Photoconductively Loaded Plasmonic
Nanoantenna as Building Block for
Ultracompact Optical Switches
Nicolas Large,
†,‡
Martina Abb,
§
Javier Aizpurua,
†
and Otto L. Muskens*
,§
†
Centro de Fisica de Materiales CSIC-UPV/EHU and Donostia International Physics Center, DIPC, Paseo Manuel
Lardizabal 4, Donostia-San Sebastian 20018, Spain,
‡
CEMES/Universite´ de Toulouse, France, and
§
School of Physics
and Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
ABSTRACT We propose and explore theoretically a new concept of ultrafast optical switches based on nonlinear plasmonic
nanoantennas. The antenna nanoswitch operates on the transition from the capacitive to conductive coupling regimes between two
closely spaced metal nanorods. By filling the antenna gap with amorphous silicon, progressive antenna-gap loading is achieved due
to variations in the free-carrier density in the semiconductor. Strong modification of the antenna response is observed both in the
far-field response and in the local near-field intensity. The large modulation depth, low switching threshold, and potentially ultrafast
time response of antenna switches holds promise for applications ranging from integrated nanophotonic circuits to quantum
information devices.
KEYWORDS Plasmonics, nanoantennas, nanoparticles, ultrafast switches
P
lasmonics has emerged recently as an extremely
promising technological research area, owing to rapid
advances in nanofabrication and modeling.
1-3
Min-
iaturized nanoplasmonic devices hold the potential to be-
come one of the key nanotechnologies capable of combining
electric and photonic components on the same chip.
2
Of
special interest for nanoscale control over light are metal
nanoantennas, capable of concentrating optical fields into
a subwavelength volume.
4-7
Analogous to their radiowave
counterparts, nanoantennas support standing-wave electro-
magnetic resonances at visible and infrared wavelengths.
Nanoantennas of various geometries have been applied
successfully in nonlinear optics,
4,5,8,9
nanoscale photode-
tectors,
10
fluorescence enhancement,
11-14
high-harmonic
generation,
15
and single-molecule detection.
16
Active control over subwavelength optical fields is of
importance for optical communication, sensing, and quan-
tum information technology. In the terahertz range, the
conductivity of semiconductors has been used recently to
control the transport of terahertz waves using coupling to
plasmonic modes on surfaces and nanostructures.
17,18
All-
optical control over plasmons in the optical range has
recently been demonstrated using planar metal films,
20,21
hole arrays,
22
and waveguided gold gratings.
23
For single
small metal nanoparticles, ultrafast heating, and coherent
vibrations of the metal particle give rise to broadening and
a spectral shift of its plasmon resonances.
24-26
These effects
are however not large enough for full optical control at the
single-particle level for practical pump powers.
In this communication, we explore the functionality of
plasmonic nanoantennas as novel building blocks for ultra-
compact nonlinear photonic devices. We propose that the
small footprint, large light-matter interaction strength, and
fast dynamics of single plasmonic nanoantennas can be
used to design a new type of optical switch for controlling
both the far-field and near-field distribution of light. Tun-
ability of the antenna by impedance loading of its nanogap
using a dielectric medium has recently been described
theoretically
27
and experimentally.
28
In this work we explore
a related but conceptually very distinct approach using
photoconductive loading of the antenna gap. As many
concepts in nanoplasmonics, photoconductive switching
draws on analogies in the radiowave regime.
29
The principle
is based on the transition from capacitive to conductive
coupling between two plasmon modes when bringing two
nanoparticles into physical contact.
30-32
Recently near-field
investigations have shown control over progressive loading
of a nanoantenna, which could be understood within the
framework of circuit theory.
33
We show here that photoex-
cited free carriers can be used to short circuit the antenna
arms, leading to a strong modification of both the spectral
resonance structure and near-field mode-profile. As the
plasmonic antenna switch is based on a strong confinement
of optical fields in space rather than in time, the antenna
switch can operate at very low, picojoule, switching energies
while potentially reaching a much faster, femtosecond,
20,26
response than microphotonic switching devices.
