Plasmonic circuits for manipulating optical information

Abstract

Surface plasmons excited by light in metal structures provide a means for manipulating optical energy at the nanoscale. Plasmons are associated with the collective oscillations of conduction electrons in metals and play a role intermediate between photonics and electronics. As such, plasmonic devices have been created that mimic photonic waveguides as well as electrical circuits operating at optical frequencies. We review the plasmon technologies and circuits proposed, modeled, and demonstrated over the past decade that have potential applications in optical computing and optical information processing.

Full text

Nanophotonics 2017; 6(3): 543–559
Review article Open Access
Timothy J. Davis*, Daniel E. Gómez and Ann Roberts
Plasmonic circuits for manipulating optical
information
DOI 10.1515/nanoph-2016-0131
Received July 30, 2016; revised September 16, 2016; accepted
September 22, 2016
Abstract: Surface plasmons excited by light in metal struc-
tures provide a means for manipulating optical energy at
the nanoscale. Plasmons are associated with the collective
oscillations of conduction electrons in metals and play a
role intermediate between photonics and electronics. As
such, plasmonic devices have been created that mimic
photonic waveguides as well as electrical circuits operat-
ing at optical frequencies. We review the plasmon technol-
ogies and circuits proposed, modeled, and demonstrated
over the past decade that have potential applications in
optical computing and optical information processing.
Keywords: nanorods; optical computing; optical devices;
optical logic devices; optical properties of nanostructures;
optical signal processing; plasmonics.
PACS: 73.20.Mf; 42.79.Sz; 42.79.Ta; 42.79.-e; 78.67.Qa;
78.67.-n.
1 Introduction
Optical information processing (optical computing) has
been an active topic of research for at least six decades
already [1]. In its original form, Fourier transforms
of coherent light distributions were performed using
lenses, enabling extremely fast and highly parallel data
processing such as correlations for object recognition.
There has been renewed interest in all-optical methods
to process signals in communication networks [2, 3] with
the idea of using optical processing elements to enable
“software-defined networks” [4, 5] necessary to simplify
network reconfigurability. As data in optical communica-
tions can be encoded using amplitude, phase, intensity,
wavelength, and polarization, direct serial operations
between light signals can eliminate the complex optics-
electronics-optics conversion, thereby maintaining the
encoding during processing.
However, there are good reasons electronics is used
for computation whereas optics is used for communica-
tion [6]. Electronics is based on the movement of electrons,
with signals encoded using current or voltage. The opera-
tion frequency of electrical circuits is limited by the rate
at which electrons can move, which in turn is governed
by inductive and capacitive effects as well as resistive
losses associated with electron propagation in materi-
als. Electronic systems are capable of strong non-linear
behaviors, such as switching and state changes, because
of the strong interaction between electrons mediated by
their electric fields. More fundamentally, electrons have
mass and therefore can be confined in stationary states
in small regions of space, which is important for memory.
Electronic circuits are characterized by electron propaga-
tion through wires, resistance, capacitance, inductance,
and non-linear behavior as represented by transistors
(Figure1).
Photonics is based on the propagation of light. Unlike
electrons, the optical signal can be encoded directly on the
photon wave function, such as by modulating the polari-
zation or the phase of the beam, which takes advantage
of the coherent nature of the wave. The carrier frequency
of an optical electromagnetic wave is exceptionally high,
in the region of hundreds of terahertz, enabling very large
data transfer rates. However, photons interact very weakly
with one another, if at all, so that all-optical modulation
and switching are difficult to achieve [7]. With very intense
beams, it is possible to drive non-linear changes in mate-
rial properties, such as refractive index changes, that can
be used for modulation or by using electro-optical effects
whereby an electrical signal changes the optical proper-
ties of a material to modulate the light beam. Currently,
information in communications networks is processed by
converting the optical signal into an electronic one and
*Corresponding author: Timothy J. Davis, School of Physics,
University of Melbourne, Parkville, Victoria 3010, Australia,
e-mail: timd@unimelb.edu.au
Daniel E. Gómez: School of Applied Science, RMIT University,
Melbourne, Victoria 3000, Australia
Ann Roberts: School of Physics, University of Melbourne, Parkville,
Victoria 3010, Australia
©2016, Timothy J. Davis et al., published by De Gruyter.
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

