# Investigation of dust grains by optical tweezers for space applications

A. Magazzù  CNR-IPCF, Istituto per i Processi Chimico-Fisici, Messina, Italy
D. Bronte Ciriza  CNR-IPCF, Istituto per i Processi Chimico-Fisici, Messina,
Italy  Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e
Scienze della Terra, Università di Messina, Italy  A. Musolino  Dipartimento
di Scienze della Terra, Università di Pisa, Pisa, Italy  INAF-IAPS, Istituto
Nazionale di Astrofisica, Istituto di Astrofisica e Planetologia Spaziali,
Rome, Italy  A. Saidi  Dipartimento di Scienze Matematiche e Informatiche,
Scienze Fisiche e Scienze della Terra, Università di Messina, Italy  P.
Polimeno  CNR-IPCF, Istituto per i Processi Chimico-Fisici, Messina, Italy
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze
della Terra, Università di Messina, Italy  M. G. Donato  CNR-IPCF, Istituto
per i Processi Chimico-Fisici, Messina, Italy  A. Foti  CNR-IPCF, Istituto per
i Processi Chimico-Fisici, Messina, Italy  P. G. Gucciardi  CNR-IPCF, Istituto
per i Processi Chimico-Fisici, Messina, Italy  M. A. Iatì  CNR-IPCF, Istituto
per i Processi Chimico-Fisici, Messina, Italy  R. Saija  Dipartimento di
Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra,
Università di Messina, Italy  N. Perchiazzi  Dipartimento di Scienze della
Terra, Università di Pisa, Pisa, Italy  A. Rotundi  Dipartimento di Scienze e
Tecnologie, Università degli studi di Napoli Parthenope, Italy  L. Folco
Dipartimento di Scienze della Terra, Università di Pisa, Pisa, Italy  CISUP,
Center for Instrument Sharing of the University of Pisa, Università di Pisa,
Italy  O. M. Maragò  CNR-IPCF, Istituto per i Processi Chimico-Fisici,
Messina, Italy

###### Abstract

Cosmic dust plays a dominant role in the universe, especially in the formation
of stars and planetary systems. Furthermore, the surface of cosmic dust grains
is the bench-work where molecular hydrogen and simple organic compounds are
formed. We manipulate individual dust particles in water solution by
contactless and non-invasive techniques such as standard and Raman tweezers,
to characterize their response to mechanical effects of light (optical forces
and torques) and to determine their mineral compositions. Moreover, we show
accurate optical force calculations in the T-matrix formalism highlighting the
key role of composition and complex morphology in optical trapping of cosmic
dust particles. This opens perspectives for future applications of optical
tweezers in curation facilities for sample return missions or in
extraterrestrial environments.

Cosmic dust — Optical trapping — Raman tweezers — T-Matrix formalism

Cosmic dust — Optical trapping — Raman tweezers — T-Matrix formalism

##  I Introduction

In the frame of astrophysical science and its related technology (space
missions, optical and radio telescopes), cosmic dust has attracted the
interest of scientists due to its role in the cycling processes active in the
universe. Cosmic dust is a comprehensive term indicating small solid particles
with sizes ranging from a few nanometers to tenths of millimeter. They are
floating around in the interstellar medium or in the interplanetary space in
the solar system. Interstellar dust is mainly generated by the lifecycles of
many generations of stars: it is released by radiation pressure and solar wind
or ejected during the end-time explosion of stars or during the blowing off of
their outer layers (Calura, Pipino, and Matteucci, 2008; Woosley, Heger, and
Weaver, 2002; Woosley and Weaver, 1995). Interplanetary dust consists of small
solid particles generated by collisions between solid bodies (e.g asteroids,
planets and their satellites) or evaporation of icy bodies (e.g. comets
(Rietmeijer, 1998)). If interstellar dust is almost exclusively analysed
through remote observations (Draine, 2003; Lodders and Amari, 2005), on the
other hand interplanetary dust is available through sample-return space
missions from interplanetary medium, planets and minor bodies (Westphal  _et
al._ , 2014; Brownlee  _et al._ , 2003; Frank  _et al._ , 2014), from the
Earths’ stratosphere (Testa Jr  _et al._ , 1990; Taylor, Baggaley, and Steel,
1996; Della Corte  _et al._ , 2012; Lauretta  _et al._ , 2017) and at the
Earth’s surface in the form of micrometeorites (e.g., (Genge  _et al._ , 2008;
Folco and Cordier, 2015; Taylor, Messenger, and Folco, 2016)). Samples are
analysed at terrestrial facilities by the state-of-the-art analytical
techniques – since the size of some instruments is still too large to fly to
the space (Rietmeijer, 2001; Rauf  _et al._ , 2010; Della Corte  _et al._ ,
2014).

Physico-chemical properties of cosmic dust can be studied by different
techniques, such as X-rays diffraction (Mackinnon and Rietmeijer, 1987), SEM,
TEM (Lewis  _et al._ , 1987), IR, Raman (Rotundi  _et al._ , 2008; Davidson,
Busemann, and Franchi, 2012), mass spectroscopy (Floss  _et al._ , 2006).
However, these techniques may induce shielding effects by the substrates or by
other particles. In this work, to overcome these unwanted effects, we develop
and test our setups of optical and Raman tweezers, that are contactless and
non-destructive techniques useful for the manipulation and investigation of
individual grains of cosmic dust (Alali  _et al._ , 2020). Optical tweezers
(OT) (Jones, Maragò, and Volpe, 2015) are tools based on focused laser beams,
that allow the trapping and manipulation of micro and nanoparticles without a
physical contact. This contactless and non-destructive technique in its
simplest configuration is based on a single laser beam focused down to the
diffraction limit by a high numerical aperture objective (Ashkin and Dziedzic,
1971; Ashkin  _et al._ , 1986). Optical forces are strongly dependent on
particle size, shape and composition (see also Section A). However, OT enable
trapping and characterization of particles in a wide size range, from single
atoms to cells (Jones, Maragò, and Volpe, 2015; Polimeno  _et al._ , 2018).
Furthermore, Raman tweezers, i.e. OT coupled to a Raman spectrometer, are able
to spectroscopically characterize optically trapped samples allowing accurate
information on their composition (Thurn and Kiefer, 1984; Lankers, Popp, and
Kiefer, 1994; Pan, Hill, and Coleman, 2012; Gong  _et al._ , 2018; Gillibert
_et al._ , 2019).