34,35
The response of cylindrical gold nanoantennas is cal-
culated using the boundary element method (BEM) in a
* To whom correspondence should be addressed, O.Muskens@soton.ac.uk.
Received for review: 01/17/2010
Published on Web: 04/20/2010
pubs.acs.org/NanoLett
© 2010 American Chemical Society
1741 DOI: 10.1021/nl1001636 | Nano Lett. 2010, 10, 1741–1746
full electromagnetic calculation, thus including retarda-
tion.
36,37
This method consists in solving Maxwell’s equa
-
tions by means of a distribution of surface charge densi-
ties and currents at the surfaces of the objects that interact
self-consistently with the incoming field. The nanoanten-
nas consist of two closely spaced cylindrical rods with
their long axes aligned parallel as shown schematically
in Figure 1. The rods are taken to have a hemispherical
end-cap morphology. We consider gap antennas in ab-
sence of a substrate as this provides the simplest model
system, to which additional elements like a dielectric
substrate can be added. In experiments a suitable geom-
etry can be chosen to decouple the substrate from the
nanoantenna or match the surrounding dielectric. For the
antenna switches the interparticle gap is loaded with
amorphous silicon (a-Si). Amorphous silicon is chosen for
its large electronic band gap of 1.6 eV, high free-carrier
nonlinearity, and further for its wide application range
and compatibility with many technological processes.
38
The nonlinear optical response of crystalline silicon has
been shown to be dominated by free carrier absorption,
with a much weaker contribution from gap filling and
band structure renormalization.
39,40
As similar arguments
hold for a-Si, we have calculated the dielectric function
˜(ω) of photoexcited a-Si by combining experimental
dielectric function ˜
exp
taken from Aspnes et al.
41
with the
free-carrier Drude response,
39
resulting in
where ω
pl
) (N
eh
e
2
/
0
m
opt
*m
e
)
1/2
denotes the plasma fre-
quency, with N
eh
the free carrier density, m
opt
* ) (m
e
*
-1
+ m
h
*
-1
)
-1
the optical effective mass of the carriers, and
τ
D
∼ 10
-14
s the Drude relaxation time. The optical
effective mass for a-Si, m
opt
* ) 0.17, is estimated to be
close to the value of crystalline silicon.
39
The dielectric
function ˜(ω) was calculated from eq 1 for values of the
free-electron density N
eh
ranging from 0 to 10
22
cm
-3
.
Results are shown in Figure 2a, where we have plotted
the real and imaginary parts of the refractive index ˜
1/2
≡
n + iκ. For values of N
eh
above 10
21
cm
-3
, a strong
modification of the refractive index occurs corresponding
to the formation of a free-carrier plasma. A critical density
N
eh
crit
can be defined as the transition from a primarily
capacitive (dielectric) to primarily conductive (metallic)
loading of the antenna gap, given by the condition κ(ω) >
n(ω), or equivalently Re[˜(ω)] < 0. This condition yields
an expression for the critical density
The critical threshold depends quadratically on the optical
frequency ω, while the influence of τ
D
becomes prominent
for τ
D
< 1/ω ∼ 10
-15
s, where it results in an overall shift
of N
eh
crit
to higher carrier densities.
The principle of operation of the nanoantenna switch is
illustrated in Figure 1. In the unswitched case (denoted as
“OFF”), the antenna supports half wavelength resonances
over its individual arms. For gap sizes below 50 nm, these
half-wave modes are hybridized into a symmetric combina-
tion by the capacitive interaction between the two rods.
42
Figure 1b shows the response of the same antenna above
the free-carrier switching threshold (denoted as “ON”) given
by eq 2. As the antenna arms are conductively coupled, the
antenna now supports a half-wave resonance over the full
antenna length. As we will show below, the conductive gap
FIGURE 1. Illustration of the principle of antenna switching using a
photoconductive gap, showing the fundamental mode of an un-
switched (“OFF”) (a) and a switched (“ON”) (b) nanoantenna.
