Science Progress (2013), 96(1), 1–18
Doi: 10.3184/003685013X13592844053451

Optical trapping of nanoparticles by ultrashort laser
pulsesANWAR USMAN, WEI-YI CHIANG and HIROSHI MASUHARA
Dr Anwar Usman gained his PhD from Tohoku University (Japan),and extended his researches in several places including Universiti
Sains Malaysia, Max-Born-Insitut für Kurzzeitspektroskopie im
Forschungsverbund Berlin, Osaka University, and École Normale
Supérieure de Chimie Paris. He is now a research fellow working with theMasuhara group in the Laser Bio/Nano Science Laboratory of National
Chiao Tung University, which is supported by a project on laser trapping
accompanying photochemical and photophysical processes financed by
National Science Council of Taiwan. E-mail: usman@faculty.nctu.edu.tw
Wei-Yi Chiang is a PhD student in the Department of Applied Chemistry,
National Chiao Tung University. His research is supported by a project
operated in the Masuhara group. He is carrying out research on laser
trapping with femtosecond laser pulses on target particles ranging from
dielectric nanoparticles, nanocrystals, and quantum dots.
E-mail: dominik.ac99g@nctu.edu.tw
Dr Hiroshi Masuhara graduated from Tohoku University (1966) andobtained his PhD degree from Osaka University (1971). After hisretirement from Osaka University, he joined the Department of Applied
Chemistry and Institute of Molecular Science of the National Chiao Tung
University in Taiwan as a Chair Professor. He is foreign fellow of the
National Academy of Sciences India and of the Royal Flemish Academyof Belgium and received the Asian Photochemistry Association Award(2012), the Medal with Purple Ribbon of the Japanese Government (2008),
the Porter Medal (2006), Chemical Society of Japan Award (2006), Osaka Science Prize (1994),
and Moet-Hennessy-Louis-Vuitton International Prize “Science for Art” Da Vinci of Excellence(1993). He has published more than 500 papers and 19 books and is now extending his seminal
researches on (1) laser-induced crystallisation of molecules and proteins and (2) exploration of
new laser-induced molecular phenomena by time-resolved spectroscopy and imaging. He may becontacted at Department of Applied Chemistry, National Chiao Tung University, 1001 Ta Hsueh
Road, Hsinchu 30010, Taiwan. E-mail: masuhara@masuhara.jp

ABSTRACT
Optical trapping with continuous-wave lasers has been a fascinating field in the opticalmanipulation. It has become a powerful tool for manipulating micrometer-sized objects, and has
been widely applied in physics, chemistry, biology, material, and colloidal science. Replacing thecontinuous-wave- with pulsed-mode laser in optical trapping has already revealed some novel
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phenomena, including the stable trap, modifiable trapping positions, and controllable directionalejections of particles in nanometer scales. Due to two distinctive features; impulsive peak powers
and relaxation time between consecutive pulses, the optical trapping with the laser pulses has been
demonstrated to have some advantages over conventional continuous-wave lasers, particularly
when the particles are within Rayleigh approximation. This would open unprecedented opportunities
in both fundamental science and application. This Review summarizes recent advances in the
optical trapping with laser pulses and discusses the electromagnetic formulations and physicalinterpretations of the new phenomena. Its aim is rather to show how beautiful and promising thisfield will be, and to encourage the in-depth study of this field.
Keywords: optical trapping, optical manipulation, continuous-wave lasers, laser pulses, microand nano-sized particles, geometrical-optics and Mie regimes, Rayleigh approximation, optical
Lorentz force, attractive and repulsive optical forces.

