1
Raman Spectra of Optically
Trapped Microobjects
Emanuela Ene
Diffraction rings of
trapped objects
Oklahoma State University
2
Content

Background:
Optical Tweezing
Confocal Raman Spectroscopy
Testing
and calibrating an Optical Trap
Building
a Confocal Raman-Tweezing System
Experimental spectra
Future
plans
3
Laser trapping
Ashkin: first experiment

Acceleration and trapping of particles by
radiation pressure,
Phys Rev Lett, 1970, Vol.24(4), p.156
Ashkin et al.

Observation of a single-beam gradient
force optical trap for dielectric particles,
Opt Lett, 1986, Vol. 11(5), p.288
Spatially filtered 514.5nm, ~100mW, beam
incident upon a N.A. 1.25 water-immersion
microscope objective traps a 10μm glass
sphere (Mie size regime ) with m=1.2;
FA is the resulting force due to the refracted
photons’ momentum change. The image of
the red fluorescence makes the beam
geometry visible.
4
Optical trapping
The refraction of a typical pair of rays
“a” and ”b” of the trapping beam gives
the forces “Fa” and “Fb” whose vector
sum
“F” is always restoring
for axial and transverse displacements
of the sphere from the trap focus f.
Typically, the “spring” constant (trap
stiffness) is 0.1pN/nm.This makes the
optical tweezing particularly useful for
studying biological systems.
A. Ashkin, Biophys. J. 61, 1992
5
Photons and scattering forces
p photon 
p photon
F 

d p photon
p absorbed
 ns
photon
h
c0
Pi
 ns
c0
dt
pi

pf
h
c0
red
p backscatte
(per second )  2ns
photon
F

h 
 2ns sin
c0
2
red
p backscatte
 2ns
photon
absorption

h
2P
h Pi

 ns i  F mirror
c0 h
c0
 I inc 
Fr  
 p photon dS
h
S

Δpphoton
Ray optics (Mie) regime
6
Large particle:
2a

 1
 I inc x, y, z  
Fr  
 p photon dS
h
S

Fr  Q


ns
Pi
c0
The radiation force has an axial (scattering) and
a gradient (transversal) component.
Pi affected by losses on the overfilled aperture and by spherical aberrations
Q- trapping efficiency (depends on the geometry of the particle, relative refractive
index “m”, wavelength, radial distribution of the beam)
Some numbers
For a sphere with 2a=5μm, the value of 2πa/λ is
30 for the 514.5nm laser
25 for the 632.8nm laser
Pi=1mW; ns=4/3 (water);
Qmax=0.3 (immersion objective, glass sphere with m=1.2)
Fr,max=1.3pN
7
Light forces
in the ray optics regime
A single incident ray of power P
scattered by a dielectric sphere;
PR is the reflected ray; PT2Rn is an
infinite set of refracted rays
r
As before, for one photon the momentum is
a
p photon 
h
h
 ns

c0
and the photon flux in the incident ray is
Ni 
Pi
h

ns Pi ns Pi 

2 n
Fz 

R cos(  2 )  T R cos(  n )

c0
c0 
n 0

ns Pi
Fy  0 
c0



2 n
 R sin(  2 )  T R sin(  n )
n 0


8
F = Fz + iFy
nP
F  s i
c0


i 2
2 i
 1  Re  T e   R ei
n 0

n 


ns Pi
T 2 [cos(2  2r )  R cos(2 ) 
 1  R cos(2 ) 

