Oklahoma State University

1

Raman Spectra of Optically Trapped Microobjects 

Emanuela Ene

Diffraction rings of trapped objects

2

Content

Building a Confocal Raman-Tweezing System Experimental spectra

Future plans

Testing and calibrating an Optical Trap

Background: Optical Tweezing Confocal Raman

Spectroscopy

3

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, beamincident upon a N.A. 1.25 water-immersion microscope objective traps a 10μm glasssphere (Mie size regime ) with m=1.2;FA is the resulting force due to the refractedphotons’ momentum change. The image of the red fluorescence makes the beam geometry visible.

Laser trapping

4

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

Optical trapping

5 Photons and scattering forces

0c

hnp s

absorbed

photon

h

pphoton

0

2c

hnp s

redbackscatte

photon

mirroris

is

redbackscatte Fc

Pn

h

P

c

hnp

photon

00

secondper 2

2)(

0c

PnF is

absorption

2sin2

0

c

hnp sphoton

dt

pdF photon

pi

pf

Δpphoton

dSph

IF photon

S

incr

6

Ray optics (Mie) regime

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)

is

r Pc

nQF

0

12

a

Large particle:

dSp

h

zyxIF photon

S

incr

,,

Pi=1mW; ns=4/3 (water); Qmax=0.3 (immersion objective, glass sphere with m=1.2)

Fr,max=1.3pN

For a sphere with 2a=5μm, the value of 2πa/λ is 25 for the 632.8nm laser

30 for the 514.5nm laserSome numbers

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

0

2

00

)cos()2cos(n

nisisz nRTR

c

Pn

c

PnF

0

2

0

)sin()2sin(0n

nisy nRTR

c

PnF

As before, for one photon the momentum is

0c

hn

hp sphoton

and the photon flux in the incident ray is

hP

N ii

r

a

8

0

22

0

Re1n

niiiis eReTc

PnF

F = Fz + iFy

02

2

0 )2cos(21

)2cos()22[cos()2cos(1)(

c

PnQ

rRR

RrTR

c

PnFeF is

sis

scat

02

2

0 )2cos(21

)2sin()22[sin()2sin()(

c

PnQ

rRR

RrTR

c

PnFmF is

gis

grad

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.

(1)

(2)

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.

The best trapping is for the bigger sphere and the focus outside the sphere.

The best trapping is for the smaller waist and the focus outside the sphere.

0.5μm-radius silica sphere (m=1.09)

for different laser spots

Silica spheres (m=1.09) with different radii when the minimum beam waist is 0.4μm

10

y

Gradient, scattering and total forces as a function of the distance S’ of the trap focus from the origin along the y-axis (transversal). The transverse force is symmetric about the center of 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.

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).

Transversal forces in ray-optics regime as calculated by A. Ashkin, ( Biophys. J 61, 1992)

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

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

Cells modeled as transparent spheres

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

distributionτ<1/2 : untruncated Gaussian beam

13 Wave-optics (Rayleigh) regime

incincscatscatp

scat IaICPc

nF 46

0

Electric dipole-like (small) particle :

12

a

incgrad IaF 3

Theory applies for metallic/semiconducting particles as well, if dimension comparable to the skin depth.

Dipole polarizability:

32

22

2

1a

m

mns

Fgrad

2

2)( EB

t

pEpF

- the scattering cross-sectionscatC

Ep The dipole moment:

14

The diffraction limit in water, for an uniform irradiance, of this objective is dzero≈ 3.4μm

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.

2z trp =0.18μm

2w trp=0.24μm2w0=1.25

d4=320d1=175 d2=425 d3=1500 z=1.84

f1=-100 f2=300 f3=+160

Laser632.8nm

d5=160

fobj=+1.82

R=160

R=106

2w2=6.262w3=6.26

2wmin=5.2μm

15 MicroRaman Spectroscopy

excscatteringRamanscattered IVI

exc

4

Vscat = 8π2/3 x wtrp4 /λ ≈ 3*10-8mL

Imax = (w0/wtrp)2 I0 =5.5x108 I0

42

0

2222

3

8/12 trp

z

trptrp

z

z

scat

wdzwzwdzwV

RR

R

2

trpR

wz

20mLII 0Ramanscat

w0 =3.76mmλ =632.8nmw trp =0.16μmZ trp =0.17μm

Our numbers:Focused Gaussian beam

zR zR

2wtrp

Imax Imax /2

Vscat- scattering volume

Imax /2

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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

Screen calibrated with a 300lines/inch Ronchi ruler

Vtrap≈ 8π2/3 x wtrp4 /λ≈ 0.02μm3

Vobject ≈ 10μm3

Vobject / Vtrap ≈ 500

2z trp=0.83μm

LED2w0=0.9

d4=310d1=750 d2=850 d3=300 z=1.88

f1=100 f2=750

f3=+150

2w trp=0.27μmP=19mW

Laser632.8nm

Pinhole

CCD camerawith absorption

filters

BS

d5=160

d6=127

d7=310 Camera lens

f=55mm

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Calibrating the screen

A 5μm PS tweezed bead, in a high density solution, imaged with the

100x objective

The sample stage with white light illumination and green

laser trap

Ronchi rulers at the object plane were used

to calibrating the on-screen magnification

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

For the 100X objective,

the magnification in the image is 1162.5

Magnification:M=Δlscreen x 300/1”

14μm

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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 hoursPMMA =

polymethylmethacrylate

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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.

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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

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

in two different traps

Coated PSS in a 0.8mW trap

4.88μm PSS in a 0.8mW trap

22

Estimating the trapping force

Thmeas vvv

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

22max )( fallthmeas vvvkF

Slow, uniform motion in the fluid.Stokes viscosity, Brownian motion.