1. Introduction
It has been more than four decades since the first experimental demonstration of astable trap in micrometre-sized particles by a single continuous-wave (cw) laser beam.1
The basic concept of optical trapping is the employment of a tightly focused beam
into a diffraction-limited size to produce a steep gradient light intensity, which is
responsible to generate optical gradient forces or trapping potential wells.1-4 This noninvasive technique (termed as optical trapping or optical tweezers)5 is not only useful toconfine but also to move micro-scale objects to desired positions in three-dimensional
space; hence, it has become an indispensable tool to immobilise and manipulate single
particles or cellular organelles.6-10 Therefore, since its invention, optical trapping has
been showing tremendous, consistent, and increasing impacts on many research areasin physics, chemistry, biology, and materials science.4,10-14 Potential applications of laser
trapping have received much attention particularly in particle deposition,15-19 particle
aggregation,3,4,20-22 polymerisation,23 and crystallisation of organic compounds.14,24-29 For
the latter, in particular, this topic is reviewed in detail by Sugiyama et al.14 On the other
hand, optical trapping of biological particles extends from living cells,30,31 bacteria,32,33
viruses,30 DNA strains,34,35 to proteins.36 These have been reviewed by Moffitt et al.37
With the idea that the momentum change of light scattering can generate forces on
small objects, laser trapping has also been applied to trap target particles with diameters
down to the few tens of nanometres scale, such as fluorescent macromolecules,38
dielectric nanospheres,5,13 carbon nanotubes,39 semiconductor nanowires,40 and metallic
nanoparticles.7,41-49 Reducing the size of the target particle results in an abrupt decreasein the optical gradient force, a shallower trapping potential well, and a higher intrinsic
thermal diffusion coefficient. All these effects lead the particle to delocalise and escapefrom the optical trap; hence, conventional optical trapping is limited to particle sizes forstable traps.4,5,10,38 The minimum potential depth of ~10 k BT (where k B is the Boltzmann
constant and T is the absolute temperature in the trap) is usually required to overcome
thermal diffusion.5,50 Both a stronger optical gradient force and a deeper trapping potential
well can be achieved by increasing either the intensity of the incident cw beam or the
steepness of its gradient. These two approaches, however, are extremely limited by thelaser and optical systems. Although, plasmonic effects of metallic nanostructures havebeen introduced to increase the gradient of the laser intensity, and with these effects a
few tens of nanometre-sized polystyrene beads, quantum dots, or even proteins can be
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optically trapped by incident cw lasers with the power density as low as 0.1 W cm-1,2,51-53
temperature elevation effects remain a key issue in the nanostructures.54
An important step in the development of the optical trap is the utilisation of ultrashortlaser pulses instead of cw lasers. Such laser pulses have been demonstrated to be able
to control the crystal polymorph of glycine,55,56 to trap a few nanometre-sized quantum
dots,57 and to manipulate the dimensions and crystalline properties of nanodeposits.58
Furthermore, optical trapping with laser pulses revealed several new phenomena, whichcannot be induced when the trapping beam is a cw laser, particularly when the dimensionsof the target particles are much smaller than the incident wavelength.57,59,60 This article may
not cover the full area of laser trapping, but it will give readers an overview of the growing
and future challenges in this topic, particularly optical trapping with ultrashort laser
pulses. It is organised as follows; in the next section we explain in brief the basic principle,
experimental, and theoretical concept of optical trapping with cw lasers. We follow this bya discussion of the optical trapping of single particles or biological molecules that has beenachieved by employing nanostructures. We then discuss the novel phenomena attributed to
optical trapping experiments with ultrashort laser pulses. By describing nonlinear opticaleffects and three-dimensional optical forces exerted on dielectric particles in the trappingsite that have been performed,59,60 we give particular emphasis to the electromagnetic
formulations of the optical forces and physical interpretations of the new phenomena.
With these interpretations, we propose a new concept of the optical trap for ultrashortlaser pulses. Finally, we describe their possible future applications to challenging themesin the field of optical trapping, such as optical manipulation of biological molecules, single
particle trapping, and dynamics and sorting of Rayleigh particles driven by laser pulses.

2. Optical trapping
2.1. The principles of optical trapping
The key point of the laser trapping phenomenon is the light–matter interaction
accompanied with a change in photon momentum that generates attractive and repulsive
optical forces. For particles with dimensions in the order of the laser trapping wavelengthor larger, namely they are in the geometrical-optics or Mie regimes, the refraction of thelight field at the surface of a dielectric sphere results in gradient forces.5 As long as therefractive index of the particle is higher than its surrounding fluidic medium where it issuspended, the gradient force attracts the particle towards the highest light intensity. In
addition, reflection of the light field generates a scattering force that pushes the particle inthe direction of light propagation. The spatial gradient of the light intensity is one of the
key factors to determine the magnitudes of the gradient and scattering forces as well as
the equilibrium position of the particle in the trapping site.
On the other hand, for particles with sizes being sufficiently smaller than the
wavelength of the laser trapping beam, the Rayleigh approximation is applied.3,5,7,50,61
With this approximation, the optical forces exerted on the small dielectric sphere canbe calculated by treating the particle as a point dipole that minimises its energy in thelight field gradient. The attractive force is associated with the Lorentz force acting on
the dipole, whereas the repulsive forces are associated with momentum transfer orabsorption of the electromagnetic wave due to the scattering or absorption by the particle,
respectively.3,5,7,50,61,62
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Irrespective of the dimensions of the target particles, optical traps involve the balanceof the attractive and repulsive forces.5 The magnitudes of the attractive and repulsive
forces are basically determined by the laser power, as they are proportional to the lightintensity, and optical properties of the trapped particles. More detailed information on thebasic principles of optical trapping is given in the excellent reviews by Molloy et al.12 or
Dholakia et al.13

2.2. Experimental setup
The optical trapping setup which is based on a microscope system has been addressedin many reported works.1,4,5 Briefly, a monochromatic laser beam is tightly focused at
normal incident to a sample cell mounted on the microscope stage. Since the steepnessof the gradient light intensity determines the strength of the gradient force and ensuresa three-dimensional confinement, a spatially collimated and a tightly focused light beam
are required. To achieve such a condition, a high-magnification microscope objective lenswith a high numerical aperture (NA) is necessary. A sensitive detection of the position of
the particle in its trapping site is also a key feature of the optical trapping experiments.
The detection system varies from micro-imaging to micro-spectroscopic techniques, andthe information at the trapping site is collected and detected either through a condenser
lens or via the same objective lens.3,4,12,13,49
We should note that the utilisation of a high NA objective leads to several consequences.
Firstly, in the focal spot, the electric field of a linearly polarised incident beam is distributed
into the transverse and longitudinal components, and the distribution of their intensities
are determined by the NA.63,64 In Section 3.3, we will discuss that, with the transverseand longitudinal fields, the objective lens can be used as a handle to control the trapping
behaviour of the Rayleigh particles. Secondly, a higher NA corresponds to a higher
divergence angle and a shorter working distance of the focused beam. Since the working
distance is typically within a few hundreds of micrometres, and since the sample cell itself
consists of 130-μm-thickness coverslips, the trapping position is restricted to 100‒200 μm
inside the sample cell.