˜
(ω) )
˜
exp
(ω) -
(
ω
pl
ω
)
2
1
1 + i
1
ωτ
D
(1)
FIGURE 2. (a) Real (left panel) and imaginary (right panel) parts of
the refractive index ˜
1/2
≡ n + iκ, calculated using eq 1 as a function
of the wavelength and the photoexcited free-carrier density N
eh
. (b)
Optical extinction spectra for an S ) 50 nm antenna, under
unswitched (blue, “OFF”) and switched (red dash, “ON”) conditions,
corresponding to respective carrier densities of N
eh
) 0cm
-3
and
10
22
cm
-3
. The 3D radiation patterns are associated to the λ
1
and λ
1
′
resonances of each switching mode. The inset represents the 2D
cross section of these radiation patterns.
N
eh
crit
(ω) )
Re[
˜
exp
(ω)]ε
0
m
opt
*
e
2
(ω
2
+ 1/τ
D
2
) (2)
© 2010 American Chemical Society
1742
DOI: 10.1021/nl1001636 | Nano Lett. 2010, 10, 1741-–1746
loading results in strong modifications of both the far-field
antenna response and the near-field mode profiles.
Figure 2b presents the effect of photoconductive switch-
ing on the far-field resonances of a nanoantenna with a gap
width S of 50 nm. We present here the effect of a stationary
carrier density; dynamic effects will be discussed further
below. For this antenna, the capacitive interaction between
the two nanorods is relatively weak and the resonances
resemble those of the individual nanorods. Far-field extinc-
tion spectra were calculated for free carrier densities N
eh
below (0 cm
-3
, solid blue) and far above (10
22
cm
-3
, dashed
red) the switching threshold. The unswitched antenna shows
a strong resonance at a wavelength λ
1
of 980 nm, which can
be attributed to the fundamental dipole modes of the
uncoupled antenna arms.
37
Photoconductive switching in
-
duces a shift of the resonance position from λ
1
to λ
1
′ over
350 nm, or a relative shift (λ
1
′ - λ
1
)/λ
1
of 36%. This switching
effect is many times larger than that typically observed using
dielectric loading.
22,28
Importantly, the sharp resonance
profile of a dipole antenna results in a large switching
contrast of the extinction σ
on
/σ
off
of 44 at the new resonance
wavelength λ
1
′ ) 1.33 µm and inverse contrast σ
off
/σ
on
of
11at λ
1
) 980 nm. Calculated far-field radiation patterns
corresponding to the two resonances of the unswitched and
switched antenna are shown in the inset of Figure 2b. As
both resonances correspond to a dipolar mode, no change
is observed in the angular distribution pattern apart from
an overall increase in radiative efficiency. This increase
indicates that a larger antenna is formed under short-circuit
conditions compared to the capacitive situation where there
are two smaller antennas.
Figure 3 explores into more detail the antenna far-field
response with progressive conductive loading for antennas
with varying gap dimensions. We have calculated the optical
extinction of nanoantennas with gap sizes S ranging from 0
to 50 nm. The dashed white lines in Figure 3 indicate the
strongly wavelength dependent switching threshold for
N
eh
crit
for our model a-Si. The results of Figure 3f correspond
to the antenna of Figure 2b (S ) 50 nm). The general
behavior of the resonance structure with increasing free-
carrierdensitycanbeunderstoodusingbasic circuit theory.
27,33
The blue shift of the antenna resonance below the switching
threshold, as the carrier density is increased, can be under-
stood using a simple resistor model. One can think of this
coupled-antenna resonance as a pure capacitive cavity
where the positive and negative polarization charges act as
a capacitor. As we increase now the carrier density in the
bottleneck of the cavity, there is a reduction of the charges
(reduction of the Coulomb interaction), and there will be a
blue shift which is proportional to the reduction of the area
of the capacitive coupling. There is a point where the current
flow is so large that this capacitive mode at the cavity cannot
be sustained any more; thus it gets completely damped and
dies out.
