Tailoring Light-Matter Interaction with a Nanoscale Plasmon Resonator
Nathalie P. de Leon,1,2 Brendan J. Shields,2 Chun L. Yu,1 Dirk Englund,2 Alexey V.
Akimov,2,3 Mikhail D. Lukin,2* and Hongkun Park1,2*
1Department of Chemistry and Chemical Biology, and 2Department of Physics, Harvard
University, Cambridge, MA 02138, 3Lebedev Institute of Physics, Moscow, Russia
*To whom correspondence should be addressed. Email: firstname.lastname@example.org,
(Received January 12, 2012)
We propose and demonstrate a new approach for achieving strong light-matter
interactions with quantum emitters. Our approach makes use of a plasmon
resonator composed of defect-free, highly crystalline silver nanowires surrounded
by patterned dielectric distributed Bragg reflectors (DBRs). These resonators have
an effective mode volume (Veff) two orders of magnitude below the diffraction limit
and quality factor (Q) approaching 100, enabling enhancement of spontaneous
emission rates by a factor exceeding 75 at the cavity resonance. We also show that
these resonators can be used to convert a broadband quantum emitter to a
narrowband single-photon source with color-selective emission enhancement.
PACS numbers 73.20.Mf, 42.50.Pq, 81.07.Gf, 81.07.Bc
Techniques for controlling light-matter interactions in engineered electromagnetic
environments are now being actively explored. Understanding these interactions is not
only of fundamental importance but also of interest for applications ranging from optical
sensing and metrology to information processing, communication, and quantum science
[1-3]. To enhance the coupling between an optical emitter and a desired mode of the
radiation field, two approaches can be used . One strategy is to increase the lifetime of
the confined optical excitation in high-Q dielectric resonators, such as whispering gallery
structures, micropillars, and photonic crystals [3, 5]. Another strategy is to reduce the
effective mode volume (Veff) of confined radiation [6-9], as is currently explored using
plasmonic nanostructures capable of confining light to dimensions well below the
Plasmonic resonators, which combine the benefits of both strategies, have potential
for engineering light-matter interaction at nanoscales and achieving large coupling
between an emitter and the radiation field [2, 10]. However, experimental realization of
these structures has remained an outstanding challenge [2, 11, 12]. Prior attempts to
control and engineer surface plasmon polariton (SPP) propagation have relied on
patterning of metal films using techniques such as focused ion beam and reactive ion
etching [13, 14]. Unfortunately, these patterning methods introduce defects that act as
scattering centers. Moreover, standard metal deposition techniques typically generate
polycrystalline films with short SPP propagation lengths. Consequently, plasmonic
cavities demonstrated thus far typically had large mode volumes to minimize absorption
and scattering in the metal [15-17].
In this Letter, we propose and experimentally demonstrate the new strategy to realize
a plasmonic resonator with an exceptionally small mode volume and a moderate Q that
can drastically modify the interaction between a quantum emitter and SPPs. Our new
approach, illustrated in Figure 1, takes advantage of chemically synthesized silver
nanowires for tight confinement and reduced group velocity of optical radiation.
Owing to their high crystallinity, these NWs support propagation of surface plasmon
polaritons (SPPs) over several micrometers in the visible range . We define plasmon
distributed Bragg reflectors (DBRs) and cavities by patterning polymethylmethacrylate
(PMMA), a low-index dielectric. Unlike metal/air structures that have been previously
employed to manipulate SPP propagation [13-17], patterned PMMA does not suffer from
high scattering losses because the relatively low index contrast (compared to metal/air
boundaries) reduces susceptibility to lithographic imperfections.
Thin silver NWs surrounded by air support a fundamental SPP mode whose spatial
extent is on the order of the wire radius . The effective refractive index for this mode
increases when the surrounding medium changes from air to PMMA (
air > 1),
providing the index contrast needed to define DBRs for SPPs. FDTD simulations show
that a quarter-wave stack composed of several PMMA slabs reflects the incoming SPPs
with > 90% efficiency (Fig. 1(c)). The stopband (the wavelength range over which the
quarter-wave stack acts as an efficient plasmon mirror) can be tuned over the entire
visible range by varying the stack period, with a bandwidth exceeding 100 nm. A sharp
resonant feature appears within the stopband when two DBRs are placed together to
define a plasmon cavity. Specifically, for a 100-nm diameter NW with DBRs composed
of 6 PMMA slabs, a plasmon cavity with Veff ~ 0.04 (!/n)3 and Q ~ 100 can be achieved
(Fig. 1(d), see also Supplementary Material).
