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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 26 — Dec. 29, 2003
  • pp: 3562–3567
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Optical trapping of three-dimensional structures using dynamic holograms

H. Melville, G.F. Milne, G.C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin  »View Author Affiliations


Optics Express, Vol. 11, Issue 26, pp. 3562-3567 (2003)
http://dx.doi.org/10.1364/OE.11.003562


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Abstract

We demonstrate the use of a spatial light modulator (SLM) to facilitate the trapping of particles in three-dimensional structures through time-sharing. This method allows particles to be held in complex, three-dimensional configurations using cycling of simple holograms. Importantly, we discuss limiting factors inherent in current phase only SLM design for applications in both optical tweezing and atom trapping.

© 2003 Optical Society of America

1. Introduction

Holograms allow a single laser beam to be transformed into a number of independent traps. Encoding computer generated holographic patterns onto a spatial light modulator (SLM) allows us to tie this advantage with the reconfigurability and dynamic control offered by these devices. In this paper we demonstrate the use of a nematic SLM to create three-dimensional arrangements of microscopic particles through time-sharing. This technique relies on the fast update speeds of the SLM providing us with a simple, powerful and versatile method of constructing three-dimensional structures.

Sending a stream of holograms to the SLM allows us to create dynamic patterns and hence we can time-share between trap sites. This means that we can create, for example, a dual beam trap by switching between the holograms for each of the individual trap sites. If the frequency of this switching is high enough then the particle diffusion time will be too low to enable it to leave the trap site before the trapping light returns to that position. Time-sharing is a well established technique for creating arrays of trap sites, usually relying on acousto-optic deflection techniques (AOD) [7

7. G. J. Brouhard, H. T. Schek, and A. J. Hunt, “Advanced optical tweezers for the study of cellular and molecular biomechanics,” IEEE Trans. Biomed. Eng 50, 121–125 (2003), [CrossRef] [PubMed]

, 8

8. R. Nambiar and J. C. Meiners, “Fast position measurements with scanning line optical tweezers,” Opt. Lett. 27, 836–838 (2002), [CrossRef]

] to provide the beam deflection and rapid switching. The use of AODs provides the ability to trap many tens of particles since the switching time of these devices is very high (e.g., kilohertz). However, although there has been some work [9

9. A. van Blaaderen, J. P. Hoogenboom, and D. L. J. Vossen, et al., “Colloidal epitaxy: Playing with the boundary conditions of colloidal crystallization,” Faraday Discussions 123, 107–119 (2003), [CrossRef]

] using time-sharing AOD techniques to create three-dimensional structures, this has been limited to two planes created one after the other. Time-sharing with an SLM has previously been used to create multiple trap sites in two dimensions using a ferroelectric SLM [10

10. W. J. Hossack, E. Theofanidou, and J. Crain, et al., “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 11, 2053–2059 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-2053. [CrossRef] [PubMed]

]. Here the multiple bit-planes of the ferroelectric device were used to create both static and dynamic holograms simultaneously. These ferroelectric devices have relatively high refresh rates but low efficiency compared to the nematic devices used here.

Holograms can be used to produce, among other things, an array of trap sites. The holograms are calculated using the Gerchberg-Saxton (GS) algorithm [11

11. R. W. Gerchberg, “Superresolution through Error Function Extrapolation,” IEEE Trans. Acoustics Speech and Signal Processing 37, 1603–1606 (1989), [CrossRef]

13

13. L. B. Lesem, P. M. Hirsch, and J. A. Jordon, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Develop. 150–155 (1969), [CrossRef]

] as shown in [14

14. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002), [CrossRef]

]. The trap sites created by these holograms all lie in the same xy plane (the focal plane of the objective assuming the incoming light beam is collimated). We can also create a lens function[14

14. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002), [CrossRef]

], for display on the SLM, according to:

Φz(ρ¯)=2πρ2zλf2mod2π
(1)

where Φz(ρ_) is the phase modulation imposed on the beam, ρ_ denotes a radial position in the diffractive optic element’s (DOE) aperture, z is the desired displacement of the optical trap(s) relative to the focal plane in an optical train (including relay optics and objective lens) with effective focal length f and λ is the wavelength. The lens function has the effect of moving the beam focus in z, either in the positive or negative direction. Adding the lens to another hologram will therefore simply translate the generated pattern.