544T.J. Davis etal.: Plasmonic circuits for manipulating optical information
then applying electronic signal processing methods. This
is not a coherent process, and the phase information asso-
ciated with the light beam must be decoded and converted
into an electrical signal. Moreover, photons have no mass
and therefore cannot remain stationary in space, which
is problematic for optical memory. Photonic circuits are
characterized by waveguides and linear effects such as
interference, diffraction, and resonance.
Intermediate between electronics and photonics lies
plasmonics. Surface plasmon polaritons (SPPs), often
abbreviated to plasmons, are collective oscillations of
the conduction electrons driven by light at the surfaces
of metals [8, 9]. As such, the plasmons oscillate at optical
frequencies, around hundreds of terahertz, and are associ-
ated with strong electric fields. The plasmons maintain the
phase relationships with the incident light and are there-
fore coherent excitations. As plasmons can be confined to
regions 100 times smaller than light focused to a diffrac-
tion-limited spot [10], they provide a means to manipu-
late optical energy at the nanoscale. This size regime lies
in between that of photonics, where device feature sizes
are typically above 1000 nm, and that of electronics, for
which transistor feature sizes are now approaching 10 nm.
Plasmons propagating on metal structures such as plane
surfaces, grooves, or wires or even confined to small metal
particles [where they are known as localized surface plas-
mons (LSPs)] have been described as light on a wire [11].
It is fair to say that very little has been done using
plasmonics for optical computing or optical information
Electron propagation
Voltage & current
Low frequency
Electron-electron interaction strong
Light propagation
Amplitude, phase, polarisation
Very high frequency
Photon-photon interaction weak
Waveguide
Interference
Diffraction
Wires
Resistance
Inductance
Capacitance
Non-linearity
Electronics
Photonics
Plasmonics
Electric charge oscillations on metal surfaces
Oscillations at optical frequencies
Propagate on wires as waves – maintain phase coherence
Resonate on particles like electrical circuits
Plasmon-plasmon interactions strong but linear
Figure 1:A comparison between electronic and photonic circuits.
The field of plasmonics lies in between.
processing. To date, most of the effort has been directed
to understanding the basic principles and demonstrat-
ing devices in proof-of-principle experiments. The resur-
gence in the study of surface plasmons has been driven by
the optics community, and as such, most applications of
plasmonics mimic configurations in optics or photonics,
such as waveguides, devices for converting polarization,
optical filters, and so on [12]. However, plasmons repre-
sent the extreme frequency limit of the classical skin effect
well known in radio frequency engineering, which has led
to descriptions of plasmons in terms of electric circuits,
antennas, and electrical filters.
In this review, we examine the optical and electrical
circuit descriptions of plasmonics and then present some
recent ideas on plasmonic systems that may have applica-
tions in optical-domain information processing.
2 A brief overview of surface
plasmons
Research into SPPs has burgeoned in the last 16 years,
driven largely by the emergence of methods for nanoscale
structuring of metals [13–20]. Although strictly a quantum
quasi-particle composed of coherent charge oscillations,
plasmons can be described classically using Maxwell’s
equations of electromagnetism, which predicts the pres-
ence of propagating electromagnetic waves trapped at
the interface between a dielectric and a metal (Figure
2). These are SPPs. They are the combined effect of the
electron plasma at the metal surface coupled to the
polarization charges induced in the dielectric. Light with
a free-space wavenumber k0 = ω/c will create surface
plasmons with a wavenumber spp0 /( ),
md
md
kk
=+
εε
εε
which depends on the relative electric permittivity of
the metal εm(ω) and that of the adjacent dielectric εd. At
optical frequencies, εm < 0 is negative and large |εm|  εd
so that spp0 .
d
kk>ε This means that the plasmon wave-
length is smaller than that of the light and the plasmon
is unable to radiate into the dielectric, becoming trapped
at the surface (Figure2A andB). Furthermore, it is then
quite difficult to excite surface plasmons as light from the
dielectric cannot be phase-matched to it. However, plas-
mons radiate at discontinuities such as ridges or pits in
the surface or abrupt changes in the dielectric, and like-
wise, light incident on these discontinuities can excite
surface plasmons (Figure2C). These discontinuities can
also reflect and scatter plasmons [20, 21].
A thick metal film with dielectric materials adjacent
to both surfaces will support two independent plasmon

T.J. Davis etal.: Plasmonic circuits for manipulating optical information545
waves, one for each surface, with wavelengths depend-
ing on the permittivities of the dielectrics. If the metal
film becomes thinner than the skin depth of the elec-
tromagnetic wave, the plasmon electric fields penetrate
the full thickness of the film leading to coupled modes
and mode splitting [22]. For such thin films, it is pos-
sible to excite surface plasmons using special geom-
etries (Kretschmann, Otto) and appropriately chosen
di electrics [8, 9].
As plasmons propagate as waves, they can reflect,
scatter, diffract, and interfere, which enables them to be
used in much the same way that light is used in photon-
ics. At certain frequencies, plasmons excited on the sur-
faces of metal particles exist as standing waves (Figure
2D and E), which are known as LSPs. The characteristic
frequencies correspond to LSP resonances [23] and are
associated with a large number of possible standing wave
modes [24]. As these particles are generally much smaller
than the wavelength of light, with dimensions typically
between 10nm and 200 nm, no phase-matching condition
is necessary and LSPs can be excited simply by shining
light on the particles at an appropriate frequency, but only
those modes that have non-zero electric dipole moment
are excited, the other modes, appearing “dark”. Because
of losses in the metal (essentially Ohmic losses), the
resonances are much broader than those usually found
in spectroscopy on atoms and molecules, with quality
factors around Q ~ 10 (for example, see Figure 6A). Metals
such as aluminum, gold, and silver are commonly used in
plasmonics because of their relatively low loss at optical
frequencies.
In the following sections, we will discuss different
devices created using surface plasmons. Most of these
devices have been used for proof-of-principle demon-
strations and may not be practical in real applications.
We begin by examining research into devices based on
plasmon waveguides that use the wave-like properties
of plasmons propagating over surfaces or within special
guides to demonstrate both linear and non-linear optical
devices for manipulating light at the nanoscale. As
plasmon emission and detection is important, we briefly
present some research into plasmon emitters and detec-
tors as well as coupling to fluorescent materials. We then
examine plasmonics from the point of view of electronics
and review research on LSPs that mimic inductor-capac-
itor circuits operating at optical frequencies. Within this
topic, we consider optical antennas, optical circuits, and
concepts for performing mathematical operations on light
fields. A brief mention of quantum plasmonics follows.
Finally, because of the losses encountered with metals,
−−
+
++
−
−−
300
400
500
600
700
200
A
DE
C
B
600 700 800 900
Free space wavelength (nm)
Wavelength in medium (nm)
Glass
Plasmon on silver
Plasmon on gold
+−
++
−−
Propagation direction
Metal substrate
Dielectric
Surface plasmon polaritons (SPP)
SPP scattering and radiation
Localised surface plasmon (LSP) eigenmodes
+
−
+
+
−
Figure 2:Plasmons propagating on surfaces: (A) The wavelength of an SPP is shorter than the free space wavelength of light or the
wavelength within the dielectric, which prevents the plasmon from radiating; (B) the electric field associated with an SPP propagating over
the surface of a thick metal film; (C) illustration of a plasmon scattering at a discontinuity with some energy converted to radiation in the
dielectric; (D–E) examples of LSPs on different metal particles. These show the charge distributions (blue positive, red negative) of different
resonant modes. The fundamental mode is a half wavelength with a strong dipole moment.