When a quantum emitter is placed within this plasmon cavity, its spontaneous
emission rate can be dramatically modified. The Purcell factor (F), which is defined as
the ratio of the spontaneous emission rates within the cavity (") and in free space ("0),
scales as Q/Veff (see Supplemental Material). Equivalently, F can also be expressed as
F0!, where F0 and ! are the Purcell factor of a bare silver NW and the cavity
contribution, respectively. We note that ! is also the finesse of the cavity. For a plasmon
cavity with a 100-nm diameter silver NW (Fig. 1(d)), F0 ranges from 1 to 10 depending
on emitter placement , and ! ~ 20. F can therefore be as high as 200 when a quantum
emitter is placed at the peak electric field of the cavity mode.
Our plasmon resonator architecture offers distinct advantages over other photonic and
plasmonic cavity structures [3, 15, 19, 20]. First, the Purcell enhancement achievable in
our architecture improves dramatically as the device dimension is pushed well below the
diffraction limit . As the NW radius (R) decreases, Veff " R3, while Q can be kept
constant by choosing the cavity length to be the half the SPP wavelength (see
Supplemental Material). Therefore, the Purcell enhancement also scales as 1/R3,
indicating that extraordinarily strong coupling can be achieved for small diameter NW
devices. This is in stark contrast to dielectric photonic waveguides, in which the field
confinement decreases exponentially when the structure dimensions shrink below the
diffraction limit [21, 22].
In addition, due to its ultrasmall mode volume, our resonator can be used to direct the
emission of a broadband quantum emitter into a single cavity mode whose resonant
wavelength is selected by the cavity design. When a broadband emitter (e.g. a solid state
emitter with a broad phonon sideband) is coupled to a cavity with a much narrower
resonance, the total Purcell factor becomes independent of Q and increases only when Veff
is decreased (see Supplemental Material). Therefore, in this broadband emitter regime,
ultra-small mode volume plasmon resonators provide the only means to achieve efficient
single photon sources in which the color of emission can be selected, and the rate into
that mode can be enhanced over emission into free space.
We realize the plasmon resonator experimentally by first spin-coating PMMA on a
Si/SiO2 wafer, drop-casting silver NWs, and then spin-coating another layer of PMMA.
Electron beam lithography and subsequent development yield suspended NWs in periodic
PMMA slabs (Fig. 1(a)) [19, 23]. These plasmon DBRs and cavities were characterized
via transmission measurements of single nanostructures as a function of wavelength. Due
to the wavevector mismatch between propagating SPPs and free space photons, SPPs
couple to the far field only at defects or wire ends. We obtain a transmission spectrum by
focusing a supercontinuum laser to a diffraction-limited spot at one end of the NW, and
recording the scattered intensity at the other end as a function of wavelength using a
charge-coupled device (CCD) (Fig. 2(a)).
The data in Fig. 2(b) clearly show that the plasmon DBR exhibits a stopband in
transmission, as predicted by the simulations. By comparing the transmission intensity
just inside and outside of the stopband (over which range the propagation losses,
collection efficiency, and in/out-coupling efficiencies should be constant, see
Supplemental Material), we estimate the reflectivity of the DBR to be 90-95%. The drop-
offs in intensity at shorter and longer wavelengths are due to material absorption and the
near-IR cutoff of our optics, respectively.
Transmission spectra of cavities show a peak in the middle of the stopband. In the
device shown in Fig. 2(c), the peak is at 638 nm and the full width at half maximum is 11
nm, corresponding to a Q of 58. The highest Q observed to date in our plasmon cavities is
94, close to the theoretically simulated maximum value. The transmission intensity on
resonance is attenuated compared to that outside of the stopband due to higher absorption
losses caused by the longer effective path length on resonance, leff. From the measured
value of Q, we determine that leff is ~5 µm (see Supplemental Material). This value is
comparable to the SPP propagation length in bare silver NWs , and indicates that
losses in our resonators are dominated by material absorption.