The emergence of a new resonance at longer wave-
lengths above the critical switching threshold corresponds
to the transition of a capacitively coupled to a conductively
coupled cavity, where the strong dispersion results from
the peculiar charge density pattern which piles up positive
and negative charges at the end of the antenna. Starting
from the purely conductive mode at 10
22
cm
-3
, as the
carrier density decreases and therefore the gap becomes
less conductive, this mode would present net charge in
one of the arms of the antenna and negative in the other.
As this configuration is not physically possible, this modes
shifts dramatically to longer wavelengths, and eventually
damps and dies out.
31,33
We point out that the spectral
mode in the strongly dispersive regime is relatively nar-
row, which indicates a reduced damping of this mode. As
a consequence of the strong wavelength dependence of
N
eh
crit
, the antenna can be simultaneously switched and
unswitched in different parts of the spectrum. In this
FIGURE 3. Color density maps of the antenna spectral response as a function of photoexcited free-carrier concentration N
eh
, for antennas
with gap sizes 0 (a), 2 (b), 5 (c), 10 (d), 20 (e), and 50 nm (f).
© 2010 American Chemical Society
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DOI: 10.1021/nl1001636 | Nano Lett. 2010, 10, 1741-–1746
transitional regime, the antenna supports both conduc-
tively coupled modes at longer wavelength and capacitive
modes at shorter wavelengths, which could be of interest
for device applications.
The S ) 50 nm gap width in Figure 3f represents the
virtually uncoupled regime, where capacitive interaction is
very weak. For these wide-gap antennas, the far-field pho-
toconductive switching effect is the strongest, first because
of the absence of the red shift associated with capacitive
coupling, and second because the total antenna length is the
largest, leading to a longer wavelength fundamental mode.
In comparison, for the S ) 2 nm antenna of Figure 3b,
switching from the capacitive to conductive state does not
produce a marked wavelength shift. For the S ) 0nm
antenna, the presence of a conductive singularity results in
a strongly renormalized mode structure.
31
Photoconductive
antenna switching in this case strongly modifies the conduc-
tive area between the antenna arms, allowing a proper
antenna mode to be formed. Similarly, for the photoconduc-
tive switch to operate according to Figure 3, the contact
between the antenna and semiconductor needs to be con-
ductive, as any small (nanometer) separation will act as a
vacuum gap which will suppress the photoconductive switch-
ing effect.
Together with the switching of the far-field radiative
properties, active manipulation of the local near-fields around
plasmonic nanoantennas will be of importance for applica-
tions involving nonlinear optics and SERS,
4
quantum emit
-
ters,
16
and coherent control.
43
We calculated the near-field
intensity at various positions around a photoconductive
antenna switch. Panels a and b of Figure 4 show the intensity
at the center of the antenna gap and 5 nm from the antenna
ends for a dimer antenna with S ) 10 nm gap width. This
narrow-gap antenna supports a fundamental mode at a
wavelength λ
1
of 1100 nm with a high local intensity
enhancement of around 35 times the incident intensity in
the gap region. The mode profile of this antenna resonance
can be observed in detail in the near-field maps of Figure
4c-f. Photoconductive switching of the antenna results in
a strong quenching of the midgap intensity by an order of
magnitude, due to the redistribution of charges associated
with the suppression of the gap capacitor (Figure 4e,f). A new
mode is formed at a wavelength λ
1
′ of 1290 nm, where the
intensity is mainly concentrated around the end points of
the antenna and the midgap intensity is absent (Figure 4c,d).
Remarkably, Figure 4a shows that a transitional regime
exists above N
eh
crit
where the new mode shows a large
midgap intensity, even exceeding that of the purely capaci-
tive antenna. It should be noted that here the semiconductor
still is partly dielectric, as otherwise the fields in the gap
would be suppressed. The physical origin of this enhance-
ment is again related to the particular charge distribution in
the antenna in the crossover regime as discussed above.
