DOI: 10.1038/NNANO.2015.69 Mode-matching in multiresonant ... · Figure 3S. Experimentally acquired spectra from the two most significant lines of the array sketched in the main manuscript

Mode-matching in multiresonant plasmonic nanoantennas

for enhanced second harmonic generation

Michele Celebrano, Xiaofei Wu, Milena Baselli, Swen Großmann, Paolo Biagioni, Andrea

Locatelli, Costantino De Angelis, Giulio Cerullo, Roberto Osellame, Bert Hecht, Lamberto Duò,

Franco Ciccacci, & Marco Finazzi

Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic

generation

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NNANO.2015.69

NATURE NANOTECHNOLOGY | www.nature.com/naturenanotechnology 1

© 2015 Macmillan Publishers Limited. All rights reserved

http://dx.doi.org/10.1038/nnano.2015.69

Contents

1. Nanostructure arrays fabricated on large single-crystal gold flakes

2. Single nanostructure scattering spectroscopy setup

3. Experimental setup for SHG detection and characterization

4. Linear extinction maps

5. Numerical method to evaluate single nanostructure SHG signal

6. SH emission polarization and its dependence on the incident polarization.

7. Power and spectral characterization of the SH emitted by the nanostructure.

8. Evaluation of the nonlinear coefficient of the nanoantenna

9. SHG efficiency evaluated on standard 100 nm gold spheres

10. Resistence of the nanoantennas to photodamage

References


1. Nanostructure arrays fabricated on large single-crystal gold flakes

Figure 1S. The single-crystalline gold flake, chemically grown directly on glass [1], is transferred on the

patterned substrate and aligned to a slightly smaller hole in such a way that the edge of the gold flake is in

contact with the conductive coating, while most of it adheres on the bare fused silica to ensure optical

access to the sample from the back side. Inset: a zoom of the area investigated in the present work.


2. Single nanostructure scattering spectroscopy setup

The scattering spectra are measured using an

asymmetric dark-field scattering setup (see

Fig. 2Sa). In this experimental geometry an

almost-collimated incoherent white-light

beam generated by a halogen lamp (Axiovert,

Zeiss) is focused by a microscope objective

(Plan-Apochromat, Zeiss, NA = 1.4) on the

sample under investigation. The 2 mm-wide

beam enters the objective largely off-axis and

consequently hits the sample above the

critical angle, leading to total internal

reflection. This experimental approach can

only be applied to objects which are close

enough to the glass surface since it involves

the scattering of solely the evanescent

component of the impinging light. The beam is

chosen to be s-polarized (i.e. parallel to the

long axis of the nanorod). This configuration,

which is opposed to the one used in the main

text to efficiently excite SHG, ensures an

efficient excitation of the only antenna modes

appearing in the visible portion of the

spectrum, V2A and V2

B. After being recollected

by the objective, the reflected beam is blocked

by a beam-stopper, whereas the light

scattered by the nanostructures is transmitted

to the detection path. A flip mirror allows

performing dark field imaging maps of the

sample, which helps selecting exclusively the light scattered by a single nanostructure. Eventually, the light

is redirected to the spectrometer (Shamrock SR-303i, iXon3 897-BVF, Andor) to acquire each individual

spectrum, which is normalized to the reference spectrum of the halogen lamp. As shown in Fig. 2Sb,

separate spectra are recorded for the three different polarization states of the detected light using a

broadband polarization analyzer (LPVIS, Thorlabs): longitudinal (i.e. parallel to the impinging light – red

line), transverse (blue line) and unpolarized state (black line). As expected the detected light is mostly

polarized parallel to the incident polarization where the two antenna modes, V2A and V2

B, are best excited.

Here we would like he to emphasize that by exciting the nanostructure with polarization orthogonal to the

long axis of the rod one obtains a much lower signal (comparable with the blue curve in Fig. 2S), due to the

weak coupling of this polarization with the antenna modes (see Fig. 1c in the main text). Since all spectra

present identical features, thus the unpolarized state spectra were used for the comparison in the main

text.