We next demonstrate the utility of our cavities to control both the color and rate of
spontaneous emission of solid-state optical emitters. First, we show emission
modification in an ensemble of CdSe quantum dots. These quantum dots were coupled to
the devices by mixing them homogeneously in PMMA before fabrication. A fluorescence
spectrum of the quantum dots coupled to the NW was obtained by exciting one NW end
with green light (! = 532 nm) and collecting quantum dot fluorescence at the other NW
end. Fig. 3(a) clearly shows that the plasmon-coupled emission is narrowed and shifted
toward the resonance peak when compared to the fluorescence spectrum of uncoupled
The fluorescence lifetime is also modified by the plasmon cavity. The emission from
uncoupled quantum dots exhibits a single-exponential decay, characterized by a lifetime
(#free) of 16 ns ± 3 ns. In contrast, the emission from quantum dots coupled to the NW
exhibits a multiexponential decay because the quantum dots are distributed throughout
the PMMA, and the detected emission originates from an ensemble of quantum dots
along the NW. Notably, the initial slope of this decay yields the shortest lifetime (#coupled)
of less than 250 ps (Fig. 3(b)). This value suggests that the largest effective Purcell factor
Feff = #free/#coupled is >75, despite the detuning of the cavity resonance relative to the peak
of quantum dot emission. It is difficult to disentangle effects of nonradiative decay from
lifetime data alone, but we note that quantum dots coupled to a silver NW in unpatterned
PMMA show a multiexponential decay with initial slope corresponds to a lifetime of 4
ns. This evidence indicates that the much shorter lifetime observed in the cavity-coupled
decay is due to radiative emission enhancement rather than nonradiative decay (see
We next demonstrate control over emission properties of individual diamond nitrogen
vacancy (NV) centers using plasmon resonators. Diamond nanocrystals were coupled to
silver NWs by co-depositing them during fabrication. Approximately 10% of
nanocrystals exhibited stable, broad fluorescence characteristic of NV centers (Fig. 4(b))
. Once a single NV coupled to the wire was identified, the resonator structure was
defined by electron beam lithography around the NV center.
Fig. 4(a) shows scanning confocal microscope images of a resonator device with a
coupled NV. The top panel shows a reflection image of the device, and the middle panel
shows the fluorescence image recorded as the laser is scanned over the device. When the
NV is excited (circled), using an independently scanning collection channel (bottom
panel) we observe fluorescence from three locations: one corresponding to direct
emission from the NV, and two corresponding to the ends of the NW. The direct
emission from the NV exhibits strongly anti-bunched autocorrelation (inset of Fig. 4(b)),
indicating that it originates from a single NV center. Photon-correlation measurements
between the NV fluorescence spot and the NW end also show strong anti-bunching (inset
of Fig. 4(c)), showing that the emission from the wire end also originates from the NV [6,
9]. Assuming an SPP out-coupling efficiency of ~5% for these NWs [6, 24], we estimate
that 50-60% of the emission couples into SPPs for a typical device.
The NV fluorescence changes drastically when it is coupled to the plasmon cavity.
Before resonator fabrication, the plasmon-coupled NV fluorescence exhibits a broad
spectrum spanning a range of 630-740 nm (small, superimposed Fabry-Perot oscillations
originate from scattering by the NW ends: see Supplemental Material) [9, 16]. After
resonator fabrication, the plasmon-coupled NV spectrum exhibits a peak on resonance
with the cavity mode and suppressed fluorescence within the stopband (Fig. 4(c)). The
peak position can be placed anywhere across the NV fluorescence spectral range by
changing the cavity design, thereby enabling the selection of the wavelength of single
photon emission. The plasmon-coupled fluorescence intensity outside of the stopband (#
> 720 nm), Iout, is essentially unaltered by the cavity, and gives the baseline SPP-coupled
fluorescence. Notably, the fluorescence intensity on resonance (# = 637 nm), Ires, is
higher than Iout. In contrast, the transmission spectrum measured by launching SPPs at the
wire end with the supercontinuum laser shows that the transmitted intensity on resonance,
Tres, is lower than that outside of the stopband, Tout.
Comparison of these intensities gives the radiative Purcell enhancement due to the
cavity on resonance ! = (Ires/Iout)(Tout/Tres); for the device shown, we find that ! is 11 ±
3. This resonant enhancement is in addition to a broadband enhancement, F0, due to the
bare silver NW, which is estimated to be in a range of 1.5-2.5 for NWs of these
dimensions [6, 9]. Combining these factors together (F = F0!), we estimate the overall
Purcell enhancement to be as high as 35 at the resonance peak, a value that exceeds the
largest Purcell enhancement reported to date for NV centers coupled to dielectric cavities
[26, 27]. We note that the observed Purcell enhancement is still lower than the theoretical
maximum value expected for these devices, most likely because the NV center is not
located optimally within the cavity.
