Basic Principles

1
Light Takes Shape Advanced micromanipulation
for colloidal and biological scienceKishan
DholakiaSUPA, School of Physics and
AstronomyUniversity of St Andrews,
Scotlandwww.st-and.ac.uk/atomtrapkd1_at_st-and.ac
.uk
SFM 2008
2
This talk

• Optical trapping
• Basic considerations
• Advanced Studies
• Multiple beams,
• Optical binding
• Vortices
• non-diffracting beams
• White light studies
• Biophotonics with trapping
• Cell sorting
• Raman studies
• Cell Transfection

Industrial Physicist 1999
SPIE 2003
Recent review Dholakia et al., Chem Soc Rev vol
37, 42 (2008) available on our wesbite
3
Johannes Kepler Comet Tails
http//antwrp.gsfc.nasa.gov/apod/ap980717.html
http//sohowww.nascom.nasa.gov/hotshots/
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Size Scale
Human Hair 60mm (0.06mm)
Red Blood Cell 10 microns (0.01mm)
Light may interrogate, trap and separate objects
at this scale 1 micron 1 millionth of a metre!
5
From Thinking like a physicist, N Thompson
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• Knock the block over?
• The rubber bullet maximum momentum
• transfer

• Damage the block?
• The aluminium bullet maximum energy transfer

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Optical force on a mirror
F?
Very small!! But for a microscopic sphere use
Newtons laws..
Independent of wavelength
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At what scale are we working?
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http//www.st-and.ac.uk/atomtrap
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Optical levitation (suspending drops of water)
Expt of K Volke-Sepulveda and V Garces-Chavez
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Two counter-propagating beams
- A basic optical trap
Ashkin, Phys Rev. Lett. 24, 156 (1970)
Cell dimensions 3?3?20 mm
2 Gaussian beams
Counter-propagating
Long working distance
Works well in fiber traps
Also allows guiding
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Fibre optic trap
NO HIGH-N.A. OPTICS Compatible with
microfluidics
Potentially self-aligning -- some versions
interesting for integrated systems. Also
interesting for studies in microfluidics, Raman
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A true 3D traphow do we get it?
The same applies for light
As light is bent by a particle it exerts a force
allowing us to use light to trap
microscopic particles. REFRACTION
13
A Ashkin et al, Opt Lett 11, 288 (1986)
Quake group Phys. Rev. Lett. 91, 265506 (2003)
Nature Protocols, 2, 322 (2007) and references
therein
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? Objective Lens Choice
At the heart of a basic trap
? Laser Choice
Pick frequency to minimize absorption
(no optocution). Power depends entirely
upon application Beam Quality M2 lt 1.1,
TEM00 typical Pointing stability critical
for high-res. work
Magnification doesnt
matter, aberrations do A numerical
aperture (N.A.) gt 1.2 is desired
if 3D traps are required
52
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High N.A. lens required
to produce strong axial gradients needed for 3D
trapping with a single beam
?
Moreover, the laser should fill the back aperture
of the objective
Optic Axis
Optic Axis
Optic Axis
Focal Plane
Focal Plane
Focal Plane
OL
OL
OL
Underfilled
Filled
Overfilled
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Electrostatic Energy
Argument 2
is reduced by the presence of a polarizable
particle Rayleigh regime


_
?

_ _ _ _ _
_ _ _ _ _
Conclusion System minimizes energy by having the
polarizable particle wherever the field is highest
? Potential wells are created by local maxima in
the fields
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Analagous to dielectrophoresisGRADIENTS ARE THE
KEY
Argument 3
If one creates local minima in the potential
energy, there will be restoring forces
Uniform Field
Non-uniform Field

_ _ _ _ _
No Net Force
Net Force!
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3D trap
So, whether you like to think in terms of
momentum, energy, or forces,
When an optical physicist says everything goes
right to my waistthey arent talking about
fitting into their blue jeans
Focused Light creates a
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Three of the Earliest Geometries
Weve just shown
for Optical Trapping
There are many possible trapping geometries
only the one on the left is called an optical
tweezers.
21
Arthur Ashkin, Proc. Natl. Acad. Sci. 94, 4853
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Scattering and gradient forces
Small objects - the interaction forces between an
irradiated object and a light wave incident upon
it can be formally divided into two classes
Scattering force
Gradient force
Slide courtesy of P Zemanek
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Geometric optics
Validity