Here, we characterize the dust particle response to optical forces and
torques, providing accurate information on the particle dynamics in the
optical trap. Furthermore, we identify dust particle mineralogical
compositions by Raman tweezers. We compare our findings with optical force
calculations based on the T-matrix formalism showing how the composition and
the complex shape of dust particles play a key role in their light-driven
dynamics.

##  II Materials and Methods

The samples trapped and characterized with our Raman tweezers have known
textures and mineralogic compositions documented in this work and in previous
studies. The aim is to reproduce the well-known composition of the trapped
particles to validate the application of optical manipulation techniques to
cosmic dust.

Figure 1: Samples preparation and sketch of the experimental setups. a) SEM
image of DEW 12007 lunar meteorite powdered sample, showing the poly-
crystalline nature of each individual grains. b) Dust samples are dispersed in
distilled water by ultrasound sonication and c) this solution is placed within
a cavity glass slide and sealed by a coverglass. d) Screenshots of four
different 3D optically trapped grains of cosmic dust in water solution having
different size and morphology. e) Standard optical tweezers setup. f) Raman
tweezers setup.

The samples used have terrestrial and extraterrestrial origins. They are (1) a
quartzarenite from Kamil Crater in Egypt (M26) (Fazio  _et al._ , 2014), (2) a
hawaiite from Etna volcano in Italy (HE-1), (3) the CV3-OxA carbonaceous
chondrite Allende (A-1), and (4) a lunar meteorite (polymict regolith breccia)
found in Antarctica (DEW 12007) (Collareta  _et al._ , 2016). Previously,
mineral grains used to calibrate the dust analyser Giada on board of Rosetta
space mission (Colangeli  _et al._ , 2007) were used as the simplest possible
starting material (monomineralic, uniform size range). In this work, we have
chosen more complex non-uniform samples: the terrestrial rocks M-26 and HE-1,
considered inasmuch analogues of planetary materials (mono and polymineralic);
and the extraterrestrial rocks as representative of primitive (A-1) and
differentiated (DEW 12007) bodies of the solar system.

Once powdered, the samples are analysed using microanalytical scanning
electron microscopy for a textural characterization (shape, grain size). Their
main mineralogy is determined using X-ray powder diffraction (Section D). The
characterization was conducted at the Dipartimento di Scienze della Terra and
at the Center for Instrument Sharing of the University of Pisa (CISUP).

All the analysed samples were provided as dried powder, whose grains showed a
non-homogeneous size and shape distribution, as showed in Fig. 1(a,d). The
first step of the sample preparation was the dispersion of the powder in
distilled water by ultrasound sonication with an appropriate concentration
suitable for optical trapping (e.g. few particles / microliter). The water-
dust solution was then placed in a glass cavity slide and sealed by a
coverglass, as showed in Fig. 1(b,c). The sealed cavity glass slide was then
placed on the sample holder of our optical tweezers for the investigation Fig.
1(c). For the investigation of individual grain dust particles dispersed in
water we used two different customised setups: i) standard OT, where an
optical trap was generated by highly focusing a laser beam through an
objective, the trajectory of the trapped particle was acquired by a quadrant
photodiode (QPD) and analysed by a computer to calculate optical forces and
rotations arising from the interaction of the particle with light, Fig. 1(e);
ii) Raman tweezers, where the back scattered light from the particle was
collected through the same focusing objective and reflected to a Raman
spectrometer for phase identification, Fig. 1(f). See Section B for more
details.

##  III Results

###  III.1 Optical forces and torques on dust particles

The output signals from the QPD, proportional to the particle displacement of
the trapped particle from its equilibrium position, are analysed by MATLAB
routines to calculate the trap stiffness and to detect any rotation of the
particle in the perpendicular plane $x-y$. In particular, we use the
autocorrelation functions (ACFs) and power spectral density (PSD) calibration
methods (Jones, Maragò, and Volpe, 2015; Gieseler  _et al._ , 2021) to obtain
the relaxation frequencies of the trapped particles as fitted parameters and
hence to calculate the trap stiffness, Figs. 6(b), 2(a). See Section B for
more details. We observe that the stiffness of terrestrial and extra-
terrestrial samples, optically trapped by linear polarised light, increases
with the laser power, as showed in Fig. 2(a) for a single trapped grain of the
lunar meteorite DEW 12007. Here it is possible to notice that the stiffnesses
$\kappa_{x}$, $\kappa_{y}$ and $\kappa_{z}$ increase almost linearly with the
laser power and the difference between the stiffnesses along the $x$ and $y$
directions can be due to a possible asymmetry of the trapped grain with
respect to the propagation axis $z$. Usually the values of the stiffness
$\kappa_{z}$ are lower than the values of $\kappa_{x}$ and $\kappa_{y}$ due to
the longer extension of the gaussian beam along the $z$ axis (Jones, Maragò,
and Volpe, 2015). Due to the linearity of the stiffness with power it is
possible to obtain the stiffness efficiency $q_{i}=k_{i}/\rm{Pw}$ (with
$i=x,y,z$) as fitting parameter from the values of $\kappa_{i}$ reported in
Fig. 2(a), where $\rm{Pw}$ is the value of laser power measured at the
objective output by a power meter. In particular, by a linear fit, we obtain
that $q_{x}=1.38$ ${\rm pN}\mu{\rm m}^{-1}{\rm mW}^{-1}$, $q_{y}=1.104$ ${\rm
pN}\mu{\rm m}^{-1}{\rm mW}^{-1}$ and $q_{z}=0.536$ ${\rm pN}\mu{\rm
m}^{-1}{\rm mW}^{-1}$ respectively. Radiation pressure on complex shaped or
absorbing particles can also have a destabilising effect by pushing the
trapped particles in regions of lower intensity along the $z$ axis. For
example, grains from Allende meteorite are difficult to trap in 3D and were
often investigated while trapped in 2D against the cell wall.