2.3. The basic theory
As mentioned above, optical trapping should be based upon the interaction between
the focused light with the particle. Electromagnetic theory is therefore obviously thepreferred approach to obtain quantitative descriptions of the optical forces exerted on theparticles. By considering the relative particle size with respect to the incident wavelength,
in principle, we can adopt two distinct approaches, namely the ray optics treatment forparticles in the geometrical-optics or Mie regimes and the perturbative formulation forparticles in the Rayleigh regime.5 Here we will take a brief look at a description of opticaltrapping based on both approximations.
With the ray-optics treatment, the attractive force acting on a transparent object isrelated to the change in photon momentum of the trapping beam due to refraction by theparticle.61 The force F is given by61,65
n P(1)
F =Q mc
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where nm is the refractive index of the surrounding medium, P is the laser power, c is the
speed of light, and Q is a dimensionless quantity which is related to the configuration of
the trapped object.61 In other words, the Q value, which has been accurately estimated to
be around 0.03– 0.2,12,65 is a measure of the coupling between the optical momentum of thetrapping light field and the trapping force exerted on the object. Thus, the Q value is also
related to the trapping efficiency of the particles in the geometrical-optics or Mie regimes.
For the case of a tightly focused light impinging on the particles in the Rayleigh regime, theattractive force is associated with the Lorentz force of the dipole in the electric field, while
the scattering and absorption forces are related to the scattering and absorption process ofthe electromagnetic wave by the dipole.2,50,62 The optical forces are given by 2,50,62

[ ]


 
 
FLorentz = P.∇ E + αµ 0 ∂ t E × H Fscattering = (nmσ p / c) E × H 
Fabsorption = (nmσ a / c) E × H

(1a)
(1b)
(1c)

Here, P = χ(1)E + χ(2)EE + χ(3) EEE + ... is the light-induced polarisation; χ(1) , χ(2), χ(3)are the linear and nonlinear susceptibilities. The linear susceptibility is expressed as χ(1)= n2mɛ0α, where α = 4πα3[((np / nm)2 – 1)/((np / nm)2 +2)] is the real part of the polarisability,
α is the radius, np is the refractive index, and σp = k4|α|2 / 6π and σa = kα" are the scatteringand absorption cross-sections of the individual particles, respectively. In these expressions,k = 2πnm / λ is the wavenumber in the medium, λ is the wavelength, α" is the imaginary
part of the polarisability, E and H are the electric and magnetic fields of the laser light,and ɛ0 and μ0 are the vacuum permittivity and permeability, respectively. It is apparent
that the directions of the optical forces are governed by the vectors of the electric field
and the wavefront of the incident light. As the linearly-polarised light, tightly focused bya high NA objective lens posseses orthogonal field components in the focal spot,64 the
distribution of the transverse and longitudinal component fields, and not just the intensityof the incident light field, should be taken into account.
Notably, since conventional optical trapping experiments employ monochromatic cw laser
sources, temporal dependence does not become an issue and the second term in Eqn (1a) isnaturally neglected. For isotropic particles with negligibly low nonlinear susceptibilities,
the gradient force is equivalent to the spatial Lorentz force and it can therefore be written
as,2,50,66

 2
1
Fgradient = nm2 ε 0α∇ E
2(2)

As |E|2 is proportional to the light intensity, the force depends on the polarisability andgradient of the light intensity. For an incident beam linearly polarised along the x-axis, theelectric field of the beam is expressed as


i
ρ2 
2ζρ 2 (3))
exp−
E x = E0
exp i (ω0t − kz −22i + 2ζ
ζ
ζ
1
4
1
4
+
+




where E0 is the electric field at the central intensity peak, ρ2 = ξ + η2 , ξ = х / w0 , η = y / w0 ,and ζ = z / kw20 are the normalised spatial coordinates in the focal spot, w0 is the beamwww.scienceprogress.co.uk

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waist, and ω0 is the carrier frequency of the beam. By substituting Eqn (3) into Eqn (2), thegradient force can be written as:
2 (ξ 2 +η 2 )
nm2 ε 0α E02 − (1+ 4ζ 2 )ξ
(4)
Fgradient = − xˆ×ew0
(1 + 4ζ 2 ) 2
In Figure 1, panel (a) shows F gradient as a function of ξ, indicating that it acts as a restoring
force to attract the particles from the radial distances up to a few times of the beam waist to
the focal point. Thus, it is likely to create a trapping potential well within which the particle
is trapped. Such a potential trapping well in the area around the focal spot is related to thepotential energy of the polarisation in the electric field; 
U trap = − P.E = −nm2 ε 0α E x2

(5)

Utrap [kBT]Fgradient [pN]