Figure 2S. a) Dark-field spectroscopy experimental

setup. b) Single nanoantenna spectra acquired with

different detection polarization.


Figure 3S. Experimentally acquired spectra from the two most significant lines of the array sketched in the

main manuscript (see Figure 2a) and corresponding to the contour plots in Figure 3 of the main text. a)

Spectra corresponding to the experimental contour plot in Figure 3a in the main text. b) Spectra with which

the contour plot of Figure 3b is generated.


3. Experimental setup for SHG detection and characterization

An ultrafast Erbium-doped ultrafast fiber laser centered at

1560 nm with a pulse length of about 70 fs (FemtoFiber Pro

NIR - Toptica Photonics AG) is coupled to a home-made

inverted microscope (see Fig. 4S). The excitation light,

reflected by a 70:30 (transmission: reflection) cube beam

splitter onto the back aperture of a 1.3 N.A. objective (UAPON

40x O340 - Olympus), is focused on the fused-silica substrate

(see Section 1). The SHG signal from the nanostructure array is

collected through the same objective while the sample is

raster-scanned in the x-y plane by means of a piezoelectric

scanner (P517.3CL - Physik Instrumente GmbH & Co.). The

collected nanoantenna emission, together with the residual

excitation light reflected at the glass-air interface, travels back

through the beamsplitter onto a dichroic short-pass mirror

(DMSP, DMSP1000 - Thorlabs Inc.), which transmits the SH

and reflects the FW to a CMOS camera used for beam

optimization and alignment. Residual background on the

transmitted SHG radiation is further rejected using a set of

filters. The SHG emitted intensity is measured with a single

photon avalanche detector (SPAD, PDM-C Series, MPD S.r.l.)

positioned after a band-pass (25 nm FWHM) filter centered

at 775 nm (NBF, 775WB25 - Omega filters). The emission

spectrum is acquired with a VIS/NIR spectrometer (Acton

SpectraPro SP2300 + CCD Camera PIXIS 1024B, Princeton

Instruments Inc.) placed after a short-pass filter with ultra-

steep cutting edge (SPF, SP01-785RU-25, Semrock Inc.).

Figure 4S. Nonlinear microscopy

experimental setup.


4. Linear extinction maps

cExtinction maps of the sample array were collected at wavelengths close to the fundamental (1550 nm)

and to the second-harmonic (785 nm) respectively, by coupling CW diode lasers centered at the two

wavelengths of interest (LP785-SF100 and LPSC-1550-FC, respectively - Thorlabs Inc.) to the confocal

microscope developed for nonlinear microscopy described in the previous section. To adapt the system to

these measurements we have replaced the SPAD detector with either a photomultiplier tube (H9306-04 -

Hamamatsu Photonics K. K.), to acquire the extinction maps at 780 nm, or an IR-extend SPAD (InGaAs SPAD

- Micro Photon Devices S.r.l.), to record the extinction signal at 1550 nm. The upper panels of Fig. 5Sa recall

the same nanostructure array SEM images reported in Fig. 2a and 4b of the main text, while the bottom

panel shows a SEM picture taken on single rods with length varying from 80 to 155 nm (same lengths as in

the coupled structures). Figure 5Sb shows the linear confocal maps recorded at 780 nm on the arrays

presented in panel a, obtained with linearly-polarized light aligned along the rod long axis (double-headed

arrow). Conversely, Figure 5Sc shows maps at the same excitation wavelength collected with orthogonal

Figure 5S. Confocal microscopy linear maps acquired on the sample. a) SEM map of the areas of

interest. b) Extinction maps of the antennas at 780 nm with horizontal polarization. c) Extinction maps

of the antennas at 780 nm with vertical polarization. d) Extinction maps of the antennas acquired at

1550 nm with vertical polarization.


