Optical Manipulation and Spectroscopy Of Silicon Nanoparticles

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Optical manipulation and spectroscopy of silicon nanoparticles exhibiting dielectric resonances Ana Andres-Arroyo, Bakul Gupta, Fan Wang, J. Justin Gooding, and Peter J. Reece Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b05057 • Publication Date (Web): 05 Feb 2016 Downloaded from http://pubs.acs.org on February 6, 2016

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Optical manipulation and spectroscopy of silicon nanoparticles exhibiting dielectric resonances Ana Andres-Arroyo,† Bakul Gupta,‡ Fan Wang,¶ J. Justin Gooding,‡ and Peter J. Reece∗,† †School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia ‡ARC Centre of Excellence in Convergent Bio-Nano Science and Technology, Australian Centre for NanoMedicine, School of Chemistry, The University of New South Wales, Sydney, NSW 2052, Australia ¶ARC Centre of Excellence for Nanoscale BioPhotonics (CNBP), Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia E-mail: [email protected]

Abstract We demonstrate that silicon (Si) nanoparticles with scattering properties exhibiting strong dielectric resonances can be successfully manipulated using optical tweezers. The large dielectric constant of Si has a distinct advantage over conventional colloidal nanoparticles in that it leads to enhanced trapping forces without the heating associated with metallic nanoparticles. Further, the spectral features of the trapped nanoparticles provide a unique marker for probing size, shape, orientation and local dielectric environment. We exploit these properties to investigate the trapping dynamics of Si nanoparticles with different dimensions ranging from 50 nm to 200 nm and aspect ratios

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for achieving directed nanoscale optical manipulation, for example, through anti-reflection coating. 10 This approach has a certain appeal in that it may extend the range of conventional optical tweezers whilst retaining its most desirable properties, i.e. dynamic control, multiplexing, precision tracking, and compatibility with imaging modalities. Materials that exhibit a large permittivity can be used to maximise the gradient forces experienced in an optical tweezers, which can offset the overall reduction in the polarisability due to diminishing particle dimensions. Most research in this area has focused on the use of metallic nanoparticles which exhibit a large extinction coefficient in the infra-red at typical trapping wavelengths. 11,12 However, this type of enhanced polarisability in metallic structures is also intimately linked to absorption, which results in strong localised heating in the surrounding fluid. Whilst trapping can be achieved with as little as 20 mW, such trapping powers yield very weak restoring forces, placing severe practical constraints on applications involving force transduction and confinement. In addition, even modest heating of optically trapped nanoparticles can affect the motion of the trapped particle, the local viscosity, and the thermodynamics of mechanically coupled systems (e.g. molecular motors, proteins folding, etc.). Recently we showed that even small differences in particle dimensions could potentially lead to a significant variability in the degree of heating generated by the trapping process. 13 All-dielectric resonators have seen growing attention in the field of nanophotonics as an alternative to the inherently lossy plasmonic structures. 14,15 High refractive index dielectrics demonstrate geometric scattering resonances similar to those of plasmonic structures, however, resonances are associated with distinct magnetic and electric dipole moments and higher multipole modes. These resonances are achieved without the associated large absorption coefficient and therefore do not suffer from intrinsic optical loss and Joule heating compared with their metal counterparts. Subsequently, they have found applications in areas such as metamaterials, 16–19 nanoantennas 20–23 and thin-film photovoltaics. 24–26 Resonant spectral features can be tuned through geometric means, and may also interact with neighbouring

