron transfer kinetics
result in low exchange current densities. Both of
these metrics depend not only on the intrinsic
electronic properties of the catalyst, but also
on the solvent and the catalyst morphology. Re-
cently, we reported that three-dimensional (3D)
bulk molybdenum disulfide (MoS
) catalyzes CO
reduction to CO at an extremely low overpo-
tential (54 mV) (12) in an ionic liquid (IL). Here,
we report 2D nanoflake (NF) architectures of
this and other transition metal dichalcogenides
for electrocatalytic CO
reduction in the IL 1-ethyl-
3-methylimidazolium tetrafluoroborate (EMIM-BF
reduction activities of similarly sized
(~100 nm) TMDC NFs including MoS
, and WSe
were tested using a rotating
disc electrode. All TMDCs were grown using a
chemical vapor transport technique (13). Fig-
ure 1A shows cyclic voltammetry (CV) results of
NFs, and bulk MoS
as well as Ag nano-
particles (Ag NPs) and bulk Ag as a representa-
tive noble-metal catalyst. All experiments were
performed inside a two-compartment, three-
electrode electrochemical cell (fig. S6) using an
electrolyte of 50 volume percent (vol %) EMIM-
and 50 vol % deionized water; this compo-
sition gives the maximum CO
reduction activity
(13). The polarization curves of all studied cata-
lysts were obtained by sweeping potential be-
tween +0.8 and 0.764 V versus RHE (reversible
hydrogen electrode; all potentials reported here
are based on RHE) with a scan rate of 50 mV s
(Fig. 1A and fig. S8). We also performed chrono-
amperometry at different applied potentials for
NFs. The results indicate that the obtained
current densities for all applied potentials are
10 to 20% less than the CV results with 50 mV/s
scan rate (fig. S9). The difference is attributed to
the charging current (capacitive behavior) in the
CV measurements.
The CO
reduction began at 0.164 V (over-
potential of 54 mV) for WSe
NFs, as confirmed
by faradaic efficiency (FE) measurements (Fig.
1B). At this potential (overpotential of 54 mV), a
current density of 18.95 mA/cm
on the basis of geometrical surface area) was ob-
tained for WSe
NFs; by comparison, current den-
sities were 0.19 mA/cm
for bulk Ag, 1.57 mA/cm
for Ag NPs, and 3.4 mA/cm
for bulk MoS
CO formation FEs for WSe
NFs (Fig. 1B) and
bulk MoS
(12) were 24% and 3%, respectively.
However, the Ag NPs and bulk Ag did not reduce
at this overpotential. At 0.764 V potential,
the recorded current density for WSe
NFs was
330 mA cm
, versus 3.3 mA cm
for bulk Ag,
11 mA cm
for Ag NPs, and 65 mA cm
for bulk
. The CO formation turnover frequency (TOF)
(Fig. 1C) (13), a measure of per-site activity of
catalysts to produce CO, was 0.28 s
for WSe
NFs versus 0.016 s
for bulk MoS
produce CO at this overpotential (54 mV). Figure
1C also shows that the CO formation TOF of
was approximately three orders of mag-
nitude higher than that of Ag NPs in the over-
potential range of 150 to 650 mV.
Gas chromatography and differential electro-
chemical mass spectroscopy analyses indicated
that CO and H
0.764 V (13). The measured FE for WSe
(Fig. 1B) showed that this system is highly sel-
ective for CO formation at high potentials (0.2
to 0.764 V). However, at smaller potentials (0.164
to 0.2 V), it produces a mixture of CO and H
(synthesis gas). Figure S13 shows the selectivity
(FE) results of all TMDCs tested in this study (13).
