11institutetext: CNR-IPCF, Istituto per i Processi Chimico-Fisici, I-98158,
Messina, Italy 22institutetext: Dipartimento di Scienze Matematiche e
Informatiche, Scienze Fisiche e Scienze della Terra, I-98166, Università di
Messina, Italy 33institutetext: Dipartimento di Scienze della Terra,
Università di Pisa, Pisa, Italy 44institutetext: CISUP, Centro per
l’Integrazione della Strumentazione dell’Università di Pisa, Pisa, Italy
55institutetext: INAF Osservatorio Astronomico di Palermo, Palermo, Italy
66institutetext: ASI Agenzia Spaziale Italiana, Roma, Italy 77institutetext:
Dipartimento di Scienze e Tecnologie, Università di Napoli "Parthenope",
Napoli, Italy 88institutetext: INAF-IAPS, Istituto di Astrofisica e
Planetologia Spaziali, Roma, Italy

# Optical tweezers in a dusty universe

Modeling optical forces for space tweezers applications

P. Polimeno 1122 A. Magazzù 11 M. A. Iatì 11 R. Saija _Email:_
<EMAIL_ADDRESS>L. Folco 3344 D. Bronte Ciriza 11 M. G. Donato 11 A. Foti 11
P. G. Gucciardi 11 A. Saidi 22 C. Cecchi-Pestellini 55 A. Jimenez Escobar 55
E. Ammannito 66 G. Sindoni 66 I. Bertini 7788 V. Della Corte 88 L. Inno 77 A.
Ciaravella _Email:_<EMAIL_ADDRESS>A. Rotundi _Email:_
<EMAIL_ADDRESS>O. M. Maragò _Email:_<EMAIL_ADDRESS>
(Received: date / Revised version: date)

###### Abstract

Optical tweezers are powerful tools based on focused laser beams. They are
able to trap, manipulate and investigate a wide range of microscopic and
nanoscopic particles in different media, such as liquids, air, and vacuum. Key
applications of this contactless technique have been developed in many fields.
Despite this progress, optical trapping applications to planetary exploration
is still to be developed. Here we describe how optical tweezers can be used to
trap and characterize extraterrestrial particulate matter. In particular, we
exploit light scattering theory in the T-matrix formalism to calculate
radiation pressure and optical trapping properties of a variety of complex
particles of astrophysical interest. Our results open perspectives in the
investigation of extraterrestrial particles on our planet, in controlled
laboratory experiments, aiming for space tweezers applications: optical
tweezers used to trap and characterize dust particles in space or on planetary
bodies surface.

###### pacs:

42.50.Wk(light pressure) and 42.25.Fx(light scattering) and 96.30.Vb (dust,
extraterrestrial materials)

##  1 Optical tweezers

Mechanical effects of light were first argued by Kepler to explain comet tails
kepler1619cometis . The advent of the laser technology in the 60s enabled to
reproduce these effects on our planet starting a real scientific revolution
ashkin1970acceleration ; ashkin1970atomic . Optical tweezers
ashkin1986observation ; jones2015optical ; marago2013optical ; Polimeno2018
are tools based on tightly focused laser beams capable to trap, manipulate,
and characterize a wide range of microscopic and nanoscopic particles, in
liquids, air, and vacuum marago2013optical ; Polimeno2018 . Since the
pioneering work by Ashkin ashkin1970acceleration ; ashkin1970atomic ;
ashkin1986observation , that led him to the Nobel prize in Physics 2018, key
applications of this contactless manipulation technique have been developed in
a wide range of fields: from biology, soft matter, and ultra-sensitive
spectroscopy to atomic physics, nanoscience, photonics, spectroscopy, and
aerosols science jones2015optical . A crucial advancement has been the
realization of Raman tweezers, i.e., the coupling of optical tweezers with a
Raman spectrometer petrov2007raman . This allows the chemical and physical
analysis of a trapped particle through its vibrational fingerprints
gillibert2019raman ; donato2018optical .

Despite this tremendous experimental progress, the accurate light scattering
modeling of optical tweezers, that takes into account particle size, shape,
and composition, has been developed only recently Polimeno2018 ;
borghese2007optical ; borghese2008radiation . In the limiting cases of
particles much smaller or much larger than the laser wavelength, optical
forces in optical tweezers can be divided in two components jones2015optical :
a gradient force, proportional to the intensity gradient of the laser spot,
responsible for trapping; and a scattering force, proportional to the light
intensity that tends to push particles away from the laser focus destabilizing
single-beam trapping of particles with large extinction. Such detrimental
effects can be suppressed through the use of two counter-propagating beams to
null the opposite scattering forces zemanek2003theoretical . These dual-beam
traps are based on the use of low numerical aperture (NA) lenses and allow the
trapping of particles with reduced incident power in a focal region that is
wider than for standard optical tweezers donato2018optical . Thus they are
well suited for operation in air or vacuum where detrimental effects by
radiation pressure are enhanced by the reduced viscous damping gong2018optical
; svak2018transverse ; alali2020laser .

Notwithstanding the remarkable improvement in optical trapping techniques,
their application to planetary exploration (see the pictorial representation
in Fig. 1) is still to be developed, even though already conceived by, e.g.,
NASA NASA2014 . The development of the optical trapping technique to collect
and analyze in situ or return to Earth a variety of extraterrestrial particles
will open doors to information on space materials that is currently
unreachable: 1) as the dust volatile component, not measurable in situ by dust
instruments, e.g., those onboard Rosetta/ESA, and not retrievable by samples
return missions, e.g., Stardust/NASA, Hayabusa; 2) have biases due to
collection media contamination, e.g., aerogel used by the Stardust/NASA space
probe rotundi2008combined ; rotundi2014two ).

Here, we first review the role of dust in the universe: from interstellar, to
interplanetary, cometary and planetary dust particles. Thus, we describe the
models and methods we use to calculate light pressure and optical trapping
properties on a variety of realistic dust particle models. Then, we show
results on solar radiation pressure calculations that can help to a greater
understanding of micro-particle dynamics as well as to estimate its
detrimental role in optical trapping in space. Finally, we consider and
compare results of calculations for optical trapping of dust particles in
standard optical tweezers in water (typical laboratory conditions) with those
calculated for OT in air or in space.

Figure 1: Pictorial representation of space tweezers, space applications of
optical tweezers. Interplanetary or planetary dust can be collected and
investigated directly in situ (open space or extraterrestrial surfaces). The
inset represents a closeup up of a grain of interplanetary dust trapped by a
single-beam optical tweezers.

##  2 A dusty universe

We live in a dusty galaxy, one of the billions of galaxies in the universe.
Almost all of them are dusty. Up to the mid-20th century, all of this dust was
considered as an unfortunate impediment to making precise observations of
stars and galaxies, regarded as the most important items in the universe. The
modern view of dust as a cosmic component is almost entirely the reverse of
that earlier view. We now know that almost every aspect of the formation of
planets, stars, and galaxies is influenced in some way by interstellar dust
CCP12 . The involvement of dust grains in providing molecules important for
the origin of life, and in the safe transmission of those species to newly-
forming planets orbiting Sun-like stars McGuire , has been one of the greatest
surprises of all. It is no wonder that considerable efforts are currently
placed in trying to understand nature, composition, and evolution of dust in
the interstellar medium of galaxies.