polarization orientation (double-headed arrow). These maps aim at characterizing the optical response of

each isolated nanoparticle at the peak of the expected SH emission in comparison with the SHG maps

presented in the main text. As expected, systematic extinction variations are only observed when the

linear light polarization is set parallel to the nanorod long axis. In particular, two separate trends can be

spotted in the map of the coupled structures: (i) a marked reduction of the extinction signal occurs while

moving from top to bottom and (ii) a sensible modulation of the extinction can be noted when moving from

left to right, with distinct dips occurring at the third and fourth column. The first behavior is ascribed to the

V2B resonance, which peaks around 800 nm for the smaller V-shapes (first row) and shifts to the IR when

the V-shape arm length is increased. The second behavior is purely associated with the V2A

resonance that

is mainly determined by the rod resonance, which changes from left to right in the array and matches the

laser line for a rod length between the ones of the structures in row 3 and 4. This is also pointed out by the

two maps featuring the isolated nanostructures (rods: bottom panel, V-shapes: top-right panel).

The extinction maps collected at 1550 nm are displayed in Fig. 5Sd, which shows that, indeed, the antennas

fabricated in row 2 and 3 feature a fundamental mode matching the ultrashort laser pulse wavelength. In

particular, the right panel of Fig. 5Sd, which shows the extinction maps acquired on the isolated V-shape

structures, reproduces the SHG map acquired on the same region of the sample (see right panel of Fig. 4a

in the main text). Furthermore, a careful observation of the left panel of the same figure reveals lower

extinction from the antennas in column 2, which agrees with the lower SHG recorded in Fig. 4a in the main

text, possibly indicating the presence of some fabrication inaccuracy (e.g. thinner structures, wider gaps).


5. Numerical method to evaluate single nanostructure SHG signal

The intensity of the second harmonic (SH) field generated by nanoparticles is always orders of magnitude

weaker than the intensity of the pump field; it follows that a perturbative approach may be adopted and in

the so called undepleted-pump approximation we can assume the SH field does not couple back to the

fundamental field (FF). Therefore, the nonlinear problem can be decomposed into two linear scattering

problems: we first solve the linear electromagnetic problem at the FF using a frequency-domain finite-

element solver and then we use the calculated fields to specify the SH polarization source currents which

give rise to the radiated electromagnetic field at the SH frequency [2, 3]. It is certainly true that, as a rule of

thumb, boundary element methods are more efficient in problems where there is a small surface/volume

ratio and might require, therefore, a much smaller number of elements to evaluate the fields than volume

integral based methods. However, boundary element methods involve a complex parameterization of the

boundary elements. This is why in our manuscript we have decided to resort to a commercial finite-

element method (COMSOL Multiphysics). Although SH polarization sources in metals are due both to free

and bound electrons, we consider here only contributions of free electrons, as it has been proven they are

responsible for the dominant nonlinear terms in this process [4]. The current density source of SH light may

then be expressed as the superposition of two contributions: one coming from the volume of the antenna,

, the other, , located at the metal surface. As it has been already discussed in the literature [2, 5,

6] the source component due to normal surface currents ( ) is dominant with respect to both the

source component related to tangential surface currents and to the source component due to the volume.

Thus in our simulations we neglect these latter terms and we relate our SH sources to the FF electric field

and to the free electron hydrodynamic parameters as follows:

(1)

where = 5.9×1028

m-3

is the free electrons density in gold assuming the effective electron mass is =

= 9.11×10-31

kg, e is the elementary charge, = 3.33×1013

s-1

is the electron gas collision frequency in

gold, is the bulk gold permittivity at the FF taken from Palik [7], and the angular frequency of the FF

field. Moreover, is a unit vector pointing outward and normal to the metallic surface, is the

normal component of the FF electric field (evaluated inside the metal region). In all our numerical

simulations, we have checked that the employed discretization (with a cell size equal to 10 nm) provides

sufficient accuracy by verifying that reducing the element size to smaller values does not change the

numerical solution. Moreover, to avoid numerical instabilities due to diverging fields at the sharp corners of

the structure, we introduced a small radius of curvature, mimicking the real morphology of metallic

nanostructures.