The catalytic performance of TMDC NFs was
compared with that of other reported catalysts
(Fig. 1D) by multiplying current density (activity)
by CO formation FE (selectivity). At 100 mV
overpotential, the performance of WSe
NFs ex-
ceeded that of bulk MoS
and Ag NPs tested under
identical conditions in an ionic liquid by a factor
of nearly 60. The performance of WSe
NFs also
exceeds those of Au NPs (17)andCuNPs(18)by
three orders of magnitude. Additionally, at this
overpotential, the performance of WSe
that of WS
and MoSe
NFs by factors of 3 and 2,
respectively (Fig. 1D). We also performed chro-
noamperometry experiments to examine the elec-
trochemical stability of WSe
NFs in 50:50 vol
% IL/deionized water. At the applied potential of
0.364 V (0.254 V overpotential), a small decay
(10%) was observed after 27 hours of continuous
operation of the three-electrode two-compartment
cell (fig. S14) (13).
The photochemical performance of WSe
was also studied using a custom-built wireless
setup. This artificial leaf mimics the photosynthesis
process in the absence of any external applied
potential. The cell (Fig. 2A) (13) is composed of
three major segments: (i) two amorphous silicon
triple-junction photovoltaic (PV-a-si-3jn) cells in
series to harvest light, (ii) the WSe
/IL cocatalyst
SCIENCE 29 JULY 2016 VOL 353 ISSUE 6298 467
Department of Mechanical and Industrial Engineering,
University of Illinois, Chicago, IL 60607, USA.
of Mechanical Engineering, Chungbuk National University,
Cheongju 361-763, South Korea.
Materials Science Division,
Argonne National Laboratory, Argonne, IL 60439, USA.
Department of Physics, University of Illinois at Chicago,
Chicago, IL 60607, USA.
Department of Civil Engineering,
University of New Mexico, Albuquerque, NM 87131, USA.
Materials Research Laboratory, University of Illinois at
Urbana-Champaign, Urbana, IL 61801, USA.
Conn Center for
Renewable Energy Research, University of Louisville,
Louisville, KY 40292, USA.
*These authors equally contributed to this work. Corresponding
author. Email: (A.S.-K.); (L.A.C.)
on July 29, 2016 from
(6298), 464-467. [doi: 10.1126/science.aaf8533]353Science
Longhi, Natalia M. Litchinitser and Liang Feng (July 28, 2016)
Pei Miao, Zhifeng Zhang, Jingbo Sun, Wiktor Walasik, Stefano
Orbital angular momentum microlaser
Editor's Summary
, this issue p. 464Science
the rate of information transmission. increaseThese microlasers could find application in telecommunication and information technologies to
controlled amount of optical angular momentum is generated internally to the designed device structure.
demonstrate a possible route for an integrated optics approach in which a twisted-light source with a
et al.optical angular momentum, or twist, has usually been achieved with bulk optic devices. Miao
encode information for optical communications. Creating light beams with the desired amount of
Structured light, in the form of helical wavefronts, provides an additional degree of freedom to
Microlasers with a twist
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on July 29, 2016 from
... Non-Hermitian systems have recently engrossed considerable attention in quantum and classical physics [1] including optics [2]. Designing non-Hermitian optical systems with balanced distribution of gain and loss allows to have the salient feature of parity-time reversal symmetry [3,4], which gives rise to a multitude of seductive phenomena and applications such as realizing laserabsorber devices [5][6][7], single-mode lasing [8,9], generation of orbital angular momentum (OAM) lasing [10], unidirectional invisibility [11][12][13], sensing [14][15][16], and so forth. Concerning isotropic optical media, parity-time reversal symmetry is achieved by properly engineering the effective permittivity (or dielectric constant) in space such that the real and imaginary parts of this effective parameter are even and odd functions with respect to the position vector, respectively [17]. ...
... For k z → k 0 this condition simplifies to k 0 d χ 2 − 1 = π(1/2 + m). Note that the tangent term tends to both plus and minus infinity at these points, which means that they simultaneously correspond to nulls and poles, according to Eq. (10). For m = 0 and k 0 d = 2 we find χ = 1 + (π/4) 2 ≈ 1.27, which agrees with Fig. 2(b). ...