• object is spherical and much larger than the
  wavelength (agt10 l)

Ashkin BiophysJ 1992
Slide courtesy of P Zemanek
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Forces in the Rayleigh regime
(particle much smaller than the illuminating
wavelength, technically R lt l/20, but good
agreement can be found up until R w0)
nrel is the ratio of the refractive index of the
particle to that of the medium
Harada Asakura, Opt. Comm. 124, 529 (1996),
Eqns 16 , 10, 11
Tightly focused light beams require higher-order
corrections
The gradient force must compete with radiation
pressure!
However, whats found in real experiments depends
upon many factors!
?
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24
Force-measuring system
Key point If we have calibrated the trap
stiffness, measurements of displacement within
the trap yields sensitive force measurements at
the pico-Newton level. Careful versions extend
this down to 25 fN.
1 picoNewton (pN, 10-12 N) is roughly equal
to the gravitational attraction between you
and a book at arms length the radiation
pressure on a penny from a flashlight 1 yard
away 1 millionth the weight of a grain of salt
Alex Rohrbach (EMBL)
Motors
Antibody-antigen
b-avidin
Fibroblasts
Unexplored Opportunities
FORCE (pN)
1
10
100
1000
10,000
0.01
0.1
Optical Tweezers
Atomic Force Microscope
Extended from http//yakko.bme.virginia.edu/lab/l
aserpresent.htm
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A Parabolic Potential Energy Well
For a given laser power and particle size,
trapped matter experiences
(for small displacements)
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Eric Dufresne, Ph.D. thesis, 2000
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A Classical Oscillator
A parabolic well implies a linear relationship
between force and displacement, as with a mass on
a spring.
-- where ? is the elastic constant or stiffness
of the optical trap and ? is the damping
parameter.
With no damping (e.g., in vacuum) the result
would be a resonant frequency as follows
Mass of object 5 x 10-16 kg
?
Typical trap stiffness
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Trap Stiffness
is typically a linear function of laser power
k 1000 kBT/nm2
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Eric Dufresne, Ph.D. thesis, 2000
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In typical biological applications, the stiffness
of the optical tweezers is around 0.05 pN/Nm and
the trapped objects are around diameter 1
micron, corresponding to a mass of 10-16kg..
Hence, the resonant frequency would be around
50kHz. Biological experiments must be
performed in an aqueous medium, so significant
damping force arises. For a particle of radius r
, moving in a fluid of viscosity, the Stokes
drag constant We find that the roll-off
frequency well below 1 kHz. Since this is much
lower than the resonant frequency, the motion is
very over-damped. In
fact, it means that inertial and gravitational
forces can be ignored altogether
29
Tethering or Clamping of Single Molecules
Single-Molecule Biology study of molecular
motors (rowers and porters) requires
From S. Block lab www.stanford.edu/group/blocklab
/ResearchMain.htm
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• Living cells use molecular motors that take
  chemical energy and convert this to work.
• Functions that are essential to life from DNA
  replication, RNA transcription and protein
  synthesis to cell division, vesicle trafficking,
  cell locomotion, endocytosis.
• There are two types of motor
• Rotary motors are embedded in membranes and are
  driven by the flow of ions across transmembrane
  electrochemical gradients eg the bacterial
  flagellar motor.
• Linear motors work in an isotropic chemical
  environment energy from chemical reactions,
  usually the hydrolysis of the chemical, adenosine
  triphosphate (ATP) to adenosine diphosphate (ADP)
  and phosphate.

