# Controlled Second Harmonic Generation with Optically Trapped Lithium Niobate Nanoparticles

Zacharie Behel, Yannick Mugnier, Ronan Le Dantec, Yann Chevolot, Virginie

Monnier, Pierre-François Brevet

► To cite this version:

Zacharie Behel, Yannick Mugnier, Ronan Le Dantec, Yann Chevolot, Virginie Monnier, et al., Controlled Second Harmonic Generation with Optically Trapped Lithium Niobate Nanoparticles. Nano Letters, 2024, 24 (19), pp.5699-5704. 10.1021/acs.nanolett.4c00353. http://dx.doi.org/10.1021/acs.nanolett.4c00353

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Distributed under a Creative Commons Attribution 4.0 International License
Controlled Second Harmonic Generation

with Optically Trapped Lithium Niobate Nanoparticles

Zacharie Behel,¹ Yannick Mugnier,² Ronan Le Dantec,² Yann Chevolot,³ Virginie Monnier,³

Pierre-François Brevet¹*

¹ Institut Lumière Matière, UMR CNRS 5306 and Université Claude Bernard Lyon 1, F-69622 Villeurbanne, France.

² Université Savoie Mont-Blanc, SYMME, F-74000 Annecy, France

³ Université Lyon, Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR5270, Ecully 69130, France.

*Corresponding author : Pierre-François Brevet, e-mail: pfbrevet@univ-lyon1.fr

**KEYWORDS :** Nanoparticle, Lithium Niobate, Second Harmonic Generation, Optical Trapping, Holographic Optical Tweezers
ABSTRACT

We report experiments where the second harmonic generation (SHG) response from a single 34 nm diameter lithium niobate nanoparticle is observed. The experimental set-up involves a double arm structure with a first beam devoted to the optical trapping of single nanoparticles whereas the second arm involves a femtosecond laser source at 800 nm leading to the SHG emission from the trapped nanoparticles. SHG operation where one to three nanoparticles are present in the optical trap is first demonstrated, thus highlighting the transition between coherent and incoherent SHG, the latter also known as hyper Rayleigh scattering (HRS). With the use of a spatial light modulator to move the optical trap in and out of the focus of the fundamental femtosecond beam, the observed SHG intensity response is switched back and forth between a low and a high level of intensity. This controlled SHG operation opens new avenues for nanoparticle characterization and applications in sensing or communication and information technologies and constitutes the first step in the design of active substrate-less metasurfaces.
INTRODUCTION