Incorporating both gain and loss into electromagnetic systems provides possibilities to engineer effects in unprecedented ways. Concerning electromagnetic effects in isotropic media that have concurrently electric and magnetic responses, there is in fact a degree of freedom to distribute the gain and loss in different effective material parameters. In this paper, we analytically scrutinize wave interactions with those media, and, most importantly, we contemplate the extreme scenario where such media are anti-Hermitian. Considering various conditions for excitation, polarization, and geometry, we uncover important effects and functionalities such as lasing into both surface waves and propagating waves, conversion of evanescent source fields to transmitted propagating waves, full absorption, and enhancing backward to forward scattering ratio. We hope that these findings explicitly show the potential of anti-Hermiticity to be used in optical physics as well as microwave engineering for creating and using unconventional wave phenomena.
... [45][46][47] Yet for many years, the challenges have been generally to remove the unwanted strong sidelobes from the superoscillatory light patterns. [25,48] In addition, photonic structures such as subwavelength angular gratings, [49] waveguide arrays, [50] metamaterials, [51] can significantly squeeze the light field into extremely small scale; however, they only support several specific light modes that are difficult to be tuned; [52] if these subwavelength modes emit from the structure to free space, they exhibit serious diffraction and expand rapidly during propagation. We emphasize that the diffraction limit restricts spot size of light to about half the wavelength. ...
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Spatially or temporally structured light has attracted considerable attention for its intriguing beam characteristics, which have found extensive applications in classical and quantum optics. Extending structured light from macroscale and microscale to nanometricscale brings more prospects both for fundamental and applied science. However, sculpting light at the subwavelength scale remains a challenge since its transverse structure is fragile in the nanometric scale. Here a novelholography for arbitrary light sculpting at the subwavelength scale is demonstrated. A wave phenomenon of diffractive focusing from an amplitude‐only nanometric (50‐nm‐thick) film is introduced, and use of the induced high‐spatial‐frequency waves as carriers to encode information of an object is considered. Using this technique, nanometric holograms are designed and fabricated for generating the well‐defined eigen modes including the zero‐order Bessel beam, vortex beam, vector beam, Airy beam, as well as an arbitrary light pattern, with feature sizes on the deep‐subwavelength scale. The broadband performance of the hologram is examined, and a white‐light nondiffracting beam at the deep‐subwavelength scale is realized. This demonstration paves a way toward on‐demand light sculpting at the nanometric scale, which may find applications such as optical super‐resolution imaging, nanoparticle manipulation, and precise measurements.
In general, a high‐quality (Q) microresonator can accommodate abundant whispering gallery modes (WGMs) with the mode number increasing with the dimensional sizes of the microresonator. Removing the unnecessary modes while reorganizing the remaining modes is of vital importance, which, however, has been proved challenging and usually results in a tradeoff with the Q of the microresonator. Here, an effective and controllable mode trimming and clustering mechanism is revealed underlying the generation of polygon and star modes in weakly perturbed tapered fiber‐coupled lithium niobate whispering gallery microresonators. Experimentally, various polygon and star modes are observed in sequence within a single microresonator by tuning the excitation wavelength or varying the coupling position between a tapered fiber and the circular microresonator, which can be well reproduced with the theoretical model. The finding offers a ubiquitous solution for a broad range of applications requiring elaborate selection and organization of the high‐Q WGMs.
Open systems with non-Hermitian degeneracies called exceptional points show a significantly enhanced response to perturbations in terms of large energy splittings induced by a small perturbation. This reaction can be quantified by the spectral response strength of the exceptional point. We extend the underlying theory to the general case where the dimension of the Hilbert space is larger than the order of the exceptional point. This generalization allows us to demonstrate an intriguing phenomenon: The spectral response strength of an exceptional point increases considerably and may even diverge to infinity under a parameter variation that eventually increases the order of the exceptional point. This dramatic behavior is in general not accompanied by a divergence of the energy eigenvalues and is shown to be related to the well-known divergence of Petermann factors near exceptional points. Finally, an accurate and robust numerical scheme for the computation of the spectral response strength based on the general theory and residue calculus is presented.