For the rational design of antenna switches, we define
figures of merit of antenna performance for far-field extinc-
tion and near-field intensity enhancements. For applications
requiring large spectral shifts and extinction contrast, we
calculate the relative resonance shift (λ
1
′ - λ
1
)/λ
1
and the
on-off extinction ratio σ
on
/σ
off
at λ
1
and λ
1
′. For the near-
field switching, key parameters of interest are the off-on
ratios I
off
/I
on
of the local intensity at the midgap A for the
capacitive antenna resonance λ
1
, and at the antenna end
position B for the conductive antenna resonance λ
1
′. Result-
ing values are shown in Figure 5 for the antennas with
various gap sizes. The increasing capacitive loading for
decreasing gap width S drives the individual particle reso-
nances λ
1
toward that of the half-wave antenna λ
1
′,
4
resulting
in a reduced far-field switching performance, i.e., values
close to 1. Therefore, for far-field switching, antennas with
a large gap are favorable for achieving a large spectral shift
FIGURE 4. Near-field intensity maps calculated for a antenna of L
) 100 nm arm length and S ) 10 nm gap size, as a function of
wavelength and free-carrier density, for the antenna midgap (a) and
5 nm away from the antenna arms (b). (c-f) Near-field intensity
maps around the antenna of (a) for resonance wavelength λ
1
′ (c, d)
and λ
1
(e, f), under unswitched (N
eh
) 0cm
-3
) (c, e) and switched
(N
eh
) 10
22
cm
-3
) (d, f) conditions.
FIGURE 5. Figures of merit for switching operation for operation in
far-field (a) and near-field (b). (a) Relative resonance shift (λ
1
′ - λ
1
)/
λ
1
(left scale, linear) and on-off extinction ratio σ
on
/σ
off
at wave-
lengths λ
1
and λ
1
′ (right scale, logarithmic), against antenna gap
width S. (b) Near-field intensity off-on ratios I
off
/I
on
at λ
1
, point A
(midgap) and λ
1
′, point B (5 nm from tip).
© 2010 American Chemical Society
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DOI: 10.1021/nl1001636 | Nano Lett. 2010, 10, 1741-–1746
and high switching contrast. We should bear in mind though
that antennas with a large gap require more energy for
switching and do not benefit as much from reduced switch-
ing thresholds at antenna resonances. For the near-field
switching, antennas with a narrow gap are generally more
favorable as these produce higher local field enhancements.
However, the near field switching contrast depends strongly
on the desired position and wavelength as observed in Figure
5b. Active manipulation of the local near-fields around
plasmonic nanoantennas will be of importance for applica-
tions involving coherent control over local field amplitudes
and phases
43
and for active manipulation of quantum emit
-
ters.
16
The free carrier densities required for nanoantenna switch-
ing at near-infrared wavelengths are higher than those in the
terahertz range.
17,18
However such densities are routinely
achievable using ultrafast laser excitation of an electron-hole
plasma.
39,40
In order to compare the switching energies
required for photoconductive antenna switching with state-
of-the-art microphotonic devices, we estimate the pumping
energies for direct and two-photon optical excitation. In this
estimate, we do not consider dynamical effects occurring
on the time scale of the optical pump pulse, which will be
discussed further below. For pulsed optical excitation on a
time scale much shorter than carrier relaxation process in
the system, the free carrier density N
eh
can be estimated
from the incident optical fluence F
0
using
38
where ω ) 2π/λ, R
0
and β are the linear and two-photon
absorption coefficients, and t is the time duration of the
pulse. For excitation of a-Si in the telecommunication range
using an ultrafast laser, a critical density N
eh
crit
of around 10
21
cm
-3
is achieved via two-step absorption (β = 120 cm/GW)
at a fluence of F
0
) 0.73 mJ/cm
2
.