Quantitative characterization of single nano-objects with dimensions much smaller than the wavelength of light is still a great technical challenge in nanoscience [1]. This can be achieved when these nano-objects are supported onto a substrate with routine microscopy-based methods, such as Scanning or Transmission Electron Microscopy (SEM or TEM), thus providing their morphological parameters with great accuracy [2]. A full description of a sample containing large size and shape distributions of nanoparticles though requires several TEM images to derive relevant statistics. Improved reproducibility in the fabrication method may alleviate this problem, using top-down lithography-based approaches or similar advanced routes, as it is the case for arrays of nano-elements constituting metasurfaces, for instance [3, 4]. However, *in-situ* observation of single nanoparticles remains a challenge in liquid suspensions where the nano-objects are not supported by a substrate and thus undergo permanent Brownian motion. Their individual characterization is however highly demanded since ensemble measurements only lead to average physic-chemical properties resulting from most bottom-up chemical syntheses. Influence of their size and shape is the first obvious example since large deviations from the average value may arise within the corresponding ensemble distributions. Therefore, besides ensemble characterization methods, there is still a need for characterization tools at the single nano-object level in solution. Regarding optical methods, determination of the linear properties of individual metallic nanoparticles, in particular their extinction and absorption cross-sections, has been proposed and compared with their UV-visible absorption spectra derived from large ensembles [5]. At the single particle level, experimental sensitivity is the limiting factor for the smallest sizes although nanoparticles as small as 5 nm in diameter have been studied [6]. For the nonlinear optical properties like the first hyperpolarizability, reports at the single particle level are scarcer
despite the necessity to perform them because of the strong size, shape and crystalline
structure dependence [7]. Indeed, for centrosymmetric metallic nanoparticles, the first
hyperpolarizability leading to the effective second harmonic generation (SHG) cross-section
originates from surface contributions while a volume response accounts for the SHG emitted
by non-centrosymmetric nanocrystals [8]. SHG is a nonlinear phenomenon whereby two
photons at a fundamental frequency are converted into one photon at the harmonic frequency.
For materials belonging to point groups with an inversion symmetry center, this phenomenon
is forbidden within the electric dipole approximation so that it can only occur at their surface.
As a result, SHG scattering is a perfect tool to investigate the surface of gold or silver metallic
nanoparticles of various sizes and morphologies [9]. In the case of acentric structures and
among the well-known non-centrosymmetric oxide nanomaterials [10], lithium niobate
(LiNbO₃, LN) is an illustrative example of a reference optical material with a very rich
nonlinear optical response [11] stemming from the core volume down to nanocrystal size of
about ~5 nm [12]. Interestingly, for hybrid nanostructures consisting of LiNbO₃ cores
decorated with gold seeds and gold nanoparticles, the surface contribution remains to be
clarified [13, 14]. Therefore, experimental parameters including size, shape, crystalline
structure or possibly exact morphology, as it is the case with core-shell nanoparticles for
instance, play a major role in the origin of the SHG phenomenon. In terms of characterization,
by using the original hyper Rayleigh scattering (HRS) configuration [15], an incoherent SHG
signal may be detected arising from the orientation fluctuations of the randomly dispersed
particles in the liquid suspension. Such an ensemble technique has been extensively used in
the past to determine the first hyperpolarizability of molecules and then nanoparticles.
Extremely large first hyperpolarizability values were thus derived for metallic nanoparticles
with diameter ranging from a few to hundreds of nanometers [16]. Besides these ensemble
measurements, the question of the SHG characterization from single nanoparticles has already been addressed and demonstrated for diluted suspensions but at the detriment of the acquisition time [17]. Another strategy is to thicken the liquid solvent and to make the suspension idle so that the nanoparticles are no longer subjected to Brownian motion. Under these conditions, if polarization analysis of the HRS intensity is reported and compared to ensemble measurements [18, 19], a time-consuming procedure needs to be implemented since 3D-translation of the whole cell containing the sample is required to bring a single nanoparticle within the focus of the fundamental beam. Note that such a cumbersome method performing single nano-object characterization has also been applied on several dielectric non-centrosymmetric oxide nanocrystals after casting a drop of a suspension onto a glass substrate followed by solvent evaporation. As already outlined, assessing the first hyperpolarizability tensor elements values from the polarization-resolved traces is then severely complicated, especially for low-symmetry point groups with more than two independent elements in their second order susceptibility tensor. Knowledge of the nanocrystal size, shape and possible agglomeration state as well as their spatial orientation is required [20, 21] again highlighting the urgent need to develop new optical approaches dedicated to the nonlinear optical characterization at the single nano-object level.

Besides, a strategy based on optical tweezers [22, 23], combining SHG measurements with optically trapped nanoparticles opens new avenues for nonlinear metasurfaces, a topic of great interest with high stake perspectives in fields as diverse as light converters, light communication, photo-voltaics, light-based sensors, ... as discussed in recent reviews [24-26]. Metasurfaces as prepared by top-down methods with lithography are prepared once for
all with fixed geometrical parameters and materials. Although there exist proposals to go
towards active systems using phase change materials or combination with an externally
applied non-photonic stimulus, those metasurfaces are defined once for all. The present work
proposes to go around this lock by removing the substrate in order to have a mobile motif,
externally controlled by light. Therefore, the substrate-less metasurface can be reconfigured
on demand according to the desired application. Also, with respect to nonlinear optics and
nonlinear metasurfaces, nanostructures are affected in shape and polarization by the substrate
and this feature can be crucial up to the point where the substrate-nanostructure response
dominates over the nanostructure response itself. Abandoning the substrate allows to remain
with a device where the response is controlled by the nanostructure only, without any
perturbation by a substrate. Note that this active strategy may also be used in practice for
linear metasurfaces.