Solvent effect plays an important role in catalytic reaction, but there is little research and attention on it in electrochemical CO2 reduction reaction (eCO2RR). Herein, we report a stable covalent‐organic framework (denoted as PcNi‐im) with imidazole groups as a new electrocatalyst for eCO2RR to CO. Interestingly, compared with neutral conditions, PcNi‐im not only showed high Faraday efficiency of CO product (~100%) under acidic conditions (pH ≈ 1), but also the partial current density was increased from 258 to 320 mA cm–2. No obvious degradation was observed over 10 hours of continuous operation at the current density of 250 mA cm−2. The mechanism study shows that the imidazole group on the framework can be protonated to form an imidazole cation in acidic media, hence reducing the surface work function and charge density of the active metal center. As a result, CO poisoning effect is weakened and the key intermediate *COOH is also stabilized, thus accelerating the catalytic reaction rate.
Solvent effect plays an important role in catalytic reaction, but there is little research and attention on it in electrochemical CO2 reduction reaction (eCO2RR). Herein, we report a stable covalent-organic framework (denoted as PcNi-im) with imidazole groups as a new electrocatalyst for eCO2RR to CO. Interestingly, compared with neutral conditions, PcNi-im not only showed high Faraday efficiency of CO product (~100%) under acidic conditions (pH ≈ 1), but also the partial current density was increased from 258 to 320 mA cm-2. No obvious degradation was observed over 10 hours of continuous operation at the current density of 250 mA cm-2. The mechanism study shows that the imidazole group on the framework can be protonated to form an imidazole cation in acidic media, hence reducing the surface work function and charge density of the active metal center. As a result, CO poisoning effect is weakened and the key intermediate *COOH is also stabilized, thus accelerating the catalytic reaction rate.
On‐chip optical nonreciprocity is one of the essential functions to fully advance the development of integrated optical systems, which remains technically challenging in many aspects. There is a great need for mechanisms and approaches to facilitate the large‐scale implementation of nonreciprocal light propagation. Recently, unconventional phenomena, such as chiral optical modes and directional light propagation, have been unraveled at exceptional points (EPs), which are unique degeneracies in the energy spectrum and eigenspace of non‐Hermitian systems. Here, this work theoretically and experimentally demonstrates that by steering a single microresonator with thermo‐optic nonlinearity to chiral EPs, nonreciprocal light propagation is achieved with an isolation ratio up to 24 dB and insertion loss less than 0.5 dB. The nonreciprocity is dependent on the chirality and could be optimized near the EPs. Their results pave new avenues for the nonreciprocal control of light propagation enabled by non‐Hermitian degeneracies and hold great potential for microscale and nanoscale on‐chip nonreciprocal devices.
Here, we theoretically demonstrate a strategy for efficiently turning whispering-gallery-mode (WGM) responses of a subwavelength dielectric disk through their near-field couplings with common low-order electromagnetic resonances of a dielectric block. Both simulations and an analytical coupled oscillator model show that the couplings are Fano interferences between dark high-quality WGMs and bright modes of the block. The responses of a WGM in the coupled system are highly dependent on the strengths and the relative phases of the block modes, the coupling strength, and the decay rate of the WGM. The WGM responses of coupled systems can exceed that of the individual disk. In addition, such a configuration will also facilitate the excitation of WGMs by a normal incident plane wave in experiments. These results could enable new applications for enhancing light-matter interactions.