38
Two-step absorption is
an upconversion process where the electron is excited by
two photons through an intermediate state, which in a-Si can
be a midgap defect state. Similar switching fluences are
obtained using linear absorption above the bandgap, where
R
0
> 10
5
cm
-1
.
40
For excitation using a diffraction-limited
spot of around 1 µm
2
area, the above fluence gives a
switching energy of 7.3 pJ. This energy compares well to
values achieved using microphotonic ring resonators (25
pJ)
34
and photonic crystal nanocavities (∼100 fJ),
35
which
are however intrinsically several orders of magnitude slower
than plasmonic devices.
20
The above switching energies are valid for ultrafast pulsed
excitation. Under stationary (CW) pumping conditions, the
carrier density will be limited by different relaxation mech-
anisms such as surface recombination, Auger processes, and
electron diffusion. The ultrafast response of a-Si thin films
has been extensively studied by Esser et al.,
40
who have
shown that carrier densities in the 10
21
cm
-3
can be achieved
using ultrafast laser absorption. Carrier trapping into local-
ized states leads to a considerable reduction of the free
carrier lifetime for a thin film compared to bulk crystalline
Si. Above densities of 8 × 10
19
cm
-3
another contribution
to the relaxation time appears due to Auger processes
involving spatially overlapping electron-hole pairs. The
combined processes result in a relaxation rate of the order
of 10
13
s
-1
at carrier densities around 10
21
cm
-3
.
40
An
additional limiting factor to the carrier concentration is
carrier diffusion out of the gap region. For an S ) 20 nm
gap region and a carrier diffusion constant of D
e
= 40 cm
2
/
s, electron diffusion will contribute to a relaxation rate of
around S
2
/D ∼ 10
13
s
-1
, i.e., comparable to the Auger
process.
In practice these relaxation rates balanced against the
pumping rate will determine the stationary free carrier
population that can be achieved. However they also provide
the ultrafast time response of the nanoantenna switch
desirable for many applications. Eventually all the energy
deposited into the system will be converted into heat by
electron-phonon relaxation on a time scale of picosec-
onds.
26
In the extreme case that all this energy is dissipated
entirely in the nanoantenna, it produces a temperature rise
of around 30 K. For this estimation we have used the lattice
heat capacity of gold C
L
= 2.5 × 10
6
J/m
3
K and a total
amount of 10
6
generated electron-hole pairs per antenna
and per pump pulse. This number of carriers follows from
eq 3 for the switching fluence of 0.73 mJ/cm
2
and the
antenna gap dimensions. Effects of overheating can be
substantially reduced by embedding the antenna into an
environment with a good thermal conductivity.
The combination of strong optical resonances with a high
local field enhancement in the antenna gap opens up op-
portunities for optical pumping employing the mode struc-
ture and its dynamic modulation. Since only a nanometer-
sized active volume has to be pumped, which is strategically
located in the antenna gap, the estimated pump intensity
required for switching can be significantly reduced through
funneling of pump energy into the resonant antenna mode.
Considering a typical 100 times resonant intensity enhance-
ment in the antenna gap,
4,37
we estimate an ultimate
switching energy of around 100 fJ. In addition, it may be
possible to employ the strong resonant enhancement of
nonlinear optical phenomena in the feed gap, such as second
harmonic and supercontinuum generation,
4,5,9
to produce
a nonlinear absorption complementary to two-step absorp-
tion. The above resonant reduction of the pumping threshold
assumes that this energy can be deposited into the resonant
mode before the switching itself changes the antenna mode
structure. In the other limit of stationary resonant pumping,
the dynamic switching of the antenna will result in optically
bistable behavior.
35
We propose that the nanoantenna
switch can thus be used as a saturable absorber element.
N
eh
)
F
0
pω
[
α
0
+
βF
0
2
√
2πt
0
]
(3)
© 2010 American Chemical Society
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DOI: 10.1021/nl1001636 | Nano Lett. 2010, 10, 1741-–1746