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particles and the local environment - this makes them useful for nanosensing applications. In this work we investigate the possibility of using silicon (Si) nanoparticles exhibiting dielectric resonances for trapping experiments. Our motivation is that the large refractive index of Si provides an enhancement to the polarisability that improves trapping at the nanoscale. In addition, the characteristic scattering spectrum, as interrogated by dark-field spectroscopy, can be used as a signature of size, geometry and orientation of individual trapped particles. We show that trapping can be achieved for sizes up to 200 nm in diameter with aspect ratios varying between 0.4 and 2, where trap stiffnesses are comparable to metallic nanoparticles. We observe preferential orientation of elongated particles to the laser polarisation axis, which can be manipulated using a half-wave plate. We believe that optically trapped Si nanoparticles have significant potential in both nanoscale manipulation and sensing application. Experimental Methods. A schematic diagram of the experimental set-up used for this study is presented in Fig. 1. The optical tweezers comprise of a linearly polarised continuous wave (CW) infra-red (IR) 3W Nd:YAG laser (Laser Quantum, 1064 Ventus, λ = 1064 nm, TEM00 ) propagating in the z direction, which is focused using an oil-immersion microscope objective (Nikon, E-plan 100x, Numerical Aperture (NA) = 1.25), via relay optics, in order to create a diffraction limited spot in the front focal plane. Automated control of the position of the laser within the objective field-of-view with a fast response time is achieved with a twoaxis acousto-optic deflector (2D-AOD) (Gooch and Housego, 45035 AOBD), and aberrations in the beam profile are corrected by a spatial light modulator (SLM) (Hamamatsu LCOSSLM x10468-03) thus optimising the trap shape. The polarisation of the trapping beam is controlled by two half-wave plates (WP), the first one (WP1) serves the purpose of setting the optimal polarisation for the 2D-AOD and SLM, and the second one (WP2) is employed to rotate the polarisation of the laser in the trapping plane. The absolute power at the focus is measured using a calibrated photodetector taking into account the transmission losses of the optical system and microscope objective.

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The forward-scattered light from the trapped particles is collected by the condenser (Nikon, S-plan Fluor ELWD 40x, NA = 0.6) and its back-focal plane (BFP) is imaged onto a position sensitive detector (PSD) (First Sensor, DL16-7-PDBA4). The measured signal is used to observe the lateral position fluctuations of trapped particles in the x and y axes by relating the displacement from the centre to the interference pattern formed at the back-focal plane, a technique called back-focal plane interferometry. 27 A field-programmable gate array (FPGA)-based data acquisition card (NI PCIe-7852R) is used to synchronize the timing of the 2D-AOD and the PSD detector for calibration of the optical trap. Dark-field (DF) microscopy can be combined with optical tweezers to measure scattering spectra of single trapped nanoparticles by using a backscattered light to image the sample, thus no compromise on the strength of the optical trap is required. 28 An axicon lens was used to form a ring of light, which is imaged onto the back focal plane of the objective. The reflected light is simultaneously collected by a charge-coupled device (CCD) (AVT Stingray F145-C) for dark-field imaging, labelled as CCD1 in Fig 1, and a spectrometer (Acton SP2300, Princeton Instruments) with a scientific thermoelectrically cooled CCD optimised for spectroscopic applications (PIXIS 256, Princeton Instruments), labelled as CCD2 in Fig. 1. The reflected DF ring is excluded from being collected by both CCDs by placing a circular aperture before each of these elements ensuring that the only collected light is that which is scattered by the particle. The focal plane for the spectroscopy was selected by placing a 100 µm pinhole as the spectrometer aperture to ensure that the signal from other particles was eliminated and our spectroscopy measurements were performed only on the trapped particle. Samples for optical tweezers experiments were prepared in the following manner: Si nanoparticles (20 mg) were dissolved in 2 mL of MilliQTM water and sonicated for 5 minutes using an ultrasonicator Q500 (Qsonica,Australia). Following sonication, the suspension was filtered through a 0.22 um filter to remove any remaining large aggregates. For tweezer experiments, further dilution (50x) was carried out in MilliQ water. Dynamic light scat-