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• What can we measure?
• Force
• required to rupture a covalent bond 1000pN
• convert DNA from a double helix to a ladder
  50pN
• break most protein-protein interactions 20pN
• force produced by most motor proteins 5pN.
• Length diameter of a bacterium and optimal size
  for beads held in optical tweezers 1 micron
  resolution of light microscope 300nm diameter
  of eukaryotic cell organelles 100nm large
  protein assemblies and virus particles 30nm
  work stroke produced by motor protein 5nm

Adapted from Molloy and Padgett, Contemp. Phys
(2002)
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Optical Tweezers act as Anchors
for studying biological objects..
Quad Photodiode Detector
From review in optical tweezers, Padgett and
Molloy, Contemp. Phys. 43, 241 (2002)
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Force is proportional to Displacement
Project a magnified image of the trapped sphere
onto a quadrant photodiode.
A
B
C
D
The position of the sphere is defined by
differential signals from the quadrants.
Use of a quadrant photodiode provides higher
capture rate than CCDs while retaining
nanometer-scale position detection (centre of
gravity)
? Use dark field, phase contrast or
interferometric methods.
54
Christoph Schmidt group www.nat.vu.nl/compl/resea
rch_tech.html
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Force measurements in OT
From sphere displacements and trap stiffness,
infer macromolecule forces/dynamics
From Molloy and Padgett, Contemp. Phys (2002)
see also Berg-Sorenson and Flyvbjerg Rev Sci
Instrum (2004) Dholakia et al. Chem Soc Rev
(2008)
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Recent work has achieved angstrom resolution
Abbondanzieri et al. Nature 438, 460-465 (2005)
36
Abbondanzieri et al. Direct observation of
base-pair stepping by RNA polymerase. Nature 438,
460-465 (2005)
37

• Virtually all traps use CW lasers.
• Light in 700-1100nm popular
• Eg Yb Fibre lasers have great beam quality
• Near IR diodes/Ti-Sapphire laser
• Beam pointing/amplitude fluctuations
• M2
• what about white light? Ultrashort pulse lasers?

• The wavelength dependence of photodamage in E.
  coli compared to Chinese hamster ovary (CHO)
  cells. (Solid circles and solid line, left axis,
  half lethal dose time for E. coli cells sLD50d
  open circles and dashed line, right axis, cloning
  efficiency in CHO cells determined by Liang et
  al. Lines represent cubic spline fits to the
  data). The cloning efficiency in CHO cells was
  determined after 5 min of trapping at 88 mW in
  the specimen plane. Optical damage is minimized
  at 830 and 970 nm for both E. coli and CHO cells,
  whereas it is most severe in he region between
  870 and 930 nm (reprinted from Ref. 95).

From Neuman and Block Rev Sci Instrum 2004
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• Why create multiple traps/structured fields?

• Gaussian beam limiting depth of focus, selective
  excitation (STED)
• Novel beam shapes useful eg trapping low index
  particles, spectroscopy, mixing droplets
• Rotation studies of angular momentum and
  microrheology
• Multiplexed studies in biology enhacned depth of
  focus
• Cell organisation in 2D/3D
• Studies of colloid in 2D/3D
• Multi-particle interactions
• Creation of optical potential energy landscapes
• Chemical reactions single droplet control

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Multiple traps creating optical landscapes
Fallman, E. Axner, O. Design for fully
steerable dual-trap optical tweezers. Applied
Optics 36, 2107-2113 (1997)
Holographic Image
Lens
Liquid Crystal Spatial Light Modulator (SLM)
Acousto-Optic Deflectors (AODs) can be scanned at
hundreds of kHz
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Time sharing the light field can create multiple
traps positions. (This video in collaboration
with I Poberaj group).
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For a typical biological application, a 1 micron
diameter object has a diffusion coefficient,
given by Einsteins relation and a diffusion
distance, , over time, , given by For
example, for this object suspended in water, the
diffusion coefficient is. If the optical
tweezers are absent for 25 microsecs, the
diffusion distance is about 5nm. This represents
a maximum limit to the accuracy to which the
spheres can be positioned or their position
measured.
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Steering with a Phase-Only Optic
is equivalent to
Beam steering
a phase retardation
43
The phase modulating optic (a Diffracting
Optical Element) is effectively positioned at
the entrance of the objective lens, by making the
DOE/SLM conjugate to the back aperture. See next
talk for GPC method
D. G. Grier and Y. Roichman, Holographic optical
trapping, Applied Optics 45, 880-887 (2006).
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eg. Holographic trapping of droplets
Burnham and McGloin Opt Express 14, 4175 (2006)
Droplet new studies in mixing, atmospheric
chemistry, micro-reactions ..\..\Desktop\whiteligh
t\4175.MOV
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Vortices are ubiquitous in Nature..
Credit G Swartzlander, Tucson, Arizona
46
Credit NASA Langley Research Center (NASA-LaRC).
Wake vortex study at Wallops Island
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Laguerre-Gaussian modes an optical vortex