In this paper, we also avoid considering the nonlocal nature of light interaction with free electrons and

adopt the local approximation, i.e., we assume that the Fermi velocity of the free electrons satisfies the

inequality , where is the inverse of the characteristic length of variation of the

electromagnetic field [8]. Despite nonlocality may also affect the nonlinear response, simple models like

the one adopted here usually provide good qualitative agreement with experiments, properly describing

near- and far- field properties of SH light [8-11]. For the same reason we also avoid considering quantum

volJ surfJ

surfˆ ⋅n J

( ) ( )

320 FF

surf FF,2 2* 0 0

3ˆ

2 2

n ei E

m i i

ε

ω γ ω γ⊥

+⋅ =

+ +n J

0n *m

em 0γ

FFε ω

n̂ FF,E ⊥

/Fv qω<< q


effects in the gap region; quantum tunneling currents induced in sub-nm gaps increase absorption losses at

the FF and may add quadratic and cubic nonlinear sources that are predicted to interfere with the metal

nonlinearities [12-14].

Note that the focusing conditions achieved in the experiment correspond to a Gaussian beam diameter on

the sample equal to 1.4 µm (Rayleigh criterion), i.e. quite larger than the size of the nanoantenna; for this

reason, in the numerical experiment we have approximated the beam with a single plane wave.


6. SH emission polarization and its dependence on the incident polarization.

Figure 6S. SHG polarization dependence. a) SH emission (diamonds) from a single doubly-resonant

nanoparticle as a function of the impinging FW polarization angle. The SHG is collected with no

polarization selection. The line represent the best fit with a cos(θ)4 function. b) SH emission (dots) from the

same particle as a function of the angle. The detected polarization is selected using a polaroid. The

incident light polarization is set to obtain the highest signal (i.e. vertically). Vertical polarization (oriented

along the y-axis) correspond to 90° orientation. While a) best fit is a cos(θ)4 function, b) best fit correspond

to a cos(θ)2 function, as expected. c) Polar plot of the data points of a). d) Same as c) for b). Panel d)

corresponds to panel d) of Figure 4 in the main text.


7. Power and spectral characterization of the SH emitted by the nanostructure.

Figure 7Sa presents the bi-logarithmic plot of the power emitted by the doubly-resonant nanostructure

around 775 nm as a function of the power incident on the sample. The ~2 slope of the linear fit (blue line)

highlights the nonlinear second-order nature of the process. The count rates reported are corrected for the

losses in the collection and detection paths, and for the quantum efficiency of the SPAD detector.

Figure 7Sb shows the nonlinear coefficient extracted from the power curve for each incident power value.

The reproducibility of γSHG demonstrates the absence of photodamage during irradiation. By superimposing

the spectrum calculated through FDTD simulations (black dashed line in Fig. 7Sc) for the doubly-resonant

particle with both the excitation laser band (red curve in Fig. 7Sc) and the SH emission spectrum (blue curve

in Fig. 7Sc) one readily observe the very good matching between the V1 mode of the structure and the first,

and the excellent overlap of the mode V2A with the second. Third harmonic generation (THG) and two-

photon photoluminescence (TPPL) can also be observed in the nanostructure emission spectrum excited at

50 µW (see Fig. 7Sd). Using a double-peak Gaussian fit (red-dotted line), the SH and TH emission peaks can

be estimated to be centered around 776 nm and 519 nm, respectively. Once the losses in the collection

path are accounted for, THG signal is evaluated to be less than one order of magnitude higher with respect

to the SHG one, for an impinging power of 50 µW. The dark solid line in Fig. 7Sd represents the light

detected upon illuminating an edge of the single crystal gold flake not exposed to FIB milling with about 5

mW power (2 orders of magnitude higher than the one used with the nanoantennas), demonstrating that

nonlinearity is highly enhanced by nanostructuring. This ratio is significantly lower than the ones reported

in literature so far [15], highlighting the remarkable SH generation efficiency achieved by these structures.

Figure 7S. SHG characterization. a) Bi-logarithmic power curve (blue hollow diamonds). Linear fit (solid

line). b) Nonlinear second-order coefficient extrapolated from the power curve (blue filled diamonds).