The plot of Utrap as a function of ξ is also shown in Figure 1 (panel (b)).
Although the optical trapping process can be considered as acting as a transducer of lightforces to micro- and nano-sized particles to attract them to the focal point, it is always
confronted with the issue of Brownian motions that can expel the particle out of the trappingsite. A trap is considered to be stable when the potential trapping well is deep enoughto overcome the kinetic energy of the particles due to Brownian motion. Practically, theoptical forces exerted on the particle can be treated as if it works as a microscopic spring,and the potential trapping well can be approximated as harmonic. With this approximation,
the optical gradient force is proportional to the displacement of the particle from the beam
centre, and the stiffness of optical trap (κ) is used as the parameter related to the equilibrium
between the optical, viscous, and Brownian forces.12,13 For particles in geometrical-optics
or Mie regimes, typically, the κ value is inversely proportional either to the particle size67
or to the NA of the objective lens.68 The
κ is of the order of 1.6×10-4 N m-1 W-1 for
0.16 (a)polystyrene microparticles,67 2.4×10-3 N m-1
W-1 for quantum dots,69 and 4.1×10-3 N m-1
0.08
W-1 for gold or silver particles.43
0.00
In the work by Ashkin et al.,5 thenecessary potential depth to compensate-0.08
the stochastic kicks of the particle out of
the trapping site due to thermal Brownian-0.16
motion has been established to be ~10 kBT.
(b)With such a criterion, one can estimate the0smallest limit of the particle size in optical-4
trapping experiments. For example, by using
a power of sub-W level of the focused beam
-8
close to the limiting spot diameter of 1 μm,
the minimum sizes of metallic or dielectric-12
polystyrene particles that can be trapped-2 -1 0
1
2
are about 10–20 nm.5,48,50 However, such aξcriterion for a stable trap is not applicable for
optical trapping experiments with ultrashort
Figure 1 Plots of (a) Fgradient [Eqn (4)], and (b) Utrap[Eqn (5)] as a function of ξ for isotropic spherical pulsed lasers, as will be addressed in detaildielectric nanoparticles under focused cw lasers. in Section 3.4.
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2.4. Optical trapping of single particles
Optical trapping that can precisely manipulate the target particles on the micrometre or
nanometre scales has opened up a new area of researches in so-called micromanipulation.
Though 10–20 nm-sized metallic or dielectric polystyrene particles can be trapped byconventional optical trapping with cw lasers,5,48,50 to achieve stable traps the minimum
particle size of biological objects is about the size of living cells,31 bacteria,32 or viruses.32
For smaller sizes, such as DNA, tethering the biomolecules to microparticles is required.34,70
Since conventional optical trapping of single particles, molecules, or biomaterials without
tethering to a bead is restricted by the minimum size of the objects,4,5,10 several approaches
have been developed to overcome this size limit as well as to increase the trapping
efficiency. Among the different approaches, the utilisation of surface plasmonic effects
based on gap-mode-excitation of adjacent metallic nanoparticles and the use of a doublenanohole on a gold-thin-film substrate have been of interest for applications.51,54,71,72
The bottom line of these approaches is to increase the steepness of the gradient of theelectromagnetic field at the focal spot. By exploiting the surface plasmonic field at the
nanogap between adjacent metallic nanoparticles of a patterned substrate that localises theincident field beyond the diffraction limit known as hot spots,73-75 small target particles canbe trapped.71,72,76-78 The size limit then has been reduced down to the nanometre-scales,such as single fluorescent molecules,76 Escherichia coli bacteria,78 or 10-nm-sized quantum
dots.72 With a tip separation of 15–30 nm, optical trapping of a 12 nm silica sphere or asingle protein molecule has been demonstrated.52,53 By simultaneously reducing the limit
size and strengthening the local optical fields, the surface plasmonic effects in the opticaltrapping with cw lasers become powerful for nanobioimaging,79 stacking,80 and nonlinear
optical imaging.81
Since the laser power necessary to trap a particle is inversely proportional to the fourth
power of the particle size, there remains the difficulty of trapping single nanometre-sized
dielectric particles, although the particle itself has been shown to have a positive rolein the trapping.51,82,83 In addition, metallic nanostructures themselves strongly absorb thephoton energy. This causes the temperature around the focal spot to increase,84 and suchphotothermal effects should increase the diffusion of the nanoparticles and destabilise theoptical trap.44

3. Optical trapping with ultrashort laser pulses
3.1. Substituting cw- with pulsed-mode lasers
As laser trapping has become a key tool in the field of micromanipulation, an aim should
be to manipulate single nano-sized particles. The obvious requirement is to utilise a steep
and intense light field at the focal spot. Thus, one may ask the question: can we use laser
pulses to replace cw lasers? Such a question reflects the fact that the peak powers of laser
pulses can generate a very intense light field;85 hence, a steep gradient at the focal spot canbe achieved.
The first uses of nano- or femto-second (ns or fs) laser pulse irradiations were reported
in 1996 in the laser-induced crystallisation of urea.86 This was followed by laser-induced
crystallisation of glycine55 and laser-induced crystal growth of 4-dimethylamino-N-methyl4-stilbazolium tosylate in 2002.87 Then, this method was applied in the fs laser pulsewww.scienceprogress.co.uk

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induced crystallisation of lysozyme, where protein crystals were obtained by the focusedlight irradiation from normally unfavourable conditions for spontaneous crystallisation.88
These results indicate that focused laser irradiation with intense ultrashort laser pulses
opens a new approach to generate nuclei of organic compounds or protein crystals andto grow them into sizeable crystals. On the other hand, the optical forces of microsecond
laser pulses have been applied in the optical levitation and manipulation of microscopic
particles that are stuck on a glass surface.89
The optical trapping of dielectric particles by fs laser pulses was started with thetrapping of a 1.28-μm silica sphere.90 In this study, the highly repetitive laser pulses were
demonstrated to have an ability to trap the microscopic particle equal to that of cw lasers.
This finding offered the conclusion that the average power, rather than peak power, is the
key parameter for laser trapping.90 The advantage of laser pulses over cw lasers, however,
was realised for the first time when picosecond (ps) laser pulses at a laser power as low
as 100 mW could stably trap 3.3-nm-sized quantum dots, which cannot be achieved bycw lasers as this would require a laser power of more than 20 W to induce similar opticaltrapping.57 This provided a hint that optical trapping with laser pulses would be fruitfuland give some advantages when the target particles are in the Rayleigh regime.57 This idea
has been supported by our recent work in which we have shown that larger numbers of the
50-nm-sized polystyrene or silica spheres are optically trapped upon replacing a cw- withan fs pulse-mode laser as the trapping beam.60,91