• circularly symmetric modes, characterised by
• radial mode index p
• azimuthal mode index l (determines helicity)
  this leads to helical wavefronts and orbital
  angular momentum

L. Allen et al., PRA 45, 8185 (1992)
p 0, l 0
p 0, l 1
p 0, l 4
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Generating LG beams

• They can be produced using computer generated
  holograms

l1
l6
l3
l2
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Laguerre-Gaussian Light beams

• Helical phase front (compare a plane wave)

Orbital angular momentum

• Poynting vector S follows a helical path

l0
l3
Rotation using OAM He et al, PRL 1995
(absorption) Rotation with spin AM Friese et
al. Nature 1998 (birefringent)
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Visualising the helical wavefront
- May be used for rotation Science 292, 912
(2001) and 3D structures Science 296, 1101 (2002)
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Ability to apply quantifiable torques is
essential.

• Fundamental studies of optical angular momentum.
• Micromachines optically actuated micro-gears,
  pumps and motors.
• Explore deviations, at the microscale, from
  oft-assumed no-slip hydrodynamic boundary
  conditions.
• Study uncoiling DNA, twisting fragments of known
  length.
• Study shear thinning at the microscale in
  membranes or polymeric fluids.
• Lab-on-a-Chip clinical application examining
  mechanical properties of liquids that
  characterize the onset of arthritis, where there
  is a desire to limit the amount of fluid that
  must be extracted for diagnosis. Perhaps such
  studies could help in the study of arthritis
  treatments (which typically only offer pain
  treatment at present).

82
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The angular momentum of light
L. Allen et al PRA, 45, 8185 (1992)
Spin due to polarisation state (rotating E-field)
Orbital due to inclined wavefronts
Spin transfer birefringence, absorption Orbital
transfer astigmatism, absorption, scattering
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Rotation using birefringence
LH circularly polarised
RH circularly polarised
Trapped birefringent microsphere
Per photon transferred
Plus points no need for complex beam shapes,
fast rotation rates USEFUL FOR MICRORHEOLOGY
LOCAL VISCOSITY
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Simultaneous transfer of spin and orbital AM to
an optically trapped particle.
Spin rotation around particle axis (INTRINSIC)
Orbital rotation around beam axis (EXTRINSIC or
INTRINSIC)
V. Garcés-Chávez et al., Phys Rev Lett 91, 2803
(2003) Intrinsic/extrinsic AM A.T. ONeil et
al. Phys. Rev. Lett. 88, 053601 (2002). OAM,
absorption He et al. PRL (1995)
spin
orbital
Conclusive demonstration of intrinsic/extrinsic
AM. Particle may probe of local AM of the light
field.
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White Light Studies Supercontinuum source
http//www.fianium.com/products.htm
Knight et al. Anomalous dispersion in photonic
crystal fibre. IEEE Phot. Tech. Lett. 12, 7
(2000)
56
Double slit experiment (Thomas Young)
Cosinusoidal fringes
Incident light
Light diffracted from slits
Interference fringes show wave nature of
light. Relationship to vortices H. I. Sztul,
and R. R. Alfano, "Double-slit interference with
Laguerre-Gaussian beams," Opt. Lett. 31, 999-1001
(2006).
57
Determining the azimuthal index of a white light
vortex