546T.J. Davis etal.: Plasmonic circuits for manipulating optical information
there has been work towards low loss materials support-
ing surface plasmon propagation.
3 Plasmonic waveguide circuits
Surface plasmons can propagate as waves over metal sur-
faces, and because plasmon wavelengths can be much
smaller than light at the same frequency, they have poten-
tial in highly compact optical devices. The optical proper-
ties of these waves on surfaces have been studied [20] and
applied to simple optical elements. For example, it was
shown that a converging lens for surface plasmons can
be created by slits cut into the metal film, which performs
an optical Fourier transform analogously to macroscopic
lenses, enabling traditional optical computing on-chip
[25]. One of the issues with “free” plasmon propagation
over surfaces is creating the plasmon in the first place.
One solution is to etch a slot through the metal film to
the transparent substrate. When the slot is illuminated
through the substrate, the electric field penetrates to the
top surface, launching plasmon waves that propagate in
either direction away from the normal to the slot edge.
By including slot reflectors in the surface, it is possible
to interfere the plasmon waves enabling devices such
as binary encoders [26], logic discriminators [27], and
multiplexers [28]. Similarly, arrays of holes can be used
to launch plasmons and to convert the energy back into
freely propagating light [29].
Plasmon waves can be confined and guided by a thin
metal strip. The motivation for such work is based on the
idea that light can form high-speed and low-loss inter-
connects for electronic circuits and the use of plasmons
enables very compact devices, an order of magnitude or
smaller than the wavelength of light [14, 15, 17, 30–32].
Similar to light travelling in optical waveguides, the plas-
mons propagate with one or more different modes on
the metal strip, depending on the strip geometry and the
electric permittivities of the metal and the surrounding
medium. A systematic study of the propagation in these
guides [33–35] demonstrated the existence of a short-
range and a long-range mode. The short-range mode is
lossy because there is strong penetration of the plasmon
electric field into the metal, creating electrical currents
that lose energy by Ohmic resistance. The long-range
mode has the plasmon electric field predominantly in
the dielectric region about the waveguide, thereby reduc-
ing losses. Transmission of optical signals by plasmons
in strip waveguides has been demonstrated at telecom
wavelengths with data rates of 10 Gbs [36]. There have
Metal
Insulator
Metal
Metal – insulator – metal Insulator – metal – insulator
Wedge SPP
Hybrid plasmon polariton
Dielectric – loaded SPP Metal on insulator
Channel plasmon-polariton
Gap plasmon-polariton
Figure 3:Cross sections of different types of plasmon waveguides
(adapted from Ref. [18]).
also been investigations of plasmon propagation in more
complicated multi-layer guides [22, 37] as well as arrays of
particles [38–41].
As loss is a big problem with plasmon propagation
in metals, there have been many studies looking for con-
figurations of metals and dielectrics that minimize the
penetration of the electric field into the metal [18]. These
include grooves, slots, metal-insulator-metal designs, and
so on (see Figure3 with typical parameters in Table 1).
Important factors in plasmon waveguides are the propa-
gation distance, operating wavelength, and mode area.
The propagation distance is limited by absorption, which
is problematic in complex plasmonic circuits. The mode
area describes the cross sectional area of the region con-
taining the optical energy. Large mode areas reduce the
ability to create compact devices. For example, subwave-
length plasmon-polariton guiding by triangular metal
wedges has been demonstrated [42] with propagation
lengths ~ 120 μm and mode widths ~ 3 μm. Other proposed
strategies to mitigate Ohmic losses in plasmon oscillation
and propagation include the interaction of plasmons with
gain media [43–47].
Metal-insulator-metal (MIM), sometimes referred
to as metal-dielectric-metal (MDM), and gap plasmon
polariton (GPP) waveguides have the advantage of simple