In the present work, we report a first step towards active substrate-less metasurfaces with the
proposal and experimental demonstration of the SHG response generated by a single optically
trapped lithium niobate nanoparticle, the diameter of which is about 34 nm. The method is
based on a substrate-free and liquid cell scanning-free method allowing for rapid single
nanoparticle assessment in the native solvent. The liquid solution is here allowed to flow in a
microfluidic channel before the nanoparticles are trapped by an optical beam, independent
from the fundamental source performing the SHG operation. In this respect, the operation
differs from previous works on micrometer long nanowires where a single beam performs
trapping and SHG operation [27, 28]. The operation can be easily extended to other
nanoparticle types, like metallic ones with suitable modifications [29]. The trapping
conditions are then modified in order to spatially manipulate the nanoparticle, thereby fully
controlling their individual SHG response. As a result, this work demonstrates that it is
possible to envisage active optical trapping of single nanosized particles as the first active
building block of nonlinear metasurfaces. The next step, already demonstrated elsewhere for
quantum operation systems with cold atoms and molecules, would then entail the trapping of
several nanoparticles in individual traps arranged in a regular network [30-31].

## EXPERIMENTAL

The experimental set-up performing both the optical trapping and the SHG operation is composed of two distinct arms, the first one corresponding to classical optical trapping (Thorlabs, Optical Trapping Kit) whereas the second is dedicated to the SHG excitation and collection, see Figure 1. Note that the use of such a commercially available set-up was decided for simplicity and rapidity of development but that a home-made one would have led to a similar design. Here, we revert to the SHG nomenclature instead of HRS when the recorded signals arise from a single nanoparticle. The set-up is an improved version of that previously described for operation on 1 µm diameter silica microbeads [32].
<figure><img src="image_2.png" /><figcaption>**Figure 1:** Schematic of the experimental set-up including the two arms to perform both optical trapping and the single nanoparticle SHG. Acronyms are DM for Dichroic Mirror, SLM for Spatial Light Modulator, PM for Photomultiplier Tube, CCD for Charge Coupled Device, LED for Light Emitting Diode, fs for femtosecond and IR for Infra-Red.</figcaption></figure>

The optical trapping arm consists in a continuous near infrared laser emitting at 975 nm (Thorlabs, Laser Diode Controller model 1A LDC 210C) which is first adjusted in diameter using a threefold magnification telescope to illuminate a Spatial Light Modulator (SLM, Holoeye, model Pluto-BB) with an incidence angle of 10°. The SLM is incorporated into a 4-f
system in order to conjugate, with a pair of 50-cm focal length lenses, the planes at the
entrance of the microscope objective with the SLM screen. The SLM unit is controlled with
the Labview Red Tweezers software developed by R.W. Bowman et al. [33, 34]. A dichroic
mirror is then used to combine the trapping beam with the 800 nm femtosecond laser
(Coherent, model Chameleon Ultra) allowing SHG emission from single nanoparticles. The
two combined beams are passed through a low-pass filter ensuring that no short wavelengths
can irradiate the sample. The two beams are then focused by an immersion objective with a
magnification of X100, numerical aperture NA=1.25 and a working distance of 0.23 mm.
These characteristics are necessary for a comfortable double operation : they allow to obtain a
trapping beam with a strong intensity gradient favoring the trapping force while minimizing
the excited volume required for the most efficient SHG emission. However, as this objective
is not achromatic, the difference in wavelength between the two laser beams leads to a
longitudinal position shift of their respective focal points due to refractive index dispersion.
The solution chosen to remedy to this problem was to add a telescope with a magnification
close to 1 along the path of the femtosecond laser in order to make it slightly convergent at
the objective entrance.