There is now a robust evidence that dust grains condense in circumstellar
environments, mainly AGB (Asymptotic Giant Branch) stars gail2014  and
supernovae sarangi15 ; gall14 , from which they are ejected in the general
interstellar medium. There, dust is found to be tightly mixed with the gas,
with the dust representing only a minor fraction of the total mass. The gas-
to-dust mass ratio locally assumes the fairly constant value of 100
giannetti17 . The dependence of this ratio on the metal content among galaxies
and within a galaxy is an important issue from a cosmic perspective for a
number of reasons zafar13 , including the appearance of the first solids in
the early universe gall11 . In late-type galaxies, like our own, this ratio
scales with the metallicity, decreasing with the galactocentric radius, a
clear indication that dust growth in the interstellar medium dominates over
destruction mattsson14 . As a consequence, stardust, literally dust formed
around stars, is not the same as interstellar dust, and must be regarded as
the raw material from which true interstellar grains are formed. Such a
material is modified and destructured by violent interstellar processes
Bocchio14 , before being reformed and reassembled in denser interstellar
regions Draine09 .

Modifying processes continue to act throughout the lifetime of a dust grain,
some hundreds of millions of years in the Milky Way galaxy. In some cases,
such modifications may be catastrophic, as during the formation of a planetary
system, a filter that severely modifies the composition of interstellar dust.
Those materials passing through the filter are the most robust to destruction
and erosion. In the solar system, the patterns of isotopic abundances that are
found in survived presolar grains clearly identify their origins in the cool
envelopes of evolved low mass stars and in supernovae ejecta. These particles
have passed through many episodes of possible destruction, including their
ejection from the stellar envelopes, their passage through the interstellar
medium, where they have been subjected to intense radiation fields and
dynamical shocks, their incorporation into the molecular cloud that formed the
solar system, and through all the varied and violent processes involved in the
formation of the Sun and its planets. As near-stellar dust is modified in the
interstellar medium and becomes interstellar dust, so interstellar dust may be
severely modified, when not obliterated, when it is incorporated in the gas
that forms newly-born planetary system.

Figure 2: Scattering models with shape and composition inspired by
interstellar, interplanetary (DUSTER mission rietmeijer2016laboratory ), and
planetary oliva2019database  particles. On the top, the models emulate
hypothetical interstellar dust grains whose constituents are olivine and
aliphatic carbon. In (a) and (b), the constituents refractive indexes are
mixed according to the Bruggeman criterion. Instead, in (c) and (d), the
olivine is considered covered by a carbon layer. In (e), the model of a silica
particle arranged in quenched melt spheres shown in the FESEM image
rietmeijer2016laboratory  (f). In (g), the model of condensed Ca[O] nanograins
that are accreted onto a larger melted aggregate of tiny carbonate grains
shown in the FESEM image rietmeijer2016laboratory  (h). The larger sphere is
calcite and the other spheres are CaO. In (i), a spherical model of the
particle Fe, Mg-rich ’TP2’ rotundi2014two , in which we consider an effective
refractive index constructed mixing iron (67%) and magnesium (33%), according
to the Bruggeman criterion. In (j), a spherical model of Martian hematite
oliva2019database . In (k), a spherical model of Lunar regolith
egan1973optical . In (l), a model of an ellipsoidal fassaite shown in the
FESEM image (m). Here, we consider an effective refractive index constructed
mixing silica (53%), CaO (27%), FeO (10%), Al2O3 (10%), according to the
Bruggeman criterion bohren2008absorption .

###  2.1 Interstellar dust

Most of the information that we have about interstellar dust is obtained
remotely, by the influence of dust on various kinds of astronomical
observations. These observations may be carried out at a very wide range of
wavelengths, from X-rays to radio waves, but traditionally the most important
and defining data have come from the infrared, visible, and ultraviolet parts
of the spectrum, summarized through a wavelength-dependent extinction curve
along the lines of sight to individual stars.

There are detailed extinction measurements along hundreds of lines of sight in
the Milky Way Galaxy Fitzpatrick19 , and less accurate extinction data for the
interstellar media of external galaxies Naveen20 . Such observed extinction
profiles are different, but are clearly members of the same family showing a
basic similarity in their shapes: the extinction typically increases from low
values in the infrared to high values in the far ultraviolet, a near-linear
portion in the optical region, (in most cases) a pronounced and broad "bump"
near 217.5 nm, and a final rise of varying slope into the far ultraviolet.
Both the general aspect of the extinction and the details of specific curves
along particular lines of sight provide useful information, and generally
indicate that grains of a wide range of sizes (roughly nanometers to
micrometers) are required CCP15 .

The dominant feature in the extinction curve is the prominent bump in the near
ultraviolet. Its central position is fixed, although the width of the feature
can vary significantly from one line of sight to another. It is widely
attributed to $\pi^{\star}\leftarrow\pi$ transitions in aromatic carbon solids
gadallah11  or polycyclic aromatic hydrocarbons tielensbook . The far-
ultraviolet rise may be decomposed in a linear contribution, due to nano-sized
particles, and a non-linear component belonging to the partially invisible
(because located beyond the Lyman continuum) $\sigma^{\star}\leftarrow\sigma$
resonance in aromatic carbon. In the near-infrared, there is a weak absorption
feature at a wavelength of 3.4 $\mu$m, detectable on long paths through
diffuse gas. It is characteristic of absorption in the $sp^{3}$ (aliphatic)
C-H stretching bond Sandford91 . Further into the infrared are two stronger
absorption features, at 9.7 and 18 $\mu$m, ascribable to silicate materials,
from Si-O stretching and O-Si-O bending modes, respectively. Taken together,
these features strongly support the presence of some form of
carbon/hydrocarbon and silicate in the dust. X-ray scattering and absorption
edges provide constraints on grain size and composition, specifically O, Mg,
Si, Fe, and C atoms Draine03 . There is also a set of detected infrared
emission features occurring at 3.3, 6.2, 7.7, 8.6, and 11.3 $\mu$m, indicative
of aromatic CH groups. The mechanism responsible for the excitation of such
infrared emission may involve non-equilibrium emission from polycyclic
aromatic hydrocarbons stochastically heated to high temperatures by the
absorption of individual photons from the interstellar radiation field Leger84
. However, the requirement on microscopic sizes can be relaxed if the emitters
of the 3.3 $\mu$m and other infrared bands are heated by the chemical energy
released from reactions within larger carbon interstellar grains of mixed
$sp^{2}/sp^{3}$ carbon composition DW11 . Such structures have been in fact
observed in some extragalactic objects dartois07 . Exploiting a ternary phase
diagram where the hydrogen content and the two main bonding types ($sp^{2}$
and $sp^{3}$) for carbon constitute the poles, Dartois et al. (2007) dartois07
were able to identify the carrier of the spectral features as an interstellar
hydrocarbon belonging to the class of polymeric-like hydrogenated amorphous
carbon (a-C:H), dominated by an aliphatic/olefinic backbone structure. The
change from aliphatic to aromatic structures may occur in environments that
selectively dehydrogenate the a-C:H, providing an opportunity for aromatic
molecules to form. These observations, together with observations of very
evolved stars (protoplanetary and planetary nebulae), suggest an evolution in
which aliphatics are converted into aromatic structures antonia2008stratified
; CCP10 .