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tering (DLS) measurements were performed using a Malvern Zetasizer Nano ZS. The time dependent intensity fluctuations are characterised with the autocorrelation function in order to obtain the hydrodynamic diameter of the nanoparticles. Supporting Fig. S1 (a) shows the relative distributions of nanoparticle sizes in the prepared sample measured with DLS (black curve), where the broad peak is indicative of the polydispersity of the sample. The histogram (blue bars) corresponds to the trapped particles studied in this work, using spectroscopy to characterise their geometry. The studied Si nanoparticles not only present a range of different sizes but also vary in shape as can be seen in the transmission electron microscopy (TEM) (FEI Tecnai) images shown in Fig. S1 (b-i). A 10 µL volume of the nanoparticle suspension was pipetted into a sealed microfluidic chamber with a height of approximately 100 µm. Trapping measurements were performed on individual nanoparticles at a height of approximately 40 µm from the cover slip, with the trapping power at focus being about 120 mW. For each trapped particle the fluctuations in its position within the trap were measured with the PSD using BFP interferometry and its dark-field spectra was collected through the spectrometer with the CCD2 (1 second of exposure time). Whilst Si nanoparticles of an extended range of sizes present good trapping properties, some particles in the sample were too large to be trapped. Trapping high refractive index particles at larger size-scales suffer from the same limitations as those of metallic nanoparticles. Stable three-dimensional trapping is somewhat dictated by the ability of the axial gradient force to overcome the scattering forces, which tend to push the particle in direction of propagation. With increasing particle size the scattering forces dominates the axial gradient forces and a stable trapping position cannot be achieved. This is somewhat analogous to the problems associated with radiation pressure generated by reflections of high refractive index particles in the ray-optics limit. 10 Trapping Properties. Nanoparticles dispersed in an aqueous medium undergo rapid Brownian motion that is determined by the temperature and hydrodynamic properties of the particle and surrounding fluid. 29 A gradient force optical tweezers imposes a confining

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potential that limits this stochastic motion to a small volume about the focus of the trapping laser. The resulting equations of motion can be approximated by a series of uncoupled overdamped harmonic oscillators, where each translational coordinate ~q = (x, y, z) is associated with an optical restoring force of the form Fi = κi qi . From the Equipartition Theorem the probability of the trapped particle being displaced from the centre of the trap is given by the Boltzmann distribution, 30 shown in Eqn. 1, where U (qi ) is the confining potential in the qi dimension, κi the trap stiffness, kb Boltzmann’s constant, and T = 296 K the temperature.

P (qi ) ∝ exp

−U (qi ) kb T

= exp

−κi qi2 2kb T

(1)

The optical tweezers is calibrated for lateral position measurement of a particle by recording the PSD signal for different known displacements of the particle from the centre of the trap, achieved by synchronized switching of the 2D-AOD as detailed by Pearce et al. 28 Fig. 2 (a) shows the measured PSD signal vs. particle position along the x-axis (black dots) and the theoretical curve calculated by Gittes and Schmidt 27 (dashed blue curve). The PSD signal is linear (red solid line) for small displacements of the particle, allowing the position of the trapped particle to be tracked. A similar calibration curve is obtained for displacements of the particle along the y-axis, however, absolute measurements for the z-axis are unavailable using this calibration method. The time-dependent position of the nanoparticle in the x-y trapping plane measured over 1.5 seconds at a sampling rate of 20 kHz is filtered in the low-frequency range (below 400 Hz) to exclude non-thermal mechanical motion. Fig. 2 (b) depicts the position of a single trapped particle in the x-y trapping plane, which is observed to fluctuate around the centre of the trap within the linear region of the detector. Although not apparent, the particle is more constrained by the optical trap in the y-axis as can be seen in Fig. 2 (c), where a histogram of the particle position along the x (black) and y (red) axes is presented. The Gaussian fits based on Eqn. 1 yield trap stiffnesses of κx = 5.02 ± 0.13 pN/µm and κy = 6.57 ± 0.18 pN/µm in the x and y axes respectively for a trapping power of 120 mW. 8


