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We acknowledge discussions with Y. Bahri, E. Kapit, O. Kyriienko,
M. F. Maghrebi, V. Oganesyan, V. N. Smelyanskiy, and G. Zhu.
P.R. and C.N. performed the experiment. J. T., V.M.B., and
D.G.A. provided theoretical assistance. P.R., C.N., J. T., V.M.B., and
D.G.A. analyzed the data and cowrote the manuscript. All of the
UCSB and Google team members contributed to the experimental
setup. At CQT, this research was supported by Singapore
Ministry of Education Academic Research Fund Tier 3 (grant no.
MOE2012-T3-1-009); National Research Foundation (NRF)
Singapore; and the Ministry of Education, Singapore under the
Research Centres of Excellence Program. The data that support the
plots presented in this paper and other findings of this study are
available from the corresponding author upon reasonable request.
The authors declare no competing financial interests.
Materials and Methods
Figs. S1 to S7
18 June 2017; accepted 16 October 2017
Giant nonlinear response at a
plasmonic nanofocus drives efficient
Michael P. Nielsen, Xingyuan Shi, Paul Dichtl, Stefan A. Maier, Rupert F. Oulton*
Efficient optical frequency mixing typically must accumulate over large interaction lengths
because nonlinear responses in natural materials are inherently weak. This limits the
efficiency of mixing processes owing to the requirement of phase matching. Here, we
report efficient four-wave mixing (FWM) over micrometer-scale interaction lengths at
telecommunications wavelengths on silicon. We used an integrated plasmonic gap
waveguide that strongly confines light within a nonlinear organic polymer. The gap
waveguide intensifies light by nanofocusing it to a mode cross-section of a few tens of
nanometers, thus generating a nonlinear response so strong that efficient FWM
accumulates over wavelength-scale distances. This technique opens up nonlinear optics to
a regime of relaxed phase matching, with the possibility of compact, broadband, and
efficient frequency mixing integrated with silicon photonics.
Nonlinear optics, especially frequency mix- ing, underpins modern optical technologies and scientific exploration in quantum op- tics (1, 2), materials and life sciences (3, 4), and optical communications (5, 6 ). Four-
wave mixing (FWM) is an important nonlinear
frequency conversion technique used in photonic
integrated circuits and telecommunications for sig-
nal regeneration (6), switching (7 ), phase-sensitive
amplification (8), metrology (9), and entangled
photon-pair generation (10). As a third-order
nonlinear effect, FWM is extremely sensitive to
enhancement by the optical confinement of na-
noplasmonic systems (11). For example, FWM has
been demonstrated in a variety of metallic nano-
structures, including nano-antennas (12), rough
surfaces (13), and at sharp tips (14). Nonetheless,
efficient frequency conversion has remained elu-
sive. Although metals can be highly nonlinear and
afford extreme optical localization, at telecommu-
nications wavelengths only a small fraction of a
plasmonic mode interacts with the metal, and
increasing this only exacerbates absorption. An
alternative strategy is to incorporate low-loss non-
linear materials within nanoplasmonic systems
(15, 16 ). Indeed, recent theoretical studies of FWM
in plasmonic waveguides incorporating nonlinear
polymers are promising (17). Nonlinear polymers
defy Miller’s rule by exhibiting large Kerr indices
(18, 19) for relatively low refractive indices, and
this has been exploited in recent studies (20). In
the context of plasmonics, this brings two ad-
vantages: polymers are straightforward to inte-
grate within metallic nanostructures by means
of solution processing (21), and their low refrac-
tive index minimizes propagation loss.
Illustrated in Fig. 1 is the silicon hybrid gap
plasmon waveguide (HGPW) (11, 17, 22) that we
have used to mediate pump degenerate FWM
(DFWM) in the nonlinear polymer poly[2-methoxy-
PPV) (18). The device consists of input and output
gratings to launch and collect optical signals,
either side of a metallic waveguide of length, L,
and width, W, as narrow as W = 25 nm, which is
accessed via two tapered sections. In recent work
(11), we demonstrated this system’s capability to
enhance more than 100-fold the intensity of light
within the narrow gap, a process known as adia-
batic nanofocusing (24). In this work, the non-
linear polymer infiltrates the narrow gap section,
where the optical field is expected to be maximal.
Unlike conventional DFWM, our approach does
not require operation near zero-dispersion wave-
lengths for phase-matching (23). In our approach,
phase-matching is irrelevant because the prop-
agation distances are considerably shorter than
the DFWM coherence lengths under investiga-
tion. Near a wavelength of l = 1500 nm over a
pump-to-signal bandwidth of Dl = 30 nm, the
W = 25 nm waveguide has a coherence length
of hundreds of micrometers, which is far longer
than its 2-µm propagation length. Even a band-
width of Dl = 300 nm near 1500 nm would have
a coherence length greater than the propagation
length. More details on phase-matching and dis-
persion in the HGPWs are available in (23).
The nanofocusing mechanism is illustrated
in Fig. 1 (11, 22). An input beam polarized par-
allel to the gratings couples to transverse elec-
tric (TE)–like waveguide modes, with dominant
electric field component in the plane. For wide
gap widths, the fundamental TE-like mode prop-
agates primarily in the silicon layer over dis-
tances >100 µm because its modal overlap with
metal is minimal. For W < 50 nm, the mode be-
comes concentrated in the gap region. Although
the mode only propagates for a few micrometers
in this state, the gap’s field enhancement is dra-
matic (11). The taper angle to access this con-
fined mode is selected to minimize propagation
loss and reflections or scattering that would re-
duce the nanofocusing efficiency. More details on
the taper/grating coupling efficiencies and the
waveguide propagation losses are provided in (23).
In order to investigate DFWM in this plasmonic
device, two spectrally distinct pulses centered
Department of Physics, Imperial College London, London,
SW7 2AZ, UK.
*Corresponding author. Email: firstname.lastname@example.org