The interpretation of dust observations must take also account of the
available abundances along the line of sight. The hydrogen abundance is often
well-determined; abundances of other elements relative to hydrogen are
assumed, using solar or other relative values as a standard. It is unclear
which of these standards is the appropriate one to use Nieva08 , but whichever
one is adopted, the inventory of some materials is demonstrably incomplete. In
fact, silicates alone are unable to account for the entirety of either the
oxygen solid phase or Fe abundances Jenkins09 . The remainder of the Fe could
be in iron oxides or in metallic form Draine13 . The unaccounted oxygen is
less readily explained Whittet10 . There is an evident problem of oxygen
budget in the dense interstellar medium, as the combined contribution of
gaseous CO and silicate/oxide dust are by far less of the lowest reference
abundances Asplund09 . Solid H2O is an obvious O-bearing candidate.
Astronomers have known for decades that water is fairly common in the
universe. Interstellar water ice, as distinct from gaseous water molecules,
was first identified toward the embedded protostellar Becklin-Neugebauer
object by Gillette & Forrest (1973) Gillett73 . It is now widely detected in
interstellar dark clouds. These ices, composed mainly of water, also contain
carbon monoxide and dioxide, simple hydrides such as methane and ammonia, and
a few other species boogert15 . Still, ice contribution is not enough.
According to Whittet (2010) Whittet10 , the most plausible candidate for the
depleted oxygen appears to be a form of O-bearing carbonaceous matter similar
to the organics found in cometary particles returned by the Stardust mission.
Such materials may share some similarities with refractory organic residues
arising in the irradiation of icy mixtures by ions baratta14  or X-rays
ciaravella19 .

For its very nature, astronomical dust is likely to be an amalgam of a number
of different materials, very chaotic in composition and structure, with
different individual substances dominating at different wavelengths. These
materials are thus fundamentally different from terrestrial materials. Nuth &
Hecht (1990) Nuth90  introduced the concept of chaotic silicates in which the
level of disorder is even greater than for glasses, that are characterized by
the absence of long-range order in the atomic arrangement beyond nearest
neighbours. Since materials may be assembled in the agglomerate, an
astronomical silicate cannot be considered a solid with a definite
stoichiometric composition. They may also occur in groups that recall solid
solutions, in which one or more types of atoms or molecules of the solid may
be partly substituted for the original atoms and molecules without changing
the structure. Olivine and enstatite are excellent examples of solid
solutions. Forsterite, Mg2SiO4, and fayalite, Fe2SiO4, have identical
structures because the ions Mg2+ and Fe2+ are very nearly the same size and
are chemically similar. Very frequently amorphous silicates in space are
misleadingly described in terms of the optical properties of these materials.
Indeed, as pointed out by Rietmeijer and Nuth (2013) Rietmeijer13 , there are
no amorphous silicates, as the word "silicate" already implies that the
material is crystalline and could be a mineral. Moreover, astronomical solids
may be porous and therefore of much lower density than a glass. Ultimately,
the nature of an astronomical silicate is rather loosely constrained, to same
extent just limited to a material whose infrared spectrum is dominated by Si-O
stretching and bending vibrations. Thermal annealing (e.g. in shocks) or
intense X-ray irradiation Ciaravella16  of precursor materials, that were
probably amorphous, may explain the presence of crystalline silicates (see
however Ritmejer and Nuth 2013 Rietmeijer13 , for petrologic constraints) in
circumstellar regions and protoplanetary disks juhasz10 .

Even carbonaceous materials in space are difficult to constrain. A striking
example is given by the nature of the carrier of the interstellar ultraviolet
extinction bump at 217.5 nm, that was originally attributed to small
crystalline graphite particles Stecher65 , followed by a plethora of proposals
including mixture of spheres composed of graphite, amorphous carbon, and
silicate Mathis89M , irregular or fractal arrangement of graphite and
amorphous carbon Wright87 , polycyclic aromatic hydrocarbons Joblin92 ,
natural coal Papoular96 , and even electronic transitions of OH- ions in sites
of low coordination in silicates Steel87 . In general, carbonaceous materials
contain greater or lesser hydrogen fractions, varying proportions of different
chemical bonding, and different degrees of long-range order. All these forms
of carbon can, under suitable conditions, be readily converted from one to
another. The manifold of possible bonding arrangements produces several
allotropes of carbon of which the best known are graphite, diamond and
amorphous carbon. The physical properties of carbon vary widely with the
allotropic form. Amorphous carbonaceous materials cover a wide range of
compositions, from wide band gap, H-rich, aliphatic-rich a-C:H to narrow band
gap, H-poor, aromatic-rich a-C materials. The properties of a-C:H materials
are determined by the $sp^{3}/sp^{2}$ ratio for the carbon atoms and the
hydrogen concentration. A C-H bond contributes to the formation of $sp^{3}$
bonding and the reduction of the defects in the amorphous carbon network. In
general, it is found that the optical energy gap increases with hydrogen
concentration Higa06 .

Remote observations such as extinction profiles were at one time the only
sources of information about interstellar dust. However, even if challenging
it is now also possible to study in situ interstellar grains entering the
heliosphere by spacecrafts, and to collect them using stratospheric aircrafts
and balloons, and satellite probes. Rare interstellar dust grains can now be
examined in the laboratory being returned by the Stardust/NASA mission. During
the Cassini mission around Saturn, millions of dust particles have been
analyzed and now, thanks to the Cosmic Dust Analyzer on board the probe, 36
grains of dust supposed coming from outside our solar system have been
detected altobelli16 . Results from different missions generally deviate one
from another, and typically they are not very consistent with the dust picture
obtained by remote observations Draine09 . Obviously, this is a field in which
much work is required.

Figure 3: Optical forces distributions exerted by the Sun on dust particles
modeled as shown in Fig. 2. The optical force parallel,
$f_{\parallel}(\lambda)$ (blue line), and perpendicular, $f_{\perp}(\lambda)$
(red line), are intended respect to the light propagation direction
$\hat{\mathbf{k}}$. In (a-d) we show calculations on olivine-aliphatic carbon
structures. In (a) and (b), the constituents refractive indexes are mixed
according to the Bruggeman criterion bohren2008absorption . While in (c) and
(d) the olivine and the carbon are distributed in a core-shell structure. In
(e) we show results for the quenched melt silica particle, in (f) for the
bunch-of-grape carbon Ca-rich, in (g) for the ’TP2’ sphere, in (h) for the
martian hematite sphere, and in (i) for the fassaite ellipsoid.

###  2.2 The interplanetary dust complex

The interplanetary space of the solar system is very dusty, appreciable to the
naked eye through the faint solar colour cone of light above the western
horizon after sunset, or above the eastern horizon just before sunrise: the
Zodiacal Light, a huge amount of fine dust particles that scatter solar
radiation in the interplanetary space. The brightness of the Zodiacal Light
provides information on the overall space density of the dust known as the
interplanetary dust complex.