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Fig. 2 (d) shows a plot of the measured trap stiffness values along the x and y axes for a number of different Si nanoparticles. We observe that the particles experience a stronger restoring force along the polarisation direction (y-axis), indicative of having the long aspect of the particles aligned to this axis. This is consistent with the expected behaviour observed in other elongated geometries such as nanorods. 31,32 Further polarisation dependent spectroscopic measurements on trapped Si nanoparticles (see the "Spectroscopic Characterisation" section of this letter) provide corroborating evidence of a fixed trapping orientation determined by the polarisation of the trapping laser. The range of trap stiffness values indicates a significant size and shape dispersion within the sample volume, which are corroborated with our expectations based on the electron microscopy measurements. Metallic nanoparticles are known to experience a considerable amount of heating in an optical trap 13,33–35 making them unsuitable candidates for applications involving biological samples or in statistical mechanics studies that require a well defined thermodynamic temperature. The trapping of Si nanoparticles bears a clear advantage to that of metallic nanoparticles in this regard. Supporting Fig. S2 shows the absorption cross-section of Au and Si nanospheres of varying size calculated using Mie theory. 36 In Fig. S2 (a) the absorption cross-sections are presented for sizes that are relevant to trapping 37 (∼ 50 − 200 nm). Owing to its relative transparency at the trapping wavelength, absorption in Si is one to two orders of magnitude smaller than Au, hence minimising unwanted heating effects. The absorption cross-section Cabs and the intensity of the laser at the trapping position Itrap can be used to estimate the power absorbed by the trapped nanoparticle that will dissipate as heat 38 Pabs = Cabs · Itrap . The increase in temperature in the vicinity of a trapped 100 nm diameter gold (Au) nanoparticles and can be in excess of 500 K/W of trapping laser power for the same experimental setup as used in this work. A Si nanoparticle of equivalent size which is trapped with the same optical power will only absorb 2% of the power absorbed by the Au nanoparticle, thus the heating of a trapped Si nanoparticle can be estimated to be around 10 K/W. The heating was measured by quantifying the spectral shift of trapped

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Figure 2: (a) Calibration measurements of a typical position sensitive detector (PSD) signal for known positions of the nanoparticle in the x-axis show the linearity of the detector for small lateral displacements of the particle from the centre of the trap. (b) Lateral position of a nanoparticle trapped with 120 mW of laser power and measured with the PSD. (c) Experimental histograms (dots) and Gaussian fits (lines) of the particle position in the x (black) and y (red) directions yield trap stiffnesses of κx = 5.02 ± 0.13 pN/µm and κy = 6.57 ± 0.18 pN/µm respectively. A dark-field image of a trapped Si nanoparticle taken with the CCD1 is presented in the inset. (d) Trap stiffness measured in the y-axis, κy , vs. trap stiffness measured in the x-axis, κx , for trapped Si nanoparticles of different sizes and geometries. The stronger restoring force observed along the y-axis is consistent with having the particle aligned with the trapping laser polarisation direction.

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Au nanoparticles as a function of trapping laser power; 13 for Si nanoparticles, no spectral shift was observed. For decreasing particle size of both Au and Si the absorption crosssection becomes negligibly small, however, in this region the trapping forces also diminish and maintaining a stable trapping potential becomes impractical. For the larger particle dimensions, shown in Fig. S2 (b), the absorption cross-section of Si presents clear resonances that can exceed the absorption cross-section of Au. These features are associated with the onset of electric and magnetic resonances that are highly dependent on both geometry and local dielectric environment. Whilst these spectral resonances occur for 1064 nm in particles sizes that exceed the trapping limits for Si, nanoparticles of the order of a few hundred of nanometres in diameter, exhibit strong dielectric resonances in the visible spectral range 14,15 and provide a useful handle for further characterisation (see Fig. 3). Spectroscopic Charaterisation. The scattering spectra of spherical dielectric particles can be calculated from the exact Mie solution of light scattering, 14,15 however, for particles with alternative geometries one must resort to numerical calculations such as the discrete dipole approximation (DDA) 39 or finite-difference time-domain method. 40 Different multipole modes - e.g. electric dipole, magnetic dipole - contribute to different resonance peaks in the spectra, which are sensitive to particle size and geometry 41 as well as the dielectric properties of the surrounding medium. This makes Si nanoparticles ideal for single particle sensing applications. A dark-field microscope (Olympus BX53) image of a concentrated sample of Si nanoparticles is shown in Fig. 3 (a), where the nanoparticles appear as bright spots on a dark background. Their precise size is below the diffraction limit of the microscope and cannot be determined from this image, however, the varying colour of the nanoparticles reflects the dielectric resonances’ dependence on the particle size and geometry. Fig. 3 (b) shows an typical dark-field backscattering spectra of a trapped Si nanoparticle; the shorter wavelength resonance peak is responsible for the particle’s green hue shown in the dark-field image inset. We have used a freely available open-source Fortran-90 software package DDSCAT 7.3 42