The sample is visualized by Kohler illumination : a light-emitting diode at 680 nm is
collimated by a lens and focused by an X10 objective with a 0.25 numerical aperture acting as
a condenser. This condenser is placed in such a way as to form an afocal doublet with the
immersion objective, so that the sample image follows the reverse path of the laser to a
dichroic mirror with a cut-off wavelength of 750 nm. Light transmitted by the sample is then
focused and collected by the image acquisition system consisting of a CMOS camera
(Thorlabs, model DCC1240C). Similarly for the trapping beam that interacts with the sample,
the transmitted intensity is measured by a four-quadrant photodiode after collimation and
focusing with a condenser.

The fundamental beam at 800 nm is produced by a femtosecond laser (Coherent, model
Chameleon Ultra) delivering at 80 MHz pulses of about 140 fs duration. The average power
measured at the sample location was about 16 mW. For the nonlinear optical arm, the SHG
signal is epi-collected by the X100 objective and spectrally filtered by a 660 nm cutoff-
wavelength dichroic mirror thus reflecting the SHG signal at a wavelength of 400 nm. Thus
the experimental conditions, although they cannot be directly compared with previous single
nanoparticle works, are rather similar considering the high magnification objective used here
as compared to X16 or less normally used in ensemble measurements. The harmonic beam is
then focused by a 150 mm focal length lens before detection. Because the SHG intensity
arising from a single nanoscale source is rather weak, the detection line incorporates a high-
pass filter located at the entrance of a spectrometer (Acton, model SectraPro-150, 500 nm
grating, 1200 lines/mm, resolution of 0.1 nm) equipped with a Peltier-cooled photomultiplier
tube (Hamamatsu, R943-02). Noise from the amplified signals is systematically subtracted
with a dual channel photon counter (Stanford Research Systems, model SR400) operating at
the optical chopper frequency fixed at 135 Hz. Acquisitions involve scanning the detection
wavelength to ensure that only SHG is detected without spurious broadband signal. As
illustrated in Figure 2, the SHG intensity presents a Gaussian profile as a function of
wavelength, centered at 400 nm, namely half of the fundamental wavelength.
The neat lithium niobate nanoparticles were synthesized by a solvothermal process already reported, see reference for the neat lithium niobate synthesis [13]. Briefly, an autoclave equipped with a 23 mL Teflon cup is filled with 2.25 mL of lithium niobium ethoxide and 1.25 mL of butane-1,4-diol. The mixture was then heated for three days at 235°C. After cooling down to room temperature, the precipitate was transferred to Nalgene centrifuge tubes. Three centrifugation rounds at 13500 rpm for three minutes were carried out to collect the powder which was then washed with ethanol. The final LN nanoparticles were dried at 75 °C before being re-dispersed in deionized water at a mass concentration of 1 g/L. Their typical size and shape distributions were previously assessed [13, 35] leading to a mean diameter of (34 +/- 12) nm as derived from the Le Bail fit refinement along the [012] direction and TEM observations.

LN nanoparticles were then injected into a microfluidic channel itself placed on a controllable three-dimensional translation stage (ThorLabs, model NanoMax Axis Flexure Stage). This stage, driven through a computer interface, has a 20 µm scanning range with 20 nm steps in each direction using three piezoelectric controllers (ThorLabs, model T-Cube TPZ001). The sample holder, i.e. the microfluidic channel, is then aligned with the setup optical axis in contact with the oil of the immersion objective.