In this paper we demonstrate that, through the use of lensed holograms, we can create three-dimensional arrays via time-sharing. In doing so we illustrate some important issues regarding the speed and efficiency of dynamic holographic tweezers and their applications, not only for optical tweezers but also in atom optics [17

17. D. McGloin, G. C. Spalding, and H. Melville, et al., “Applications of spatial light modulators in atom optics,” Opt. Express 11, 158–166 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-158. [CrossRef] [PubMed]

].

2. Experiment

An optical tweezers setup (as shown in Fig. 1) was used for this experiment, with the laser beam expanded to fill the active area of the SLM. This allowed us to control and update the beam pattern as described previously. In order to demonstrate the accessibility of this three-dimensional trapping technique we used two different setups with two different phase only SLMs. The first SLM is a Hamamatsu PPMX8267 optimised for light of wavelength 532nm. The light from the SLM was passed into an Olympus IX71 research microscope, which acted as an inverted tweezer setup (similar to that in fig. 1 but with the objective below the sample). The second SLM is a Boulder Nonlinear Systems 5128 optimised for light of wavelength 1064nm. The light from this SLM was passed through a homemade tweezer system as shown in figure 1. The Hamamatsu SLM is optically addressed and has a 768×768 pixel display with 255 phase levels. The Boulder SLM is electrically addressed and has a 512×512 pixel display with 128 phase levels, although a non-linear response reduces the effective number of phase levels significantly. The refresh rate of the Boulder is nominally higher than the Hamamatsu, 75Hz compared to 10Hz [15

15. V. Bingelyte, J. Leach, and J. Courtial, et al., “Optically controlled three-dimensional rotation of microscopic objects,” App. Phys. Lett. 82, 829–831 (2003), [CrossRef]

].

Fig. 1. A simple optical Tweezer setup including a spatial light modulator for holographic tweezing (beam expansion optics not shown)

As outlined above we are using a time-share method to allow us to trap particles in three-dimensional configurations. The holograms are calculated for each plane and cycled. For the Hamamatsu this is done by creating an MPEG file with each frame of the movie corresponding to a plane in the structure. The computer interface used with the Boulder SLM allows us to run the images in sequence directly and at a chosen frequency.

For the experiments using the Hamamatsu SLM 2µm silica spheres suspended in a water and detergent solution were trapped. The first configuration consisted of just two particles in separate planes, as shown in Fig. 2(a). More complicated configurations were also created, as shown in Figs. 2(b) and (c).

Fig. 2. Trapping configurations demonstrated using the Hamamatsu SLM with 2µm silica spheres. (a) two particles trapped in two different planes, the out of focus particle has been lifted above the focal plane of the microscope objective. (b) a triangular pyramid with the out of focus particle again lifted above the others. (c) an inverted pyramid, this time with the central trap site lower than the other particles.

For the Boulder system 2.3µm silica spheres suspended in water were used. These were successfully trapped in configurations as shown in Fig. 3. Further to this it was possible to trap in up to six separate planes, as shown in Fig. 4.

Fig. 3. 2.3µm spheres trapped in three dimensional configurations using the Boulder SLM (a) two planes in a star of david configuration and (b) three particles in three different planes

The higher refresh rate of the Boulder SLM means that it is possible to trap in a larger number of planes than with the Hamamatsu system, as shown in Fig. 4. This should allow the creation of more complex patterns and structures. As the number of trap sites is increased the trapping potential decreases, therefore the particles move slightly between successive cycles of the holograms.

Fig. 4. Six particles trapped in six separate planes using the Boulder SLM.

The higher refresh rate of the Boulder SLM is advantageous as the number of holograms being used is increased. However, despite our Boulder SLM being rated as running at 75Hz and possibly even greater, in practice this was not the case. The results shown above (Fig. 4) were achieved at approximately 10Hz and we found that trapping in more than six planes was difficult. The reason for this is that the SLM is designed for use with light of wavelength 1064nm, therefore the liquid crystal layer is quite thick. This thickness impedes the response time of the SLM resulting in ‘clipping’, see Fig. 5. A slower refresh rate of around 10Hz is therefore the maximum frequency achievable for this SLM. If we run the SLM at higher frequencies the full phase modulation is not available, the efficiency drops and the holograms are not properly formed. This currently places severe restrictions on their use in any sort of dynamic application. Although we believe that the use of a wavelength requiring a thinner liquid crystal layer would allow a greater range of possible refresh rates, many optical tweezer experiments use near-infrared light and therefore for any such experiment requiring dynamic reconfigurability the use of SLMs is limited. This result also has implications for applications in atom optic experiments discussed in our earlier paper [17