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spectra calculated with DDSCAT for both oblate (0.4 ≤ AR ≤ 1) and prolate (1 ≤ AR ≤ 2) spheroids, where the effective diameter deff was constrained by the data obtained from DLS and TEM measurements (deff = 50 − 200 nm). The optimal matches (solid black curves) were obtained by minimising the cost function resulting from the difference squared between the measured and simulated spectra over a selected wavelength region encompassing the relevant spectral features of each nanoparticle. It is important to note that considering the Si nanoparticles as spheroids for the purposes of the DDA calculations is just an approximation as the particles present a much varied geometry in the TEM images shown in Fig. S1 (b-i). However, the modelling of each particle’s exact geometry is unfeasible as we do not have a means of determining the precise shape of trapped single particles. Both trap stiffness and backscattered spectra were measured for most trapped Si nanoparticles, where the particle numbers from Fig. 2 (d) correspond to the spectra from Fig. 4 as follows: 1-d, 2-c, 4-i, 5-f, 6-l, 7-e, 9-j. As both the size and the refractive index of our nanoparticles fall well outside the range where the dipole approximation is valid, full optical force calculations using, for example, a combination of T-Matrix and DDA methods could be used to correlate gradient forces with the particle geometry. The trapped particles shown in Fig. 4 present effective diameters ranging from deff = 100 nm to deff = 200 nm. In addition, the sample possessed both larger and smaller Si nanoparticles; the smaller particles were able to be trapped but their spectra did not present any dielectric resonances within the measured wavelength region; on the other hand, the larger particles could not be trapped. The polydispersity in the Si nanoparticle sample is evident not only in the effective size of each particle but also in the diversity of particle geometries. The particles presented in Fig. 4 were found to present varying shapes ranging from oblate spheroids with low AR (a-d) to prolate spheroids of moderate AR (e-j) and high AR (k-l). The dependence of the dielectric resonances on particle geometry is reflected in the dark-field images (presented as insets), where different coloured particles are observed. In addition, we performed polarisation dependent spectroscopic measurements of a trapped

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Si nanoparticle. We show that the orientation of the nanoparticle can be controlled with the polarisation of the trapping laser due to its non-spherical shape, which has been previously observed for trapped particles of irregular geometries such as nano diamonds. 44 When the trapped particle was oriented along with the y-axis - as a result of the polarisation of the trapping laser - and the DF was perpendicularly polarised, the particle’s effective cross-section was small and the backscattered intensity minimal as shown in Fig. 5 (a). A half-wave plate (labelled WP2 in Fig. 1) was used to rotate the polarisation of the laser 90◦ thus rotating the orientation of the trapped nanoparticle to be aligned with the electric field of the incident DF, increasing the particle’s cross-section. This resulted in an increased DF scattering intensity as shown in Fig. 5 (b). Similarly, a subsequent 90◦ rotation of the DF’s polarisation results in a reduction of the particle’s cross-section and scattering intensity as the particle is now oriented perpendicularly to the DF’s electric field as shown in Fig. 5 (c). Hence, polarisation dependent spectroscopic measurements of trapped nanoparticles can be used to characterise not only particle size and geometry, but also trapping dynamics. The unique combination of trapping properties make Si nanoparticles an ideal system for delivering directed nanoscale sensing in a range of potential applications that may exploit the presence of optical resonances for nanoscale optical sensing. Specifically, we envisage that changes to the spectral properties may be used to report on changes in the local environment, whilst the optical trapping provides directed control over the position of the sensor within the target environment. Conclusion. We have experimentally investigated the optical trapping and spectroscopic properties of Si nanoparticles that exhibit strong geometric resonances at visible wavelengths. We use the unique scattering properties to characterise the size, shape and orientation of a range of objects, which can then be used to correlate trapping behaviour. We have observed a tendency of the non-spherical particles to align along the polarisation of the trapping laser, thus allowing the control of their orientation. High refractive index dielectric nanoparticles are of significant interest as an alternative to plasmonic particles for nanoscale trapping and

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photonic force sensing applications. We also believe that the geometric resonances will play important role in future applications combining nanoscale optical sensing with trapping.

Supporting Information Available DLS and TEM characterisation of Si nanoparticles. Absorption cross-section of Au and Si nanospheres at the trapping laser wavelength. Unpolarised backscattering intensity of Si spheroids calculated with DDA. This material is available free of charge via the Internet at http://pubs.acs.org/.

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