T.J. Davis etal.: Plasmonic circuits for manipulating optical information547
fabrication in that they can be constructed by cutting a
slot in a metal film and filling the slot with a dielectric [31,
48]. Likewise, dielectric loaded plasmon waveguides only
require patterning of a dielectric layer on top of a metal
film, which can be done directly using lithographic resist
such as PMMA. Guiding in “V”-shaped grooves in metals
has been demonstrated along with typical waveguide
elements [17, 30] such as splitters and ring resonators. A
theoretical analysis of plasmons in channels showed that
increasing wavelength caused the fundamental mode to
shift from the bottom of the channel and become more like
wedge plasmons, being guided by the upper edges [49].
The plasmons guided by wedges at telecom wavelengths
are better confined (smaller mode area) without increas-
ing loss [50].
The choice of one waveguide geometry over another
depends on the application. If long propagation distance
is required, then one might choose a V-groove or hybrid
plasmon-polariton geometry, or if small mode area is
necessary, then an insulator-metal-insulator design may
be preferred. However, these waveguides may not be
compatible with the overall microfabrication process, in
which case some trade-off will be required.
3.1 Emitters and detectors for integrated
plasmonics
With the development of plasmon waveguide devices,
there has been some research into methods of launch-
ing plasmons directly on-chip. Most of these works have
been proof-of-principle demonstrations of devices with
potential for integration in plasmonic circuits, but they
are significantly less advanced than corresponding
devices used in photonics. In one example, a nanoscale
light emitting diode with a subwavelength footprint
directed some of its emission into a single-mode slot
plasmon waveguide [51]. Additionally, the prospect of
stimulated emission of plasmon radiation has been
studied [19, 43, 52] and a device was fabricated and
demonstrated [53]. This nanoscale plasmon emitter was
constructed from 44-nm-sized nanoparticles with a gold
core and a dye-doped silica shell. Surface plasmon oscil-
lations were outcoupled to photonic modes at a wave-
length of 531nm. At the quantum limit, there have been
experimental demonstrations of the excitation of surface
plasmons by single photon emitters. Importantly, these
experiments reveal that the radiative decay of a plasmon
excited by a single photon also yields a single photon,
even though a surface plasmon is a collective phenom-
enon consisting of the in-phase oscillations of a large
number of electrons [54–58].
Active plasmonic devices including those with gain
have been reviewed elsewhere [59]. Gain media consist
of materials with electronic states that can be optically
excited and subsequently de-excited in phase by another
light beam, as occurs in solid-state lasers. Plasmon gain
requires the gain media to emit in phase with the propa-
gating plasmon. Amplified spontaneous emission from a
polymer waveguide film containing laser dye molecules
excited by surface plasmons and pumped by another laser
has been observed [60], and there has been a demonstra-
tion of plasmonic propagation with net positive gain pro-
vided by an optically pumped layer of fluorescent polymer
in a dielectric-metal-dielectric waveguide [61]. Incoherent
plasmonic gain has been predicted with three-level fluo-
rescent semiconductor nanocrystals in the presence of
another semiconductor with negative electric permittivity
Table 1:Comparison of plasmon waveguide optical confinement (mode area), propagation length L and free space wavelength λ (from
Ref.[18]).
Waveguide typeMode width/λMode height/λMode area/(λ/)L/λλ (nm)
GPP . . %  
Wedge ~. N.A. N.A. 
MIM . . % 
IMI . ~. ~%  
V-groove . >. >% ~
DL-SP P . N.A. N.A.  
DL-SP P N.A. N.A. % 
. . .%  
. . % N.A.
HPP . . %  
. . %  
.theory .theory %  
    
N.A., not available.

548T.J. Davis etal.: Plasmonic circuits for manipulating optical information
[62]. Spontaneous emission from nanosized particles and
plasmon resonators has been studied theoretically [63].
Plasmon detectors have also been integrated into
devices, such as a Schottky contact device with an asym-
metric metal stripe waveguide [64]. Superconducting
plasmon detectors were used to detect single plasmon
quanta in a quantum interference experiment [65]. Plas-
monic components have been used in detectors to alter
the responsivity in the mid-infrared [66] as well as in the
visible region [67]. In principle, such detectors can be as
sensitive as those used in photonics, which is determined
largely by the quality of the semiconductor photo-diode
fabrication process.
3.2 Linear devices for optical computing
Linear devices based on waveguides tend to mimic those
used in photonics. Linear devices use plasmon wave
properties such as constructive and destructive interfer-
ence to perform addition and subtraction operations,
respectively. Moreover, plasmon excitation relies on
the correct alignment of the incident electric field with
respect to the ridges or grooves that launch the plas-
mons, as the field is required to induce a surface charge.
In other words, such launching methods are sensitive to
the incident polarization, which provides a means for
polarization sensitivity.
Examples of photonic devices created for plasmons
are shown in Figure4 and include “Y” junctions for com-
bining or separating plasmons [68–72], “X” junctions
[70], proximity couplers [73], directional couplers [74],
Mach-Zehnder interferometers for interfering plasmons
A
B
A+B
Y-junction OR gate
A
B
XOR gate
180° phase shift
A + B
A
B
Control
A+BA+B
180° phase shift
NOR gate
Half adder
A
B
Control
(Radiation dump
)
A+B = bit 1
A + B = bit 0
Ring resonator
Mach-Zehnder
interferometer
Bragg grating
Phase shift control
Figure 4:Plasmonic waveguide devices for performing optical
processing. The logic circuits operate using phase shifts and
interference.
[73,75–78], Bragg grating filters [69, 79], add-drop filters
[80], and ring resonators [69, 79, 81] that transmit or reflect
plasmon waves depending on frequency and switching
using phase shifts [82]. A novel plasmon filter was created
using two wires of different materials joined together that
provided a large electric permittivity mismatch resulting
in unidirectional propagation [83].
Additive logic operations have been proposed and
modeled with such circuits or their variants [84–90].
There have been demonstrations of logic functions such
as a NOR gate built from OR and NOT gates [91]; XNOT,
XOR, and NOT gates using an air slot etched in gold on
silicon dioxide [92] and an XOR gate [93]; an OR gate [94];
a logic comparator [95]; NOT, AND, OR, XOR [96]; a half-
adder [97]; demultiplexers [28]; binary encoders [26, 98];
and discriminators [27]. The operations of these gates
depend on phase shifts or on frequency (wavelength) dif-
ferences, which presuppose specific encoding schemes
for the digital information. These devices have been used
to demonstrate logic operations, but there has been no
concerted attempt at fulfilling the requirements of logical
optical processes as required in communications net-
works or optical computing.
More complex arrangements are possible leading to
coupling between waveguide modes [22]. Such coupling
can be used to create highly compact waveguide interfer-
ometers, such as the Mach-Zehnder [77, 78, 99]. As inter-
ferometers are very sensitive to phase shifts, they have
applications where non-linear effects can be used to mod-
ulate the plasmon phase.
3.3 Non-linear devices for optical computing
Linear devices have limited use in many photonic circuits,
as they cannot demonstrate bistability or static behavior
but require a continuous propagation of plasmon waves
to operate (such as required for interference). While plas-
mon-plasmon interactions and plasmon-material interac-
tions are generally linear, the plasmons have electric field
strengths one or more orders of magnitude larger than the
light wave electric fields that excite them, which makes
it easier to induce non-linear behaviors in materials,
enhancing modulation [100]. The non-linearities generally
change the local electric permittivity that shifts the phase
of propagating plasmons. When combined with plasmon
interferometers, these can be quite effective modulators.
In addition, it is possible to use electrical signals to induce
material changes, particularly in semiconductors where
the electron density, and therefore the “metallic” proper-
ties, can be altered. These are termed “active plasmonic”