3.2. Nonlinear optical effects
A distinctive advantage offered by ultrashort laser pulses is that high impulsive peak
powers can induce nonlinear optical (NLO) processes in the trapped particles. The firstexperimental observation was the fs laser trapping-induced two-photon fluorescenceof optically trapped dye-doped microscopic polystyrene beads; and such two-photon
fluorescence was absent when using a cw laser.90 The most astonishing behaviour of the
NLO effects, however, is the splitting of the trapping site of gold nanoparticles into two
off-axis positions parallel to the laser polarisation.59
Electromagnetic formulations of the optical forces have been the key to detailed
understanding of laser trapping with ultrashort laser pulses. To avoid complexity, theformulations of the NLO effects have been limited to the impulsive peak powers of thelaser pulses and the NLO properties of the trapped particles. In this case, consideringa nonzero third-order susceptibility of light-induced polarisation, one can rewrite thegradient force related to the spatial Lorentz force in Eqn (1b) as,59

{

}


1 
2
Fgrad = α∇ 1 − (4 / 3)~
a E E22(6)where ã = –(3/4) χ (3) / χ (1). Here, the time-dependent electric field along the x-axis is given
by,50,92

E x = E0

8

MASUHARA.indd 8
ρ 2   t 2 i2ζρ 2 )exp
exp − 2 −
exp i (ω0t − kz −2i + 2ζ
1 + 4ζ 2 
 1 + 4ζ 
 τ 

(7)

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where τ is the pulse duration. By substituting Exof Eqn (7) into Eqn (6), we obtain thegradient force as given by

{[

]


2
Fgradient = −xˆ 2α nmε 0 c E x 2ξ / ω0 − K 2ξ / ω0 + 2 K 2ξ 3 / ω0 +[2
+ 4a~α nmε 0c E x 2ξ / ω0 − K 2ξ / ω0 + 4 K 2ξ 3 / ω0 − 2 K 4ξ 3 / ω0 + K 4ξ 5 / ω0]} (8)The trapping potential well is expressed as

(

([

)

]

)

1
2
2 2
U trap = − α  1 + K 2ξ 2 E x − ~a 1 + K 2ξ 2 E x

2 


(9)

In Figure 2 panels (a) and (b), the Fgradient and Utrap of Eqns (8) and (9) are plotted againstξ for different values of ã|Eх|2. The curvature of Fgradient and Utrap are modified as ã|Ex|2
increases. For ã|Ex|2 >0.5, the trapping site is no longer a single spot at the focal centre,
but it splits into two off-axis positions as there are two minima parallel to the incident
polarisation direction (x-axis).59 Since this finding, such utilisation of laser pulses has
opened new horizons in both the fundamental science and application of optical trapping.
2~
a E x = 0.802~a E = 0.75

0.5 (a)x

2~
a E x = 0.50
2
~
aE =0

F gradientx

0.0
Figure 2 NLO effects in optical trapping; (a)Fgradient [Eqn (8)], and (b) Utrap [Eqn (9)] plottedagainst the distance ξ for different values of
a|Ex|2 , when spherical gold nanoparticles aretrapped by the laser pulses.

-0.5

U trap

0.00

(b)

-0.18

-0.36
-2

-1

0
ξ

1

2

3.3. Three-dimensional attractive and repulsive optical forces
One of the very recent findings in the field of optical trapping based on ultrashort laser
pulses is our report on the optical trapping and directional ejections of nanoparticles.60 In
our experiment with tightly focused 800 nm laser pulses, 50-nm sized polystyrene beads
were optically trapped and ejected in the directions perpendicular to the laser polarisation.
This experimental observation of a unique feature driven by laser pulses has been beyond
theoretical elucidation of optical trapping hitherto. As this is a fundamentally different
phenomenon from that generally regarded as a stable trap by a focused cw laser beam, we
have to consider that, as compared with the cw laser the utilisation of impulsive peak powers
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in optical trapping actually induces much more complicated three-dimensional opticalcontrols. Although the one-dimensional field along the laser polarisation is sufficient to
explain the trapping behaviour of gold nanoparticles, in the case of the directional ejectionsof nanoparticles, it is important to take the transverse and longitudinal fields that coexist
at the trapping site into account. In addition to the optical gradient, the second term of theLorentz force [see Eqn (1)] is related to the instantaneous momentum transfer that induces
temporal pulse radiation forces (also called temporal forces) which acts as a repulsive
force.62,92,93 As the NLO susceptibilities of the trapped dielectric particles are negligibly
low, in this case we have introduced the presence of temporal forces and the transverseand longitudinal components of electric fields produced by the high NA objective lens in
the electromagnetic formulations of the optical forces.60 The transverse and longitudinalcomponents have been derived using the paraxial approximation,63,64 namely using therelations of Ez = (–i / k)∂xEx and Ey = (1 / k2)∂y∂xEx , giving

E z = − KE0

 t2 
2ζρ 2 ξ (1 + i 2ζ )
ρ2 
− 2  (10a)
exp
(
)
exp
exp
i
t
kz
ω
−
−
−
 0


2
 τ 
(i + 2ζ )(1 + 4ζ 2 )1 + 4ζ 2 
 1 + 4ζ E y = K 2 E0
 t2 
ρ2 2ζρ 2 iξη (1 + i 2ζ ) 2
− 2  (10b)
ω
exp
(
)
exp
exp
i
t
kz
−
−
−
 0


2
 τ 
(i + 2ζ )(1 + 4ζ 2 ) 2
1 + 4ζ 2 
 1 + 4ζ where K = 2 / kw0.59,64
By combining Eqns (1), (7), and (10), we obtained expressions for the optical forces asa function of the parameters of the laser beam, spatial positions of single NPs in the focal
spot, and optical properties of the NPs, as given by K 4ξ 2η 3
ξK 4ξ 2η  × (1 − 12ζ 2 ) 2 + ζ 2 (6 − 8ζ 2 ) 2 +ˆ+−Fgradient = − xˆ
y
2 2
2 7
2 6