The interplanetary dust complex consists of microscopic (mainly rocky)
particles, typically less than a few millimetres in size, called
micrometeoroids, moving in the interplanetary space of the solar system
rubin2010meteorite . Dust is produced by collisions among solid bodies, by
disruptions of icy bodies nesvorny2006physical ; flynn2009dust  and by
cometary activity fulle2020comets ; guttler2019synthesis . As such the
interplanetary dust complex is an inventory of the constituent materials of a
large variety of solid bodies in the solar system. Their cosmochemical study
thus allows investigation of great diversity of astrogeobiological processes
occurred on their parent bodies. Remarkably, these include the most primitive
bodies not further processed by planetesimal accretion after aggregation in
the protoplanetary disk blum2017evidence . In addition, since the bulk of
extraterrestrial matter accreted by the Earth is in the form of cosmic dust
from the interplanetary dust complex, understanding its composition provides
also clues on outstanding issues like the contribution of extraterrestrial
matter to the Earth’s geochemical budget peucker1996accretion , including its
bearing on the emergence of life sandford2016organic . Based on particle-
impact detection at the Long Duration Exposure Facility/NASA, the main mass
fraction of the submillimetre dust particles in the Zodiacal cloud in the
vicinity of the Earth have characteristic diameters of $\sim$100-200 $\mu$m,
and the flux of micrometeoroids entering the Earth’s atmosphere is
40000$\pm$20000 tonnes per year love1993direct . Grün et al.
grun1985collisional  reached a similar conclusion and quantified the spatial
mass of cosmic debris at 1 AU as $10^{-16}$ g m-3, with the largest fraction
in the $10^{-6}$ to $10^{-4}$ g mass range, based on the lunar microcrater
record and spacecraft micrometeoroid detectors.

How much asteroid collisions versus cometary activity contribute to the
interplanetary dust complex is an outstanding issue. Matter is complicated
since such contributions are expected to vary through the solar system’s
history; this is due to the stochastic fluctuations in the number of mutual
collisions in the asteroid belt and the number and level of activity of comets
entering the inner solar system. If astronomical observations carried out by
the Infrared Astronomical Satellite (IRAS) and Cosmic Background Explorer
(COBE) satellites in the 1980’s indicated that collisions in the Main Asteroid
Belt (MAB) are the dominant source of dust in the near-Earth space
kortenkamp2001sources , dynamical simulations predict in turn that the bulk of
the Zodiacal cloud can be best produced by debris derived from Jupiter Family
Comets (JFCs) through spontaneous disruption nesvorny2010cometary . Oxygen
isotopic data from relatively large micrometeorites in the 100-1000 $\mu$m
size range collected at the Earth’s surface cordier2014oxygen ;
suttle2020extraterrestrial ; suttle2020isotopic  indicates that the
interplanetary dust complex is dominated by dust produced by cometary activity
and by collisions between primitive hydrous asteroids of carbonaceous
chondrite compositions, with a subordinate contribution from more evolved
anhydrous asteroids (mainly ordinary chondritic and Vesta-like). An additional
small fraction of micrometeorites, with heavy oxygen isotope composition, may
sample an unknown body in the solar system, namely a body not yet sampled by
macroscopic meteorites. The isotopic statistics shows that primitive,
volatile-rich material dominates the small size fraction, whereas evolved
anhydrous material dominates the large size fraction of the dust complex.

#### Physical and compositional properties of the interplanetary dust complex.

Most of the compositional properties of the interplanetary dust complex
derives from the cosmochemical analyses of samples recovered from the Earth’s:
1) surface, e.g., micrometeorites collected in Antarctica cordier2014oxygen ;
dionnet2020x ; suttle2020extraterrestrial ; 2) stratosphere, by balloon born
instruments as, e.g., DUSTER, designed for non-destructive and uncontaminated
collection of solid particles from tens of microns down to 200 nm in size
della2012situ  and by stratospheric NASA/aircraft passive sticking on silicon
oil coated plates rietmeijer2002earliest . A critical contribution is also
given by laboratory analyses of samples, i.e., collected, and brought back to
Earth, from asteroid surfaces dionnet2020combining  and in a cometary coma
rotundi2008combined ; rotundi2014two . In addition, cometary dust was studied
in situ from the onset of cometary activity to its cessation after perihelion
by the Rosetta/ESA space mission della201667p ; fulle2015density ;
rotundi2015dust .

The pristine mineralogy of micrometeorites is best unravelled by the study of
a specific class: the unmelted, i.e., particles that did not experienced
alteration by frictional heating during atmospheric passage
luigi15micrometeorites . Based on petrographic and geochemical data, most of
the micrometeorite flux reaching Earth today is dominated (>50% of unmelted
micrometeorites across all size fractions) by fine-grained and hydrated
carbonaceous chondrite material affine to the CM, CR matrices and CI
chondrites, with some specimens similar to the ungrouped meteorite Tagish
Lake. They are therefore a major component of the near-Earth dust complex in
agreement with isotopic statistics cordier2014oxygen . Coarse-grained
micrometeorites, which are primarily fragments of chondrule, and CAI (Ca-, Al-
rich inclusions) represent a smaller component (<25%) of the micrometeorite
flux van2012chondritic ; suttle2020extraterrestrial . Thus, the major
constituent minerals are olivine, low-Ca pyroxene, magnetite, sulphides, metal
and hydrous Fe-Mg silicates like serpentine and saponite. The density of
unmelted micrometeorites varies greatly according to their mineral
composition. Mean density for unmelted fine-grained micrometeorites is
$\sim$1.4 g cm-3 (average data from Kohout et al. kohout2014density ), but can
be more than twice for coarse-grained micrometeorites. Micrometeorites range
in size from 10 $\mu$m to 2000 $\mu$m rubin2010meteorite , however particles
up to 3000 $\mu$m in size have been reported in the Transantarctic Mountains
micrometeorite collection rochette2008micrometeorites ; suavet2009statistical
, and their mass varies within the nanogram to the milligram range. A
statistically significant number of micrometeorites in the 200-700 $\mu$m size
range shows that the micrometeorite size distribution is bimodal, with peaks
centred at $\sim$145 and $\sim$250 $\mu$m. This suggests that the
micrometeorite flux is composed of multiple dust sources with distinct size
distributions: fine-grained material from primitive objects and coarse-grained
material from evolved bodies suttle2020extraterrestrial .

DUSTER particles, collected with a strict contamination protocol during
different stratospheric balloon flight campaigns at 30-40 km altitudes, are
the smallest (down to 200 nm) meteoritic objects available for laboratory
investigation (see Fig. 2f,h,l). These are the residues of porous,
structurally weak bolides crossing the Earth’s atmosphere. They contribute to
the daily input of stratospheric extra-terrestrial material with: 1)tens of
microns down to sub-micrometre aggregates of nanometer-sized spherical grains,
produced by vaporization and quenching; 2) partially annealed minerals; and 3)
unprocessed minerals corte2013meteoric ; rietmeijer2016laboratory . DUSTER
particles composition includes alumina, aluminosilica, plagioclase, fassaite,
silica, CaCO3, CaO, extreme F-rich C-O-Ca particles, and oxocarbon. These are
particle linked to the friable CI and CM carbonaceous chondrite, and
unequilibrated ordinary chondrite meteors that are the most common source of
bolides and fireballs rietmeijer2016laboratory .