The strong emitter-cavity coupling observed in the present study can be improved in
several ways. Precise placement of NV centers at the peak electric field of the cavity
mode would ensure maximum Purcell enhancement for a given device. Furthermore,
because the Purcell enhancement scales as 1/R3, it can be made substantially higher using
thinner wires [7, 8]. In the present study, we were limited to larger (~100 nm) diameter
NWs because we relied on far-field excitation and detection of SPPs. While out-coupling
to the far field is less efficient in thinner wires, efficient coupling to thinner NWs can be
accomplished with near-field techniques such as evanescently-coupled optical fibers 
and electrical detection [24, 29]. Other resonator geometries, such as those that make use
of recently developed hyperbolic metamaterials can potentially be used to further
enhance the coupling .
The realization of nanoscale plasmon resonators with exceptionally small mode
volumes and high quality factors opens new possibilities for integrated plasmonic
systems, novel realization of nanoscale lasers and spasers , sub-diffraction sensing,
and optical interfacing of solid-state qubits. For instance, color-selective single photon
sources could have applications in quantum cryptography, and these resonators can be
used to direct NV emission into the zero-phonon line for coherent optical manipulation, a
crucial requirement for the realization of such applications as single photon transistors
. Other possibilities include high spatial resolution imaging and enhanced coupling of
individual molecules. Furthermore, the use of patterned, low-loss dielectrics for
controlling SPP propagation in nanoscale plasmonic structures can potentially be
extended towards other applications such as plasmonic circuit elements [33, 34], out-
coupling gratings , and meta-materials [35, 36].
We acknowledge J. T. Robinson, A. L. Falk, F. Koppens, and J. D. Thompson for
helpful discussions. We also gratefully acknowledge support from NSF, DARPA, the
Packard Foundation, and the NSF and NDSEG graduate research fellowships (NdL).
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FIG. 1 (color online). (a) Schematic of device concept (top) and SEM image using an
Inlens detector (bottom) of the DBR resonator fabricated around a silver NW. The
sample is tilted at 30° from two different orientations to demonstrate that the NW is
suspended from the substrate in PMMA. Scale bar = 1 µm. (b) Simulated electric field
intensity of a plasmonic cavity at wavelengths inside the stopband (top left), outside the
stopband (bottom left) and on resonance (right). (c) Simulated transmission spectrum of a
DBR consisting of a 100 nm silver NW and PMMA slabs with a period of 200 nm. A
quarter-wave stack composed of 6 PMMA slabs reflects the incoming SPPs with a
reflectivity exceeding 90%. (d) Simulated transmission spectrum of plasmon cavity
composed of two DBRs. The nominal cavity length corresponds to !SPP, and the
linewidth gives a Q of 100.
FIG. 2 (color online). (a) CCD image of SPP propagation overlaid on an SEM image of a
device. (b) Transmission spectrum of plasmonic DBR. The minimum intensity in the
stopband indicates a reflectivity of 90-95%, and sideband oscillations can be seen outside
the stopband. (c) Transmission spectrum of plasmon resonator. The peak in the stopband
at 638 nm has a width of 11 nm, corresponding to a Q of 58. SEM images of both devices
are shown in the insets, with scale bars that correspond to 1 µm.
FIG. 3 (color online). (a) Fluorescence spectrum of CdSe quantum dots in the substrate
(blue, dashed) and coupled to the plasmon resonator (red). The transmission spectrum of
the device is overlaid (gray, crosses). The fluorescence of coupled quantum dots is
shifted and narrowed by the cavity resonance. (b) Lifetime measurements obtained by
excitation with a pulsed laser of coupled (red) and uncoupled (blue, dashed) quantum
dots. Uncoupled quantum dots have a lifetime of 16 ns, while coupled quantum dots
show multi-exponential behavior, with the initial slope corresponding to a lifetime of less
than 250 ps.