Figure 2: Effects of the laser light on trapped particles. a) Trap stiffnesses
$\kappa_{x}$ , $\kappa_{y}$ and $\kappa_{z}$ as a function of the laser power
measured at the objective for a single trapped grain of the lunar meteorite
DEW 12007. b) Rotational frequencies $\Omega_{\rm rot}$ of different samples
as a function of the laser power measured at the objective. c) Rotational
frequencies, $\Omega_{\rm rot}$, of an optically trapped single dust grains of
HE-1 for different polarised light: left circular polarised (LCP), linear
polarised (LP) and right circular polarised (RCP) light. Negative/positive
frequency values correspond to a rotation anticlockwise/clockwise with respect
to the z axis, respectively.

Figure 3: Theoretical trap efficiencies. a) Black line represents the
theoretical trap efficiency $Q_{z}^{\rm th}$ along the longitudinal direction
$z$ with $x=y=0$. Dark blue line represents the theoretical trap efficiency
$Q_{xy}^{\rm th}$ along the transversal direction $x-y$ with $z=0$. In the
inset is showed the theoretical particle, modelled as a micro-sphere with
homogeneous refractive index according to the Bruggeman mixing rule. Light
blue line is a reference line at $y=0$. b) Black line represents the
theoretical trap efficiency $Q_{z}^{\rm th}$ for a particle model showed in
the inset. Here the particle is modelled again as a micro-sphere with
homogeneous refractive index according to the Bruggeman mixing rule but has 4
inclusions made of the secondary constituents of the lunar meteorite, $2$
inclusions made of olivine having a $10\%$ each of the total volume and $2$
inclusions of ilmenite with a $2\%$ each of the volume. $Q_{z}^{\rm th}$
presents only two stable equilibrium points at $x=-0.38$ and $x=0.75\ \mu{\rm
m}$, but, according to our forces calculations, only at $x=0.75\ \mu{\rm m}$
trapping along the $x$ and $y$ direction is possible. c) Theoretical (lines)
and experimental (dots) stiffness efficiencies $q_{xy}$ and $q_{z}$ within the
transversal plane $x-y$ and along the longitudinal direction $z$ respectively.
Blue lines and dots represent the theoretical and experimental efficiency
$q_{xy}^{\rm th}$ and $q_{xy}^{\rm ex}$ respectively, along the transversal
direction $x-y$, while the black lines and dots represent the theoretical and
experimental efficiency $q_{z}^{\rm th}$ and $q_{z}^{\rm ex}$ respectively,
along the longitudinal direction $z$.

In order to compare our experimental results with theoretical expectations, we
calculate optical forces through the Maxwell stress tensor exploiting the
multipole expansion and T-matrix formalism (Borghese, Denti, and Saija, 2007a;
Polimeno  _et al._ , 2018, 2021). We consider particle models emulating the
dust grains of the lunar meteorite DEW 12007. Although all the trapped dust
grains showed irregular shapes, for simplicity, we modelled our particles as
micro-spheres having an average diameter $d=1\ \mu\rm{m}$ with a refractive
index given by the Bruggeman mixing rule for the constituent minerals of DEW
12007, as showed in the inset of figure 3(a) (Bohren and Huffman, 2008;
Polimeno  _et al._ , 2021).

In our calculations we consider a single Gaussian laser beam having a
wavelength $\lambda=830\ \rm{nm}$ and a power $\rm{Pw}=50\ \rm{mW}$, focused
by a high-NA objective (NA=1.3), mimicking the experimental conditions used
during the investigation of the lunar dust grains. In figure 3(a), we show the
theoretical transversal and longitudinal trap efficiencies defined
respectively as: $Q_{xy}^{\rm th}=(F_{x}^{\rm opt}+F_{y}^{\rm opt})/2\rm{Pw}$
and $Q_{z}^{\rm th}=F_{z}^{\rm opt}/\rm{Pw}$. Thereafter, we refined our
particle model to take into account the anisotropy and heterogeneity of the
real dust grains. We still considered an homogeneous sphere, with a refractive
index obtained according to the Bruggeman mixing rule but now we add $4$
spherical inclusions, 3(b) inset. These inclusions are made of the secondary
constituents of the lunar meteorite, in particular we consider $2$ inclusions
made of olivine having a $10\%$ each of the total volume of the modelled
grain, and $2$ inclusions of ilmenite with a $2\%$ each of the total volume.
Similarly to the previous model, we calculate the optical forces and the
theoretical longitudinal trap efficiency $Q_{z}^{\rm th}$, as showed in Fig.
3(b). Here it is possible to notice how the trap efficiency is affected by the
internal structure of a dust grain, presenting several equilibrium points with
$Q_{z}^{\rm th}=0$, and only two stable equilibrium points at $x=-0.38$ and
$x=0.75\ \mu{\rm m}$, conversely, the homogeneous model was showing an only
stable equilibrium point at $x=0\ \mu{\rm m}$, Fig. 3(a,b).

Aiming at validating our theoretical model, we compare the theoretical $q^{\rm
th}_{xy,z}$ and experimental $q^{\rm ex}_{xy,z}$ stiffness efficiencies on the
transverse $x-y$ plane and in the longitudinal direction $z$. In particular,
in the former case the mean transverse efficiency $q_{xy}=(q_{x}+q_{y})/2$ is
considered. Moreover, in the case of the theoretical stiffness efficiencies,
$\rm{Pw}$ is the value of power set for the simulation.

In figure 3c it is possible to notice a relative good agreement between the
theoretical and experimental values of the stiffness efficiencies $q^{\rm th}$
and $q^{\rm ex}$, validating the theoretical model used for the calculation of
optical forces acting on cosmic dust. The small discrepancies are due to the
spherical shape used in our model which is a simplification of the complex
particle shape, mass distribution, and mineral composition. In fact, a
linearly polarised laser light does not produce any radiation torque on a
spherical and homogeneous particle because of symmetry (Marston and Crichton,
1984). However, for anisotropic and asymmetric particles two additional
mechanical effects of light occur: i) a transverse component of radiation
pressure which is responsible for the optical lift effect, i.e., a transverse
displacement of the particle with respect to the incident light propagation
direction (Swartzlander  _et al._ , 2011); ii) a radiation pressure torque
inducing particle rotations and known as windmill effect (Jones, Maragò, and
Volpe, 2015)

Rotations of a trapped particle induce a correlation among its $x$, $y$
trajectories. In these circumstances, we can use optical tweezers also for
photonic torque microscopy to quantify these rotations (Irrera  _et al._ ,
2016; Schmidt  _et al._ , 2018). In particular, particle rotations in the
$x-y$ plane can be highlighted by calculating the differential cross
correlations ${\rm DCCF}_{xy}(\tau)=\left\langle
x(t)y(t+\tau)\right\rangle-\left\langle y(t)x(t+\tau)\right\rangle$ of the
acquired signal from the QPD, Fig. 6(a), for different lag times $\tau$. The
rotational frequency $\Omega_{\rm rot}$ can be obtained as fitting parameter
of the ${\rm DCCF}_{xy}$ by a sinusoidal model (Pesce  _et al._ , 2009; Jones
_et al._ , 2009).