Similar particles are collected at lower quotes in the stratosphere by
NASA/aircrafts: Interplanetary Dust Particles (IDPs), numerous and fine-
grained, are available for laboratory analyses rietmeijer2002earliest ;
rotundi2007combined . They have a chondritic overall composition, masses in
the order of pico- to nano-grams and sizes of few microns rubin2010meteorite ,
but they can reach hundreds of microns for the Giant Cluster IDPs class. They
mainly consist of extremely fragile aggregate of crystalline and amorphous
materials with grain-size typically in the order of 100s of nm or smaller.
Hydrous IDPs are mainly massive objects with fibrous or platy surface
textures. They consist mainly of hydrous mineral assemblages, mostly smectite
and lesser serpentine and silicate glass, with minor amounts of diopside,
forsterite, chromite, Fe- and Ni-sulfides, schreibersite (Ni-phosphide),
magnetite, glasses of silicatic composition and disordered carbonaceous
material. Among IDPs are the aggregate anhydrous IDPs, which are extremely
fine-grained, highly porous (up to 70%) and low-density (0.3-0.6 g cm-3).
Following Rietmeijer’s classificationrietmeijer2002earliest , they consist of
a matrix aggregates of generally spherical entities, $\sim$0.1 to $\sim$1
micron in size, with embedded variable amounts of $\sim$5 micron-sized Mg, Fe-
and Ca, Mg, Fe-silicates, Ni-free and low-Ni pyrrhotite, iron oxides, and
amorphous materials. Aggregate IDPs are supposed to have a cometary origin
brunetto2011mid  testified also by the comparison with cometary dust particles
returned by the Stardust/NASA space probe rotundi2008combined ; rotundi2014two
. In fact, dust particles after ejection from the nucleus form a dust flux
della2019giada , which undergoes to solar radiation pressure effects, as
observed in situ by GIADA onboard the ESA Rosetta space probe della2016giada ,
to gas drag and to gravity force zakharov2018asymptotics . These dust
particles either remain tied to the nucleus or they are liberated into space
feeding the interplanetary dust complex, where their orbital evolution is
mainly controlled by radiation pressure and the Poynting-Robertson light drag
dermott2001orbital . This causes particles from 1 to 1000s of $\mu$m in size
to spiral slowly into the Sun, i.e., to gradually reduce the orbit’s
eccentricity and semi-major axis, in a $10^{4}$ to $10^{6}$ year time scales,
intercepting in some cases Earth’s atmosphere, where they are collected as
IDPs.

###  2.3 Planetary dust

Many terrestrial planets and satellites of both terrestrial and giant planets
in our solar system show dusty environmental conditions. In particular, the
mostly explored dusty bodies are the Moon and Mars.

#### The Moon.

The Moon is the only Earth’s natural satellite. Since the Moon has neither a
magnetic field nor a significant atmosphere, the lunar regolith and the near-
surface environment are mainly affected by space weathering processes such as
meteoroid impacts, solar ultraviolet radiation, solar wind, galactic cosmic
rays and plasma processes in the tail of the Earth’s magnetosphere.

On the Moon, all the locations explored so far have cratered surfaces covered
with loose regolith of several meters. We can therefore assume that the entire
surface is covered by regolith although the thickness may vary (about 5 m in
the maria, up to 20 m in the highlands). Such regolith layer is a cohesive,
dark grey to light grey, very-fine-grained, clastic material consisting of a
mixture of a wide variety of materials including fragments of highland
anorthosites, some forms of KREEP volcanic rocks, mare basalts and volcanic
glass, plus a small meteoritic component lucey2006understanding . The
influence of the solar wind and high-energy particles of solar and cosmic
origins induces the implantation of H, He, and many rare elements into the
regolith. Continued reworking by micrometeoroids of the hydrogen-enriched
regolith particles causes the material melting and the reactions
(particularly, H with FeO), producing water vapor and submicron grains of
metallic iron sintered into glass mckay1991lunar .

Considering the samples returned by the Apollo and Luna missions, the fine
fraction of the lunar regolith (45-100 $\mu$m in mean size) comprises about a
half of the lunar regolith by weight; the superfine fraction (particles
smaller than 10 $\mu$m) about 10%, while the particles smaller than 2 $\mu$m,
the finest regolith fraction, make up 1-2% of the mass. The shape of dust
particles is extremely irregular and highly variable, ranging from angular
with sharp edges to spheroidal. The density of individual particles is usually
assumed in the range from 2.7 to 3.0 g cm-3 carrier1991physical . Individual
particles may be glass-bounded aggregates mckay1991lunar  called agglutinates.
Agglutinate particles may have lower density (higher porosity), they are
usually <1 mm and contain minute droplets of Fe metal (much of which is very
fine-grained, single domain FeO), and troilite (FeS). They formed by the
melting and mixing produced by micrometeoritic bombardment of the lunar
regolith.

The optical parameters of the dust particles (i.e., the real and imaginary
parts of the complex refractive index) depend on the composition and can vary
significantly, not only over a wide region, but even locally in a microscopic
scale. For the glassy component, the real part values range from 1.570 to
1.749 and they vary directly with the total Fe and Ti contents and inversely
with the Al content chao1970lunar . The imaginary part of the complex
refractive index is more variable and can span from 0.0005 up to 0.15
according to the composition and wavelength of interest.

Electrical properties of the dust particles are characterized by the extremely
low electrical conductivity (approximately $10^{-14}$ ohm/m in shadowed areas
carrier1991physical , but about a hundred times higher under solar-light
exposure) permitting accumulation of electrostatic charge under ultraviolet
irradiation.

#### Mars.

Mars, the fourth planet of our solar system, has many features in common with
the Earth. Much of the Martian surface is covered by unconsolidated soils
(dust) derived from impact, aeolian and other sedimentary processes. Such dust
is likely produced by impacts early in Mars’ history and subsequently recycled
at its surface. Sometimes the wind in Mars’ thin atmosphere blows the dust on
the surface into dust storms, carrying dust particles up to altitudes of about
50 km. The composition of the Martian dust grains was obtained from several
space missions, starting from the mission Mariner 9 in 1971 toon1977physical .

It is possible to build a mineralogical model of the dust using all the data
acquired from the Mariner 9 and Viking Landers clark1982chemical  space
missions. Best fit results are those obtained by mixing different kinds of
clay, with montmorillonite Si2Al4O10(OH)2 $\cdot$nH2O as a base, mixed with
nontronite (where part of Al is replaced by Fe3+) and saponite (where Al is
replaced by Mg). Indeed, data by the X spectrometer aboard the Pathfinder
showed higher abundances of magnesium and aluminum, and lower abundances of
iron, chlorine and sulphur foley2003final  respect to what expected. The rocks
analyzed were similar to andesites, terrestrial materials derived from the
fractionation of basalt in intrusive conditions.