Q
s

2
1

R

2
R
cos(
2
r
)
c0 (1)


Fscat
nP
 e( F )  s i
c0
Fgrad
ns Pi
 m( F ) 
c0

ns Pi
T 2 [sin(2  2r )  R sin(2 ) 
  R sin(2 ) 
  Qg
2
1  R  2 R cos(2r )
c0


(2)
These sums (1) and (2), as given by Roosen and co-workers (Phys Lett 59A, 1976),
are exact. They are independent of particle radius “a”.
The scattering and the gradient forces of the highly convergent incident beam are
the vector sums of the axial and transversal force contribution of the individual
rays of the beam. T (transmitivity) and R (reflectivity) are polarization dependend,
thus the trapping forces depend on the beam polarization.
Computational modeling uses vector equations.
The beam is resolved in an angular distribution of plane waves.
Modeling in this regime ignores diffraction effects.
9
Axial forces in ray-optics regime
as calculated by Wright and co-workers (Appl. Opt. 33(9), 1994)
Vector-summation of the contributions of all the rays with angles from 0 to
arcsin(NA/ns) for a Gaussian profile on the objective aperture with a beam
waist-to-aperture ratio of 1. Linearly polarized laser of 1.06μm assumed. On
the abscise: the location of the sphere center with respect to the beam focus.
0.5μm-radius silica sphere (m=1.09)
for different laser spots
The best trapping is for the smaller waist
and the focus outside the sphere.
Silica spheres (m=1.09) with different radii
when the minimum beam waist is 0.4μm
The best trapping is for the bigger sphere
and the focus outside the sphere.
10
Transversal forces in ray-optics regime
as calculated by A. Ashkin, ( Biophys. J 61, 1992)
An axially-symmetric beam, circularly polarized,
fills the aperture of a NA=1.25 water immersion objective (max=70°)
and traps a m=1.2, polystyrene, sphere.
S’=r/a and Q are dimensionless parameters
(a=radius of the sphere; r=distance from the beam axis).
Gradient, scattering and total forces
as a function of the distance S’ of the
trap focus from the origin along the yaxis (transversal). The transverse
force is symmetric about the center of
y
the sphere, O.
The gradient force Qs is negative,
attractive, while the scattering force
Qs is positive, repulsive.
The value of the total efficiency, Qt,
is the sum of two perpendicular forces.
11
Gaussian profile on the objective aperture
Transparent Mie spheres:
•Both transversal and axial maximum trapping forces
are exerted very close to the edge of the transparent sphere
•Trap performances decrease when the laser spot is smaller than the
objective aperture
•The best trapping is for the smaller waist and bigger particle radius
Cells modeled as transparent spheres
Reflective Mie particles:
2D trapped with a TEM00 only when the focus is located near
their bottom
 trapped inside the doughnut of a TEM01* beam, or in the
dark region for Bessel or array beams

12
Modeling optical tweezing in ray
optics (Mie) regime
For trap stability, Fgrad >>Fscat
 the objective lens filled by the incident beam
 high convergence angle for the trapping beam
Usually a Gaussian TEMoo beam is assumed for calculations. But Gaussian
beam propagation formula is valid only for paraxial beams (small )!
Truncation: τ= Dbeam/ Daper
dspot = 2wtrap = K(τ)*λ*f/#
dAiry= dzero (τ >2) = 2.44*λ*f/#
τ=1: the Gaussian beam is truncated to the (1/e2)-diameter;
the spot profile is a hybrid between an Airy and a Gaussian distribution
τ<1/2 : untruncated Gaussian beam
13
Wave-optics (Rayleigh) regime
2a
Electric dipole-like (small) particle :

 1


The dipole moment: p   E

p  
F  ( p ) E 
 B  E 2
t
2



m2 1 3
a
Dipole polarizability:   n 2
m 2
Fgrad
2
s
Fgrad  a3  I inc
Fscat 
np
c0
Pscat  Cscat I inc  a 64  I inc
Cscat - the scattering cross-section
Theory applies for metallic/semiconducting particles as well, if dimension
comparable to the skin depth.
14
Our modeling for Gaussian beam
propagation uses ray matrices
The values for the trap parameters are estimated:
the beam is truncated and no more paraxial
after passing the microscope objective.
Distances are in millimeters unless stated otherwise.
f1=-100
f2=300
f3=+160
fobj=+1.82
2w2=6.26
R=106 2w0=1.25
2w3=6.26
2wmin=5.2μm
2w trp=0.24μm
2z trp =0.18μm
Laser
632.8nm
R=160
d5=160
d1=175
d2=425
d3=1500
d4=320
z=1.84
The diffraction limit in water, for an uniform irradiance, of this objective is
dzero≈ 3.4μm
MicroRaman Spectroscopy
15
Raman
I scattered
 exc4Vscattering Iexc
Our numbers:
Focused Gaussian beam
w0 =3.76mm
λ
=632.8nm
w trp =0.16μm
Z trp =0.17μm
Vscat- scattering volume
Imax /2
Imax
Imax /2
2wtrp
zR
zR
2
wtrp
zR 