T.J. Davis etal.: Plasmonic circuits for manipulating optical information549
devices [101]. The methods for non-linear modulation of
plasmons are summarized in Figure5.
There have been many devices proposed and simu-
lated, such as modulation based on an external electri-
cal signal interacting with graphene to create NOR/AND,
NAND/OR, XNOR/XOR gates [102]; third-order non-linear
optical materials in which the electric field intensity |E|2 of
the plasmon induces refractive index changes, also known
as Kerr-nonlinearity [103–107]; intense optical pulses to
induce refractive index changes in GaAsInP [108]; polari-
zation sensitive four-wave mixing non-linearity coupled to
a plasmon ring resonator [109, 110]; metal-dielectric cavi-
ties filled with non-linear materials to create bistability
[111] or switching [112]; a three-level system showing gain
[62]; beam steering by modulating refractive index [113,
114]; electro-active materials to shift refractive index [115,
116]; and change in resonance by changing refractive index
[117] or by changing material properties by electron excita-
tion pumped by light [118, 119] (changes absorption prop-
erties within a waveband). One novel device modulated
a plasmon wave on a diffraction grating by changing the
refractive index of a surface layer of fluid [120].
It is one thing to propose a device but much more dif-
ficult to fabricate and demonstrate one. Plasmonic devices
based on non-linear effects can be classified into several
different categories: those where the plasmon does the
modulation, those where an external light signal does the
modulation, and those where an external electrical signal
does the modulation. These methods are summarized in
Figure 5.
3.3.1 Direct plasmon modulation
Surprisingly, there have been few experiments demon-
strating plasmon-plasmon modulation. As the plasmon
is associated with a strong electric field, a propagat-
ing plasmon wave can directly induce enough refrac-
tive index change in a material to affect the phase of
another plasmon. Nevertheless, the Kerr non-linearity
Modulation of metal
permittivity
Modulation of background
dielectric
Light pulse
Light pulse
Plasmon
Electric field
Change in metal permittivity
Broadband signals >10 THz
High intensity pulses required
Fast modulation <100 fs
Non-linear glass
Broadband signals >10 THz
High intensity fields required
Fast modulation <ps
Phase-change material
Broadband signals >10 THz
Low intensity fields required
Slow switching >µs
Resonant molecules
Narrowband signals
Low intensity fields required
Fast switching <ps
(depends on FWHM)
Non-linear glass
Broadband signals >10 THz
High intensity fields required
Fast modulation <ps
Phase-change/photo refractive
Broadband signals >10 THz
Low intensity fields required
Slow modulation >µs
Electro-optic material
Broadband signals >100 TH
Switching 10 ps to s
(depends on material)
Electro-thermo-optic/
Electric-induced phase change
Broadband signals >10 THz
Slow modulation >µs
Semiconductor charging
Broadband signals >10 THz
<10 ns to > 1 µs
(limited by capacitance)
Modulation type
εb
εb
εb
εm + δεm
εb + δεb
εm
εm
εm
Control signal Physical process Rate
Figure 5:Comparison of plasmon modulation methods.