Data from recent rovers (e.g. MSL Curiosity at Rocknest, Oct 2012) and orbital
spacecraft show that Martian surface is dominated by a soil (dust grain
dimension <150 $\mu$m) of basaltic composition with primarily pyroxene,
plagioclase feldspar, and olivine, as well as minor amounts of Fe and Ti
oxides (e.g., magnetite, ilmenite, and hematite) and alteration minerals
(e.g., sulfates, phyllosilicates, and carbonates) morris2006 ;
yen2005integrated ; mcsween2010determining ; bish2013x . Dust particles
properties changes during dust storms chen2020dust . In general, dust particle
sizes range from 1.2 to about 4.1 $\mu$m with a mean dust radius of about
1.6-1.8 $\mu$m oliva2018properties ; wolff2009wavelength  and a positive
correlation between dust opacity and particle sizes.

Phase function results show asymmetry parameter values of $g=0.601$ $\pm$
0.108 for high atmospheric dust loading scenarios and $g=0.710$ $\pm$ 0.065
for non-dusty periods. Regarding the shape of the particles, considering a
modified log-normal aspect ratio distribution for a mixture of spheroids, data
suggest more elongated particles are present during dust storms, with aspect
ratios of 2.8 $\pm$ 0.9 for high-opacity days, in contrast to values of 1.8
measured during post-storm period. The particles single scattering albedo is
found ranging in the solar band between 0.89-0.90 (dark regions) and 0.92-0.94
(bright regions) wolff2010ultraviolet .

Moreover, there are a very strong and a fast feedback between sand/dust
emission and electric field enhancement and a linear relation between the
concentration of lifted dust and the generated electric field esposito2016role
.

Figure 4: Extinction cross-sections, $\langle\sigma_{\mathrm{ext}}\rangle$,
and optical trapping force, $F$, components along $x$ (blue line), $y$ (red
line), and $z$ (yellow dots) when the particle is trapped in water (center
column) or in air (right column). Results in (a-c) are related to the olivine-
aliphatic carbon core-shell sphere. (d-f) show calculations for the olivine-
aliphatic carbon core-shell cluster. (g-i) concern the quenched melt silica.
(j-l) show the results for the bunch-of-grape carbon Ca-rich. (m-o) are the
results for the ’TP2’ sphere. For the optical trapping calculations the laser
power is fixed at 50 mW and the wavelength at $0.83$ $\mu$m.

##  3 Methods and models for space tweezers calculations

Optical forces and optical trapping are the consequence of the electromagnetic
momentum conservation during a light scattering process jones2015optical ;
borghese2007scattering . To understand theoretically how light interacts
mechanically with matter, Maxwell’s equations and the integration of the
averaged Maxwell stress tensor have to be performed mishchenko2002scattering ;
borghese2007scattering . However, such calculations can be computationally
complex, $e.g.$ when we deal with non-spherical or non-homogeneous particles,
and the use of approximations can be also advantageous jones2015optical ;
polimeno2019optical . The range of validity of the different approximations is
determined by the size parameter $x=k_{\mathrm{m}}r$, where
$k_{\mathrm{m}}=2\pi n_{\mathrm{m}}/\lambda_{0}$ is the radiation wavenumber
in the medium surrounding the particle, $r$ is the particle size,
$\lambda_{0}$ is the wavelength in vacuum, and $n_{\mathrm{m}}$ is the medium
refractive index jones2015optical . When $x\ll 1$, the particle size is much
smaller than the wavelength, and the dipole approximation can be adopted,
treating the particle as a dipole chaumet2000time ; arias2003optical ;
albaladejo2009scattering . In the opposite case, when $x\gg 1$, the ray optics
regime appears computationally the most suitable, and the optical fields are
simply represented as a collection of $N$ light rays according to the
geometrical optics ashkin1992forces ; jones2015optical . Each ray has a $N$-th
portion of the total incident power $P_{\mathrm{i}}$, and a linear momentum
per second $n_{\mathrm{m}}P_{\mathrm{i},N}/c$ born1999principles . According
to the Snell’s law, a single ray which impinges on a surface with an certain
incident angle is partly reflected and partly transmitted. Therefore, the ray
changes its direction and, consequently, its momentum causing a reaction force
on the center of mass of the particle callegari2015computational .

In the intermediate regime, that is when the particle size is comparable with
the light wavelength ($x\simeq 1$) or for non-spherical and non-homogeneous
particles like cosmic dust, we need to resort to full electromagnetic theory
and the T-Matrix formalism has proved to be computationally advantageous
waterman1971symmetry ; borghese1980addition ; borghese2007scattering . Any
particle can be modeled through a sphere, clusters or aggregates of spheres,
spheres with spherical (eccentric) inclusions, and multilayered spheres
borghese2007scattering . This formalism consists in the expansion of the
electromagnetic fields into a basis of vector spherical harmonics applying the
boundary conditions across the particle surface mishchenko2002scattering ;
borghese2007scattering . The incident, and the internal fields inside the
particle have to be regular at the origin while the scattered field is such as
to satisfy the radiation condition at infinity borghese2007scattering ;
fucile1997optical ; ishimaru1991wave . The transition matrix, $\mathbb{T}$,
connects the amplitudes of the scattered fields to the amplitudes of the
incident ones upon a multipole expansion of the fields. Its order is, in
principle, infinite and thus it must be truncated to a multipole index value
$L_{M}$ borghese2007scattering . Such value is chosen to ensure the required
accuracy of the transition matrix elements. However, for a cluster of $N$
spheres this implies the solution of a system of order
$D_{M}=2NL_{M}(L_{M}+2)$, which may become too large borghese2007scattering .
Actually, the inversion of the scattering matrix is responsible for most of
the computation time required for the calculation that scales as $D_{M}^{3}$.
Thus, on account of the definition of $D_{M}$, the computation time scales as
$L_{M}^{6}$ whereas the storage requirements scale as $L_{M}^{4}$, so that it
pays, in terms of both CPU time and storage requirements, to keep $L_{M}$ as
low as practicable. Thus, the choice of an appropriate value of $L_{M}$, in
order to satisfy computation time and storage requirements, is of crucial
importance iati2004optical ; saija2003efficient .

