Table Of ContentPlasmon ruler with gold nanorod dimers: utilizing the second-order resonance
Anton T. Le,1 Maxim R. Shcherbakov,1 Natalia Dubrovina,2 Anatole Lupu,2 and Andrey A. Fedyanin1,a)
1)Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
2)Univ. Paris-Sud, Institut d’Electronique Fondamentale, UMR 8622, 91405 Orsay Cedex,
France
(Dated: 16 January 2014)
The idea of utilizing the second-order plasmon resonance of the gold nanorod π-dimers for plasmon rulers
is introduced. We report on a qualitatively different dependence of the plasmon resonance shift on the
interparticle distance for the first- and second-order longitudinal modes, extending the working range of
plasmon rulers up to the distance values of 400nm.
4
1
PACS numbers: 36.40.Gk, 73.20.Mf, 78.67.Bf, 78.20.Ci
0
2
n Optical properties of gold nanoparticles have con- system.
a tributedtomanyareasofscienceandtechnology,suchas In this contribution, we obtain the dependence of the
J drugdelivery1,cellimaging2,photothermaltherapy3and SPR position λ on the distance between the rods d for
0
5 others. Inparticular,apossibilityofmeasuringnanoscale a set of π-dimers by means of microspectroscopy of gold
1
length utilizing pairs of gold nanoparticles—i.e., plas- nanorod samples and corresponding numerical calcula-
monic dimers—was demonstrated4,5 producing the idea tions. The first- and second-order longitudinal dipolar
]
s of so-called plasmon ruler. Operating principles of plas- plasmon resonances are considered. It is shown that one
c
monrulersarebasedonthefactthatthespectralposition can use the λ (d) dependence for the second-order res-
i 0
t of the surface plasmon resonance (SPR) of a plasmonic onance to form a plasmon ruler with working distance
p
o dimerstronglydependsonthedistancebetweenthe par- range of up to 400nm. On the contrary, far-field inter-
. ticles forming the dimer6. This phenomenon makes it ference effects hinder the possibility of using this system
s
c possible, e.g., to measure length of a sub-100-nmmacro- as a plasmon ruler for the same working range if one
i molecule with gold nanoparticles bound to its ends by considers the first-order resonance.
s
y measuring the SPR position and comparing it to one of Theaimofthe presentstudyisto performacompara-
h the uncoupled nanoparticles4. Tailorable nature of SPR tivestudy ofadimer plasmonruleoperatingatthe first-
p allows flexible tuning of plasmonic dimer optical prop- or the second-order dipolar resonance. We designed and
[ erties by changing the shape, mutual arrangement, or fabricated two sets of plasmon ruler structures with sig-
1 polarization of the incoming light and, hence, the type nificantly different dimensions of the resonant elements
v of the resonance7–9. In plasmon rulers, however, the but providing very close resonance frequencies when op-
1 maximum measurable distance is still limited to roughly erating accordingly to the design at the first- or second-
7 100nm. order resonance. Gold nanoparticle dimer samples were
6 Nanorods are one of the frequently used shapes to fabricatedusing electronbeamlithographywith positive
3
analyze the physics behind the near-field coupling of electron resist. All the measured nanostructures were
.
1 plasmonic nanoparticles10. One distinguishes between located on the same 0.5mm-thick fused silica substrate.
0 two types of nanorod dimers—the so-called π-dimer Thenanorodswere50nminheight,50nminwidth;their
4 and σ-dimer, referring to the analogy from the orien- lengthaandthedistancedbetweentheedgesofnanorods
1
tation of coupled atom p-orbitals. Providing subwave- within the dimer varied from sample to sample and con-
:
v length fieldlocalizationinthe gapbetweenthe inline ar- stitutedatableofparameterswitha=50,100,150,200,
Xi rangednanoparticles,theσ-dimerisusedinnanoantenna 300, 400, and 500nm, and d = 50, 100, 150, 250, 350,
research11 and applications, such as improved surface- 450, and 650nm. Examples of SEM images are shown
r
a enhancedRamanscattering12. Theπ-dimer,ontheother in Figs.1(a-d) for different combinations of a = 100nm,
hand, is a system conventionally considered for obser- a = 400nm, d = 50nm, and d = 350nm. Each nanos-
vation of optical magnetism happening when the free- tructured area had lateral dimensions of 100×100µm2
electron currents are out of phase in the nanorods form- and contained approximately 104 periodically arranged
ing the dimer13. Finally, for nanorods long enough it nanorod dimers. The separation distance between adja-
is possible to excite several longitudinal SPR modes14. cent dimers was of approximately 1.5µm; the density of
Nevertheless considered theoretically15,16, the coupling eachdimerarraywaschosenintentionallysparseinorder
properties of the higher-order resonances were neither to minimize the interaction effects between the nearest
providedexperimentallysofar,norwerethey considered neighbors.