550T.J. Davis etal.: Plasmonic circuits for manipulating optical information
of most optical materials, which determines the change
in refractive index with optical intensity, is in the order
of ~ 10−17 m2/W [121]. That is, to change the refractive
index by 1% requires light or plasmon intensities around
1015 W/m 2. While this is very large, compressing a 1-W
laser beam with a cross section area of 1 mm2 into a region
30 × 30 nm2 will create such an intensity. A more practi-
cal method for modulating one plasmon by another has
been demonstrated using semiconductor nanoparticles,
which have an electronic excited state near the plasmon
frequency. The excitation of an electron into this state
by one plasmon changes the absorption and refractive
properties experienced by another plasmon at a different
frequency, leading to all-plasmon modulation [122, 123].
An alternative is to use a photochromic dye in which the
refractive index is altered by the presence of the plasmon
[124] although such processes are slow, taking millisec-
onds or even seconds to occur.
3.3.2 Modulation by external light
It is well known that light can induce non-linear changes
in material properties, which in turn can be used to
modify the phase or absorption of propagating electro-
magnetic waves. In one class of devices, a high intensity
light pulse directed onto a metal disturbs the free elec-
tron distribution changing the electric permittivity of the
metal or an adjacent semiconductor. This is an extremely
fast effect, usually induced by femtosecond laser pulses,
which perturbs the plasmon [125–128]. A similar effect was
observed recently in indium tin oxide nanorods support-
ing plasmons in the infrared [129]. There are interferom-
eters in which refractive index modulation by a light pulse
on a photo-refractive material induces a phase shift in one
beam path changing the interference state and therefore
the plasmon intensity [130–133]. This method can be used
with magneto-optical materials [134]. Light pulses can
induce phase transitions in materials, such as vanadium
dioxide, which are accompanied by large refractive index
changes [135], or light can induce mechanical strain to
change the periodicity of a grating, thereby modulating
the propagating plasmon [136]. A variant on this method
was to use a light pulse to induce scattering centers by the
local decomposition of silver oxide [137].
3.3.3 Modulation by an electrical signal
A plasmon ring resonator was constructed with a dielec-
tric host-matrix doped with an electro-optic material that
changes refractive index on application of an electri-
cal signal, modulating the plasmon transmission. Such
devices can be slow depending on the electrical response
time of the material [138]. Recently, a plasmonic Mach-
Zehnder modulator was demonstrated, which used an
electro-optic material to modulate the phase. The on-chip
modulator was integrated into a silicon waveguide of
10-μm length with a frequency response up to 70 GHz
[139]. A novel plasmon memory device was based on mem-
ristor technology in which the growth of a metal filament
under action of an applied electric field modulates the
plasmon propagation [140] in a MIM waveguide structure.
It is possible to control the electron density by an electric
field [141–144] by using a semiconductor or electro-optic
material, which can be used to modulate plasmons, or
by using Tamm-plasmon-polaritons, which are plasmon
states formed at the boundary between a metal and a
dielectric Bragg mirror [145]. A similar phenomenon is
the Faraday effect in which a static magnetic field applied
to a magneto-optic material alters the optical properties,
which can be coupled to plasmonic devices [146].
Variants of this method use electrical signals to induce
temperature changes that modify the refractive index of a
thermo-optic dielectric, again by using interferometry to
alter the plasmon intensity [147] or by using electrochemi-
cal switching of material properties [148, 149].
It is clear that the most promising methods for
plasmon modulation use electrical effects. These are
easily integrated into existing electronic circuit designs
and can show superior performance [139].
4 Plasmonics as electronics at light
frequencies
So far, we have reviewed plasmonics technologies derived
from photonics based on waveguide devices such as “Y”
junctions, Mach-Zehnder interferometers, and ring reso-
nators. These exploit the wave-like properties of plasmons
propagating on surfaces. However, as we discussed in
the introduction, it is possible to excite surface plasmons
on small metal particles. When illuminated at a specific
frequency, LSP resonances are excited (Figure 6A). Physi-
cally, these are oscillations of the conduction electrons
at the surface of the particle. If we consider these oscil-
lations from the point of view of electrical engineering,
we would describe them in terms of traditional circuit ele-
ments, such as inductance, capacitance, and resistance.
A correspondence between electrical circuit ele-
ments and metal and dielectric particles was given by

T.J. Davis etal.: Plasmonic circuits for manipulating optical information551
Enghetaetal. [153, 154] in terms of the electric permittivi-
ties and independently by Davis [155] in terms of lumped
circuit elements determined from considerations of power
flow. This same procedure was used more recently to
extract lumped values from complicated arrangements
of particles [156]. In essence, a metal particle supporting
LSPs can be represented by a combination of inductance,
capacitance, and resistance (Figure 6B). The inductance is
a consequence of the negative electric permittivity of metals
at optical frequencies [154]. The capacitance is related to
the influence of the surrounding dielectric, and resist-
ance arises from loss in the metal when a current flows or
when the plasmon re-radiates light (radiation resistance).
Similarly, a dielectric particle acts like a capacitor [154].
Formulae that accurately predict the circuit values for
arbitrary-shaped plasmonic structures are not available.
For a metal sphere of radius R and complex permittivity
,
mm m
i=+
′′′
εε
ε the equivalent inductance is given approxi-
mately by 2
sph1/
()
,
m
L
Rωπ≈− ′
ε which depends on the real
part of the permittivity. The capacitance associated with
the external electric fields Cfringe ≈ 2πωRε0 depends on the
permittivity of the surrounding space. The resistance of
the sphere depends on the imaginary part m
′′
ε of the per-
mittivity [154].
The plasmon circuit model provides a means for
designing optical elements using LSPs in the same way
one would design an electrical circuit (Figure 6). This is
a radical departure from the usual interpretation of plas-
monics as an optical phenomenon and creates new ways
of approaching optical information manipulation. The
proximity of one metal nanoparticle to another leads to
capacitive coupling between the LSPs, mediated by their
electric fields. This can result in quite complex circuits
and circuit models [156]. The coupling between plasmonic
particles is interesting because the resonant modes are
altered and generally form pairs that are split in frequency.
Such behavior is a consequence of coupled oscillators,
well known in physics and engineering. In the study of
LSPs, the mode splitting has been described in terms of
the hybridization of molecular orbitals that occurs when
two atoms bind, which leads to bonding and anti-bonding
states [157–159].
700 750 800 850
0.0
0.2
0.1
0.3
Wavelength (nm)
Intensity (arb. units)
R
LC
Gold nanorod
100 nm
Z1Z2
Z3
CsCs
CE
CE
Z
G
G
1 2
3
A
BC
Experiment
Fit
D E F
Figure 6:Plasmonics as electronics. (A) An example of the scattering spectrum from a single gold nanorod l=100 nm, w=40 nm, t=30nm;
(B) SEM image of the resist used to define a gold nanorod during lithography; (C) the equivalent circuit impedance of the rod – the spectrum
is fit to I=A+B|Z|2 where Z=(R+jωL)/(1−ω2LC+jωRC) is the circuit impedance. The fit gives the lumped component values RC=3.99×10−17s
and LC=1.64×10−31 s2 and the resonant frequency is π
==
1/2393 THz;
f
LC (D) a three-nanorod structure that mimics a Wheatstone
bridge circuit [150, 151]; (E) the equivalent electrical circuit; (F) an alternative analysis using plasmon coupling theory [152] that gives
plasmon excitation amplitude on nanorod 3 ã3=[Gp·(E1−E2)]/[(δω+iΓ/2)2−2G2] directly in terms of parameters associated with the optics
of nanoparticles – the detuning δω from the single rod resonance of FWHM Γ, dipole moment p and interparticle coupling G. The LSP
amplitude depends on the difference in the electric fields E1−E2 of the light incident on the two parallel rods, 1 and 2.