(a) l3 (b) l6 (c) l7 (d) l10
Interference patterns after young slits of Laguerre Gaussian beams with higher azimuthal indices (a) l3, (b) l6, (c) l7 and (d) l10. The lower images show the modeled interference patterns using 550nm radiation. Interference patterns after young slits of Laguerre Gaussian beams with higher azimuthal indices (a) l3, (b) l6, (c) l7 and (d) l10. The lower images show the modeled interference patterns using 550nm radiation. Interference patterns after young slits of Laguerre Gaussian beams with higher azimuthal indices (a) l3, (b) l6, (c) l7 and (d) l10. The lower images show the modeled interference patterns using 550nm radiation. Interference patterns after young slits of Laguerre Gaussian beams with higher azimuthal indices (a) l3, (b) l6, (c) l7 and (d) l10. The lower images show the modeled interference patterns using 550nm radiation.
58
Supercontinuum source

• Simultaneous trapping and spectroscopy of a
  microsphere

• Trapping and spectroscopy of aerosols to
  determine droplet size

• Investigations into longitudinal optical binding
  without interference effects

P. Li et al, Manipulation and spectroscopy of a
single particle by use of white light optical
tweezers. Optics Letters, 30, 2 (2005)
M. Guillon et al. Optical trapping and spectral
analysis of aerosols with a supercontinuum laser
source. Opt. Express, 16, 11 (2008)
D.M Gherardi et al. A dual beam photonic crystal
fiber trap for microscopic particles.Applied
Physics Letters, 93 (2008)
59
Generation of white light vortices
60
White light trapping vortices and multiple traps
All spectral components may accrue the azimuthal
phase OAM transfer from a broadband light field.
In general white light trapping offers prospect
of trap spectroscopy (eg droplet analysis see
Guillon et al. Opt Express (2008)
Opt Express 16, 10117 (2008)
61
Bessel light beams
Bessel beams have an intensity cross-section that
does not change as they propagate termed
propagation-invariant. THE CENTRE DOES NOT
SPREAD.
Durnin et al, JOSA A and PRL 1986/1987
With and being the radial and
longitudinal components of the wavevector
Radial intensity profile
Zeroth order Bessel beam
intensity
The zeroth order Bessel beam showing the narrow
central maximum
62
Bessel beams an optical rod of light
White light Bessel modes P. Fischer et al. Opt
Express 13, 6657 (2005)
Reformation or self-healing
63
CW guiding
femtosecond guiding visualise the beam using
fluorescent dye
H. Little et al., Opt Express 12, 2560 (2004) K.
Dholakia et al. New J. Phys. 6, 136 (2004)
Create optical conveyor belts eg Cizmar et al.
APL (2005) Applied Physics B-Lasers and Optics
84 197-203 and for cold atoms , see S Schmid et
al. NJP (2007)
64
The Bessel beam may self heal around obstacles
Vertical Bessel beam self-heals around
obstacles See V Garces-Chavez et al., Nature
419, 145 (2002)
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ACTIVE SORTING
Nature Biotechnology  23, 83 - 87 (2004)
Published online 19 December 2004
doi10.1038/nbt1050 Microfluidic sorting of
mammalian cells by optical force switching Mark M
Wang, Eugene Tu, Daniel E Raymond, Joon Mo Yang,
Haichuan Zhang, Norbert Hagen, Bob Dees, Elinore
M Mercer, Anita H Forster, Ilona Kariv, Philippe
J Marchand  William F Butler
74
Cell sorting
75
Particle Activation Fluid Flow
In a single trap the particle
escapes in line with the
drag force
gradient force
Where a second trap is
e
-
e
ò
present the trajectory of
µ
h
0
d
V

e
the particle is affected
0
viscous drag
If the traps are linked then
ph
F 6
rv

there is a preferred route
of escape
s
viscosity
v
velocity
r
radius
In the extreme case we can
consider what happens in
a line trap
76
Potential Landscape Plus Driving Force
The landscape can also comprise of a set of
parallel ridges like this roof
77
Sorting in a Potential Landscape
But it is more interesting when the ridges go
across the fall-line
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Passive optical sorting for small cell samples
Nature 426, 421 (2003) Optics Letters 32, 1144
(2007) Appl Phys Lett (2005) See work too of
Zemanek et al (Brno, CZ), Grier et al (USA),
Volke-Sepulveda et al (UNAM, Mexico)
79
Raman spectroscopy