In quantum mechanics, with the groundbreaking discovery of parity-time symmetry (PT-symmetry), Bender and Boettcher unfold the nature of the non-Hermitian Hamiltonian to exhibit real eigenvalues. This opened a new doorway to efficiently explore all the previously ignored quantum non-Hermitian systems. The analogy between the Schrödinger equation in quantum mechanics and the paraxial wave equation in optics spurred researchers to apply the concept of PT-symmetry to optical systems. On exploring the PT-symmetric optics experimentally, by engineering loss and gain in the system, a lot of applications have been reported. It includes single-mode lasers, coherent perfect absorber lasers (CPA lasers), exceptional point sensors (EPS), spectral and spatial filters, etc. In addition to linear theoretical models on PT-symmetry, nonlinear theoretical models and the corresponding experimental results have also been reported in the last few decades. This review article begins with the fundamental idea of PT-symmetry for beginners. Subsequently, we elucidate its advancements in the field of optics. Besides, we present the recent developments of various laser systems using PT-symmetry. Thus, this review intends to focus on novel theoretical and experimental works on PT-symmetry.
Exceptional points (EPs)—non-Hermitian degeneracies at which eigenvalues and eigenvectors coalesce—can give rise to many intriguing phenomena in optical systems. Here, we report a study of the optical forces on chiral particles in a non-Hermitian system at EPs. The EPs are achieved by employing the unidirectional coupling of the chiral particles sitting on a dielectric waveguide under the excitation of a linearly polarized plane wave. Using full-wave numerical simulations, we demonstrate that the structure can give rise to enhanced optical forces at the EPs. Higher order EPs in general can induce stronger optical forces. In addition, the optical forces exhibit an intriguing “skin effect”: the force approaches the maximum for the chiral particle at one end of the lattice. The results contribute to the understanding of optical forces in non-Hermitian systems and can find applications in designing novel optical tweezers for on-chip manipulations of chiral particles.
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The angular momentum state of light can be described by positions on a higher-order Poincar\'e (HOP) sphere, where superpositions of spin and orbital angular momentum states give rise to laser beams that have found many applications, including optical communication, quantum information processing, microscopy, optical trapping and tweezing and materials processing. Many techniques exist to create such beams but none to date allow their creation at the source. Here we report on a new class of laser that is able to generate all states on the HOP sphere. We exploit geometric phase control with a non-homogenous polarization optic and a wave-plate inside a laser cavity to map spin angular momentum (SAM) to orbital angular momentum (OAM). Rotation of these two elements provides the necessary degrees of freedom to traverse the entire HOP sphere. As a result, we are able to demonstrate that the OAM degeneracy of a standard laser cavity may be broken, producing pure OAM modes as the output, and that generalized vector vortex beams may be created from the same laser, for example, radially and azimuthally polarized laser beams. It is noteworthy that all other aspects of the laser cavity follow a standard design, facilitating easy implementation.
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Gradient metasurfaces are two-dimensional optical elements capable of manipulating light by imparting local, space-variant phase changes on an incident electromagnetic wave. These surfaces have thus far been constructed from nanometallic optical antennas, and high diffraction efficiencies have been limited to operation in reflection mode. We describe the experimental realization and operation of dielectric gradient metasurface optical elements capable of also achieving high efficiencies in transmission mode in the visible spectrum. Ultrathin gratings, lenses, and axicons have been realized by patterning a 100-nanometer-thick Si layer into a dense arrangement of Si nanobeam antennas. The use of semiconductors can broaden the general applicability of gradient metasurfaces, as they offer facile integration with electronics and can be realized by mature semiconductor fabrication technologies.
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Optical systems combining balanced loss and gain provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity–time (PT)-symmetric Hamiltonians. Such systems can be used to create synthetic materials with properties that cannot be attained in materials having only loss or only gain. Here we report PT-symmetry breaking in coupled optical resonators. We observed non-reciprocity in the PT-symmetry-breaking phase due to strong field localization, which significantly enhances nonlinearity. In the linear regime, light transmission is reciprocal regardless of whether the symmetry is broken or unbroken. We show that in one direction there is a complete absence of resonance peaks whereas in the other direction the transmission is resonantly enhanced, a feature directly associated with the use of resonant structures. Our results could lead to a new generation of synthetic optical systems enabling on-chip manipulation and control of light propagation.