Vscat 
I
Raman
scat
 I0  20mL
 1  z / w   dz  83
zR
zR
 zR
0
2
2

w
dz

2

w
trp

Vscat = 8π2/3 x wtrp4 /λ ≈ 3*10-8mL
Imax = (w0/wtrp)2 I0 =5.5x108 I0
2
2
trp
2

4
wtrp

16
Confocal microRaman
Spectroscopy
Background fluorescence and light coming
from different planes is mostly suppressed
by the pinhole; signal-to-noise-ratio (SNR)
increases; scans from different layers and
depths may be recorded separately.
In vivo Raman scanning of transparent
tissues (eyes).
17
Testing and calibrating an
optical trap
CCD camera
with absorption
filters
Vtrap≈ 8π2/3 x wtrp4 /λ≈ 0.02μm3
Vobject ≈ 10μm3
Vobject / Vtrap ≈ 500
f1=100
d7=310
Camera
lens
f=55mm
f2=750
f3=+150
P=19mW
2w trp=0.27μm
2w0=0.9
LED
BS
Laser
632.8nm
Pinhole
d6=127
2z trp=0.83μm
d5=160
d1=750
d2=850
d3=300
d4=310
Screen calibrated with a 300lines/inch Ronchi ruler
z=1.88
18
Calibrating the screen
Ronchi rulers at the object plane were used
to calibrating the on-screen magnification
14μm
The sample stage with white light
illumination and green laser trap
Imaging through a 50X objective: a) a
300lines/inch target in white light transmission;
b) the 632.8nm laser beam focused and
scattered on a photonic crystal
Magnification:
M=Δlscreen x 300/1”
A 5μm PS tweezed bead, in a high density
solution, imaged with the 100x objective
For the 100X objective,
the magnification in the
image is 1162.5
19
Water immersed complex microobjects
have been optically manipulated
Cell “stuck” near a
0.8µm PMMA sphere
with 6nm gold
nanoparticles coating
SFM image of a cluster of 0.18μm PS
“spheres” coated with 110nm SWCN.
Scanning range: 4.56μm
Diffraction rings of trapped objects.
Sub-micrometer coated clusters were
optically manipulated near plant cells;
both of the objects stayed in the trap
for several hours
PMMA = polymethylmethacrylate
20
Optical manipulation
in aqueous solution and in golden colloid
The particle is held in the trap while the 3D sample-stage is moving uniformly.
The estimated errors: 0.2s for time and 4μm for distance.
Purpose:
identifying the range of the manipulation speeds and estimate (within an order
of magnitude) the trapping force; a large statistics for each trapped particle
has been used.
21
Speeds distributions
for uncoated and coated polystyrene spheres
and 632.8nm laser; optical manipulation
in aqueous solution and in golden colloid
1.16μm PSS in a 0.8mW trap
1.16μm PSS horizontally moved Coated PSS in a 0.8mW trap
in two different traps
4.88μm PSS in a 0.8mW trap
The polystyrene spheres are manipulated easier
if they are
•rather smaller than bigger
•uncoated than coated
•immersed in water than in metallic colloids
•at higher trapping power
Estimating
the trapping force
22
Slow, uniform motion in the fluid.
Stokes viscosity, Brownian motion.
Fdrag=kvfall
vfal
vth
vth
Fdrag=kv
1 (    0 )d 3 g
kexp 
6
v fall
v
ksphere  3d
Ga=kvfall
ksphere  kexp  5 108 Ns / m
Fdrag  k  v  Ftrap,||
l
Ga
Fmax
Horizontal manipulation
Free falling and thermal speeds
Particle type
and size in μm
average
Vfall(μm/s)
average
Vth(μm/s)
≈4μm clusters
of coated PSS
9
4
4.88μm
uncoated PSS
25
10
1.16 μm
uncoated PSS
17
16



