Abstract

We discuss how information available from ray-tracing techniques can be used to calculate optical forces and torques on particles. A general ray-trace computer code is augmented with the polarization and irradiance distributions of the illumination and Fresnel surface coefficients to give a reasonably accurate prediction of interaction with large particles out of the focal plane. Calculations of trapping location versus nonuniform illumination conditions are compared with an experiment. Other example calculations include trapping a hemispherical lens and a two-particle trap.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Zemax Development Corporation, http://www.zemax.com/.
  2. Optical Research Associates, http://www.opticalres.com/.
  3. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
    [CrossRef]
  4. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
  5. P. A. M. Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
    [CrossRef]
  6. A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005).
    [CrossRef] [PubMed]
  7. T. D. Milster, “Physical optics simulation in Matlab for high-performance systems,” Opt. Rev. 10, 246-250 (2003).
    [CrossRef]
  8. H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Optics, 2001).
    [CrossRef]
  9. D. G. Flagello, T. Milster, and A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53-64 (1996).
    [CrossRef]
  10. The size and variation were specified by Bangs Laboratories Inc., Fisher, Ind.
  11. M. Lang, T. D. Milster, E. Aspnes, T. Minamitani, and G. Borek, “Investigation of micro solid immersion lens mounting systems,” Jpn. J. Appl. Phys. 46, 3737 (2007).
    [CrossRef]
  12. A. L. Birkbeck, S. Zlatanovic, M. Ozkan, and S. C. Esener, “Laser-tweezer-controlled solid immersion microscopy in microfluidic systems,” Proc. SPIE 5275, 76-84 (2004).
    [CrossRef]
  13. N. K. Metzger, K. Dholakia, and E. M. Wright, “Observation of bistability and hysteresis in optical binding of two dielectric spheres,” Phys. Rev. Lett. 96, 068102 (2006).
    [CrossRef] [PubMed]

2007 (1)

M. Lang, T. D. Milster, E. Aspnes, T. Minamitani, and G. Borek, “Investigation of micro solid immersion lens mounting systems,” Jpn. J. Appl. Phys. 46, 3737 (2007).
[CrossRef]

2006 (1)

N. K. Metzger, K. Dholakia, and E. M. Wright, “Observation of bistability and hysteresis in optical binding of two dielectric spheres,” Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

2004 (1)

A. L. Birkbeck, S. Zlatanovic, M. Ozkan, and S. C. Esener, “Laser-tweezer-controlled solid immersion microscopy in microfluidic systems,” Proc. SPIE 5275, 76-84 (2004).
[CrossRef]

2003 (1)

T. D. Milster, “Physical optics simulation in Matlab for high-performance systems,” Opt. Rev. 10, 246-250 (2003).
[CrossRef]

2000 (1)

P. A. M. Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

1996 (1)

1986 (1)

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

Ashkin, A.

Aspnes, E.

M. Lang, T. D. Milster, E. Aspnes, T. Minamitani, and G. Borek, “Investigation of micro solid immersion lens mounting systems,” Jpn. J. Appl. Phys. 46, 3737 (2007).
[CrossRef]

Birkbeck, A. L.

A. L. Birkbeck, S. Zlatanovic, M. Ozkan, and S. C. Esener, “Laser-tweezer-controlled solid immersion microscopy in microfluidic systems,” Proc. SPIE 5275, 76-84 (2004).
[CrossRef]

Bjorkholm, J. E.

Borek, G.

M. Lang, T. D. Milster, E. Aspnes, T. Minamitani, and G. Borek, “Investigation of micro solid immersion lens mounting systems,” Jpn. J. Appl. Phys. 46, 3737 (2007).
[CrossRef]

Chu, S.

Dholakia, K.

N. K. Metzger, K. Dholakia, and E. M. Wright, “Observation of bistability and hysteresis in optical binding of two dielectric spheres,” Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

Dziedzic, J. M.

Esener, S. C.

A. L. Birkbeck, S. Zlatanovic, M. Ozkan, and S. C. Esener, “Laser-tweezer-controlled solid immersion microscopy in microfluidic systems,” Proc. SPIE 5275, 76-84 (2004).
[CrossRef]

Flagello, D. G.

Lang, M.

M. Lang, T. D. Milster, E. Aspnes, T. Minamitani, and G. Borek, “Investigation of micro solid immersion lens mounting systems,” Jpn. J. Appl. Phys. 46, 3737 (2007).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Optics, 2001).
[CrossRef]

Metzger, N. K.