The straight solid line represents the constant value which best fits the data. c) SHG spectrum (blue line)

and laser band (red line) overlapped with the doubly-resonant antenna calculated spectrum. d) Emission

spectra of the same particle (light blue line) and of the flake edges at 5 mW incident power (blue line).


8. Evaluation of the nonlinear coefficient of the nanoantenna

Parameter Exc. λ

(nm)

Laser rep.

rate (MHz)

Laser pulse

length (fs)*

FW average

power (mW)

Exc.

obj. NA

spot diameter

(µm)

FW Peak

Power (W)

Symbol λ ν τ PFW NA δ ��

Formula �.��×

�

� �

��

Value 1550 80 120 0.12 1.35 1.4 13

Table 1. Experimental parameters and input power levels.

Parameter SH emitted

photons (cts/s)

SHG Power

(W)

SHG Peak Power

(W)

Max. conversion

efficiency

Peak Nonlinear

Coefficient (W-1

)

Symbol N PSH �� ηSHG ��

Formula N · Eph PSH / (ν ·τ) PSH / PFW ��/(��)�

Value 7.6 × 10-13

7.6 × 10-13

8.0 × 10-08

6.4 × 10-9

5.1×10-10

Table 2. Output power levels and nanostructure nonlinear parameters. Eph: photon energy.

To estimate the peak nonlinear coefficient �� for the doubly-resonant nanostructure, we have evaluated

all the relevant parameters of our experimental setup. They are summarized in the two tables above. In

short, for the maximum employed incident power (~ 120 µW), which is well-below the nanostructure

damage threshold (see Section 9), we obtain a peak power ��

≅ 13W. In these conditions we

measured ~ 6.3 × 104 SHG counts/s at the detector from the doubly-resonant nanostructure. Assuming that

almost all the SHG is emitted towards the glass/objective side (i.e. a very conservative assumption) and

considering the losses due to the collection angle and transmittance of the objective (~ 30%) together with

the ones introduced by the optical elements in the collection path (beam-splitter: ~ 20%, dichroic-mirror:

~ 50%, narrow-band filter: ~ 50%, detector quantum efficiency: ~ 15%), we arrive to ~ 3 × 106 emitted

photons per second, corresponding to an SHG peak power ��

≅ 8 × 10#$W. The nonlinear coefficient

of the doubly-resonant antenna is thus ��

≅ 5.1 × 10#�&W#�. Using the average power levels for our

experiment, at the maximum employed input power, we find a maximum conversion efficiency '�� ≅

6.4 × 10#*. These coefficients are estimated by considering an optimized matching between the impinging

light and the nanoantenna, hence the excitation power was not scaled to account for the ratio between the

structure fingerprint and the spot size.


9. SHG efficiency evaluated on standard 100 nm gold spheres

To evaluate the performances of our device we have also studied 100 nm-diameter single spherical gold

nanoparticles grown in solution, which are successively spin-coated on a fused silica substrate and cleaned

using oxygen plasma. Fig. 8Sa shows a SHG map acquired on the spherical nanoparticle sample. The real

intensity counts are then evaluated using the same parameters employed for the antenna sample, to

account for the setup losses. The real intensity count histogram for all the investigated particles is shown in

Fig. 8Sb, revealing two main peaks. We interpret the lower and most pronounced one as due to SH

emission from single spheres while the second, which is set at about twice the intensity, is attributed to

emission from two uncoupled particles which are not resolved by the microscopy setup. Starting from this

assumption we assign a value of about 20 kcts/s for the single 100 nm-diameter nanoparticles excited with

60 µW average power, which corresponds to a nonlinear coefficient ��

=�,-./012

(�34/012

)5≅ 2.5 × 10#��W#�

almost 2-orders-of-magnitude lower than the one reported for the doubly-resonant nanostructure

developed in this paper.

Figure 8S. SH intensity characterization for 100 nm-diameter spherical isolated nanoparticles. a) SHG map

of a significant area of the spin-coated nanoparticle sample. b) Intensity histogram.