The diversity of dust particles in an astrophysical context implies a richness
of models that we need to build in order to calculate realistic optical forces
for space tweezers applications. Here, we consider several models of
extraterrestrial dusts with shape and composition inspired by interstellar
particles, DUSTER samples corte2013meteoric ; rietmeijer2016laboratory , and
Moon or Mars dust analogs. We show these models in Fig. 2. On the top row, the
homogeneous and stratified single/aggregated spheres emulate hypothetical
interstellar dust grains whose constituents are olivine and aliphatic carbon
antonia2008stratified . The olivine refractive index is provided by Draine &
Li while the carbon one by Ashok et al. draine1984optical ; palik1998handbook
. In Figs. 2a and 2b, the constituents refractive indexes are mixed in such a
way as to treat the particle homogeneously with a single effective refractive
index according to the Bruggeman criterion bohren2008absorption . On the other
hand, in Figs. 2c and 2d, an olivine core is considered covered by a carbon
layer antonia2008stratified . The spheres radius of Figs. 2a and 2c is
$r=0.15$ $\mu$m. On the other hand, the clusters of Figs. 2b and 2d are
composed by $9$ spheres of different sizes with the major semi-axis $r=0.16$
$\mu$m. In Fig. 2e, we present a model according to a Field Emission Scanning
Electron Microscope (FESEM) image of a silica particle clustering arranged in
quenched melt spheres, shown in Fig. 2f, and collected by DUSTER
rietmeijer2016laboratory . The refractive index is provided by Malitson
malitson1965interspecimen . The model is composed by 4 spheres of different
radius with the major semi-axis $r=0.23$ $\mu$m. Fig. 2g represents the model
of condensed Ca[O] nanograins that are accreted onto a larger melted aggregate
of tiny carbonate grains, shown in the FESEM image of Fig. 2h, and collected
by DUSTER corte2013meteoric ; rietmeijer2016laboratory . The larger sphere is
calcite and the other spheres are CaO. The cluster model is composed by 30
spheres with the calcite refractive index provided by Ghosh while the calcium
oxide one is provided by Liu & Sieckmann ghosh1999dispersion ;
liu1966refractive . Moreover, its major semi-axis has $r=0.25$ $\mu$m. In Fig.
2i, a spherical model ($r=1.25$ $\mu$m) of the particle Fe, Mg-rich TP2,
collected by DUSTER, is shown rotundi2014two . We consider an effective
refractive index obtained mixing iron (67 %) and magnesium (33 %), according
to the Bruggeman criterion whose the two refractive indexes are respectively
provided by Johnson & Christy and Hagemann johnson1972optical ;
hagemann1974desy ; bohren2008absorption . In Fig. 2j, a spherical model of
Martian hematite ($r=1$ $\mu$m) oliva2019database . In Fig. 2k, a spherical
model of Lunar regolith ($r=1$ $\mu$m) egan1973optical . Fig. 2l shows the
model of a microscale fassaite ellipsoidal, collected by DUSTER, and shown in
a FESEM image of Fig. 2m rietmeijer2016laboratory . We consider an effective
refractive index constructed mixing silica (65 %), and CaO (35 %) according to
the Bruggeman criterion bohren2008absorption , the major semi-axis is 2
$\mu$m. All non-spherical models are oriented in such a way that their major
axis is aligned with the incident light propagation direction.

Table 1: Summary table of radiation pressure and optical trapping properties.
For each model particle we show: the radius, $r$, or the radius of the
smallest sphere enclosing the cluster; the geometric cross-section,
$\sigma_{\mathrm{geom}}$; the integrated optical force on the solar intensity
spectrum along the parallel, $\bar{F}_{\parallel}$, and perpendicular
direction, $\bar{F}_{\perp}$, with respect to the light propagation; the
extinction cross-section $\sigma_{\mathrm{ext}}$ at the trapping wavelength
$\lambda=0.83$ $\mu$m; the real, $n$, and the imaginary part, $k$, of the
refractive index at the trapping wavelength $\lambda=0.83$ $\mu$m; and the
optical trap stiffnesses along the optical axis, $\kappa_{z}$, and
perpendicular to it, $\tilde{\kappa}$, in water and in air.

The calculation of the solar radiation pressure and optical trapping forces on
model particles of Figs. 2a - 2k is carried out with the T-matrix formalism
because their size parameters fall within the range $x\approx[0.1-6]$. On the
other hand, when the particle size parameter is too high (e.g. $x\geq 10$)
such as in the fassaite micro ellipsoid of Fig. 2l, the calculation is carried
out in the ray optics approximation. For this case we exploited the optimized
computational MATLAB codes for dielectric particles provided by Callegari et
al. callegari2015computational  (http://opticaltweezers.org/software/otgo-
optical-tweezers-geometrical-optics/).

##  4 Results on solar radiation pressure and optical trapping of dust
particles

Solar radiation pressure calculations are important to understand its
relevance in optical trapping applications in space. In general external
forces, such as solar radiation pressure, can have detrimental effects on
optical trapping of particles in space or the high atmosphere. Here we aim to
show that T-matrix methods can be used to give accurate estimates of these
effects on individual dust particles. The total radiation force,
$\mathbf{\bar{F}}$, and force spectrum, $f_{s}(\lambda)$, that the Sun exerts
on particles are calculated as:

$\bar{F}_{s}=\int_{\lambda}\mathrm{d}\lambda\ f_{s}(\lambda)\ ,$ (1)
$f_{s}(\lambda)=\frac{i_{\odot}(\lambda)}{I_{\odot}}\
F_{\mathrm{rad},s}(\lambda)\ ,$ (2)

where the index $s=(\parallel,\perp)$ specifies respectively the parallel and
the orthogonal component of $F_{\mathrm{rad},s}(\lambda)$ respect to the
radiation incident direction, $\hat{\mathbf{k}}$. The expressions of
$F_{\mathrm{rad},s}(\lambda)$ are the wavelength dependent optical forces
calculated in the ray optics approximation jones2015optical  or in the
T-matrix approach borghese2007scattering  according to the different models
under investigation. The term $f_{s}(\lambda)$ specifies the spectral force
distribution obtained scaling the computation outputs
$F_{\mathrm{rad},s}(\lambda)$ upon the solar radiation intensity distribution
$i_{\odot}(\lambda)$ normalized at the solar irradiance $I_{\odot}$, $i.e.$,
$I_{\odot}=\int_{\lambda}\mathrm{d}\lambda\ i_{\odot}(\lambda)=1.34$ kW$/$m2
standard2012g173 . Therefore, the considered spectrum is chosen in the range
$\lambda=[0.28-2]$ $\mu$m that is when the light emission by the Sun has the
maximum intensity.

In the Fig. 3, we plot the solar radiation force distributions
$f_{s}(\lambda)$ (Eq. 2) for all the models presented in Fig. 2. In
particular, we show the force, $f_{\parallel}(\lambda)$, parallel to the
propagation direction as a red line, and the perpendicular one,
$f_{\perp}(\lambda)$, as a blue line. Figures. 3a-d concern the calculation on
different models for the olivine-aliphatic carbon structures. Figure 3e is
referred to the quenched melt silica, Fig. 3f the bunch-of-grape carbon Ca-
rich, Fig. 3g the ’TP2’ sphere, and Fig. 3h the martian hematite sphere.
Finally, Fig. 3i shows the fassaite ellipsoid for which the radiation force is
calculated with ray optics. We note how the parallel component,
$f_{\parallel}$, is much larger than the perpendicular one, $f_{\perp}$. In
fact, the parallel component is proportional to the particle extinction cross
section, while the transverse one is related to the asymmetry parameters,
$g_{i}$, related to the non-sphericity of the scatterer
mishchenko2001radiation ; borghese2007scattering ; saija2005transverse . Thus,
for cylindrically symmetric particles the component $f_{\perp}$ is zero (Figs.
3a, 3c, 3g, 3h, 3i). Figures. 3b, 3d, and 3e show results for elongated
nanoscale clusters that generally align with the incident electric field
direction borghese2008radiation  yielding a low value of $f_{\perp}$. In Fig.
3f we report the highly non-symmetrical model of the bunch-of-grape carbon Ca-
rich for which $f_{\perp}$ is quite strong and $\bar{F}_{\perp}\simeq 1.46$
pN, a value comparable to $\bar{F}_{\parallel}\simeq 18.2$ pN (Tab. 1). In
summary, the parallel component of the solar radiation pressure,
$f_{\parallel}$, describes an optomechanical interaction of the solar
radiation pressure with the extraterrestrial dust models in the tens of
piconewton range. On the other hand, for non-spherical particles the
perpendicular component of the solar radiation pressure can drive more complex
transverse or rotational dynamics klavcka2001motion .