2(1 + 4ζ )  (1 + 4ζ )
 (1 + 4ζ )

(

)

2

2

2 (ξ +η )2t− 2
 4 K 2 ξ 2ζ
4 K 2 ξ 2ζ (ξ 2 + η 2 )   nm2 ε 0αE02 − (1+ 4ζ 2 )
τ

×
×
e
×
e
+ zˆ
−

2 3
2 4

w
(1 + 4ζ )0
 
 (1 + 4ζ )

(

2

(11a)

)



K 2ξ 2K 4ξ 2η 2 (1 − 12ζ 2 ) 2 + ζ 2 (6 − 8ζ 2 ) 2
1 
ˆ
+ zˆ
+
Fscattering =  xˆ
y
×
2 2
2 6
1 + 4ζ 2 (1 + 4ζ ) (1 + 4ζ )×

nm2 ε 0σ p E02
2

−

×e

2 (ξ 2 +η 2 )(1+ 4ζ 2 )

−

2t 2

×e τ

(11b)

2

(

)



K 2ξ 2K 4ξ 2η 2 (1 − 12ζ 2 ) 2 + ζ 2 (6 − 8ζ 2 ) 2
1 
ˆ
+ zˆ
Ftemporal =  xˆ
+
y
×
2 2
2 6
(1 + 4ζ )1 + 4ζ 2 
 (1 + 4ζ )
2 (ξ 2 +η 2 )

2t 2

− 2
− 2nm3 ε 0αE02t − (1+ 4ζ 2 )
τ
×
×
e
×
e
cτ 2

10

MASUHARA.indd 10(11c)Anwar Usman, Wei-Yi Chiang And Hiroshi Masuhara

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We found that the optical forces are three-dimensional. As a practical form, we havesummarised the forces into three components as follows;Fx = xˆFgradient + xˆFscattering + xˆFtemporal
Fy = yˆ Fgradient + yˆ Fscattering + yˆ FtemporalFz = zˆFgradient + zˆFscattering + zˆFtemporal

(12a)
(12b)
(12c)

 

Figure 3 shows the spatio-temporal maps of the Fx , Fy , and Fz components exerted on
a 50-nm-sized polystyrene bead optically trapped with laser pulses (800 nm, τ = 90 fs,
80 MHz)tightly focused by an objective lens (NA 0.90).60 As shown in panels (a)–(e),the Fx acts as an attractive force directing the nanoparticles towards the focal point. This
indicates that the gradient force overcomes completely the repulsive forces in the direction
parallel to the incident laser polarisation. This is commonly observed in optical trapping
experiments.5,94 The Fx increases rapidly in the first half of the pulse envelope, reaches
a maximum magnitude on the scale of nN, and then decreases in the second half of thepulse envelope. Such a transient attractive force by the fs pulsed laser is much higher
than
the constant pN attractive forces of cw laser beams.1-3,49 Panels (f )–(j) show thatFz is along the positive z-axis during the first half of the pulse envelope and turns into
the opposite direction in the second half. Thus, the attractive force is depleted along the
1.5

z/kw021.0

t = -τ

abt = -0.5τ

t = 0τ

cdt = 0.5τ

t=τ

e

nN

0.5
0.0

-0.5
-1.0
-1.5
-2

1.5

z/kw02

1.0

-1

f

0

x/w0

1

2 -2

-1

g

0

x/w0

1

2 -2

-1

h

0

x/w0

1

2 -2

-1

i

0

x/w0

1

2 -2

-1

j

0

x/w0

1

2

0.5
0.0

-0.5
-1.0
-1.5
-2
2

x/w 0

1

-1

0

x/w0

1

k

2 -2

-1

0

x/w0

1

l

2 -2

-1

0

x/w0

1

2 -2

m

-1

0

x/w0

1

n

2 -2

-1

0

x/w0

1

2

o

0

-1
-2
-2

-1

0

y/w0

1

2 -2

-1

0

y/w0

1

2 -2

-1

0

y/w0

1

2 -2

-1

0

y/w0

1

2 -2

-1

0

y/w0

1

2

9
7
5
2
0
-2
-5
-7
-9

nN
0.5
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.5

pN

10
7
5
3
1
-1
-3
-5
-7
-10

Figure 3 Representative calculated spatio-temporal maps of optical forces exerted on polystyrene
nanoparticles
at the focal spot [Eqns (11)] for polarisation of the incident laser beam along the x-axis.
The Fx , Fz , and Fy components are shown in panels (a)–(e), (f)–(j), and (k)–(o), respectively, with thescales of the forces being given at the end of each row. Each column represents the times with respect tothe existence of a single pulse in the focal spot. The positive or negative values of the forces mean theirdirections along the positive or negative x-, y-, and z-axis, respectively.
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3/26/2013 12:04:36 PMz-axis, and Fz acts as arepulsive force. We note that Fz is asymmetric with respect to thepulse propagation, as Fz reaches a maximum magnitude of +0.46 nN at t = –0.5τ in thefirst half and –0.34 nN at t = 0.5τ in the second half of the pulse envelope. Consequently,
Fz is intrinsically favourable for ejection of NPs along the beam propagation. This force
is therefore reasonably related to the ejection force to overcome the adhesive interaction
between a polystyrene microparticle
and a glass surface in optical levitation experiments.89
As shown in panels (k)–(o), Fy is positive along the positive y-axis and negative alongthe negative y-axis, irrespective of its spatial
 position along the z-axis, indicating that
Fy also acts as a repulsive force. Since the Fy is almost symmetric along the y-axis, thisforce should eject the nanoparticles equally along the positive and negative y-axis. Thus,
the theoretically calculated forces, overall, suggest that optical trapping of dielectric
nanoparticles with the ultrashort laser pulses relies solely on the attractive force along
the x-axis, whereas the nanoparticles are ejected by the resultant of repulsive forces along
the ±y- and ±z-directions, as illustrated in Figure 4. This interesting feature implies thatthe nanoparticles are ejected from the trapping site by two repulsive forces perpendicular
to the laser polarisation. The theoretical finding of the three-dimensional optical forces at
the focal spot explains fairly well the directional ejections of the nanoparticles out of thetrapping site.60
t = -τ