FIG. 4 (color online). (a) Scanning confocal microscope images of the device. The top
panel shows an image of the reflected green laser light. The middle panel shows
fluorescence in the red as the laser is scanned over the area. When the laser is focused
onto the NV in the cavity (indicated with a white circle), an independent collection
channel is scanned over the area to detect fluorescence (bottom). The bright spot in the
center results from direct excitation and detection of the NV fluorescence. Two additional
spots can be seen from the ends of the wire, where SPPs excited by the NV scatter into
free space. Scale bar = 1 µm. (b) The fluorescence spectrum from the center of the NW
shows broadband emission characteristic of NVs. The inset shows autocorrelation of the
fluorescence, which is strongly anti-bunched, indicating that emission results from a
single NV center. (c) The fluorescence spectrum from the end of the NW (red) shows
significant modification, which corresponds to the transmission spectrum of the device
(black). Cross-correlation between the SPP-coupled emission and the emission collected
directly from the NV indicates that the fluorescence at the end of the NW originates from
the same NV center (inset).
Supplementary Material for Tailoring Light-Matter Interaction with a Nanoscale
Nathalie P. de Leon1,2, Brendan J. Shields2, Chun L. Yu1, Dirk Englund2, Alexey V.
Akimov,2,3 Mikhail D. Lukin2, and Hongkun Park1,2
1Department of Chemistry and Chemical Biology, and 2Department of Physics, Harvard
University, Cambridge, MA 02138, 3Lebedev Institute of Physics, Moscow, Russia
A. Materials and Methods
The silver nanowires used in our experiments were synthesized using a modified
solution-phase polyol method described previously . Resonators were fabricated by
spin-coating 950 PMMA C4 (MicroChem) on a Si substrate with 300 nm SiO2,
dropcasting silver nanowires in ethanol, then spin-coating another layer of PMMA. Once
silver nanowires were identified, the dielectric stacks were defined by e-beam lithography
(Raith) and developed in methylisobutylketone and isopropanol.
FDTD simulations were performed using commercial software (Lumerical) with
literature values for material constants .
Transmission spectra were taken using a Koheras SuperK supercontinuum laser
coupled to an acousto-optic tunable filter, enabling the excitation wavelength to be
selected. The beam was spatially filtered using a single mode fiber (NKT) and then
focused to a diffraction-limited spot using an objective (100x, 0.8 numerical aperture).
Fluorescence spectra were taken using a CCD and a spectrometer (Princeton
CdSe quantum dots (Invitrogen, 650 nm emission wavelength) with organic capping
ligands were flocculated out of decane and dispersed in PMMA. This solution was then
used for fabrication of resonators. Diamond nanocrystals (Microdiamant, 0-0.05
micrometres) were centrifuged, washed, and dispersed in ethanol before co-depositing
with silver nanowires. We tuned the relative concentrations of nanowires and diamond
nanocrystals so that approximately 30% of the wires had a single NV coupled to them,
thus minimizing the probability that multiple NVs were coupled to one wire.
Lifetime measurements were performed using a frequency-doubled picosecond 1060
nm laser (Fianium, 400 fs pulsewidth, 80 MHz repetition rate down-sampled to 20 MHz)
an avalanche photodiode with 50 ps timing resolution (Picoquant) and a fast photodiode
with 80 ps timing resolution (Newport). Photon correlation measurements were taken
using avalanche photodiodes (Perkin Elmer). The details of the experimental setup used
for photon correlation measurements have been described previously .
B. Plasmonic DBR characterization
In our supercontinuum laser transmission measurements, the observed intensity (I) is
where I0 is the incident intensity, T is the transmission through the DBR, l is the optical
path length along the NW, l0 is the characteristic SPP propagation length in the NW
waveguide, !c is the collection efficiency, and !pl is the product of the in-coupling and
out-coupling efficiencies of the NW.
We fabricated a variety of plasmonic DBR devices with different periods and
nanowire diameters in order to tune the stopband across the visible range. The stopband
position and device dimensions can be used to calculate the effective refractive index of
the SPP mode in air,
air, for a given device from the Bragg condition for a quarter-wave
) ( 2
. Here dair and dPMMA are the widths of the slabs in air
and PMMA, respectively. Figure S1(a) shows the calculated
for devices of varying
nanowire diameter compared to simulated values from FDTD. The measured values are
within about 2% of the calculated values across the range of nanowire diameters we
Fig. S1(b) shows the dependence of stopband position on DBR period. Using the
for each device, we plot the stopband position "0/
and find that it matches the Bragg condition for a quarter wave stack.