In Fig. 2(b) we show the rotational frequencies $\Omega_{\rm rot}$ of three
different trapped samples, where $\Omega_{\rm rot}$ increases as the laser
power increases. It is noteworthy that the polarisation used to trap the
samples listed in Fig. 2(b) is linear, it does not carry any spin-angular
momentum, so the observed rotations are only due to the radiation torque
exerted by the light on the particles because their asymmetric shape.

In the case of circular polarised light, depending on the absorption
properties of the particle, a laser beam can induce a spin angular torque in
addition to the radiation one (Marston and Crichton, 1984; Jones, Maragò, and
Volpe, 2015). When a laser beam is circularly polarized, each of its photons
carries a spin angular momentum $+\hbar$ for left circularly polarised light
(LCP) $-\hbar$ for right circularly polarised light (RCP). Therefore, the
total torque acting on a non sperical particle is given by different
contributions that include a radiation torque related to the shape and the
transferred spin angular momentum. The spin angular momentum is added to to
the "windmill effect" in the case of LCP and subtracted in the case of RCP
(Jones, Maragò, and Volpe, 2015).

In Fig. 2(c) we report the rotational frequencies $\Omega_{\rm rot}$ of an
optically trapped grain of the terrestrial samples HE-1 from Etna volcano for
different light polarisation. Here, $\Omega_{\rm rot}$ decreases from -18 $\rm
s^{-1}$ for LCP to -28 $\rm s^{-1}$ for RCP with a central value of -23 $\rm
s^{-1}$ for LP indicating that the trapped particle is absorbing circular
polarised light with a spin angular momentum $+\hbar$ for LCP light and
$-\hbar$ for RCP light. Thus, negative frequency values mean a rotation
anticlockwise with respect to the $z$ axis, while positive frequency values
mean a rotation clockwise with respect to the $z$ axis. The rotational
frequency $\Omega_{\rm rot}$ reported in Fig. 2(c) is the result of rotations
induced by the total torque acting on the sample. The radiation pressure
torque, which does not depend on light polarisation, produces a particle
rotation frequency of -23 $\rm s^{-1}$, while the spin angular momentum torque
sums or subtracts depending on the helicity of light. In the case of LCP light
the contribution of the spin angular momentum torque is positive and summed to
the radiation torque increasing the rotational frequency of the particle to
-18 $\rm s^{-1}$, while in the case of RCP light the contribution is negative
decreasing the rotational frequency of the particle to -28 $\rm s^{-1}$. This
demonstrates that the total optomechanical interaction of particles with
light, depends both on the particle shape and on the helicity of the laser
beam.

###  III.2 Spectroscopic analysis and mineralogy of individual grains

We characterize the mineralogical compositions of terrestrial and
extraterrestrial dust grains with different shapes and sizes by Raman
tweezers, Fig. 1(d). All the investigated sample are trapped in 3D or in 2D,
whenever the radiation pressure is stronger than the axial gradient force. In
the latter case, a stable 3D optical trapping is not achievable because the
radiation pressure pushes the particle away along the $z$ direction, along
which the laser beam propagates. To overcome this issue, we push the particle
against the wall of the glass slide, thereby physically confining the particle
along the $z$ direction, while the particle is still confined along the $x-y$
direction by the optical gradient forces, defining the optical potential. For
each sample, a reference background spectrum, without any trapped particle, is
also acquired and used to remove the spurious signal from the glass slide and
the media (water, immersion oil). Thereafter, by a fitting routine, the peaks
of each spectrum are identified and compared with reference spectra for the
identification of the constituent phases in the trapped samples. We first
analyze the standard samples M26, HE-1 and A-1 in order to match their mineral
composition reported in literature (Fazio  _et al._ , 2014; Orlando  _et al._
, 2008; Brunetto  _et al._ , 2014; Cristofolini  _et al._ , 1987).

Figure 4: Raman spectra of optically trapped single dust particle from sample:
a) M26 from Kamil crater (black line), red line represents the Raman spectrum
of quartz used as reference (RRUFF R150074). b) HE-1 from Etna (black line)
and A-1 from Allende meteorite (blue line). Red line represents the Raman
spectrum of olivine used as standard reference (RRUFF X050088). All spectra
are offset for clarity.

In Fig. 4(a) we report a Raman spectrum (black line) collected by a single
optically trapped grain of sample M26. According to the literature it contains
mainly quartz whose reference spectrum is represented by the red line (Fazio
_et al._ , 2014). Similarly, in Fig. 4(b) we report the Raman spectra, of a
single grain of the sample HE-1 from Etna volcano (black line) and of A-1 from
Allende meteorite (blue line). According to the literature, both meteorites
contain olivine, whose reference spectrum is represented by the red line
(Cristofolini  _et al._ , 1987). For all the experimental spectra of our
samples showed in Fig. 4(a,b) there is a good agreement with the reference
spectra of their mineral composition found in literature.

Figure 5: Raman spectra and its mineralogical composition of optically trapped
dust particles of the lunar meteorite DEW 12007. Black lines represent the
Raman spectra of the trapped samples, while colored lines represent the
reference Raman spectra from the RRUFF database of: a) plagioclase (RRUFF
X050108), b) pyroxene (RRUFF R200002), c) olivine (RRUFF X050088) and d)
ilmenite (RRUFF R060149), used for the mineral identification of the trapped
single grains. All spectra are offset for clarity. e) Raman spectra of a
single grain of DEW 12007 (black line) containing several mineral components
(colored lines). f) Mineral occurrence of the mineral constituents over 70
trapped grains of the lunar meteorite DEW 12007.