552T.J. Davis etal.: Plasmonic circuits for manipulating optical information
The lumped circuit values for plasmonic circuits are
generally unknown, and the circuit element associated
with a given interaction has to be assumed. Unlike con-
ventional electronics, the inductance of plasmonic parti-
cles is strongly dependent on frequency. Furthermore, the
role of light polarization on circuit elements is unclear.
We developed, as an alternative, an approach based on
approximate solutions of Maxwell’s equations for the
interaction of electromagnetic waves with metal particles.
It is possible to write down an equation for the natural res-
onant modes of an arbitrary shaped metal particle, which
becomes relatively simple in the near-field regime where
the phase shifts due to propagation of the electromagnetic
radiation can be neglected [160–162]. These resonant
modes are the LSPs (Figure 2D and E) and are represented
by surface charge standing waves. The electric fields from
the surface charges couple nearby particles, predomi-
nantly through electric dipole interactions. When the cou-
pling between the modes is taken into account, one can
derive a simple algebra describing the effects of ensembles
of metal nanostructures on one another and on the inci-
dent and scattered light fields [152, 163–165]. This is quite
analogous to the description in terms of electrical circuits
and leads to algebraic expressions no more complicated
than those found in electric circuit analysis. The advan-
tage is the algebra is expressed in terms of the natural
quantities associated with LSPs, such as electric permit-
tivity, induced dipole moments, and coupling by electric
fields including the polarization properties of the incident
light fields. This algebraic approach has been very suc-
cessful and has enabled us to design quite complex cir-
cuits, such as the plasmonic Wheatstone bridge that can
be used for phase detection [150, 151], all-optical modu-
lation and switching [166], as well as antennas with fre-
quency-dependent beaming [167] and response tailored to
the handedness of circular polarization [168].
4.1 Optical antennas
Alongside the development of plasmonic systems as elec-
trical circuits, it has been recognized that metal nanopar-
ticles behave like antennas for light [169, 170]. The optical
cross section of a metal nanoparticle is significantly larger
than its physical cross section, meaning that a small
nano-sized particle can capture light over a much larger
area and convert it into a localized plasmon resonance.
The simplest optical antenna is a metal nanorod. The fun-
damental plasmon resonance has a large dipole moment
(Figure 2D), and it acts like a half-wave antenna. However,
the wavelength corresponds to that of the plasmon and
not the incident light, so that optical antennas can have
dimensions well below the wavelength of light. Further-
more, the fundamental mode can only be excited by light
with an electric field component parallel to the dipole
moment, which usually lies along the major axis of the
rod, making these optical antennas polarization sensi-
tive. The LSP resonance stores optical energy and, as
such, develops very strong electric fields concentrated at
the ends of the rod, at least an order of magnitude larger
than the electric field of the incident light that excites it.
The localization of energy provides efficient coupling of
optical energy into other systems, such as waveguides and
fluorescent molecules [171, 172], and likewise, the plas-
monic antenna can efficiently out-couple radiation from
molecules, enhancing emission and polarization charac-
teristics. The quality factor (Q) of the resonance depends
on the metal and the dielectric environment but is typi-
cally in the range Q ~ 10–20.
There has been a large variety of antenna configura-
tions investigated, many of which are based on designs
used in radio engineering. As light is an electromagnetic
wave, most of the concepts of radio antenna design carry
across to the optical domain, except that the conductors
are not perfect but are lossy. Optical antennas have been
reviewed extensively elsewhere [169, 170, 173], and we
give only a brief overview here. Although much has been
written on optical antennas, these are essentially metal
particles exhibiting LSP resonances and it is more useful
to describe them as such. Most optical antenna designs
are dipole antennas, even though the antenna geometry
can be complicated, as the fundamental resonant mode
is predominantly dipolar in nature. Initial studies on
optical antennas verified the field enhancement prop-
erties of plasmons [174] and the spectral dependence of
the antenna near-field [175]. Optical antennas have been
used to enhance optical coupling into materials [176],
plasmonic waveguides, and transmission lines [177–179].
Examples of different optical antenna designs are the
Yagi-Uda antenna [180, 181], cross antennas [182], J-pole
[183, 184], V antennas [183], and bow-tie antennas [185].
As with radio engineering, it is possible to create antenna
arrays [173] for controlling the divergence and radiation
direction of a light beam [186, 187] and plasmonic struc-
tures for steering the radiation direction of light depend-
ing on frequency [167] or controlling the propagation
direction of plasmons based on phase [188]. The antenna
excitation patterns [189, 190] can be altered by changing
the phase and polarization of the incident light, which
affects the plasmon modes that are excited [191].
The antennas can have a strong influence on the
optical emission properties of fluorescent molecules