asa basisforaqualitativelydifferentplasmonruler-type Extinction spectra of goldnanoroddimers with differ-
entnanorodlengthandinterparticledistancevalueswere
obtained by means of transmission microspectroscopy
technique. Transmission spectra were carried out un-
a)Electronicmail: [email protected] der normal incidence using the white-light microspecr-
2
m) 665 730
on (n685 660770 720
positi680 655760
e 675 710
nc 650
a
eson670 a= 400 nm 645750 a= 500 nm 700
R
0 200 400 600 0 200 400 600
Distance (nm) Distance (nm)
FIG. 2. Measured (connected dots) and calculated (solid
curves) position λ of the second-order longitudinal dipolar
0
plasmonresonanceofnanoroddimersasafunctionofthein-
terparticledistancedforthesetsof400nm-and500nm-long
nanorods.
first-orderSPR.Forthe400-nm-longrods,whichoperate
at the second-order SPR, the resonance is also found in
the same spectral range. The electric field z-projection
distribution is representedin Figs.1(g) and1(h) indicat-
FIG. 1. (a-d) SEM micrographs of gold nanorod π-dimers ing the two- and four-antinode structure corresponding
with a nanorod length of a = 100nm or a = 400nm, and to the first- and second-order SPRs, respectively.
an interparticle distance of d = 50nm or 350nm. (e-f) Nor- The extinction spectra displayed in Figs.1(e-f) show
malizedexperimentalextinctionspectraofnanoparticledimer that the resonance wavelength λ depends on the inter-
0
setswithananorodlengthof100nmand400nmcorrespond- particle separation distance d. This is attributed to the
ing to the first- (I) and second-order (II) resonances, respec- effect of optical coupling between the nanorods. The ex-
tively. (g-h) Calculated Ez distribution nearby the nanorod perimentally observed and numerically calculated varia-
dimersforthefirst-andsecond-orderlongitudinalresonances,
tion of the resonance wavelength λ as a function of d
respectively, in the cross-section close to the surface of the 0
for 400-nm- and 500-nm-long nanorods operating at the
dimer.
second-order SPR is shown in Fig.2. Aside the 10% dif-
ference in the absolute value of resonance wavelength,
experimental and modeling results are in good overall
toscopysetupwithaspectralrangefrom400to1400nm,
agreement. The difference in the absolute resonance
a spectral accuracy of 0.8nm, a focal spot of 50µm,
wavelength values is due to the substrate that was not
and a numerical aperture of the focusing system of 0.04.
taken into account in the calculations.
The input polarization state was controlled by a broad-
Sensitivity of λ to d was previously shown to mono-
0
band Glan-Taylor prism polarizer to be parallel to the
tonically depend on d18,19. λ is more sensitive to the
0
nanorods.
variation of d if the latter is small, and less sensitive for
The transmission spectra of all experimentally stud- larger d values. A closer inspection of Fig.2 reveals that
ied nanorod dimers were also numerically simulated us- there are some small but persistent deviations between
ing the finite-difference time-domain(FDTD) technique. the experimentaland modeled results. While the depen-
Simulations were performed using FDTD Solutions soft- dence is monotonic in the modeled case, it shows some
warefromLumericalSolutions,Inc. Goldnanorodswere oscillatory behavior in the experiment. The oscillatory-
modeled as cuboids with the width and height fixed at type features in the experimental dependences are the
50 and 30nm, respectively. The minimal number of grid consequence of periodical arrangement of the dimers in
points per wavelength was set to 22, and an additional a regular 2D array that leads to diffraction coupling be-
5nm-meshwasimplementedintheareaofnanorods. The tween the nanorods. A similar effect related to the in-
materialdielectricconstantsweretakenfromRef.17. The terference between the SPR and diffraction order for a
refractive index of the surrounding medium was set to 2D array of nanoantennas was reported in Refs.[20,21].
be 1.0. The incident electromagnetic field was polarized This effect is discussed in more details in the case of the
parallel to the nanorods. Unless otherwise noted, the plasmonruleoperatinginafirstorderwhereitsinfluence
perfectly matched layer (PML) boundary conditions are is much more dramatic.