After testing our Raman tweezers on terrestrial and extraterrestrial standard
grains, we investigate cosmic dust from the lunar meteorite DEW 12007. In
particular, we trap about 70 different particles in 2D and 3D, following an
appropriate protocol to avoid to trap the same grains twice. In Fig. 5(a-d) we
report with black lines the Raman spectra of four different trapped grains of
DEW 12007, and with colored lines the reference Raman spectra of some of their
constituents according to the literature (Collareta  _et al._ , 2016). In
particular, in Fig. 5(a-d) we can observe that the trapped grains contain the
following minerals: plagiocase (labradorite); pyroxene (augite and pigeonite);
olivine (forsterite and fayalite); ilmenite.

Figures 4(a,b) and 5(a,d) show that each single trapped grains contains only a
single mineral component, among the several ones reported in literature,
matching its own reference spectrum. We identified both monomineralic and
polymineralic grains (Fig. 5e), as expected for a rock in which the grain-size
is highly variable.

The occurrence of the mineral constituents of the lunar meteorite DEW 12007
over 70 dust grains is reported in Fig. 5(f), where it is possible to notice
that plagioclase is the most recurring mineral constituent, with an occurrence
of $50.4\%$, then we found that pyroxene is the second most abundant mineral
with an occurrence of $27.8\%$, and finally olivine and ilmenite with an
abundance of $11.3\%$ and $10.4\%$ respectively. The rank of the mineral
abundances of the constituents of DEW 12007 matches the data from literature
(Collareta  _et al._ , 2016). It is noteworthy that during the grinding
process it could happen that cosmic dust was not homogeneously ground,
producing grains with more than one or without any clear mineral component.

##  IV Conclusions

We used optical tweezers to trap individual micron-sized dust particles of
astrophysical interest to characterize their opto-mechanical response. We
calculated their trap stiffness and their rotational frequencies as a function
of the trapping laser power, showing how these quantities increase almost
linearly with the laser power. We also calculated the theoretical values of
the optical forces acting on cosmic dust by T-matrix formalism, finding a good
agreement between the experimental and theoretical values, validating our
theoretical models. Moreover, we investigated the effect of light polarisation
on cosmic dust, measuring the particle rotational frequency for different
helicity of light, showing how the total opto-mechanical interaction depends
on both the particle shape and the polarisation of the laser beam.
Furthermore, we used Raman tweezers to investigate the mineral composition of
the dust particles. The agreement of our results with the literature validates
optical trapping for the analysis of cosmic dust, opening new perspectives in
the investigation of extraterrestrial particles on our planet. Optical
trapping techniques, thanks to their contactless and non-invasive unique
combination of capabilities, can be used to maximize the scientific return
from the analyses of cosmic dust samples collected by the current and future
sample return missions (e.g. OSIRIS-Rex, Mars 2020; Chang’e 5), particularly
during the preliminary investigation procedures in receiving/curation
facilities (Smith  _et al._ , 2021). High-resolution, contactless and non-
invasive analysis of planetary dust are actually expected to provide
unprecedented information on the astrophysical origin and geologic evolution
of their parent bodies. Furthermore, they are also expected to be instrumental
for biohazard assessment for constrained sample return missions – like those
targeting Mars or the icy bodies in the outer solar system, and the detection
of past or extant extraterrestrial life. Finally, the successful trapping of
particles in a water medium is the first step towards the realization of
trapping in air/vacuum, a totally non-invasive micromanipulation fundamental
for extraterrestrial materials. For these reasons, optical tweezers are key
tools in controlled laboratory experiments, aiming for space applications to
trap and characterize dust particles directly in space or on extraterrestrial
bodies during exploratory missions.

##  V Acknowledgment

We acknowledge financial contribution from the agreement ASI-INAF
n.2018-16-HH.0, project “SPACE Tweezers” and from the MSCA ITN project
“ActiveMatter" sponsored by the European Commission (Horizon 2020, Project
Number 812780). A. Musolino acknowledges support by ASI-INAF, “Rosetta GIADA”,
I/024/12/0. The lunar regolith breccia was collected during the 2017 Antarctic
Campaign of the Programma Nazionale delle Ricerche in Antartide (PNRA) within
the “Meteoriti Antartiche" project (ID: PNRA16_00029) and the sample used in
this study was provided by the Museo Nazionale dell’Antartide di Siena.
Scanning electron microscopy (SEM) imaging was carried out the ESEM-FEG
facility of the Centro per la Integrazione della Strumentazione - Università
di Pisa (CISUP).

##  Appendix A Optical forces

Forces arising in optical trapping are a consequence of the conservation of
the electromagnetic momentum in the light-matter interaction (Jones, Maragò,
and Volpe, 2015). However, some simplifications and approximations have been
made for an easier understanding of optical forces. These approximate
approaches are often a valuable source of physical insight and have a great
pedagogical value (Magazzú  _et al._ , 2015; Polimeno  _et al._ , 2018; Jones,
Maragò, and Volpe, 2015). In the geometrical optics approximation, valid for
particle size larger than the wavelength of the trapping beam, optical forces
can be divided in a gradient and a scattering component. The gradient force
component is perpendicular to the propagation of the laser beam, it is
proportional to the intensity gradient of the laser spot and it is responsible
for trapping. While the scattering force component, having the same direction
of the propagating laser beam, is proportional to the light intensity and
tends to push particles away from the laser focus due to the radiation
pressure (Jones, Maragò, and Volpe, 2015). In this approximation the incoming
optical field can be considered as a collection of light rays, each of them
carrying a portion of the total optical power and linear momentum. When a ray
impinges on a particle, it is partly transmitted and partly reflected by the
particle surface and the exchange of linear momentum between the ray and the
particle generates an optical force $\vec{F}=\frac{\Delta\vec{P}}{\Delta t}$,
where $\Delta\vec{P}=\vec{P}_{\rm inc}-\vec{P}_{\rm ref}$ is the exchanged
momentum calculated as the difference between the incident and reflected
momentum $\vec{P}_{\rm inc}$ and $\vec{P}_{\rm ref}$ respectively during a
time interval $\Delta t$. The optical force exerted by a laser beam on a
particle is the sum of the forces generated by each constituting ray and for
specific experimental conditions and parameters (e.g. when the refractive
index of a particle is higher than the one of its surrounding medium, proper
size of the particle and laser power, etc.) these forces can confine a
particle within a equilibrium region close to the focal spot, where the force
acting on the particle is zero (Magazzú  _et al._ , 2015; Polimeno  _et al._ ,
2018; Jones, Maragò, and Volpe, 2015). When a trapped particle is displaced
from the centre of the trap to a non equilibrium point, a net optical force
acts like a restoring spring, bringing the particle back toward the centre of
the trap. For small displacement of the particle from its equilibrium position
the restoring force is, to a first approximation, proportional to the
displacement acting like a Hookean spring with a fixed stiffness (Jones,
Maragò, and Volpe, 2015; Gieseler  _et al._ , 2021), i.e