C. Theoretical limits of Q
The quality factor (Q) of a resonator can be expressed in terms of the separate loss
channels in the cavity:
where QSP results from material absorption of the SPP mode, Qff is due to far-field
scattering, and QR is due to sub-unity reflection at the mirrors. QSP represent the
theoretical limit of Q that is limited only by the material absorption. QSP is defined as the
energy stored divided by the power dissipated:
which can be rearranged to give the following relationship:
The lifetime of a plasmon in the cavity, !0, is therefore given by
Expressing !0 in terms of the SPP propagation length on resonance (LSPP) and the phase
velocity (vp) and substituting for ", we get
For a 100 nm diameter silver nanowire, we have previously measured the propagation
length at 650 nm to be around 5 µm, which would put an upper bound on Q of 101. We
find that our resonators have Q approaching 100, indicating that for our best devices
losses are dominated by propagation length in the material rather than imperfections in
the mirrors or device geometry.
D. Quantum dot lifetime on silver nanowires
Time-resolved fluorescence measurements of quantum dots coupled to silver nanowires
surrounded in unpatterned PMMA show a multi-exponential decay, with the initial slope
corresponding to a lifetime of 4 ns (Fig. S2). This indicates that the nonradiative and
radiative emission enhancement due to the silver nanowire contributes a factor of ~4 to
the overall lifetime reduction.
E. Quantum dot mixture fluorescence modification
In order to investigate the radiative contribution to Purcell enhancement, we coupled a
mixture of CdSe quantum dots spanning an emission range of 550-800 nm to the
resonators by incorporating them into the PMMA before device fabrication. The
transmission and fluorescence spectra are shown in Fig. S3. The plasmon-coupled
fluorescence emission exhibits oscillations that match the transmission spectrum, and the
intensity at the cavity resonance is three to four times higher than the intensity outside of
the stopband, while the transmission intensity on resonance is about half the intensity
outside of the stopband. This observation provides another signature of radiative Purcell
enhancement, in addition to the direct lifetime modification measurement described in the
F. Fluorescence of NVs coupled to silver nanowires
NVs coupled to silver nanowires can emit into the far field or into SPP modes. The far-
field fluorescence spectrum is essentially unmodified (Fig. S4(a)), while the SPP-coupled
fluorescence exhibits small oscillations originating from Fabry-Perot resonance in the
silver nanowire (Fig. S4(b)). As described in the main text, SPP-coupled NV
fluorescence is modified dramatically when the NV center is coupled to a plasmon cavity.
G. Purcell enhancement and mode volume in plasmon resonators
The spontaneous emission rate of an emitter in a cavity, #, is given by Fermi’s Golden
"= µ• E
% ( )#cr,%
where µ is the transition dipole moment of the emitter, E is the electric field, # is the
angular frequency, r is the position of the emitter, $e is the optical density of states of the
emission, and $c is the optical density of states of the environment. In the weak coupling
limit, an emitter placed at the peak electric field of the cavity mode exhibits a Purcell
enhancement of spontaneous emission, F, given by
Here # is the spontaneous emission rate in the cavity, #0 is the rate in a uniform dielectric
medium, Q is the quality factor of the cavity, and
max ) E
dimensionless mode volume. In an absorbing, dispersive medium such as silver, the
mode volume can be estimated using the Drude model result for the energy density [4-6].
We simulated a plasmon resonator made of a 100 nm diameter silver nanowire using
FDTD (Lumerical): in particular, this resonator was designed for a "SPP-mode with a
resonant wavelength of 630 nm. Evaluating the expression using the electric field
intensity at the resonant wavelength from simulations, we calculate a dimensionless Veff
of 0.04 ("0/n)3. We can also define an effective mode area,
2dA/max " E
2, which is 0.032 ("0/n)2 from the simulations. These
values yield an effective cavity length, Leff of 1.1875 ("0/n) = 1.57 "SPP.