meant for each side of the integration volume. The working range of a plasmon ruler, that is, the
The experimental extinction spectra of the dimer ar- range from d = 0 to the value where the first deriva-
rays with different interparticle distance d operating at tive of the λ (d) function becomes equal to zero, is the
0
the first- and second-order resonances are displayed in key parameter showing the maximum distance that can
the Figs.1e and 1f, respectively. In a good agreement be measuredwith such a ruler. To point out the key dif-
with the modeling predictions,the resonanceis observed ference in λ (d) for the I and II resonances, calculations
0
around650nmforthe100-nm-longrodsoperatingatthe of λ (d) were carried out for the dimer with a=400nm
0
3
665 680 790
m) II a= 420 nm 665
position (n11334500 I 665650 a= 100 nm III 666767055 m)665650 670 789000 780
Resonance 1330 a= 400 nm 664550 666505 ce position (n695105 a= 100 nm 696150 1372800 a= 150 nm 770
0 2D00istanc4e0 (0nm) 600 0 20D0istan4c0e0 (nm)600 esonan900 900 1300 1140
R
885 1280
FIG. 3. Calculated position of thefirst-order(I)and second- 890 1120
order(II)longitudinaldipolarplasmonresonancesofnanorod 870 1260
dimers as a function of the interparticle distance d. (Left): a= 200 nm 880 a= 300 nm 1100
for the nanorods of the same length of a=400nm. (Right): 0 200 400 600 0 200 400 600
Distance (nm) Distance (nm)
for the nanorods of different lengths of a = 420nm and a =
100nm. Note the right panel having the same scale for both
FIG. 4. Measured (connected dots) and calculated (solid
curves. Thedashedlinesshowtheupperlimitoftheplasmon
curves) position of the first-order longitudinal dipolar plas-
ruler working range based on theparticular dimers.
monresonanceλ ofnanoroddimersasafunctionoftheinter-
0
particle distance d for the sets of 100nm-, 150nm-, 200nm-,
and 300nm-long nanorods.
for both resonance orders as seen in the left panel of
Fig.3. The working range of the first-order-resonance
rulers is limited to the value of approximately 170nm.
For d>170nm the inter-particle far-field effects are be-
lieved to disrupt the monotonous dependence leading to
oscillatory behavior. On the other hand, for the second-
orderresonancethemonotonousdecayoftheλ (d)func-
0
tion is extended up to 370nm. This makes it more ben-
eficial to measure large distance and length values with
thesecond-orderresonanceofsucharuler. Onecouldar-
gue thatthe characteristicdecay functionof λ (d) scales
0
with the wavelength, and, therefore, it is not feasible to
compare graphs in the left panel of Fig.3. However,
the same rule applies if the two resonances are consid-
ered on the same wavelength scale as shown in the right
panel of Fig.3. Here, the λ (d) curves are given for the
0
lengthvaluesofa=420nm(second-orderresonance)and
a= 100nm (first-order resonance). This graph straight-
forwardly indicates the difference between the first- and FIG. 5. Normalized calculated extinction spectra of the
second-order resonances in plasmonic nanorod dimers. dimers with a = d = 300nm as a function of the packing
Highsensitivityofthefirst-orderresonanceofananopar- period. The first-order and the second-order longitudinal
dipolar plasmon resonances are indicated with I and II, re-
ticle in the presence of the other one is understood—the
spectively. Forthesakeofclarity, thespectraarenormalized
resonance is “brighter” than the second-order one due
separately;theborderbetweenthetwonormalization regions
to larger electric dipole value; the overall absolute ex-
at λ=650nm is denoted with a black vertical line.
tinction coefficient of light is approximately 3–4 times
larger for the first-order resonance than for the second-
order one. The same feature of the far-field coupling of culations with PML boundary conditions. In order to
dark modes was found in Ref.[20]: darker (quadrupolar) illustrate the difference of I and II resonances in terms
modes of plasmonic cavities are less subject to far-field of diffraction coupling the effect of the packing period
coupling that the brighter (dipolar) ones. on extinction is shown in Fig.5. Here, extinction of the
Anotherdownsideofthefirst-orderresonanceisitsde- nanorod dimer arrays with a = 300nm and d = 300nm
pendence ondiffraction originatingfromthe periodic ar- is plotted as a function of wavelength and arrangement
rangementofthe dimers. The effectofunwanteddiffrac- periodascalculatedwithFDTDusingperiodicboundary
tioncouplingofthefirst-orderresonanceisdemonstrated conditions. It is seen that for the first-order resonance
with the data provided in Fig.4 for the samples with located in the infrared range there is a strong influence
a=100nm, 150nm, 200nm, and 300nm. It is seen that of diffraction coupling between the rods. The affection
for all the samples the shape of the experimental λ (d) of diffraction on the resonant wavelength of plasmons
0
dependence does not reproduce the one obtained in cal- was reported previously for the first-order resonance21.
4
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