$F_{x}\approx-\kappa_{x}(x-x_{\rm eq})$ (1)

where, considering for simplicity only a single component of the force, $x$ is
the particle position, $x_{\rm eq}$ is the equilibrium position and
$\kappa_{x}$ is the trap stiffness. The trap stiffness can be obtained by
several calibration methods, (Jones, Maragò, and Volpe, 2015; Gieseler  _et
al._ , 2021) and by its value we can quantify an external force $F_{{\rm
ext},x}$ acting on a trapped particle by measuring the particle displacement
$\Delta x_{\rm eq}=(x-x_{\rm eq})$ from its equilibrium position, i.e.
$F_{{\rm ext},x}=\kappa_{x}\Delta x_{\rm eq}$

##  Appendix B Experimental setups

The light source of the standard optical tweezers used for the investigation
of cosmic dust is a laser diode (LD) generating a linear polarised laser beam
with a wavelength of 830 nm. The laser beam is expanded by a two lenses
($\rm{l_{1},l_{2}}$) telescope system and reflected by a dichroic mirror
towards the back aperture of a high numerical aperture (NA) oil immersion
objective, which was also used to imagine the sample on a CMOS camera, Fig.
1(e). Thanks to the telescope system, the beam overfills the back aperture of
the objective giving rise to a highly focused laser beam. The overfilling
creates the maximal optical field gradient in the focal spot for a more
efficient optical trapping. A sample holder is equipped with a 3D translation
piezo-stage to move the focal spot within the cavity glass slide containing
the sample solution. The dichroic mirror used to reflect the laser beam to the
objective acts like a short pass filter, it reflects the laser light towards
the objective and transmits the visible light to a CMOS camera, preventing the
saturation of the detector and allowing a clear view of the sample on a
monitor. The polarisation of the trapping beam can be tuned by a waveplate to
investigate the optical response of cosmic dust for different light
polarisations. In particular, changing the light polarisation from linear to
right- or left-circular, the occurrence of spin-angular momentum transfer from
light to the dust can be investigated (Donato  _et al._ , 2014; Jones, Maragò,
and Volpe, 2015). The forward-scattered light from a trapped particle,
containing information about the particle position, is collected together with
the transmitted light by a condenser. The superposition of these two beams
generates an interferometric pattern, which is reflected by a second dichroic
mirror towards a quadrant photo diode (QPD) through a lens (l3) Fig. 1(e)
(Polimeno  _et al._ , 2018; Jones, Maragò, and Volpe, 2015). A QPD converts
the interferometric pattern collected by a condenser in analogical voltage
signals, proportional to the displacement of the particle from its equilibrium
position (Gittes and Schmidt, 1998; Jones, Maragò, and Volpe, 2015; Magazzú
_et al._ , 2015). The signals from the QPD were acquired at a sampling
frequency of 50 kHz by a National Instrument acquisition board for time
intervals of 2 sec. The sampled signals were then analysed by a PC providing
information about the opto-mechanical interaction between light and a single
grain of cosmic dust.

In order to characterize the optical trapping forces on a single dust grain,
we extract some crucial parameters from the particle random trajectories in
the confining potential, such as the trap relaxation frequency. The starting
point of optical force measurements in optical tweezers is the description of
the centre-of-mass random motion of an optically trapped particle through an
overdamped Langevin equation (Jones, Maragò, and Volpe, 2015). In particular,
for small displacements around the equilibrium point a positional coordinate,
e.g. $x$, of the trapped particle, subject to the random force, $F_{\rm
random}(t)$, can be expressed in terms of the following equation:

$\gamma\frac{dx}{dt}+\kappa_{x}x=F_{\rm random}(t)$ (2)

where $\gamma$ is the Stokes friction coefficient of a particle immersed in a
fluid medium and $\kappa_{x}$ is the trap stiffness that we wish to measure.
The first term of eq. 2 is the velocity dependent viscous force, the second
one is the restoring term due to the optical potential, and the final one
describes the Brownian stochastic force. The power spectral density (PSD) of a
signal describes how its energy is distributed in the frequency domain and it
is useful to calibrate optical tweezers. Indeed, the power spectral density of
eq. 2 show a Lorentzian shape:

$S_{x}(\omega)=\frac{2D}{(\omega^{2}+\omega_{x}^{2})}$ (3)

where the half-width of the distribution is the relaxation frequency defined
as $\omega_{x}=\kappa_{x}/\gamma$ and $D=k_{B}T/\gamma$ is the diffusion
coefficient from the Stokes-Einstein equation (Jones, Maragò, and Volpe,
2015). By fitting the power spectrum of the particle coordinate with a
Lorentzian shape function we obtain the relaxation frequency $\omega_{x}$ as a
fit parameter and hence we can get the trap spring constant $\kappa_{x}$
(Gittes and Schmidt, 1998; Magazzú  _et al._ , 2015).

