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Optical forces through guided light deflections

Darwin Palima,
1,*

Andrew Rafael Bañas,
1
Gaszton Vizsnyiczai,

2
Lóránd Kelemen,

2


Thomas Aabo,
1
Pál Ormos,

2
and Jesper Glückstad

1,3


1
DTU Fotonik, Dept. of Photonics Engineering, Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark

2
Institute of Biophysics, Biological Research Centre, Hungarian Academy of Sciences, Szeged H-6701, Hungary

3
[email protected]

*
[email protected]

www.ppo.dk

Abstract: Optical trapping and manipulation typically relies on shaping

focused light to control the optical force, usually on spherical objects.

However, one can also shape the object to control the light deflection

arising from the light-matter interaction and, hence, achieve desired

optomechanical effects. In this work we look into the object shaping aspect

and its potential for controlled optical manipulation. Using a simple bent

waveguide as example, our numerical simulations show that the guided

deflection of light efficiently converts incident light momentum into optical

force with one order-of-magnitude improvement in the efficiency factor

relative to a microbead, which is comparable to the improvement expected

from orthogonal deflection with a perfect mirror. This improvement is

illustrated in proof-of-principle experiments demonstrating the optical

manipulation of two-photon polymerized waveguides. Results show that the

force on the waveguide exceeds the combined forces on spherical trapping

handles. Furthermore, it shows that static illumination can exert a constant

force on a moving structure, unlike the position-dependent forces from

harmonic potentials in conventional trapping.

© 2013 Optical Society of America

OCIS codes: (170.4520) Optical confinement and manipulation; (220.4000) Microstructure

fabrication; (230.7370) Waveguides.

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#176697 - $15.00 USD Received 21 Sep 2012; revised 22 Nov 2012; accepted 23 Nov 2012; published 7 Jan 2013
(C) 2013 OSA

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1. Introduction

Light can exert force and induce mechanical effects by exchanging momentum with matter.

This momentum exchange depends both on the spatial distribution of the illuminating light as

well as the object’s refractive index distribution. Applications of optical trapping and

manipulation rely upon controlling this exchange that, in general, will require both the control

over the light illumination [1] as well as the object shape [2]. The widespread commercial

accessibility of spatial light modulation technologies in recent years has helped channel

research activities towards light-based optimization of optical forces and torques. At the same

time, effects like ‘optical pulling force’ [3, 4], ‘stable optical lift’ [5], and optical micromotors

[6, 7] emphasize the role of the object shape for exploiting mechanical effects from optical

momentum.

#176697 - $15.00 USD Received 21 Sep 2012; revised 22 Nov 2012; accepted 23 Nov 2012; published 7 Jan 2013
(C) 2013 OSA

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Fig. 1. Simulated scattering off a circular dielectric microbead for calculating the Maxwell

stress tensor and the optical force: (a) time-averaged intensity, |E|
2
; (b) zoom-in on the

bounding box with quiver plot overlay depicting the calculated force sampled from 15 × 15
unit cells (c) snapshot of the E-field’s y-component, Ey ; (d) refractive index distribution. (λ0 =

1070 nm, nbead = 1.6, nsurrounding = 1.33)



Fig. 2. Simulated propagation of light through a bent waveguide for calculating the Maxwell
stress tensor and the optical force: (a) snapshot of the E-field’s y-component, Ey; (b) time-

averaged intensity, |E|
2
; (c) snapshot of the H-field’s x-component, Hy; (d) snapshot of the H-

field’s z-component, Hz. (λ0 = 1070 nm, nbead = 1.6, nsurrounding = 1.33).

#176697 - $15.00 USD Received 21 Sep 2012; revised 22 Nov 2012; accepted 23 Nov 2012; published 7 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 586

Page 7

The results above serves as a simple example of controlled light deflection using a

designed structure achieves an optical force exceeding that achieved when using simple

partial reflective/refractive light deflection in a microsphere. To gauge how much more we

can get with a more optimized structure for orthogonal light deflection, we also simulated the

optical force that acts on a perfectly reflecting mirror angled at 45° to deflect light

orthogonally. The simulation results, presented in Fig. 3, yield a net force,

ˆ ˆ86.98 85.62  x + zF . The corresponding transverse, axial, and net relative efficiency

factors are Qrel,x = 21.95, Qrel,Z = 21.61, Qrel,net = 30.8, respectively. The same order of

magnitude efficiency improvement, relative to a circular microbead, achieved for both the

waveguide and the perfect mirror indicates that, indeed, the waveguide serves as a good

example of optimizing the optical force using structures designed with specifications for light

deflections. Moreover, the about twice higher efficiency achieved for the perfect mirror

shows that there is still some room for optimizing the deflecting structure (e.g., minimizing

the coupling losses evident in the simulated propagation in Fig. 2).



Fig. 3. Simulated reflection off a perfect mirror for calculating the Maxwell stress tensor and
the optical force. (a) time-averaged intensity, |E|

2
; (b) zoom-in on the bounding box with

quiver plot overlay depicting the calculated force on each 15 × 15 grid unit of the simulation

(c) location of mirror (λ0 = 1070 nm, nsurrounding = 1.33) (d)–(f) snapshots of the fields Ey, Hx,
and Hz.