17. D. McGloin, G. C. Spalding, and H. Melville, et al., “Applications of spatial light modulators in atom optics,” Opt. Express 11, 158–166 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-158. [CrossRef] [PubMed]

]. In this paper it is assumed that the electrically addressed SLMs will provide fast refresh rates to facilitate their use with cold atoms. The problems encountered with rise times and clipping could reduce the effectiveness of these SLMs in this field.

Fig. 5. Graphs showing the rise time of the Boulder SLM (grey) and the resultant clipping occurring at 50Hz (black).

As we might expect based on the loss of full phase modulation at high refresh rates the achievable displacement of the trap sites is decreased when we are time sharing. Using a static hologram to displace a particle in z, with the lens function, it is possible to move through a range in excess of ±8µm comfortably. Time-sharing reduces this range to only ±3µm.

3. Conclusions

Acknowledgments

D.M. is a Royal Society University Research Fellow. G.C.S. is supported by an award from the Research Corporation and by the National Science Foundation through Grant No. DMR-0216631. This work is supported by the UK’s EPSRC.

References and Links

1.

A. Ashkin, “Accelerating and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156–159 (1970), [CrossRef]

2.

A. Ashkin, J. M. Dziedzic, and J. E. Bjorkholm, et al., “Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles,” Opt. Lett. 11, 288–290 (1986), [CrossRef] [PubMed]

3.

J.-M. R. Fournier, M. M. Burns, and J. A. Golovchenko, “Writing Diffractive Structures by Optical Trapping,” Proceedings SPIE - The International Society for Optical Engineering, 2406, 101–111 (1995),

4.

P. T. Korda, G. C. Spalding, and D. G. Grier, “Evolution of a colloidal critical state in an optical pinning potential landscape,” Phys. Rev. B 66, 024504 (2002), [CrossRef]

5.

S. A. Tatarkova, W. Sibbett, and K. Dholakia, “Brownian Particle in an Optical Potential of the Washboard Type,” Phys. Rev. Lett. 91, 038101 (2003), [CrossRef] [PubMed]

6.

M. Brunner and C. Bechinger, “Phase behavior of colloidal molecular crystals on triangular light lattices,” Phys. Rev. Lett.88, art. no.-248302 (2002), [CrossRef] [PubMed]

7.

G. J. Brouhard, H. T. Schek, and A. J. Hunt, “Advanced optical tweezers for the study of cellular and molecular biomechanics,” IEEE Trans. Biomed. Eng 50, 121–125 (2003), [CrossRef] [PubMed]

8.

R. Nambiar and J. C. Meiners, “Fast position measurements with scanning line optical tweezers,” Opt. Lett. 27, 836–838 (2002), [CrossRef]

9.

A. van Blaaderen, J. P. Hoogenboom, and D. L. J. Vossen, et al., “Colloidal epitaxy: Playing with the boundary conditions of colloidal crystallization,” Faraday Discussions 123, 107–119 (2003), [CrossRef]

10.

W. J. Hossack, E. Theofanidou, and J. Crain, et al., “High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay,” Opt. Express 11, 2053–2059 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-2053. [CrossRef] [PubMed]

11.

R. W. Gerchberg, “Superresolution through Error Function Extrapolation,” IEEE Trans. Acoustics Speech and Signal Processing 37, 1603–1606 (1989), [CrossRef]

12.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972),

13.

L. B. Lesem, P. M. Hirsch, and J. A. Jordon, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Develop. 150–155 (1969), [CrossRef]

14.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169–175 (2002), [CrossRef]

15.

V. Bingelyte, J. Leach, and J. Courtial, et al., “Optically controlled three-dimensional rotation of microscopic objects,” App. Phys. Lett. 82, 829–831 (2003), [CrossRef]

16.

J. Leach, G. Sinclair, and P. Jordan, et al., “3D Manipulation of Particles into Crystal Structures using Holographic Optical Tweezers,” Opt. Express (in press),

17.