The Raman tweezers used for the identification of the minerals constituents of
our samples is a customised setup obtained by coupling a homemade optical
tweezers with a commercial Raman spectrometer (Horiba TRIAX 190) through a
notch filter, Fig. 1(f). This filter reflects the laser light, from a laser
diode having a wavelength of $780\ {\rm nm}$, to the back aperture of an oil
immersion objective, similarly to the case of the dichroic mirror previously
described in the standard optical tweezers setup, Fig. 1(e). The notch filter
reflects only the single wavelength of the laser beam, and it is transparent
to all the other wavelengths. In such a way, the elastic component of the
scattering is cut out by the notch filter and only the Raman signal is
transmitted to the spectrometer, which is equipped with a grating having a
spectral resolution of $8\ \rm{cm^{-1}}$ and coupled to a silicon Peltier-
cooled CCD camera to acquire the spectra. The Raman spectra of our
investigated samples were obtained with a laser power of about $7\ {\rm mW}$
at the sample and acquired with an integration time of few tens of seconds.

Figure 6: Rotational and relaxation frequencies. a) Differential cross
correlation function ${\rm DCCF}_{xy}(\tau)$ of the sample HE-1 from Etna,
black circles represent experimental data, while red line represents a
sinusoidal fitting function. Discrepancy between the experimental data and the
fit are due to the presence of of a second rotational or vibrational motion of
the trapped particle due to its non-spherical geometry and anisotropy (Jones
_et al._ , 2009). b) Black line represents the power spectrum density (PSD) of
the trajectory along $z$ direction for a trapped dust grain of the lunar
meteorite DEW 12007. While the red line represent a Lorentzian fit of the
calculated PSD, where the relaxation frequency of the trapped grain is
obtained as fitted parameter.

##  Appendix C Theoretical calculations

###  C.1 Radiation force in optical tweezers

In the framework of electromagnetic scattering theory, optical forces and
optical trapping are the consequence of the electromagnetic momentum
conservation during a light scattering process (Jones, Maragò, and Volpe,
2015; Borghese, Denti, and Saija, 2007a). Using the linear momentum
conservation, the time-averaged optical force on a generic particle exerted by
a monochromatic light is:

$\mathbf{F}_{\mathrm{rad}}=\oint_{S}\mathrm{\bar{T}_{M}}\cdot\hat{n}dS$ (4)

where the integration is carried out over a surface S surrounding the
scattering particle, $\hat{n}$ is the outward normal unit vector, $\vec{r}$ is
the vector position, and $\mathrm{\bar{T}_{M}}$ is the averaged Maxwell stress
tensor in the Minkowski form (Pfeifer  _et al._ , 2007) describing the
optomechanical interaction. For a non-magnetic medium (Borghese, Denti, and
Saija, 2007a):

$\mathbf{F}_{\mathrm{rad}}=-\frac{\varepsilon_{\mathrm{m}}r^{2}}{4}\int_{\Omega}\left(|\textbf{E}_{\mathrm{s}}|^{2}+\frac{c^{2}}{n_{\mathrm{m}}^{2}}|\textbf{B}_{\mathrm{s}}|^{2}+2\Re\left\\{\textbf{E}_{\mathrm{i}}\cdot\textbf{E}_{\mathrm{s}}^{*}+\frac{c^{2}}{n_{\mathrm{m}}^{2}}\textbf{B}_{\mathrm{i}}\cdot\textbf{B}_{\mathrm{s}}^{*}\right\\}\right)\hat{\textbf{r}}\
\mathrm{d}\Omega$ (5)

where $\varepsilon_{\mathrm{m}}=\varepsilon_{0}n_{\mathrm{m}}^{2}$ is the
medium permettivity, $r$ and $\hat{r}$ are the modulus and the unit vector of
the vector position $\vec{r}$ respectively, $\varepsilon_{0}$ is the vacuum
permittivity, $n_{\mathrm{m}}$ is the medium refraction index, $c$ is the
light velocity, $\mathbf{E}_{\mathrm{i}}$, $\mathbf{B}_{\mathrm{i}}$,
$\mathbf{E}_{\mathrm{s}}$, $\mathbf{B}_{\mathrm{s}}$ are respectively the
incident electric and magnetic field and the scattered electric and magnetic
field and the integration is taken over the full solid angle $\Omega$. The
scattered electromagnetic field $\mathbf{B}_{\mathrm{s}}$ is calculated in
near zone, take into account the transmission properties of the wave inside
the nanoparticle. When we deal with spherical monomers, the expression of the
radiation force should be rewritten in terms of T-matrix formalism (Borghese,
Denti, and Saija, 2007a; Saija, 2005; Polimeno  _et al._ , 2018). Because of
the linearity of Maxwell’s equations, once the field involved in the
scattering process are expanded in terms of Vector Helmholtz Harmonics (VHH),
it is possible, through the definition of T-matrix, to obtain the relation
between the incident and scattered field imposing the boundary conditions to
the fields on the spherical surface (Borghese, Denti, and Saija, 2007b). The
T-matrix $\mathbb{T}\equiv\\{T^{(p^{\prime}p)}_{l^{\prime}m^{\prime}lm}\\}$
elements encompasses all the information on the morphology of the scattering
particle with respect to the same incident field, binding the known multipole
amplitudes of the incident field $W^{(p)}_{{\mathrm{i}},lm}$ with the unknown
amplitudes of the scattered field
$A_{{\mathrm{s}},l^{\prime}m^{\prime}}^{(p^{\prime})}$ (Borghese, Denti, and
Saija, 2007a). For the case of optical tweezers, we generalized the incident
field resorting to the angular spectrum representation of Richards and Wolf
(Richards, 1959) and then calculated the optical tweezers stiffness for each
particle (Jones, Maragò, and Volpe, 2015; Borghese, Denti, and Saija, 2007b).