t = 0.5τ

t = 0τ

t = -0.5τ

z

z

t=τ

z

z

z

y

y

y

y

y

x

x

x

x

x

12.5 ns

Figure 4 Schematic illustrations of theforcesin the focal spot during the single pulse envelope.
 optical
Blue, green, and red arrows denote Fx , Fz , and Fy components, respectively.

3.4. Trap stability
We recall that the optical trapping of nanoparticles relies solely on the periodical attractive
force parallel to the incident laser polarisation, but they might be accelerated and pushed
out of the trapping site in the directions orthogonal to the laser polarisation. Consequently,
Brownian motion of the nanoparticles in the trapping site could be completely overcomeby the optical forces during laser pulse irradiation, and we can neglect the criterion fora stable trap with a necessary energy of 10 kBT.5,50 The stiffness of the optical trap withregard to laser pulses should be therefore distinct from that with a cw laser, althoughfurther evaluation this issue is desirable and this is in progress in our laboratory.
With the concept of three-dimensional dynamics of Rayleigh particles driven bytightly focused laser pulses,60 we note that competition between the transient attractive
and repulsive forces in all directions are crucial to determine the stability and efficiency of
optical traps. A stable trap can be achieved only when the repulsive forces are overcomeby the attractive force or they are naturally suppressed. To achieve such conditions one
could consider three consequences. Firstly, one can decrease the particle size to reduce thescattering force, as σp is proportional to the sixth power of the particle radius. Secondly,
12

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expanding the pulse width will reduce the temporal pulse radiation force, which isinversely proportional to the pulse duration. Thirdly, the objective lens can act as a handle
for controlling the trapping behaviour of the Rayleigh particles through the K2 and K4
terms [see Eqn (11)]. With the two former conditions, essentially tight and stable opticaltrapping of 3.3-nm-sized quantum dots by a 3.5-ps-pulsed laser has been experimentallydemonstrated and evaluated in detail by Tamai’s group.57

4. Possible future applications of optical trapping with ultrashort laser pulses
The field of optical trapping is basically multidisciplinary, involving physics, optics, andlasers.11 The advent of optical trapping opened a new area of research on nanometre-sized
objects. It has enabled us to manipulate particles with sizes from the nanoscale upwards
and to provide insights into biological molecular machines.36,95 The long journey of thisfield leads to its widespread applications in a large variety of fields in physics, chemistry,
biology, materials, and colloidal science. Although still in its infancy, replacing cw lasers
with ultrashort laser pulses as the trapping beam has already shown some fascinating
behaviour in optical trapping, and it will develop optical trapping further to a new levelin both fundamental science and applications.57,59,60,91 Laser trapping with ultrashort laser
pulses is characterised by two distinctive features; periodical impulsive peak powers andthe relaxation time between consecutive pulses.
Repetitive Attractive and Repulsive Forces
Leading to Transient Gathering, Trapping,
Association, Binding, and Assembling.

Diffusion and Microfluidic
Convection Flow Accompanying
the Ejections of Particles fromTrapping Site.

OTLP

Repetitive Diffusion, Dissociation,
Dehydration, and Reorganization,
Processes.

Cooperative Motions
and Reorientations

Figure 5 Several aspects that govern the kinetic behaviour of nanoparticles around the focal spot
under optical trapping with laser pulses. OTLP stands for optical trapping with laser pulses.