## RESULTS AND DISCUSSION

Aqueous suspensions of LN nanoparticles were prepared at a nominal concentration of $C = 0.01$ g/L ($4.8 \times 10^{13}$ particles per liter) corresponding to a good compromise between the waiting time before a nanoparticle is trapped once the infrared beam is switched on and a low
enough particle density to achieve single particle trapping. As shown below, trapping of
several nanoparticles remains possible though. In order to ensure that a SHG signal is detected
in the 380 – 420 nm range, spectrally resolved traces of the detection arm were performed, see
Figure 2. This procedure ensures that a monochromatic SHG signal is indeed collected and
that no spurious broadband signal deteriorates the sensitivity. As expected, the observed
signal has a Gaussian profile with a Full Width at Half Maximum (FWHM) of about 5 nm
consistent with the femtosecond excitation source but precluding any further analysis as a
function of the nanoparticle number.

<figure><img src="image_3.png" /><figcaption>**Figure 2**: Spectrally resolved SHG intensity trace for an optically trapped single 34 nm diameter Lithium Niobate nanoparticle, (disks) experimental data and (dashed) corresponding Gaussian fit.</figcaption></figure>

In order to observe the possibility of multiple trapping, namely simultaneous trapping of
several LN nanoparticles, the system is left over time with both the optical trapping and the
femtosecond fundamental beams illuminating the microfluidic channel. Time-dependent variations of the transmitted trapping beam intensity monitored with the four-quadrant photodiode and of the SHG intensity recorded at 400 nm are plotted in Figure 3 and demonstrate two successive trapping events. The transmitted intensity of the trapping beam, plotted in the upper panel, is maximal for the lowest number of trapped nanoparticles. However, when a LN nanoparticle enters the trap, a decrease of the transmitted intensity is observed resulting from an increase of the linear scattering at 975 nm. Lithium niobate is indeed a transparent material over a broad range of wavelengths such that absorption can be neglected here. The two successive drops in intensity at ~5 s and ~10 s then indicate the entrance of two more nanoparticles in the trap. A simultaneous SHG intensity increase is observed in the lower panel of Figure 3. At this stage, the initial number of trapped nanoparticles can be questioned as discussed below.
<figure><img src="image_4.png" /><figcaption>**Figure 3:** Simultaneous trapping of several lithium niobate nanoparticles. (upper panel)</figcaption></figure>

Time-resolved trace of the transmitted trapping beam through the microfluidic channel containing the nanoparticles solution. (lower panel) Simultaneous time-resolved trace of the SHG intensity. Dotted lines indicate average SHG intensity over the trapping event.

Events associated with a decrease of the trapping beam intensity result from the trapping of nanoparticles whereas an increase can be ascribed to a nanoparticle leaving the trap. Interestingly, no event corresponding to a single particle leaving the trap was recorded. Only full recovery of the trapping beam intensity was indeed observed and this was attributed to an unstable situation of multiple nanoparticle trapping eventually leading to collisions with the
consequence that two of the trapped particles are ejected from the trap. At this stage, the origin of this feature is tentative only and requires further scrutiny in the future. As another feature, SHG intensities epi-collected from the trap can be determined from the averaging of the recorded time-resolved SHG traces where the error bar is standard deviation of the count number. These average SHG intensities increase linearly with the number of events observed, i.e. the number of nanoparticles in the trap as depicted in Figure 4.

<figure><img src="image_5.png" /><figcaption>**Figure 4:** Normalized SHG intensities after averaging of the corresponding time-resolved traces as a function of the LN nanoparticle number present in the optical trap. Initial condition is assumed to correspond to a single trapped nanoparticle, see text.</figcaption></figure>