v meas  v  v Th
Fmax  k (vmeas  vth ) 2  v fall
2
For 4.88μm PSS in water (0.8mW):
ρ=1.05g/cm3; vmeas=22μm/s; η=10-3Ns/m2
Fest≈2pN
The range of secure manipulation
speeds and trapping forces have been
investigated for water and colloid
immersed microobjects
23
pN
PSS = polystyrene sphere
SWCN = single wall Carbon nano tube
NP
=nano particle
Clusters size unit: μm
μm/s
24
Building a confocal Ramantweezing system from scratch
halogen
lamp
DM3000
system
PMT
objective
&
sample
P4
Monochromator
L curvature
Video
camera
Imaging
system
BS
BS
subt.
filters
LLF
P3
HeNe Laser
M – Silver mirror
P – Pinhole
LLF - laser line filter
BS – beam-splitter
BP - broad-band
polarization rotator
BPR
beam
expander
Experimental setup
M2,
M3
P1
LLF
Ar+ Laser
P2
M1
Spectrometer characteristics
25
Detecting
Raman lines

180o scattering geometry chosen
excitation laser beam is separated from the million times weaker
scattered Raman beam, using an interference band pass filter
 matching the beam in the SPEX 1404 double grating monochromator
(photon counting detection, R 943-02 Hammatsu)
 multiple laser excitation, different wavelengths, polarizations,
powers
 alignment with Si wafer
 confocal pinhole positioned using a silicon wafer
 calibration for trap and optics with 5μm PS beads (Bangs Labs)
 metallic enclosure tested

