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. Top view of waveguide (Ta 2 O 5 ) x Field distribution y F scat F gra d 1.5 μm 200 nm 3
Waveguide propulsion Transparent microparticles are attracted by strong field gradient (evanescent field). Radiation pressure propels particles along the waveguide. Top view of waveguide (Ta 2 O 5 ) Propagating field x z F scat F gra d 200 nm 4
Waveguide propulsion experimental setup CCD camera Fiber Laser 5W@ 1070nm High N.A. 80X Objective lens IR Filter Waveguide 20X Long WD Objective Lens 40X Objective Micro-chamber Lens with cells Piezoelectric Controller X-Y-Z Translation Stage Vaccum Suction X-Y-Z Translation Stage 5
Waveguide propulsion on straight waveguide Waveguides made of Ta 2 O 5 (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 Waveguide propulsion of nanowires Photon. Tech. Letters, 21, 1408, (2009) Optics Express,18, 21053, (2010) Optics Letters, 36, 3347 3349 (2011) 6
Simulation of optical forces with Comsol x y z 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: F x = F = ò T n ˆ da, T = e e æ E E - 1 ij 0 r i j 2 d E ö ç 2 è ij ø + 1 æ m B B - 1 i j 2 d B ö ç 2 è ij ø 0 ò S S s AM n x da s AM = 1 4 e n æ 2 2 n c 0 w 2 n -1 öé ç E 2 t + n 2 c 2 è w ø n E ù 2 ê r ú ë w û F scat F grad a-, 8
Simulation of optical forces with Comsol Force from MST vs. from optical pressure Zoom Polystyrene n V/m 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? 9
Optical pressure Can be found from: The field using the expression of Brevik & Kluge, s AM Difference in diagonal radial components of MST on the two sides of a surface kpa/w Laser Laser 10
Forces & pressure on red blood cells (RBC) Pressure (Pa) and direction a) From bottom, through w.g. b) Cross-section Analyst, 2015,140, 223-229 11
Force & torque on RBC Analyst, 2015,140, 223-229 12
Squeezing of red blood cells on tapered waveguide Analyst, 2015,140, 223-229 13
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 (a) (b) Laser Waveguide loop with a 2μm gap Lab Chip, 12(18), 3436-40, 2012 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 Lab Chip, 12(18), 3436-40, 2012 15
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: Lab Chip, 12(18), 3436-40, 2012 16
Verticalµforceµ(fN) Vertical force (fn) Trapping in waveguide gap: Optical levitation? Simulation frame Water Waveguide ends Polystyrene sphere, 2 mm dia., fluorescent 2mm gap = tight trapping 10mm gap = levitation? Silica Gap (10 μm) (a) 200 0 0,000 2,000 4,000 6,000 8,000 10,000-200 -400 (c) 60 50 40 30 Positive values = pushing up! -600-800 50 20 10-1000 -1200-1400 0 3,000 4,000 5,000 6,000 7,000-50 Distanceµfromµwaveguideµendµ(µm) Optics Express, 6601-6612 (2015) 0 0,000 0,500 1,000 1,500 2,000 2,500 3,000 3,500 4,000-10 -20 Vertical position (µm) 17
Relativeµz-positionµ(μm) Relativeµverticalµpositionµ(μm) Relative vertical displacment(µ m) Trapping in waveguide gap: Optical levitation! On waveguide x In gap Laser off, leaves gap 10 z 5 2.17μm 0 0 zµ=µ5.98μm Laserµoff 10 0 5 10 15 Time(s) 20 25 5 Optics Express, 6601-6612 (2015) 18
On-chip phase measurement Measurement set-up: Waveguide Young interferometer Lab Chip, 2015,15, 3918-3924 Simulation using PMLs, input and output ports. Phase and transmission found from S-parameters. 19
On-chip phase measurement Simulated Measured Resonances! (not measured) Lab Chip, 2015,15, 3918-3924 20
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 RBCs are squeezing on waveguides < 6µm wide RBC regains shape when laser is switched-off No permanent loss of RBC elasticity was observed (a) Waveguide (a) (b) ~3 µm 3 µm Waveguide Squeezed Cell Laser On (b) ~6 µm Laser off Laser on Laser Off 23