#176697 - $15.00 USD Received 21 Sep 2012; revised 22 Nov 2012; accepted 23 Nov 2012; published 7 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 587

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below and viewed by the sideview microscope. This time the BWS is used in its conventional

trapping mode (i.e., using balanced counterpropagating beams, λ = 1070 nm) to trap the

microstructure at the spherical handles and position it relative to the static beam and

illuminate different sites on the structure. The images obtained by the sideview microscope,

presented in Fig. 6(c), confirms the geometry depicted in Fig. 6(b), where light couples in

through the central portions of the structure where the supporting arms connect and then exit

through the spherical trapping handles. Moreover, Fig. 6(c) also illustrates that the spherical

trapping handles can effectively work as microlenses that serve to minimize the divergence of

the light coming out of the structure. In this experiment, the green beam power was

minimized to visualize the beam path without appreciably disturbing the counterpropating

NIR optical traps that hold the structure through its four spherical handles. As we anticipated,

illuminating the spherical handles with green light did not lead to waveguiding (a time-

reversal argument based on observed beam path in Fig. 6(c) requires obliquely illuminating

the spherical handle to guide light through the supporting arm).


Fig. 6. Motion of structure due to the superposition of optical forces from guided light

deflections. The horizontal arrangement of the snapshots, taken at equal time intervals using
the top-view microscope, enables using the structure’s spherical handle as the position data

point at each observation time. (a) Plot of the structure’s position vs. time shows two speeds–

the structure increases its speed when a second guided deflection occurs and forces from the
guided deflections reinforce each other. (b) Illustration of light deflection geometry having two

guided light deflections whose generated forces can reinforce each other. (c) Snapshots from

the sideview microscope experimentally illustrating the guided light deflection geometry
illustrated schematically in (b). The experiment is performed in a fluorescent medium to help

visualize the deflections of a green beam (λ = 532 nm). The structure is trapped at its spherical

handles by counterpropagating infrared beams (λ = 1070 nm) to position it relative to the green
beam and illuminate points that create guided light deflections; (d) (Media 1) Snapshot from

the topview microscope when using two linear illumination patterns for the simultaneous

optical manipulation of the two different structures used in Figs. 5 and 6(a) using line traps.

#176697 - $15.00 USD Received 21 Sep 2012; revised 22 Nov 2012; accepted 23 Nov 2012; published 7 Jan 2013
(C) 2013 OSA 14 January 2013 / Vol. 21, No. 1 / OPTICS EXPRESS 592

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Page 13

Having verified how beams can be guided through the structure, we can conclude that the

observed motion of the structure in Fig. 6(a) confirms that different guided light deflections in

the structure can generate transverse forces that reinforce each other. The structure initially

moves as the line pattern illuminates the first in-coupling site. The transverse motion brings

the structure’s second light-coupling point into the illumination region, which causes the

structure to speed up as the force from the additional guided light deflection reinforces the

initial force. This proof-of-principle demonstration shows that structures can be designed such

that different guided light deflections from the various inputs generate forces that reinforce

each other. Finally, for completeness, we also present a sample video clip, recorded using the

topview microscope as depicted in Fig. 6(a), which shows the structure being optically

manipulated using a line trap (Media 1). Moreover, this clip also demonstrates the

simultaneous optical manipulation of the two different structures used in Figs. 5 and 6(a).

Figure 6(d) shows a snapshot from the video clip.

4. Conclusions and outlook

Using a bent waveguide as an example, we have shown some of the features and promising

potential of shaping objects to create controlled light deflections and, thereby, achieve desired

optical forces. Our numerical simulations show that a simple bent waveguide can have an

order of magnitude improvement in the trapping quality factor when compared to a dielectric

microbead that intercepts an equal cross-section of the incident beam. The achieved

improvement is comparable to using a perfect mirror for orthogonal light deflection, which

highlights the improved efficiency with which shaped structures are able to utilize the

incident optical momentum flux. Our proof-of-principle experiments illustrate the possibility

of optical manipulation using shaped structures. Moreover the results display an interesting

optical manipulation modality where static illumination exerts a position-independent optical

force, along one dimension, in contrast to harmonic potential regimes in conventional optical

trapping. This “force clamp” (in analogy with the optical torque wrench [33], which can exert

controlled torque) can open the possibility for exerting programmed optical forces without the

need for sensitive position detection systems in various applications. An alternate approach

for creating a force clamp by shaping the structure (not using waveguides, but using tapered

structures) was recently published while this paper was in peer review [34]. Advanced

designs in the future, developed with further optimization and potential combination of

various structure-mediated light deflections, can create novel structures tailored towards

specific applications. One area of interest is in utilizing this idea to create optomechanical

microtools that are capable of exerting stronger forces. Another interesting application would

be to use the structures, instead of microspheres, for calibrated mechanical perturbations of

tethered biomolecules, where the extended structure can minimize illumination of the

biomolecules to avoid optical damage and where the position-independent force profile can

enable consistency in the applied force. Developing accurate force calibration methods for

shaped microstructures will be an important allied technology. One approach is to use tools

for calibrating trapped microspheres, e.g., position fluctuations due to thermal motion, but

adapt them to the more complex dynamics of shaped structures [35]. On the other hand,

emerging novel optical manipulation schemes can also demand novel calibration schemes.

Acknowledgment

This work was supported by the Danish Technical Scientific Research Council (FTP) and the

Hungarian Scientific Research Fund (OTKA-NK-72375).



#176697 - $15.00 USD Received 21 Sep 2012; revised 22 Nov 2012; accepted 23 Nov 2012; published 7 Jan 2013
(C) 2013 OSA

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