26
Calibrating the spectrometer
with a Quartz crystal
The (x-y) -scattering plane is perpendicular on the z-optical axis; the excitation beam
polarization is “z” (V); the Raman scattered light is unanalyzed (any).
465cm-1 is the major A1 (total symmetric, vibrations only in x-y plane) mode for quartz.
27
Axial
resolution
Backward scattered
Raman light
Silicon wafer
(n=3.88
δ=3μ[email protected])
Incident laser
beam
Oil immersion
objective
(NA=1.25)
The calibration of our confocal setting
was done with a strong Raman scatterer.
Confocal spectra have been collected
when axially moving the Si wafer in
steps of 2μm.
Cover glass
(n=1.525;
t=150μm)
Oil layers
(n=1.515)
28
Confocal microRaman
spectra
Backward
scattered
Raman light
Δz≈440μm
Slide
Aqueous
solution
of PS
spheres
(m=1.19)
Incident
laser
beam
Oil immersion
objective
(NA=1.25)
Oil layer
(n=1.515)
Cover glass
(n=1.525,
t=150μm)
Slide with 1.5mm depression, filled with
5μm PS spheres in water. Focus may
move ≈ 440 μm from the cover glass.
Results identical as in www.chemistry.ohiostate.edu/~rmccreer/freqcorr/images/poly.html
29
An optimal alignment and range of powers
for collecting a confocal Raman signal
from single trapped microobjects
has been identified
5.0μm PS sphere (Bangs Labs) trapped
10mW in front of the objective;
broad-band BS 80/20, no pinhole
Better results than in
Creely et al., Opt. Com. 245, 2005
Confocal scan
5mW in front of the objective;
double coated interference BS
30
Confocal Raman-Tweezing
Spectra from magnetic particles
1.16μm-sized iron oxide clusters
(BioMag 546, Bangs Labs)
Silane (SiHx) coating
The BioMags in the same Ar+ trap were blinking alternatively. We attributed this behavior to an optical
binding between the particles in the tweezed cluster (redistribution of the optical trapping forces
among the microparticles).
31
Future plans:
monitoring plant and animal trapped living cells in real time;
analyze the changes in their Raman spectra induced by the
presence of embedded nanoparticles
(a) Near-infrared Raman spectra of single live yeast cells (curve A) and dead yeast
cells (curve B) in a batch culture. The acquisition time was 20s with a laser power of
~17mw at 785 nm. Tyr, tyrosine; phe, phenylalanine; def, deformed. (b) Image of the
sorted yeast cells in the collection chamber. Top row, dead yeast cells; bottom row, live
yeast cells. (c) Image of the sorted yeast cells stained with 2% eosin solution.
(Xie, C et al, Opt. Lett., 2002)
32
Future plans:
using optical tweezing both for displacing magnetic micro- or
nano-particles through the cell’s membrane and for immobilizing
the complex for hours of consecutive collections of Raman spectra
0 mM
0.15 mM
15.0 mM
PC12 cells ( a line derived from neuronal rat cells) were exposed to no (left), low
(center), or high (right) concentrations of iron oxide nanoparticles (MNP) in
the presence of nerve growth factor (NGF), which normally stimulates these
neuronal cells to form thread-like extensions called neurites. Fluorescent
microscopy images, 6 days after MNP exposure and 5 days after NGF exposure.
Pisanici II, T.R. et al ,
Nanotoxicity of iron oxide nanoparticle internalization in growing neurons,
Biomaterials , 2007, 28( 16), 2572-2581
33
Future plans:
using optical manipulation for displacing microcomplexes and
cells in the proximity of certain substrates that are
expected to give SERS effect
Klarite SERS substrate
(Mesophotonics)
and micro Raman spectrum
for a milliMolar glucose solution
with 785nm excitation laser,
dried sample, 40X objective
34
Summary
•a working Confocal Raman-Tweezing System has been built from scratch
•a large range of water immersed microobjects have been optically manipulated
•sub-micrometer objects were trapped and moved near plant cells
•an optimal alignment and range of powers for collecting a confocal Raman
signal from single trapped microobjects has been identified
•our experimental Confocal Raman-Tweezing scans for calibration reproduce
standard spectra from literature
•Raman spectra from superparamagnetic microclusters have been investigated
•a future development towards a nanotoxicity application is proposed
35
Appendices
36
Some useful values
for biological applications
Energy
1 photon ( λ=1μm)
Thermal energy KBT
(room temperature)
1 ion moving across a biological membrane
Force
For optical trapping
For breaking most protein-protein
interactions
For breaking a covalent bond
Length
4 pNxnm
30 pNxnm
1 pN
20 pN
1000 pN
Typical bacteria diameter
1 μm
Typical laser wavelength for biological
applications
1 μm
Trap size
Time
200 pNxnm
Cell division
0.5 μm
1 min
Cycle time for many biological processes
1ms to 1s
Scanning time for a Raman spectrum (CCD
camera detection)
0.2s to 10s
37
Substance
Raman line (cm-1) Present in our Raman
spectra for tweezed objects
for bulk samples
Water
984
No
1648
No
3400
No
210
Yes
290
Yes
620
Yes
960
Yes
Magnetite
676
No
Maghemite
252
?
650
?
740
?
Silane
Polystyrene
1001.4
Yes
1031.8
Yes
1602.3
Yes
3054.3
Yes
38
Stability in the trap for wave regime

Fgrad/ Fscat ~ a-3 >>1
The time to pull a particle into the trap is much less than the time diffusion out of the
trap because of Brownian motion