Such a linear relationship between the average SHG intensities and the number of trapped nanoparticles indicates that the SHG response observed is incoherent [15]. The 34 nm diameter LN nanoparticles are small enough with respect to the trapping volume to undergo rotational diffusion leading to random orientational distribution. In this respect, the transition from SHG for a single trapped nanoparticle to HRS for two or more nanoparticles is observed.
In order to verify this assumption, it is reminded that the standard expression for the total HRS intensity, when both neat solvent and nanoparticles can be detected, is written as [15] :

$$I_{\text{HRS}} = G[N_{w}\langle\beta_{w}^{2}\rangle + N_{LN}\langle\beta_{LN}^{2}\rangle] \quad (1)$$

where $N_w$ and $N_{LN}$ are the number of water molecules and LN nanoparticles illuminated while $\langle\beta_w^2\rangle$ and $\langle\beta_{LN}^2\rangle$ stand for the orientational average of their respective squared first-hyperpolarizabilities. Because the fundamental beam is here linearly polarized along the vertical OX laboratory axis whereas there is no polarization selection on the output harmonic beam, the first hyperpolarizabilities can be written in the laboratory frame [36] as :

$$\langle\beta_i^2\rangle = \langle\beta_{i,XXX}^2\rangle + \langle\beta_{i,YXX}^2\rangle \quad (2)$$

where $i = w, LN$ and for a propagation direction taken along the OZ laboratory axis, see Figure 1. Eq.(1) normalized with respect to the intensity measured in absence of nanoparticles becomes then simply :

$$I_{\text{HRS}} = 1 + \frac{\langle\beta_{LN}^2\rangle}{N_w \langle\beta_w^2\rangle} N_{LN} \quad (3)$$

where the quantity $N_w\langle\beta_w^2\rangle$, product of the number of water molecules within the fundamental beam focus times the square of the water first hyperpolarizability averaged over all possible orientation, is known. Hence, the numerator $\langle\beta_{LN}^2\rangle$ directly provides the lithium niobate nanoparticle first hyperpolarizability that can be compared to that obtained from ensemble measurements. Note that it can also be compared to the first hyperpolarizability derived from the product of the quadratic susceptibility $\chi^{(2)}$ with the nanoparticle volume where the
quadratic susceptibility lithium niobate is taken from textbooks [37]. This experimental value for the first hyperpolarizability of a single lithium niobate nanoparticle becomes too small because the neat solvent provides only a faint HRS intensity, which is the present case as observed in absence of nanoparticles. A value in line with ensemble measurements or textbooks as described a few lines above is nevertheless recovered only if the quantity $N_w\langle\beta_w^2\rangle$ is replaced with $N_{LN}\langle\beta_{LN}^2\rangle$ with $N_{LN} = 1$, that is a single nanoparticle is always present in the optical trap, namely the fundamental beam focus. Note that if it is assumed that $N_{LN} = 2$ for instance, the extracted first hyperpolarizability is too small.

In the subsequent data treatment, we first used the standard internal reference method with estimation of $N_w$ within the interaction volume to determine $\langle\beta_{LN}^2\rangle$. However, this procedure leads to a first hyperpolarizability $\beta = \sqrt{\langle\beta_{LN}^2\rangle}$ far too weak in comparison with the value previously determined from ensemble measurements for a single 34 nm diameter lithium niobate nanoparticle, namely $\beta = \sqrt{\langle\beta_{LN}^2\rangle} = 0.77 \times 10^{-24}$ esu [13]. One thus has to consider that the initial number $N_{LN}^0$ of LN nanoparticles present within the optical trap is not null and that the solvent contribution to the detected intensity is negligible. According to Eq. (3) with $N_w\langle\beta_w^2\rangle$ replaced with $N_{LN}^0\langle\beta_{LN}^2\rangle$, the slope is simply $1/N_{LN}^0$. Experimentally, a value of 0.8 for this slope was derived from Figure 4, indicating that $N_{LN}^0 = 1.2$, i.e. $N_{LN}^0 \sim 1$, namely that a single nanoparticle is initially trapped during the time dependence of the HRS intensity, as seen on Figure 4. Next two events therefore correspond to the addition of a second and a third LN nanoparticle in the optical trap, respectively. This conclusion is also supported by our experimental sensitivity that does not allow us to clearly observe the neat water solution whereas the SHG signal from a single trapped nanoparticle is well-above the signal-to-noise
ratio. As a result, the transition from SHG of a single LN nanoparticle to HRS from several LN nanoparticles is indeed observed in this experiment.