N. K. Metzger, K. Dholakia, and E. M. Wright, “Observation of bistability and hysteresis in optical binding of two dielectric spheres,” Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

Milster, T.

Milster, T. D.

M. Lang, T. D. Milster, E. Aspnes, T. Minamitani, and G. Borek, “Investigation of micro solid immersion lens mounting systems,” Jpn. J. Appl. Phys. 46, 3737 (2007).
[CrossRef]

T. D. Milster, “Physical optics simulation in Matlab for high-performance systems,” Opt. Rev. 10, 246-250 (2003).
[CrossRef]

Minamitani, T.

M. Lang, T. D. Milster, E. Aspnes, T. Minamitani, and G. Borek, “Investigation of micro solid immersion lens mounting systems,” Jpn. J. Appl. Phys. 46, 3737 (2007).
[CrossRef]

Neto, P. A. M.

P. A. M. Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

Nussenzveig, H. M.

P. A. M. Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

Ozkan, M.

A. L. Birkbeck, S. Zlatanovic, M. Ozkan, and S. C. Esener, “Laser-tweezer-controlled solid immersion microscopy in microfluidic systems,” Proc. SPIE 5275, 76-84 (2004).
[CrossRef]

Rohrbach, A.

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

Rosenbluth, A. E.

Wright, E. M.

N. K. Metzger, K. Dholakia, and E. M. Wright, “Observation of bistability and hysteresis in optical binding of two dielectric spheres,” Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

Zlatanovic, S.

A. L. Birkbeck, S. Zlatanovic, M. Ozkan, and S. C. Esener, “Laser-tweezer-controlled solid immersion microscopy in microfluidic systems,” Proc. SPIE 5275, 76-84 (2004).
[CrossRef]

Europhys. Lett. (1)

P. A. M. Neto and H. M. Nussenzveig, “Theory of optical tweezers,” Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

M. Lang, T. D. Milster, E. Aspnes, T. Minamitani, and G. Borek, “Investigation of micro solid immersion lens mounting systems,” Jpn. J. Appl. Phys. 46, 3737 (2007).
[CrossRef]

Opt. Lett. (1)

Opt. Rev. (1)

T. D. Milster, “Physical optics simulation in Matlab for high-performance systems,” Opt. Rev. 10, 246-250 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

N. K. Metzger, K. Dholakia, and E. M. Wright, “Observation of bistability and hysteresis in optical binding of two dielectric spheres,” Phys. Rev. Lett. 96, 068102 (2006).
[CrossRef] [PubMed]

Proc. SPIE (1)

A. L. Birkbeck, S. Zlatanovic, M. Ozkan, and S. C. Esener, “Laser-tweezer-controlled solid immersion microscopy in microfluidic systems,” Proc. SPIE 5275, 76-84 (2004).
[CrossRef]

Other (4)

H. A. Macleod, Thin Film Optical Filters, 3rd ed. (Institute of Optics, 2001).
[CrossRef]

The size and variation were specified by Bangs Laboratories Inc., Fisher, Ind.

Zemax Development Corporation, http://www.zemax.com/.

Optical Research Associates, http://www.opticalres.com/.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

One ray incident on the surface of a particle in a fluid. k ^ i , k ^ t , k ^ r , and k ^ n are unit vectors in the direction of the incident ray, the transmitted ray, the reflected ray, and the surface normal, respectively. θ i , θ t , and θ r are the incident, transmitted, and reflected angles, respectively. V is the position vector (the location where the ray intercepts the particle) measured from the center of mass of the particle. f is the force transferred to the particle from the ray’s interaction with the particle. The free-body forces are shown emanating from the center of mass. F O is the total force transferred from all the rays. Ξ is the total torque from all the rays. F E rep resents electrostatic and magnitostatic forces. F B is the force described by Brownian motion. G is the gravitational force. F K is the kinetic force from currents in the host medium. n f and n p are the indices of refraction of the fluid and the particle, respectively.

Fig. 2
Fig. 2

Force diagram on a 10 μm particle 1 μm off the optical axis. The light is incident from above with a NA of 1.13 in water and the optical axis along the z axis. The magnitudes and directions are shown by the arrows. The lighter shade arrows in the upper-half sphere show force from the rays entering the sphere, the lighter shade arrows in the lower-half sphere show the force from the rays exiting the sphere, and the large dark arrow shows the total torque. The axes are separated into the x y plane and the y z plane on the left-hand side. The plus (+) shows the location of the center of the sphere. The total force F and the total torque Ξ are indicated to the left.