###  C.2 Optical properties of composite particles

Knowledge of the optical properties of particles that interact with radiation
is a key ingredient for the correct modelling of a matter radiation
interaction. When the medium that constitutes the particles is a multi-
component mixture, two main paths can be taken for modelling: (1)
homogenization theory (Garnett, 1904, 1906) through the use of the Bruggeman
mixing formula (Garnett, 1935, 1936); (2) the representation of complexity by
means of a random geometry of one-component inclusions whose size can respect
the fraction of volume obtained from the experimental chemical-physical
analysis of the sample. The Bruggeman mixing formula (Garnett, 1935, 1936) can
be applied to a medium composed of N kinds of inclusions with permettivities
$\varepsilon_{n}$ and volume fractions $f_{n}$ such that $\sum_{n}f_{n}=1$. In
this case, unlike Maxwell Garnett Mixing Formula that is inapplicable when the
volume fractions of all components are comparable, the Bruggeman mixing
formula is symmetric with respect to all medium components and does not treat
any one of them differently. Therefore, it can be applied, at least formally,
to composites with arbitrary volume fractions without causing contradictions
when we cannot distinguish the “host” material from the “inclusions”. From
operative point of view, the Bruggeman effective permittivity, which we denote
by $\varepsilon_{BG}$, can be obtained satisfying the following equation:

$\sum\limits_{n=1}^{N}f_{n}\frac{\varepsilon_{n}\textendash\varepsilon_{BG}}{\varepsilon_{n}+2\varepsilon_{BG}}=0$
(6)

where $\sum_{n}f_{n}=1$. In the case of a strongly inhomogeneous particle
consisting of islands of different materials, the process of interaction
underlying the optical trapping phenomena is reminiscent of the multi-
component structure of the nanoparticle and the formula of Bruggeman, derived
within the homogenization theory, tends to mask this behaviour. For this
purpose, the optical behaviours of the spherical inclusions contained within
the spherical nanoparticle, which constitute an aggregate, is studied by
applying the theory of electromagnetic scattering to cluster of spheres.

Within the T-matrix approach, the calculus of the multipole amplitudes of the
field scattered by the whole object is performed in two steps. First, we
consider the superposition of the field that would exist within the sphere in
absence of any inclusion and of the scattered fields coming from the aggregate
taking into account all the multipolar interactions. This superposition
constitutes the internal field of the host sphere. Second, we impose the
boundary conditions to the internal field and to the external field across the
surface of the host sphere to get the amplitudes of the scattered field.

As a result of the first step, we get a system of linear nonhomogeneous
equations that in symbolic form can be written as:

$\mathbb{P}=\mathbb{Z}\mathbb{W}$ (7)

where $\mathbb{P}$ is the matrix whose elements are the unknown scattering
coefficients of the internal field to be calculated, $\mathbb{Z}$ is the
T-matrix of the internal aggregate, and $\mathbb{W}$ is the matrix of the
known external incident field coefficients.

Once the amplitudes of $\mathbb{P}$ have been calculated, we proceed to the
second step which in symbolic form yields:

$\mathbb{A}=\mathbb{S}\mathbb{P}=\mathbb{S}(\mathbb{Z}\mathbb{W})=\mathbb{T}\mathbb{W}$
(8)

where $\mathbb{A}$ is the matrix whose elements are the scattering
coefficients in external medium to be calculated, S is the matrix which acts
on the matrix $\mathbb{P}$ containing the coefficients of the already
calculated internal field, and $\mathbb{T}$ is the transition matrix for the
whole scatterer (Borghese, Denti, and Saija, 1994, 1998).

##  Appendix D Samples characterization

The samples used in this work (M-26, HE-1, A-1, DEW 12007) have been analysed
under the field emission scanning electron microscope with energy dispersive
spectroscopy FEG-SEM FEI QUANTA 450 at the Center for Instrument Sharing of
the University of Pisa (CISUP) for a textural characterization (shape, grain
size). Their main mineralogic composition is determined using X-ray powder
diffraction data acquired at the Dipartimento di Scienze della Terra of the
Università di Pisa. Lithology and mineralogic composition of the samples are
reported in Table 1.

The characterization of M-26 refers to literature (Fazio  _et al._ , 2014).
In-depth characterization of DEW 12007 can be found in literature(Collareta
_et al._ , 2016). Quantitative mineralogical compositions of the samples M-26
(quartzarenite), HE-1 (hawaiite), A-1 (carbonaceous chondrite Allende), and
DEW 12007 (lunar regolith breccia) were obtained applying the Rietveld method
(Bish and Post, 1993) and given in Table 1. X-ray powder diffraction data were
collected at the Dipartimento di Scienze della Terra of the Università di
Pisa, on a Bruker D2 Phaser diffractometer, equipped with a Lynxeye detector,
operating at 30 kV and 10 mA and using Cu K$\alpha$ radiation ($\lambda$ =
1.54184 Å). The diffraction patterns were collected over the 5-70∘ 2$\theta$
range for DEW 12007 and 12-70∘ 2$\theta$ range for HE-1 and Allende, with
0.02∘ scan step size and 1 $\rm s$ counting time per step. Samples were spiked
with a known amount of rutile as internal standard (NIST SRM 674a) in order to
check for the presence of an amorphous component (Gualtieri, 2000).

Table 1: Textural and mineralogic composition of the samples used to test the
Raman tweezers set-up: (1) M-26, quartzarenite; (2) HE-1 hawaiite; (3) A-1
Allende; (4) DEW 12007. For each sample is reported: (1) its lithology (type
of rock and textural information) obtained at the FEG-SEM and literature and
(2) the overall mineralogical composition [weight %] obtained with X-ray
diffraction.

Sample |  | Lithology
---
| Overall min. compo. wt%
---
M-26 |  | Quarzarenite – Coarse-grained
---
| Quartz >99
---
HE-1 |  | Hawaiite – Fine-grained. Basalt with pyroxene
---
and plagioclase microphenocrystals with abun-
dant glass inclusions. Vesicular. 30% phenocrysts
by volume
| Plagioclase: labradorite 56
---
Clinopyroxene: augite 35
Olivine: forsterite 8
Magnetite <1
Glass <5
Allende (A-1) |  | CV3 OxA carbonaceous chondrite – chondrules
---
and CAIs ($\sim$55 vol%) embedded in a fine-grained
dark matrix ($\sim$40 vol%)
| Olivine: forsterite 80
---
Clinopyroxene: clinoenstatite 9
Clinopyroxene: diopside 7
Orthopyroxene: enstatite 2
Clinopyroxene: pigeonite 1
Chromite <1
DeWitt (DEW) 12007 |  | Lunar polymictic breccia with <1 mm sized lithic
---
clasts in aphanitic matrix
| Plagioclase: labradorite 48
---
Clinopyroxene: augite 23
Clinopyroxene: pigeonite 18
Olivine: forsterite 10
Ilmenite 1
Chromite <1

##  Appendix E Note

A. Magazzù, D. Bronte Ciriza, and A. Musolino contributed equally to this
work.

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