T.J. Davis etal.: Plasmonic circuits for manipulating optical information553
[192, 193], leading to enhanced, polarized, and directed
emission, which can be described in terms of impedance
matching [194]. Furthermore, such plasmonic antennas
can be used to convert polarization states from linear
to circular [195] or to distinguish between left and right
circularly polarized light [168]. In this regard, a self-con-
sistent electromagnetic theory of the coupling between
dipole emitters and dissipative nanoresonators has been
developed [63]. The antenna response can be modified by
placing dielectric materials or other metals nearby, which
affect the LSP resonances. This is analogous to capacitive
and inductive loading of the antenna [196, 197]. When
loaded with non-linear materials, it has been shown
theoretically that optical antennas can exhibit bistability
[198]. Tunable plasmonic antennas were created from two
suspended wires and changing their separation with an
applied voltage [199].
4.2 Plasmonic circuits
There has been relatively little work relating plasmonics
to electronics and building devices using this concept.
The concepts of distributed electronic circuit components
have been applied to optical structures such as transmis-
sion lines [153, 200], and an analysis of the optical power
associated with electromagnetic waves can be related to
lumped circuit components [155, 156, 201]. The lumped
circuit description has been demonstrated in the optical
regime (below 700 nm) in terms of an inductor-capacitor
circuit [155] in the thermal infrared regime (8–14 μm) [202]
and mid infrared (above 1.3 μm) [203].
Simple plasmonic circuits have been shown to act as
filters for waveguides [204] or for loading antennas [196,
197], as well as mimicking more complex filters, such as
a third-order Butterworth filter [205]. The correspond-
ence between metal and dielectric particles and electronic
components has been demonstrated using a scanning
probe tip to assemble together different optical filter com-
binations [206]. That the optical resonances of metal nan-
oparticles can be altered in the presence of other metals or
dielectrics is well known so it is not surprising that optical
filters can be created in this way.
There are very few complex plasmonic circuits dem-
onstrated with specific functionality. The plasmonic
equivalent of the Wheatstone bridge circuit in electronics
was suggested as a means for detecting optical signal dif-
ferences [150], and a realization of the circuit with dimen-
sions around 200nm acts as an optical differentiator to
detect optical phase differences [151]. Circuits of this type
have potential applications in optical signal processing,
such as decoders for differential phase-shift keying. The
plasmon coupling theory [152, 163, 164] shows that such
plasmonic circuits output signals that are linear com-
binations of the inputs Eout = M

· Ein, but with complex
matrix coefficients M

[166], which suggests that a variety
of different linear mathematical operations can be per-
formed. This plasmon circuit concept was used to design
a device for all-optical modulation of light, based on an
interference effect, as well as all-optical switching of light
beams [166].
The idea of performing mathematical operations on
light fields using nanoscale structures was highlighted
recently where optical Fourier transforms were demon-
strated numerically [207]. In addition to the optical dif-
ferentiator described above [151], designs for an optical
differentiator and integrator were demonstrated [208],
providing an approach to analogue optical computing.
5 Quantum plasmonics
Although plasmon properties can be described by classical
electromagnetism, the plasmons arise from long-range cor-
relations of the conduction band electrons in a metal and
appear in the form of quasi-particle boson states with both
particle and wave-like properties. In particular, the plasmons
remain coherent with the incident light, suggesting that it
should be possible to observe quantum coherence effects
with them or to use plasmons for manipulating quantum
properties of light. The resurgence of interest in plasmon-
ics has been accompanied by an interest in their quantum
properties [59, 209], which includes coherence, entangle-
ment, and wave-particle duality [209]. Plasmon waveguides
have been used to observe quantum interference [65] as
well as two plasmon quantum interference [210]. The wave-
particle duality of single SPPs has been studied using single
photon emitters coupled to a silver plasmon waveguide [57].
The quantum tunneling of electrons across sub-nanometer
gaps between coupled plasmonic particles has been inves-
tigated [211]. Plasmons also couple to quantum systems,
such as semiconductor nanocrystals [212, 213]. The strong
coupling between individual optical emitters and propagat-
ing surface plasmons has been proposed as an interface for
quantum networks [214].
6 New materials
A major issue with both classical and quantum plasmonic
devices is loss due to electron decoherence, which is

554T.J. Davis etal.: Plasmonic circuits for manipulating optical information
followed by absorption of energy in the metal lattice. This
destroys the coherence of the plasmon quantum state.
This problem of energy loss in the metal also limits the use
of plasmonic devices in telecommunications, which often
demands low loss materials and low insertion loss. While
active media or stimulated emission [43, 53] may overcome
losses, an alternative has been to seek low loss materials
that support plasmon resonances [215]. The key material
property required for plasmonic behavior is an electric
permittivity that is negative over a range of frequencies.
A review of work on new materials [216] discusses the
advantages and disadvantages of various metals and
semiconductors with the conclusion that silver, gold, and
aluminum are still the best materials for SPPs and LSP
resonances in the visible and ultraviolet regions. Recently,
titanium nitride was identified as a promising material for
the visible and near infrared regions [217] although it has a
smaller electric permittivity and greater losses when com-
pared with gold at the same frequency. In this regard, gold
is a better material for plasmonics.
7 Outlook
Despite the initial promise of plasmonics for nanoscale
optical devices, there are disappointingly few commercial
applications of plasmonics and none in the communica-
tions field [218, 219]. Most of the devices presented in this
review have scientific interest, but few are practical solu-
tions to photonics problems. Certainly, for plasmonics to
have some future in optical signal processing, it is impor-
tant that methods and materials are developed for better
integration with existing communications technology.
In this regard, devices such as the all-plasmonic Mach-
Zehnder modulator that was constructed on a silicon chip
show promise [139].
For optical signal processing or optical computing
based on plasmonics, logic and computational opera-
tions need to be developed using current encoding
schemes instead of just phase. With the advantage of far
lower losses than metals, dielectrics are likely to play an
increasing role in all-optical processing. Recent develop-
ments in silicon technology for the telecommunications
wavelengths are now competing with plasmonic devices.
These on-chip silicon devices, such as a wavelength
demultiplexer and a polarization beamsplitter, have small
footprints and are composed entirely of dielectrics [220].
However, plasmonic devices, with smaller resonator sizes,
subwavelength size scales, and potential for compatibil-
ity with conventional CMOS processing techniques, may
still have an important place in this emerging and exciting
field.
Acknowledgment: This work was funded in part through
the Australian Research Council Discovery Grant
DP160100983. D.G. also acknowledges ARC funding
FT140100514.
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