The optical trap used in these experiments involves a SLM control unit based on the Labview Red Tweezers software developed by R.W. Bowman et al. [34]. Therefore, the optical trap may be termed holographic optical tweezers and has the intrinsic possibility to adjust the trap properties. In particular, it is possible to achieve the spatial displacement of the optical trap while the SHG operation is undergoing. For a single trapped LN nanoparticle, as indicated by the measured SHG intensity, this feature enables the control of the SHG response by using the SLM placed on the trapping beam path. Hence, this way, it is no longer necessary to translate the whole sample cell to observe single nanoparticles, as discussed above in introduction. The single nanoparticle is indeed first trapped and then brought in or out of the focus of the femtosecond laser beam performing the SHG operation through the trapping beam SLM manipulation. Such an operation is reported in Figure 5 where the SHG intensity is recorded as the optical trap containing a single LN nanoparticle is positioned in and out of the femtosecond excitation. The SHG intensity therefore presents maxima when the optical trap is in focus and minima otherwise. The signal-to-noise ratio is large enough to clearly observe this operation, thus demonstrating the possibility to fully control the SHG intensity from a single nanoparticle. There remains a tendency of the SHG signal to weaken as the operation is repeated, a feature attributed to some misalignment accumulating as the operation is repeated.
<figure><img src="image_6.png" /><figcaption>**Figure 5:** SHG intensity as a function of the position of the optical trap, either (ON) inside or (OFF) outside of the femtosecond fundamental beam focus.</figcaption></figure>

Figure 5 also provides a hint on the timescale of operation. Indeed, with only three points per second recorded in such a measurement in order to provide preference to a large signal-to-noise ratio rather than speed of operation, the switch from high-to-low or low-to-high signal is about one second, something that may be improved with a detector better than the current PMT used here for example.

Finally, Figure 5 clearly demonstrates the operation of the first active and substrate-less brick of our nonlinear metasurface. The next stage where several of these bricks are used simultaneously has already been achieved in the past with cold atoms for instance and constitutes the next step into those developments.

## CONCLUSIONS
In the present work, an experimental set-up has been developed involving a double arm structure. The first arm is devoted to the optical trapping of single 34 nm lithium niobate nanoparticles whereas the second arm involves a femtosecond fundamental beam operating at 800 nm and performing SHG operation on the trapped nanoparticles. The set-up is characterized to ensure that SHG operation is indeed completed. In particular, the collected signals at 400 nm are monitored from one to three trapped nanoparticles thus demonstrating the transition between SHG and an incoherent HRS response.

In a second stage, owing to the holographic character of the optical trap designed, the SHG intensity response from a single nanoparticle is controlled through the spatial translation of the optical trap, in and out of the focus of the fundamental beam ensuring the SHG operation. This all-optical control of the SHG operation from sub-100 nm dielectric nanosources opens new avenues for sensing or communication technologies and for advanced nonlinear optical characterizations of single nano-emitters dispersed in their native solvent. The present experimental set-up therefore constitutes a first step towards the design of active substrate-less nonlinear metasurfaces for operation in the fields of sensing with parallelization of the SHG response of individual nanoparticles, communication technologies with light-controlled SHG intensity changes or quantum optics as SHG operation indicates that parametric down conversion is also achievable.

## ACKNOWLEDGEMENTS

This work is supported by the Agence Nationale pour la Recherche (ANR) within the frame of the projects RACINE (ANR-17-CE24-0029-03) and METATRAP (ANR-22-CE09-0011-01).
The authors acknowledge the authors of reference [34] for the use of the holographic tweezers program.

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