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When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a so-called "Exceptional Point" occurs which acts as a source of non-trivial physics in a diverse range of systems. Lasers provide a natural setting to study such "non-Hermitian degeneracies", since they feature resonant modes and a gain material as their basic constituents. Here we show that Exceptional Points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled micro-disk quantum cascade lasers, we demonstrate that in the vicinity of these Exceptional Points the laser shows a characteristic reversal of its pump-dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power. This result establishes photonic molecule lasers as promising tools for exploring many further fascinating aspects of Exceptional Points, like a strong line-width enhancement and the coherent perfect absorption of light in their vicinity as well as non-trivial mode-switching and the accumulation of a geometric phase when encircling an Exceptional Point parametrically.
Propagation of light in a medium is dictated by equifrequency surfaces (EFSs), which play a similar role as Fermi surfaces for electrons in crystals. Engineering the equifrequency surface of light through structuring a photonic medium enables superior control over light propagation that goes beyond natural materials. In this Letter, we show that a bulk metamaterial with a suitably designed bianisotropy can exhibit line degeneracy in its EFSs that consist of two ellipsoids of opposite helicity states intersecting with each other. Very interestingly, light propagating along the direction of the line degeneracy experiences strong spin-dependent photon deflection, or optical spin Hall effect, which may lead to applications in optical signal processing and spin-optical manipulations. We provide a realistic metamaterial design to show that the required bianisotropy can be readily obtained.
Metasurfaces are two-dimensional optical structures enabling complete control of the amplitude, phase, and polarization of light. Unlike plasmonic metasurfaces, planar silicon structures facilitate high transmission, low losses and compatibility with existing semiconductor technologies. Here, we report an experimental demonstration of high-efficiency polarization- sensitive dielectric metasurfaces with full 2pi phase control in transmission mode at telecommunication wavelengths. Such silicon metasurfaces are poised to enable a versatile optical platform the realization of all-optical circuitry on a chip.
We experimentally demonstrate a functional silicon metadevice at telecom wavelengths that can efficiently control the wavefront of optical beams by imprinting a spatially-varying transmittance phase independent of the polarization of the incident beam. Near-unity transmittance efficiency and full 0-2 pi phase coverage are enabled by utilizing the localized electric and magnetic Mie-type resonances of low-loss silicon nanoparticles tailored to behave as electromagnetically dual-symmetric scatterers. We apply this concept to realize a metadevice that converts a Gaussian beam into a vortex beam. The required spatial distribution of transmittance phases is achieved by a variation of the lattice spacing as a single geometric control parameter.
The lasing and coherent perfect absorption (CPA) properties of PT-symmetric microrings with mixed index and gain gratings, externally coupled to a bus waveguide, are theoretically investigated. For a complex grating at the PT-symmetry breaking point, perfect unidirectional (either clockwise or counterclockwise) laser emission can be realized, but the grating does not discriminate longitudinal modes and CPA can not be simultaneously achieved. Above the grating the PT-symmetry breaking point, single-mode emission, and simultaneous CPA can be obtained, with unbalanced and controllable excitation of clockwise and counterclockwise modes in the ring.
The spatial structure of light with Orbital Angular Momentum, or "twisted light", closely resembles the shape of atomic wavefunctions. It could therefore make symmetry-forbidden transitions in quantum dots possible. However, the vanishing intensity in the center of an OAM beam usually makes this effect weak. Here we show a plasmonic approach to focus OAM light to sub-wavelength dimensions using metallic nanoscale resonant optical antennas, allowing to increase the interaction strength by 3 orders of magnitude.