Fig. 3
Fig. 3

Plot of the total optical force from a NA 1.13 beam upon a 10 μm diameter polystyrene sphere in water at different locations. The circle at the beginning of each arrow gives the position of the sphere and the length and direction of each arrow gives the magnitude and direction of the force. A sphere located at position B will experience a force up and to the left. A sphere located at position A is in a stable trapping location.

Fig. 4
Fig. 4

Experiment layout.

Fig. 5
Fig. 5

Measured trapping position of an approximately 10 μm diameter sphere versus the blocking of the pupil. Without the coverslip in the simulation, the sphere displacement quickly departs from the experimental data with increasing blocking percentage. Only with the coverslip included does the model follow the experimental data.

Fig. 6
Fig. 6

Total optical force from a NA 1.13 beam on a diamond SIL in water at different locations. The circle at the beginning of each arrow gives the position of the sphere and the length and direction of each arrow gives the magnitude and direction of the force.

Fig. 7
Fig. 7

Plot of the balanced force for two 20 μm diameter spheres in a 0.25 NA two-fiber trap with a 200 μm fiber spacing. Inset, plot of the force difference between two spheres with a medium index of refraction of 1.20.

Tables (1)

Tables Icon

Table 1 Translation and Rotation Stability Tested for SILs of Different Materials

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

k ^ r = k ^ n ( k ^ i k ^ n ) .
cos θ i = k ^ i k ^ n ,
cos θ t = k ^ t k ^ n .
E s = c s x E x + c s y E y + c s z E z ,
E p = c p x E x + c p y E y + c p z E z ,
c s x = c s y β i + c s z γ i α i ,
c s y = γ i c s z α n α i β i α n β n α i ,
c s z = { γ i 2 [ ( α n α i ) 2 + ( β n β i ) 2 + ( α i β n α n β i ) γ i 2 ] } 1 2 ,
c p x = c s y γ i c s z β i ,
c p y = c s z α i c s x γ i ,
c p z = c s x β i c s y α i .
R s = [ n f cos θ i n p cos θ t n f cos θ i + n p cos θ t ] 2 ,
R p = [ n f cos θ t n p cos θ i n f cos θ t + n p cos θ i ] 2 ,
T s = 1 R s ,
T p = 1 R p .
R = ( N i B C N i B + C ) 2 ,
( B C ) = ( j = 1 q [ cos δ j i sin δ j / η j i η j sin δ j cos δ j ] ) ( 1 η m ) ,
N s = y cos θ i ,
η p = N / cos θ i ,
N = ( n i k ) ,
δ = 2 π y d cos θ i λ ,
Φ = 1 2 c n ε 0 d A | E | 2 .
Φ s = 1 2 c n d A ε o E s 2 ,
Φ p = 1 2 c n d A ε o E p 2 .
Φ i = Φ s + Φ p .
Φ r = R s Φ s + R p Φ p
Φ t = T s Φ s + T p Φ p
f l q = [ n f Φ r c k ^ r + n p Φ t c k ^ t n f Φ i c k ^ i ] l q .
f l q = n f c [ ( R s Φ s + R p Φ p ) k ^ r + n p n f ( T s Φ s + T s Φ s ) k ^ t ( Φ s + Φ s ) k ^ i ] .
f l q = n f c [ ( k ^ r k ^ i ) ( R s Φ s + R p Φ p ) + ( k ^ t k ^ i ) ( T s Φ s + T p Φ p ) ] l q .
Φ i = Φ t ,
k ^ i = k ^ t ,
f l q = n p c [ ( k ^ r k ^ i ) ( R s Φ s + R p Φ p ) + ( k ^ t k ^ i ) ( T s Φ s + T p Φ p ) ] l q .
F O = l = 1 M x q = 1 M y f l q + l = 1 M x q = 1 M y f l q .
ξ l q = V l q × f l q ,
ξ ' l q = V l q × f l q .
Ξ = l = 1 M x q = 1 M y ξ l q + l = 1 M x q = 1 M y ξ l q .
F total = F O + G + F B + F E + F K

Metrics