We now focus on the systematic characterization of optical trapping forces in
optical tweezers, $i.e$, a single Gaussian beam focused by a high-NA
objective. In our calculations we fix the laser wavelength at $0.83$ $\mu$m,
that is a typical wavelength for optical tweezers experiments in the near-
infrared, and the power $P=50$ mW. In Fig. 4, we show the three Cartesian
components of the trapping force in the neighborhood of the optical tweezers
paraxial nominal focus placed at the origin of the coordinate system
($x=y=z=0$). The trapping position of the particle in the axial $z$-direction
does not typically coincide with the origin because of the ’pushing’ effect of
the optical scattering force. To calculate the force on the particle at the
equilibrium position
$C_{\mathrm{eq}}=(x_{\mathrm{eq}},y_{\mathrm{eq}},z_{\mathrm{eq}})$, the $z$
axial coordinate at which the axial force vanishes must firstly be found.
Hence, the force plots in the transverse directions $(x,y)$ can then be
calculated. In the left column of the Fig. 4, we present the extinction cross-
sections $\sigma_{\mathrm{ext}}$ for the visible and near-infrared wavelength
spectrum. The extiction cross section, $\sigma_{\mathrm{ext}}$, takes into
account the rate at which the energy is removed from the electromagnetic wave
through scattering and the absorption, allowing us to understand how
effectively trapping takes place jones2015optical . The trapping arises when
the focused incoming field generates a restoring force proportional to the
particle’s displacement from an equilibrium point, and that, for small
displacements, behaves harmonically Polimeno2018 . Therefore, trap stiffnesses
are defined as:

$\kappa_{i}\equiv\frac{\mathrm{d}F_{i}}{\mathrm{d}x_{i}}\bigg{|}_{x_{\mathrm{eq},i}}\
.$ (3)

We calculate optical trapping in water ($n_{\rm m}=1.33$) with an objective NA
$=1.3$ (middle column of Fig. 4) and in air or vacuum ($n_{\rm m}=1$) with NA
$=0.9$ (right column of Fig. 4). We note that here we focus only on
electromagnetic calculations, neglecting thermal fluctuations and
hydrodynamics effects due to the surrounding medium volpe2013simulation .
Generally, for a given particle, optical trapping in water is stabilized by
the overdamped viscous dynamics in the fluid, while in air or vacuum the
underdamped dynamics might be more critical for stable optical trapping
svak2018transverse . Moreover, the higher NA in water causes the equilibrium
point $C_{\mathrm{eq}}$ to be closer to the nominal focus than in air. This is
confirmed by comparing the graphs in Fig. 4, central column (in water), with
those of the right column (in air). The dielectric particles, such as the
quenched melt silica (Figs. 4h, 4i), and carbonate cluster (Figs. 4k, 4l)
exhibit fairly stable trapping. Even the interstellar dust model of a sphere
aggregate can be trapped thanks to the relatively low extinction (Figs. 4e,
4f). Indeed, for these model particles we are able to extrapolate the trapping
constants along the axial direction, $\kappa_{z}$, and along the perpendicular
direction, $\tilde{\kappa}\equiv(\kappa_{x}+\kappa_{y})/2$ (Tab. 1). On the
other hand, model particles, like the interstellar dust sphere (Figs. 4b, 4c),
or the Fe-Mg sphere (Figs. 4n, 4o), can not be trapped neither in water nor in
air. A similar behavior is also exhibited by the hematite sphere, regolith
sphere, and the ellipsoidal fassaite as shown in Tab. 1 by observing the
corresponding trapping constants. The reason is to be found in their large
size (Fe-Mg sphere, hematite, regolith, and fassaite) and on their strong
absorption (interstellar dust, Fe-Mg sphere, hematite, regolith and fassaite).
To further confirm, we have calculated the trapping properties of the Fe-Mg,
hematite spheres by reducing their size such that $r_{\mathrm{Fe-Mg}}=0.05$
$\mu$m and $r_{\mathrm{hem}}=0.1$ $\mu$m. In this way, the trap stiffnesses
can be extrapolated (Tab. 1) and a quantitative indication of
$\sigma_{\mathrm{ext}}$ is provided in Tab. 1. This behaviour is similar to
the optical trapping of metal nanoparticles that can be efficiently trapped at
small size where absorption and extinction cross sections are still small in
the near-infrared amendola2017surface .

##  5 Conclusions

After a review on the role of interstellar, interplanetary, and planetary dust
in the universe, we studied computationally the solar radiation force and
optical trapping properties for different cosmic dust particles. We showed
that the radiation force exerted by the Sun is not trivially negligible: it
can actively influence the dynamics of the modeled dust particles at the nano-
and microscale when compared to, e.g., optical trapping forces. Furthermore,
we calculated single-beam optical trapping properties for cosmic dust modeled
particles both in water and in air with parameters close to typical optical
tweezers experiments in the near-infrared. We found that dielectric and weakly
absorbing particles can be captured, while microparticles with stronger
absorption show a scattering component of the optical force that prevents
optical trapping in a standard single-beam optical tweezers. This detrimental
effects can be overcome through dual-beam traps made by stationary counter-
propagating laser beams zemanek2002simplified ; donato2018optical .

This study opens perspectives for the application of optical tweezers
techniques to solar system study, $e.g.$, cometary particles analyses
including the volatile component, dust particles in the Martian atmosphere
and/or on the Martian and Lunar surfaces. Such applications will also be
strategic within curator facilities designed for the uncontaminated handling
and preliminary characterization of extraterrestrial samples returned by space
probes. The opportunity to apply optical tweezers to planetary particulate
matter in the frame of curation facilities can pave the way for space
applications for in situ physical chemical analyses. The accurate knowledge of
the (optical, microchemical and electrical) properties of extraterrestrial
dust allows the design of an appropriate optical tweezers system for space
applications, e.g., to be mounted on stratospheric platforms, onboard future
cometary probes, or landers/rovers to Mars or to the Moon.

## Acknowledgements

We acknowledge financial contribution from the agreement ASI-INAF
n.2018-16-HH.0, project “SPACE Tweezers”. M.A.I., D.B.C., M.G.D., A.F.,
P.G.G., and O.M.M. acknowledge support from the MSCA ITN (ETN) project “Active
Matter”, project number 812780.

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