Optical trapping on waveguides

Olav Gaute Hellesø University of Tromsø

Norway

Outline

• Principles of waveguide propulsion

• Simulation of optical forces: Maxwell stress tensor vs. pressure

• Squeezing of red blood cells on a waveguide

• Trapping in a waveguide gap: Interference & levitation

• Phase-change due to trapped particle: S-parameters

• Summary

2

Waveguide propulsion

• Transparent microparticles are attracted by strong field gradient (evanescent field).

• Radiation pressure propels particles along the waveguide.

Fscat y

x

Fgra

d 200 nm

1.5 μm

Field distribution Top view of waveguide (Ta2O5)

3

Waveguide propulsion

• Transparent microparticles are attracted by strong field gradient (evanescent field).

• Radiation pressure propels particles along the waveguide.

z

x

Fgra

d

Fscat

200 nm

Propagating field Top view of waveguide (Ta2O5)

4

CCD camera

X-Y-Z Translation

Stage

Piezoelectric Controller

High N.A. 80X Objective lens

20X Long WD Objective Lens

Micro-chamber with cells

X-Y-Z Translation

Stage

40X Objective Lens Waveguide

Fiber Laser 5W@ 1070nm

Vaccum Suction

IR Filter

Waveguide propulsion– experimental setup

5

Waveguide propulsion – on straight waveguide

• Waveguides made of Ta2O5 (n = 2.1) • Red blood cells: 6 µm/s (in sucrose), Polystyrene microparticles: 50 µm/s,

Nanowires: > 500 µm/s !

Waveguide propulsion of red blood cells

Photon. Tech. Letters, 21, 1408, (2009)

Optics Express,18, 21053, (2010)

Optics Letters, 36, 3347–3349 (2011)

Waveguide propulsion of nanowires

6

y

x z

Simulation of optical forces with Comsol

• Define geometry

• Define mesh

• Set boundary conditions

• Find waveguide mode

• Propagate through geometry

• Find forces by integrating Maxwell’s Stress Tensor over the surface of the particle

• Memory-intensive, using e.g. 8x128 GB on a cluster

7

Simulation of optical forces with Comsol

• Forces by integrating Maxwell’s stress tensor (MST) over surface of particle:

– Comsol: emw.unTx, unTy & unTz

• Optical pressure given by field (ref. Brevik & Kluge, JOSA B, 1999): can also be integrated over surface to give force:

Fgrad

Fscat

s AM =1

4e0nw

2 nc

2

nw

2-1

æ

èç

ö

ø÷ Et

2 +nc

2

nw

2Er

2é

ëê

ù

ûú

a-

,

F = T ×n̂daSò , T ij =e

0er EiE j -

1

2dijE

2æ

èç

ö

ø÷+

1

m0

BiB j -1

2dijB

2æ

èç

ö

ø÷

Fx = s AMnx daS

ò

8

Simulation of optical forces with Comsol Force from MST vs. from optical pressure

n V/m

Zoom

Water

Thus:

• MST gives error for small index difference

• And for high???

Cause of error:

• Triangular mesh on spherical surface?

• MST subtracting large numbers?

• Error in Comsol for MST?

Polystyrene

9

Optical pressure

• Can be found from:

– The field using the expression of Brevik & Kluge, sAM

– Difference in diagonal radial components of MST on the two sides of a surface

kPa/W

Laser

Laser

10

Pressure (Pa) and direction a) From bottom, through w.g. b) Cross-section

Forces & pressure on red blood cells (RBC)

11 Analyst, 2015,140, 223-229

Force & torque on RBC

12 Analyst, 2015,140, 223-229

Squeezing of red blood cells on tapered waveguide

13 Analyst, 2015,140, 223-229

Loop with a gap: Transport & stable trapping

• On a waveguide, particles are continuously propelled forward

• Alternative: loop with intentional gap on the far side

• Particle is stably trapped in the gap by the counter-propagating fields

Laser

(a) (b)

Lab Chip, 12(18), 3436-40, 2012

Waveguide loop with a 2μm gap

14

Trapping in waveguide gap: Simulation of 2mm gap

• Symmetric about centre of

waveguide

Simulate half the problem

• Interference fringes caused by the

two counter-propagating beams

a) 3D-model

b) Field, side-view

c) Field, top-view

15 Lab Chip, 12(18), 3436-40, 2012

Trapping in waveguide gap: Simulation of 2mm gap

Horizontal and vertical

forces as sphere is

moved across gap:

Transversal and vertical

forces as sphere is

moved sideways out of

the gap:

16 Lab Chip, 12(18), 3436-40, 2012

Trapping in waveguide gap: Optical levitation?

Gap (10 μm)

Waveguide ends

Polystyrene sphere,

2 mm dia., fluorescent Water

Silica

Simulation frame

-1400

-1200

-1000

-800

-600

-400

-200

0

200

0,000 2,000 4,000 6,000 8,000 10,000

Vert

icalµf

orceµ(

fN)

Distanceµfromµwaveguideµendµ(µm)

-50

0

50

3,000 4,000 5,000 6,000 7,000

(a)

-20

-10

0

10

20

30

40

50

60

0,000 0,500 1,000 1,500 2,000 2,500 3,000 3,500 4,000Vert

ical

forc

e (fN

)Vertical position (µm)

(c)

• 2mm gap = tight trapping

• 10mm gap = levitation?

Positive values

= pushing up!

17 Optics Express, 6601-6612 (2015)

Trapping in waveguide gap: Optical levitation!

0 5 10 15 20 25−10

0

10

0 5 10 15 20 25−5

0

5

Rel

ativ

eve

rtica

ldis

plac

men

t(µm

)

Time(s)

2.17μm

Laserµoff

zµ=µ5.98μm

Rel

ativ

eµz-

posi

tionµ

(μm

)

Rel

ativ

eµve

rtica

lµpos

itionµ(μ

m)

z

In gap On waveguide Laser off, leaves gap

x

18 Optics Express, 6601-6612 (2015)

On-chip phase measurement

19

Measurement set-up:

Waveguide Young interferometer

Simulation using PMLs, input and

output ports.

Phase and transmission found from

S-parameters. Lab Chip, 2015,15, 3918-3924

On-chip phase measurement

20

Measured Simulated

Resonances!

(not measured)

Lab Chip, 2015,15, 3918-3924

Summary

• Comsol works fine to find the field around nano- and microparticles on waveguides – But memory-hungry: Up to 1TB RAM

• Optical forces: Problem with Maxwell’s stress tensor • Optical pressure: Can be combined with mechanical model? • Interference and resonances require tight sampling • Critical to avoid reflection from PML at end of waveguide • Use PML with slit port excitation for counter-propagating

beams

21

Thanks to:

• Balpreet Singh Ahluwalia, Per Jakobsen, Pål Løvhaugen, Firehun Tsige Dullo and Øystein Helle

• Waveguide fabrication at the Optoelectronics Research Centre, Southampton, UK: James Wilkinson and Ananth Subramanian (now Ghent)

• Cell work: Thomas Huser (Bielefeld), Ana Oteiza and Peter McCourt (UiT)

• Funding: Research Council of Norway

• Computer resources: Notur - The Norwegian metacenter for computational science

22

Squeezing of red blood cells on narrow waveguide

Squeezed

Cell

Laser on Laser off

Waveguide

(a) (b)

• RBCs are squeezing on waveguides < 6µm wide

• RBC regains shape when laser is switched-off

• No permanent loss of RBC elasticity was observed

3 µm ~3 µm

~6 µm

Laser On

Laser Off

(a)

(b)

Waveguide

23