• Light is incident upon a sample. It is scattered
  and is on unit of vibrational energy different
  from the incoming light.
• No matching of energy states is required
• Input beam interacts with the e- cloud and
  polarises the molecule creating a short live
  virtual state- quickly re-radiates

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Raman Spectroscopy
Raman shift in wave numbers
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The scattered light carries information on the
molecular constituents of the cell identify cell
abnormalities
82
Trapped cell remove raman signal from the
environment
83
P. Jess et al., Opt. Express 14, 5779-5791 (2006)
84
A single human keratinocyte cell held in an
optical trap
85
S, McGreehin, R Marchington, P Reece, T Krauss .
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Shunting of a micron sized particle between two
traps
Laser
Laser
Laser
Laser
Laser
Integrated optical micromanipulation S.
Cran-McGreehin et al., Lab-on-a-chip 6, 1122 (Aug
2006) S. Cran-McGreehin at al., Optics Express
14, 7723-7729 (2006)
87
Raman studies for cervical cancer
88
Cell transfection
Transfection The transfer of exogenous DNA into
a cell. www.nature.com
89
Femtosecond nanosurgery
Related to optical breakdown in liquid (gen. free
e-) multiphoton ionisation quantum
tunneling impact ionisation thermionic
emission For fs nanosurgery we can tune the
free e- (low density plasma). These create
subtle photochemical damage of membrane
reactive ion species fs beamslow disruptive
mechanical effects Femtosecond laser
nanosurgery Vogel et al, Appl. Phys B vol81,
1015 (2005) Phys Rev Lett (2008) Quinto-Su and
Venugopalan ch4 Methods in Cell Biology vol 82
(2007)
90
CW vs pulsed lasers
Continuous wave (CW)
Pulsed

• More thermal damage
• Larger area affected
• Mechanical damage (melting, etc)

• Less thermal damage
• Smaller area affected
• Less mechanical damage
• Most material is vaporized
• Less power needed

Images Chichkov et al, Applied Physics A (1996)
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fs - Transfection Efficency
Study based on 4000 cells
D. Stevenson et al, Optics Express 14, p7125
(2006)
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Tweeze and porate with the same laser
94
A different approach?

• Multiphoton process requires exact placement of
  cell membrane.
• Error of a few µm can prevent transfection.

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Bessel Photoporation(The Optical Syringe)

• Non-gaussian light beams behave differently.
• The bessel beam preserves a non-diffracting
  central core over long distances.
• Can perform fs-poration over a much greater
  depth of focus.
• Beam also self-heals - is this a further
  advantage?

96
Beam shaping in biophotonics
X. Tsampoula et al. Appl. Phys Lett 91, 053902
(2007) T Cizmar et al.Opt Express 16, 14024(2008)
97
Opt. Express 16, 14024-14035 (2008)
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A cuvette of fluorescent dye excited by single
photon excitation (right line) and multiphoton
excitation (localized spot of fluorescence at
left) illustrating that two photon excitation is
confined to the focus of the excitation beam
(courtesy of Brad Amos MRC, Cambridge). 
99
Single and two photonexcitation revisited
Picture courtesy of C McDougall and CTA Brown
100
Acknowledgements Sorting G Milne, L Paterson, M
MacDonald, A Riches, E Papagiakoumou,
Photoporation X Tsampoula, V Garces-Chavez, D
Stevenson, B Agate, CTA Brown, W Sibbett K
Taguchi, S and K Mohanty Theory M Mazilu Bessel
beam (SLM) T Cizmar White light J Morris, A
Carruthers, M Mazilu, WM Lee, Integrated Trap S
McGreehin, T Krauss Raman P Jess, M Mazilu P
Zemanek group ISI, Brno, Czech
Republic Biology/Medicine co-Investigators F
Gunn-Moore (neuroscience) A Riches (cancer
biology) CS Herrington (pathology) Visit us at
www.st-andrews.ac.uk/atomtrap