In general, the optical, medium, and material effects, and their cooperation, that govern
optical trapping with laser pulses are summarised in Figure 5. The periodical attractive
and repulsive forces by the laser pulses dramatically influence the stability and efficiencyof the optical trap. On the material side, as a large number of nanoparticles are packed in
the trapping site, they may associate optically into a kind of transient assembly, as such an
assembly was observed for polystyrene beads optically trapped with a cw laser.21,22 We also
have to consider that the particles ejected out of the trapping site may be accompanied byconvection or microfluidic flow in the medium. One advantage offered by the laser pulses
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is that the repetitive relaxation between pulses will allow the trapped particles or biologicalsubstances to relax, diffuse, dissociate, re-associate or reorganise. Since such opticallymediated particle–particle interactions (as so-called optical binding)96 would govern theirtrapping behaviour and play an important role in the laser-induced organisation of thecolloids, clusters, or molecules into solid-state materials, they are of interest to be exploredusing laser trapping with laser pulses. The other important viewpoint is that the temperatureelevation or heating effect of the laser light97,98 could be suppressed due to the dissipation ofheat from the trapped particles to the surrounding fluid during the interval times, althoughfurther detailed experimental data are still desired. Optical trapping without a heating
effect is an ideal condition which occurs in many experiments with biological substanceswith the risk of, for instance, thermally-induced cell death or protein denaturation.
Regarding the development of optical trapping with ultrashort laser pulses, it seems thatthe ongoing research in this subject will reveal more novel phenomena and have significant
impacts in the evolving area of optical micromanipulation. The most potential advantage
offered by ultrashort laser pulses is their high impulsive peak powers that will not only
confine and manipulate single nano-sized particles or molecules with higher trapping ability
but also induce NLO processes in the trapped particles. With the NLO processes, one can
explore the effects of two- or three-photon processes in optical trapping or even optimise
them to enhance the trapping abilities. The other key features to be considered is that the
distribution of the transverse and longitudinal components of electric fields produced byhigh NA objective raises a kind of competition between the attractive and repulsive opticalforces. However, the repulsive forces associated with the controllable directional ejectionsof the nanoparticles will be a useful tool for controlling the kinetic motions of the particles
and light-driven microfluidic circulation and micromachines.60 As the repulsive force isdetermined by the polarisability of the particles, one of the most promising applications of
the repulsive forces is the sorting of nanoparticles driven by laser pulses, as illustrated in
Figure 6(a). The sorting of the dielectric nanoparticles from their mixtures in polydisperse
colloids can be based on their size and refractive index. Laser trapping can also induce
phase transitions, such as if the trapped particles form aggregates with different solubility
from their monomers, as illustrated in Figure 6(b).
In biology and biomedicines, similarly to conventional optical trapping with cw
lasers that was quickly applied as a tool in the optical manipulation of biologicalsubstances, such as viruses, bacteria, and cells, cell organelles, proteins, and DNA,6,8,30-36
ultrashort laser pulses have been utilised as tools for imaging based on linear and NLO
processes,99 as tweezers for single protein molecules,53 or as optical scissors in subcellular
nanosurgery.100,101 We consider that replacing cw lasers with ultrashort laser pulses inbiological applications would lead optical trapping to be more efficient in optical trappingand manipulation. Thus, one might be able to inject a single tagged molecule into a desired
position inside a cell. As a tool for optical sorting in biology, laser pulses may be expected
to sort different biological substances, such as red and white blood cells from a culture
medium or different proteins in purification steps.
The other fascinating application in biology is the crystallisation of proteins.55,88
Since many proteins are difficult to crystallise or the processes are time-consuming,
ultrashort laser pulses would be applicable in the crystallisation of such proteins. In thiscase, repetitive optical pulses, which induce gathering, trapping, binding, and assembling
molecular clusters coupled with diffusion, dissociation, dehydration, reorganisation, andcooperative reorientation processes14 would be beneficial for the soluble protein molecules
14

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Anwar Usman, Wei-Yi Chiang And Hiroshi Masuhara

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in the culture medium to be sorted or crystallised in situ, as illustrated in Figure 6(c).
Moreover, as laser trapping can precisely control the crystal polymorph, allowing one tofabricate a bulk solid organic crystal containing various crystal structures by switchingdifferent trapping beams. Such a solid crystal might be used, for instance, to optimise its
phase matching conditions for NLO applications or photonic crystals.

Figure 6 Illustrations for laser trapping-induced (a) particle sorting, (b) phase transition fromsoluble monomer to dissoluble aggregates, and (c) gathering, trapping, binding, and assembling
molecular clusters leading to crystallisation. The dashed arrows denote a large number ofrepetitive pulses.

In addition to biological substances, optical trapping applications have been intensively
explored for metallic particles.7,41-43,45-49,102,103 For the latter case, scattering and absorption
cross-sections operate much more strongly than for dielectric and biological particles,
thus they can easily induce non-negligible scattering and absorption forces in the frontof the gradient forces. Metallic nanoparticles usually have high refractive indices and
NLO optical susceptibilities,104 and their interparticle interactions can produce plasmonic
field effects.105,106 With these excellent optical properties, intensive research on the opticaltrapping of metallic nanoparticles with laser pulses might lead to new discoveries in opticaltrapping and manipulating nanometre-sized metallic particles, not just distinct opticaltrapping behaviours from those of dielectric particles.
Finally, we should note that theoretical modelling and numerical approaches basedon a light field continuously irradiated on the target particles, play a role in understanding
the basic concept of optical trapping, approximations, and the specific properties of thetarget nanoparticles.2,50,66,107 Since many novel optical trapping phenomena are reported
and the field of optical trapping is expanding rapidly, theoretical modelling should be
developed following the experimental observations. For instance, theoretical modelling
has recently been extended to involve resonance effects when the trapped nanoparticles
are simultaneously excited by a one-photon process.108-110 Such theoretical understandingwww.scienceprogress.co.uk

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not only explained and showed some good agreement with the experimental findings,111
but they provided detailed predictions of the resonance effects in optical trapping as well
as some clues in designing experiments to optimise the effects. Despite recent progresson the optical forces and trapping potential well of laser pulses,59,60,92,93 much theoreticaland numerical work still needs to be done to take into account the periodical attractive
and repulsive forces as well as the diffusion, kinetic, optical binding, association, anddissociation of the nanoparticles at and around the focal spot. The other interesting
viewpoints that we also need to take into account would be the NLO effects; e.g. how thetwo- or three-photon excitation and intermolecular interactions in the excited state exert
an effect on the laser trapping or even on the laser-induced organisation of the molecules
into solid-state materials. All these remain a task to be done and much work needs to beaccomplished in the future, but the basic ideas have already been started.

Acknowledgement
Professor H. Masuhara is grateful to the Ministry of Education of Taiwan (MOE-ATU
Project; National Chiao Tung University), the National Science Council of Taiwan (Grant
No. NSC 100-2113-M-009-001), and the Foundation of the Advancement for Outstanding
Scholarship of Taiwan.

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