compared with that simulated by using the NLSE
as a function of peak pump power for a HGPW of
W = 25 nm and L = 2 µm. The simulated conversion efficiency varies with peak power cubed until
a critical power at which nonlinear absorption of
the pump beam dominates. For Ppð0Þ > 30 W
in the narrowest waveguides (W = 25 nm), the
MEH-PPV degraded, setting the upper power limit for our data set. Although the conversion efficiency roll-off was not observed in experiments,
it is remarkable that nonlinear absorption should
not limit performance until peak powers approaching 100 W, owing to the short device lengths.
The observed conversion efficiencies were
~20 dB less than those expected from NLSE simulations by using the measured nonlinear parameters of MEH-PPV films. Because the discrepancy
was systematic across all measured devices (Fig. 4),
we can identify a number of reasons. First, poor
infiltration of MEH-PPV into the gap would not
only affect the waveguide’s nonlinear coefficient
but also the mode confinement. Second, the morphology of the MEH-PPV within the gap could
be distinct from that of bulk films, which were
used to assess the material’s nonlinear parameters. Last, calculating the waveguide nonlinearity,
g, from the nonlinear responses of the various
device materials could require more rigourious
theoretical treatment (25). Nevertheless, all data
broadly agrees with theory for a waveguide nonlinearity, g, that is a factor of 2.5 to 3 times less
than that inferred from Z-scan measurements.
The plasmonic waveguide width and length
clearly influence the DFWM conversion efficiency;
whereas a narrower gap boosts the effective non-
linear coefficient, the additional propagation loss
limits idler accumulation. This raises the ques-
tion: What is the optimal interaction length? The
conversion efficiency of HGPWs with W = 25 nm
and Ppð0Þ ¼ 30 W for L = 1 to 5 µm is shown in
Fig. 4A. The experiment is broadly consistent with
the theory that conversion efficiency increases
with device length until a maximum is reached
because of growing propagation loss. The fact
that the conversion efficiency is maximal near
the measured propagation length of 1.9 ± 0.6 µm
suggests that DFWM accumulates rapidly and
that the optimal gap width is <25 nm. The do-
minant role of confinement in these devices is
apparent from the much smaller CEs of HGPWs
with W > 25 nm despite the increase in peak
interaction length (Fig. 4B). Complementary data
are shown in Fig. 4, C and D, on how the conver-
sion efficiency varies with gap width for two fixed
HGPW lengths of L = 3 µm and L = 5 µm, at
Ppð0Þ ¼ 30 W. Although the gap width affects
both propagation loss and nonlinear coefficient,
broad agreement between NLSE simulations
and experiments remains, demonstrating that
this frequency-mixing approach is robust and
We have shown that the intense light at a na-
nofocus enables nonlinear optical control over ex-
tremely short interaction lengths comparable with
the vaccuum wavelength of light. Remarkably,
at the minimum gap width of 25 nm in this study,
we are still operating far from where nonlocal
and quantum effects arise at the subnanometer
scale (26), which suggests scope for improvement
through reducing the gap width, studying wider
conversion bandwidth, and exploring alternative
nonlinear gap materials. Moreover, our approach
mitigates phase-matching limitations over large
bandwidths in a nonresonant manner (27). With
efficient nonlinear processes over distances
shorter than a plasmonic mode’s propagation
length, we can also eliminate the key problem
of insertion loss that has plagued the applica-
tion of plasmonics. This shows that plasmonic
nanofocusing on a silicon platform can be a pow-
erful tool in nonlinear optics.
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The authors thank J. Nelson for discussions on nonlinear organic
polymers. The authors also thank L. Lafone for discussions on
plasmonic waveguides. This work was sponsored by the U.K.
Engineering and Physical Sciences Research Council (EPSRC;
grants EP/I004343/1 and EP/M013812/1). M.P.N. and P.D. were
supported by EPSRC studentships. M.P.N. was also supported by a
Natural Sciences and Engineering Research Council of Canada
(NSERC) scholarship. S.A.M. acknowledges the Lee-Lucas Chair.
R.F.O. was supported by an EPSRC Career Advancement
Fellowship and Marie Curie International Reintegration Grant
(PIRG08-GA-2010-277080). Data requests can be made via
dataenquiryEXSS@imperial.ac.uk. M.P.N. and R.F.O. conceived of
the experiments. M.P.N. developed the theoretical simulations,
fabricated the samples, and conducted the experiments. X.S.
prepared the MEH-PPV sample for Z-scan characterisation, which
were conducted by M.P.N. and P.D. M.P.N. and R.F.O. cowrote the
manuscript. All authors commented on the manuscript.
Materials and Methods
Figs. S1 to S7
19 June 2017; resubmitted 14 September 2017
Accepted 26 October 2017
SCIENCE sciencemag.org 1 DECEMBER 2017 • VOL 358 ISSUE 6367 1181
0 10 20 30 40 50 60 70 80 90100
Waveguide Width (nm)
0 10 20 30 40 50 60 70 80 90100
Waveguide Width (nm)
0 2 4 6 8 10 12 14 16 18 20
Waveguide Length (µm) Waveguide Length (µm)
Fig. 4. DFWM conversion efficiencies for a variety of different HGPW devices. (A and B)
Conversion efficiency versus waveguide length for HGPWs of (A) W = 25 nm at Ppð0Þ ¼ 30 W and
(B) W = 50 nm at Ppð0Þ ¼ 40 W. (C and D) Conversion efficiency versus waveguide width for
HGPWs of (C) L = 3 µm and (D) L = 5 µm at Ppð0Þ ¼ 30 W. Solid lines show theoretical conversion
efficiencies calculated with the NLSE using g/2.5.