Surface (creeping) wave generates a gradient force
Equilibrium for the metallic particle near the laser focus
( 0.5-3.0μm sized gold particles )
H. Furukawa et al, Opt. Lett. 23(3), 1998
39
Alternate trapping beams
I ( , z) 
Hermite-Gaussian TEM00
2P
e
2
w( z )
 2  2 


 w( z ) 2 


Laguerre-Gaussian
TEM01* - doughnut (with apodization or Phase Modulator)
Bessel
( with a conical lens –axicon -)
Il ( , , z) 
A Bessel beam can be represented by a superposition of
plane waves, with wave vectors belonging to a conical
surface constituting a fixed angle with the cone axis.
Bessel l=1
VCSEL
arrays
I ( ) 
l 2
2
l!
 kt P  z 



 wc  zmax 
I0
e
2
(  / w0 )
2l 1
J l2 (kt ,  )e
kt =k sinγ (γ is the wedge angle of the axicon); k=wave number
P = total power of the beam
wc= asymptotic width of a certain ring
zmax=diffraction-free propagation range ( consequence of finite aperture)
Holographic Optical Tweezers
(the hologram is reconstructed
in the plane of the objective)
 2  2 


 w2 
 0 
 2 z 2

 z 2 max





40
Gaussian optics and propagation matrix
I ( , z) 
2P
e
w( z ) 2
Beam complex q-parameter
 2  2 


 w( z ) 2 


Rayleigh range
beam waist
At the minimum waist,
the beam is a plane wave (R-> ∞)
beam radius of curvature
  zR 2 
R( z )  z 1    
  z  
 r' 
r 
   T  
 ' 
 
Transfer matrix
for light propagation
Paraxial approximation
Calculating the beam parameter
based on the propagation matrix
41
Frèsnel coefficients
Non-magnetic medium
1
r  arcsin sin 
m



tan2 (  r )
Rp 
tan2 (  r )
m
nsphere
nsurround
θ
Transmissivity
Reflectivity
sin 2 (  r )
Rs  2
sin (  r )
m
r
Ts 
Tp 
sin(2 )  sin(2r )
sin 2 (  r )
sin(2 )  sin(2r )
sin 2 (  r )  cos2 (  r )
Rp  Tp  1
Rs  Ts  1
“p” stands for the wave with the electric field vector parallel with the incidence plane
“s” stands for the wave with the electric field vector perpendicular on the incidence plane
42
Axial forces in rayoptics regime
as calculated by A. Ashkin,
( Biophys. J 61, 1992)
An axially-symmetric beam, circularly polarized, fills the
aperture of a NA=1.25 immersion objective: max=70°
and traps a m=1.2 PS sphere. S’=r/a and Q are
dimensionless parameters.
Gradient, scattering and total
forces as a function of the
distance S of the trap focus
from the origin along the zaxis (axial). The stable
equilibrium trap is located just
above the center O of the
sphere, at SE.
43
Optical binding
Basic physics:
Michael M. Burns, Jean-Marc Fournier, and Jene A. Golovchenko, Phys. Rev. Lett. 63, 1233 (1989)
•interference between the scattered and the incident light for each microparticle
•fringes acting as potential wells for the dipole-like particles
•changing phase shift of the scattered partial waves because diffusion which
modifies the position of the wells
44
Scattered intensities, theoretically:
 (n +1), for the First Order Raman, Stokes branch
 n, for the First Order Raman, anti-Stokes branch
 (n +1)2, for the Second Order Raman, Stokes branch
I anti  Stokes
n
 h / k BT

e
e
I Stokes
n 1

hc
1
( )
k BT 
Dispersion and bandwidth
45
linear dispersion is how far apart two wavelengths
are, in the focal plane:
DL = dx /d






Grating rotation angle:  [deg]
 = Wavelength [nm]
G = Groove Frequency [grooves/mm = 1800mm-1
m = Grating Order =1, for Spex1404
x = Half Angle: 13.1o
F= Focal Distance: 850mm
 cos(x   ) 106 
nm
  0.6
Dispersion[nm/mm] 
G  F m
mm


BANDWIDTH =
(SLIT WIDTH) X DISPERSION
63.2nm excitation laser: the resolution is 4cm-1
46
Photon counting
Hamamatsu R943-02 PMT
lower counting rate limit is set by the dark pulse rate:
20cps @ -20C
 15% quantum efficiency @( 650 to 850nm)
 incident 1333photons/s signal (3.79x 10-16 W): minimum count
rate should be 200counts/s for 10 S/N ratio
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Raman Spectra of Optically Trapped Microobjects