10. Resistance of the nanoantennas to photodamage

Figure 9S shows the SEM image of the sample array acquired after the optical characterizations described

here and in the main text were completed. The overview does not show any visible damage. The absence

of photodamage is further confirmed by an SEM zoom on the antenna that was mostly exposed during the

experiment (i.e. the doubly-resonant antenna, see the inset of Fig. 9S).

Figure 9S. SEM images of the sample acquired after the experiment (see also Fig. 2a in the main text). Inset:

SEM zoom image of the doubly-resonant particle.


References

1. Wu, X., Kullock, R., Krauss, E., & Hecht, B. Monocrystalline gold microplates grown on substrates by

solution-phase synthesis. Under Review.

2. Vincenti, M. A., Campione, S., de Ceglia, D., Capolino, F., & Scalora, M. Gain-assisted harmonic

generation in near-zero permittivity metamaterials made of plasmonic nanoshells. New J. of Phys.

14, 103016 (2012).

3. de Ceglia, D., Campione, S., Vincenti, M. A., Capolino, F., & Scalora, M. Low-damping epsilon-near-

zero slabs: Nonlinear and nonlocal optical properties. Phys. Rev. B 87, 155140 (2013).

4. Scalora, M., Vincenti, M. A., de Ceglia, D., Roppo, V., Centini, M., Akozbek, N., & Bloemer, M. J.

Second- and third-harmonic generation in metal-based structures. Phys. Rev. A 82, 043828 (2010).

5. Maystre, D., Neviere, M., & Reinisch, R. Nonlinear polarisation inside metals: A mathematical study

of the free-electron model. Appl. Phys. A 39, 115-121 (1986).

6. Berthelot, J., Bachelier, G., Song, M., Rai, P., Colas des Francs, G., Dereux, A., & Bouhelier, A.

Silencing and enhancement of second-harmonic generation in optical gap antennas. Opt. Express

20, 10498-10508 (2012).

7. Palik, E. D. & Ghosh, G. Handbook of optical constants of solids (Academic press, 1998), Vol. 3.

8. Rudnick, J. & Stern, E. A. Second-Harmonic Radiation from Metal Surfaces. Phys. Rev. B 4, 4274-

4290 (1971).

9. Rojas, R., Claro, F., & Fuchs, R. Nonlocal response of a small coated sphere. Phys. Rev. B 37, 6799-

6807 (1988).

10. David, C. & García de Abajo, F. J. Spatial Nonlocality in the Optical Response of Metal Nanoparticles.

J. Phys. Chem. C 115, 19470-19475 (2011).

11. Sipe, J. E., Moss, D. J., & van Driel, H. M. Phenomenological theory of optical second- and third-

harmonic generation from cubic centrosymmetric crystals. Phys. Rev. B 35, 1129-1141 (1987).

12. Esteban, R., Borisov, A. G., Nordlander, P., & Aizpurua, J. Bridging quantum and classical plasmonics

with a quantum-corrected model. Nat. Comm. 3, 825 (2012).

13. Haus, J. W., de Ceglia, D., Vincenti, M. A., & Scalora, M. Quantum conductivity for metal-insulator-

metal nanostructures. J. Opt. Soc. Am. B 31, 259-269 (2014).

14. Haus, J. W., de Ceglia, D. M., Vincenti, A., & Scalora, M. Nonlinear quantum tunneling effects in

nanoplasmonic environments: two-photon absorption and harmonic generation. J. Opt. Soc. Am. B

31, A13-A19 (2014).

15. Hanke, T. et al. Efficient Nonlinear Light Emission of Single Gold Optical Antennas Driven by Few-

Cycle Near-Infrared Pulses. Phys. Rev. Lett. 103, 257404 (2009).


Documents

DOI: 10.1038/NNANO.2015.69 Mode-matching in multiresonant ... · Figure 3S. Experimentally acquired spectra from the two most significant lines of the array sketched in the main manuscript