The overall Purcell enhancement can be decomposed into two components. One is
associated with sub-wavelength, transverse confinement of guided SPPs, while another is
associated with longitudinal confinement due to plasmonic cavity. The Purcell
enhancement for an emitter placed next to a silver nanowire without a cavity is
determined by the effective area of the SPP mode (Aeff) and the density of states (dk/d#)
We note since that the finesse of the cavity ($) is given by LSPP/Leff, and "SPP ~ vg,
the Purcell enhancement in the resonator can be written in terms of the enhancement due
to the bare wire:
. This observation indicates that the cavity introduces a factor
of the finesse to the enhancement compared to the silver nanowire. This intuitive result
shows that the mode volume confinement is due to the radial dimension of the wire, and
the Purcell factor can be further increased by the number of roundtrips of the plasmon in
To understand the scaling of Purcell enhancement with nanowire dimensions, we note
that in the quasistatic limit, Aeff scales as R2, and the group velocity scales as R, giving an
overall scaling of 1/R3. For plasmonic resonators,
can be chosen to be as small as "SPP/2. Since "SPP and LSPP both scale as R, the overall
scaling of the Purcell enhancement is still 1/R3 for the resonator case. The Purcell
enhancement can thus be significantly higher for thinner nanowires.
H. Purcell enhancement of a broadband emitter
When an emitter with emission rate #0 and bandwidth %# such that
to a cavity mode with decay rate & = #/Q < %#, the total emission rate is given by
"= "freespace+"cavity= "0+"0
is the coupling strength between the emitter and the cavity. For
emission into the cavity mode to be greater than emission into free space, we have the
This condition is independent of &, and therefore independent of Q. An enhancement of
the emission rate therefore requires that g be increased, which can be achieved by
decreasing Veff. We note that this is true only for emitters that have an incoherent
contribution to emission and therefore do not have transform-limited linewidths
I. Determination of radiative Purcell enhancement of single emitter
In order to quantify the contribution of the cavity to the Purcell enhancement of the NV
center, we compared the intensity of the SPP-coupled emission on resonance with the
intensity outside of the stopband, as described in the main text. This approximation is
complicated by several other factors, but we chose a range of comparison that gave us the
most conservative estimate of the Purcell enhancement. First, sideband oscillations
evident in Figs. 1 and 2 show can also lead to an enhancement of the decay. Our
calculated Purcell factor does not take this enhancement into account, so the actual
contribution of the cavity could be higher. Second, we account for the difference in
transmission and out-coupling losses at the different wavelengths by calibrating with the
transmission spectrum. From equation (1) above, the ratio of signal in the red and the
blue from the transmission spectrum is given by
#ll0(red )#l0(blue). The NV emission
experiences a shorter path length, thus decreasing this ratio. Therefore, our calculated
Purcell factor underestimates the enhancement by a factor of
"lNVlwirewhere lwire is the
length of the wire, and lNV is the path length from the NV to the end of the wire.
 B. Wiley, Y. Sun, and Y. Xia, Langmuir 21, 8077 (2005).
 E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1997).
 A. V. Akimov, A. Mukherjee, C. L. Yu, et al., Nature 450, 402 (2007).
 R. Loudon, J. Phys. A 3, 233 (1970).
 S. A. Maier, Optics Express 14, 1957 (2006).
 R. Ruppin, Physics Letters A 299, 309 (2002).
 D. E. Chang, A. S. Sorensen, P. R. Hemmer, et al., Physical Review B 76, 035420
FIG. S1. (a) Simulated (blue) and measured (red)
air as a function of diameter for
various devices. The simulations and measurements agree to within 2%. (b) Stopband
position (%0) versus DBR period for various devices. The silver NW diameter varies
among devices, so the stopband position is corrected by the simulated value for
FIG. S2. Lifetime measurements of CdSe quantum dots on a silver NW surrounded by
FIG. S3. Fluorescence intensity (red) collected from the end of the wire during excitation
of the other end in green, and transmission spectrum (black). The oscillations in
fluorescence match the sideband oscillations in transmission, as well as the resonance
peak. The fluorescence intensity is higher on resonance than outside of the stopband,
indicating Purcell enhancement of spontaneous emission.
FIG. S4. Far-field (a) and SPP-coupled (b) fluorescence spectra of an NV coupled to a Download full-text
silver NW. Far-field emission is broad and essentially unmodified compared to the
uncoupled NV, while SPP-coupled fluorescence exhibits small oscillations due to Fabry-
Perot resonance in the silver NW. (c) SEM images of diamond nanocrystals coupled to a
silver NW before (left) and after (right) resonator fabrication. Scale bars = 1µm.