Free falling and thermal speeds

Fdrag=kv

Fmax

Ga=kvfall

vth

v

||,trapdrag FvkF

Horizontal manipulation

For 4.88μm PSS in water (0.8mW): ρ=1.05g/cm3; vmeas=22μm/s; η=10-

3Ns/m2

Fest≈2pN

Ga

vthvfall

Fdrag=kvfal

l

dksphere 3

fallv

gdk

30

exp

)(

6

1

mNskksphere /105 8exp

23 The range of secure manipulation speeds and trapping forces have been investigated for water and colloid immersed microobjects

pN

μm/s

Clusters size unit: μm

PSS = polystyrene sphereSWCN = single wall Carbon nano tubeNP =nano particle

24 Building a confocal Raman-tweezing system from scratch

M – Silver mirrorP – PinholeLLF - laser line filterBS – beam-splitterBP - broad-band polarization rotator

Spectrometer characteristics

Experimental setup

L curvature

halogen lamp

PMTobjective&sample

DM3000 system

beam expander

P4

BS

BS

Monochromator

Video cameraImaging

systemsubt. filters

P1

HeNe Laser

Ar+ LaserM1

M2, M3

P3

P2

BPR

LLF

LLF

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

Silicon wafer(n=3.88δ=3μm@633nm)

Oil immersion objective (NA=1.25)

Cover glass (n=1.525; t=150μm)

Oil layers (n=1.515)

Backward scattered Raman light

Incident laser beam

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.

Axial resolution

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Confocal microRaman spectra

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.ohio-

state.edu/~rmccreer/freqcorr/images/poly.html

Cover glass (n=1.525, t=150μm)

Aqueous solution of PS spheres (m=1.19)

Slide

Oil layer (n=1.515)

Oil immersion objective (NA=1.25)

Backward scattered Raman light

Incident laser beam

Δz≈440μm

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 Confocal scan

5mW in front of the objective; double coated interference BS

Better results than in Creely et al., Opt. Com. 245, 2005

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

Pisanici II, T.R. et al ,Nanotoxicity of iron oxide nanoparticle internalization in growing neurons, Biomaterials , 2007, 28( 16), 2572-2581

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.

0 mM 0.15 mM 15.0 mM

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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 solutionwith 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

Appendices35

36 Some useful values for biological applicationsEnergy 1 photon ( λ=1μm) 200 pNxnm

Thermal energy KBT

(room temperature) 4 pNxnm

1 ion moving across a biological membrane 30 pNxnm

Force For optical trapping 1 pNFor breaking most protein-protein interactions

20 pN

For breaking a covalent bond 1000 pN

Length Typical bacteria diameter 1 μmTypical laser wavelength for biological applications

1 μm

Trap size 0.5 μm

Time Cell division 1 minCycle 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)

for bulk samples

Present in our Raman spectra for tweezed objects

Water 984 No

1648 No

3400 No

Silane 210 Yes

290 Yes

620 Yes

960 Yes

Magnetite 676 No

Maghemite 252 ?

650 ?

740 ?

Polystyrene 1001.4 Yes

1031.8 Yes

1602.3 Yes

3054.3 Yes

38

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

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

Stability in the trap for wave regime

Surface (creeping) wave generates a gradient force

39

VCSEL arrays

2

2

)(

2

2)(

2),( zwe

zw

PzI

2

0

22

20

0

)/()( we

w

II

max

2

22

2

12

max

2

),(!

2),,( z

z

tl

l

c

tl

l ekJz

z

w

Pk

lzI

Alternate trapping beams

Hermite-Gaussian TEM00

TEM01* - doughnut (with apodization or Phase Modulator)

Bessel ( with a conical lens –axicon -)

Holographic Optical Tweezers (the hologram is reconstructed in the plane of the objective)

Laguerre-Gaussian

kt =k sinγ (γ is the wedge angle of the axicon); k=wave numberP = total power of the beamwc= asymptotic width of a certain ringzmax=diffraction-free propagation range ( consequence of finite aperture)

Bessel l=1

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.

40 Gaussian optics and propagation matrix

Beam complex q-parameter

At the minimum waist,

the beam is a plane wave (R-> ∞)

2

2

)(

2

2)(

2),( zwe

zw

PzI

beam waist

Rayleigh range

2

1)(z

zzzR R

beam radius of curvature

Paraxial approximation

r

Tr

'

'

Transfer matrix for light propagation

Calculating the beam parameter

based on the propagation matrix

41

Frèsnel coefficients

)(tan

)(tan2

2

r

rRp

)(sin

)(sin2

2

r

rRs

)(cos)(sin

)2sin()2sin(22 rr

rTp

)(sin

)2sin()2sin(2 r

rTs

Transmissivity

1 pp TR

1 ss TR

Non-magnetic medium

“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

sin

1arcsin

mr

surround

sphere

n

nm

Reflectivity

θ

mr

42

Gradient, scattering and total forces as a function of the distance S of the trap focus from the origin along the z-axis (axial). The stable equilibrium trap is located just above the center O of the sphere, at SE.

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.

Axial forces in ray-optics regimeas calculated by A. Ashkin, ( Biophys. J 61, 1992)

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

)1

(/

1

Tk

hc

Tkh

Stokes

Stokesanti BB een

n

I

I

45 Dispersion and bandwidth

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

mm

nmx6.0

mFG

10)cos([nm/mm] Dispersion

6

BANDWIDTH = (SLIT WIDTH) X DISPERSION

linear dispersion is how far apart two wavelengths are, in the focal plane: DL = dx /d

63.2nm excitation laser: the resolution is 4cm-1

46

Photon counting

Hamamatsu R943-02 PMTlower counting rate limit is set by the dark pulse rate: 20cps @ -20C 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