D. McGloin, G. C. Spalding, and H. Melville, et al., “Applications of spatial light modulators in atom optics,” Opt. Express 11, 158–166 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-158. [CrossRef] [PubMed]

18.

M. P. MacDonald, L. Paterson, and K. Volke-Sepulveda, et al., “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002), [CrossRef] [PubMed]

OCIS Codes
(020.7010) Atomic and molecular physics : Laser trapping
(090.1760) Holography : Computer holography
(120.5060) Instrumentation, measurement, and metrology : Phase modulation
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(230.6120) Optical devices : Spatial light modulators

ToC Category:
Research Papers

History
Original Manuscript: November 24, 2003
Revised Manuscript: December 9, 2003
Published: December 29, 2003

Citation
H. Melville, G. Milne, G. Spalding, W. Sibbett, K. Dholakia, and D. McGloin, "Optical trapping of three-dimensional structures using dynamic holograms," Opt. Express 11, 3562-3567 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-26-3562


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References

  1. A. Ashkin, "Accelerating and Trapping of Particles by Radiation Pressure," Phys. Rev. Lett. 24, 156-159 (1970). [CrossRef]
  2. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, et al., "Observation of a Single-Beam Gradient Force Optical Trap for Dielectric Particles," Opt. Lett. 11, 288-290 (1986). [CrossRef] [PubMed]
  3. J.-M. R. Fournier, M. M. Burns and J. A. Golovchenko, "Writing Diffractive Structures by Optical Trapping," Proceedings SPIE - The International Society for Optical Engineering, 2406, 101-111 (1995).
  4. P. T. Korda, G. C. Spalding and D. G. Grier, "Evolution of a colloidal critical state in an optical pinning potential landscape," Phys. Rev. B 66, 024504 (2002). [CrossRef]
  5. S. A. Tatarkova, W. Sibbett and K. Dholakia, "Brownian Particle in an Optical Potential of the Washboard Type," Phys. Rev. Lett. 91, 038101 (2003). [CrossRef] [PubMed]
  6. M. Brunner and C. Bechinger, "Phase behavior of colloidal molecular crystals on triangular light lattices," Phys. Rev. Lett. 88, art. no.-248302 (2002). [CrossRef] [PubMed]
  7. G. J. Brouhard, H. T. Schek and A. J. Hunt, "Advanced optical tweezers for the study of cellular and molecular biomechanics," IEEE Trans. Biomed. Eng 50, 121-125 (2003). [CrossRef] [PubMed]
  8. R. Nambiar and J. C. Meiners, "Fast position measurements with scanning line optical tweezers," Opt. Lett. 27, 836-838 (2002). [CrossRef]
  9. A. van Blaaderen, J. P. Hoogenboom, D. L. J. Vossen, et al., "Colloidal epitaxy: Playing with the boundary conditions of colloidal crystallization," Faraday Discussions 123, 107-119 (2003). [CrossRef]
  10. W. J. Hossack, E. Theofanidou, J. Crain, et al., "High-speed holographic optical tweezers using a ferroelectric liquid crystal microdisplay," Opt. Express 11, 2053-2059 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-2053.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-17-2053.</a> [CrossRef] [PubMed]
  11. R. W. Gerchberg, "Superresolution through Error Function Extrapolation," IEEE Trans. Acoustics Speech and Signal Processing 37, 1603-1606 (1989). [CrossRef]
  12. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).
  13. L. B. Lesem, P. M. Hirsch and J. A. Jordon, "The kinoform: a new wavefront reconstruction device," IBM J. Res. Develop. 150-155 (1969). [CrossRef]
  14. J. E. Curtis, B. A. Koss and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002). [CrossRef]
  15. V. Bingelyte, J. Leach, J. Courtial, et al., "Optically controlled three-dimensional rotation of microscopic objects," App. Phys. Lett. 82, 829-831 (2003). [CrossRef]
  16. J. Leach, G. Sinclair, P. Jordan, et al., "3D Manipulation of Particles into Crystal Structures using Holographic Optical Tweezers," Opt. Express (in press).
  17. D. McGloin, G. C. Spalding, H. Melville, et al., "Applications of spatial light modulators in atom optics," Opt. Express 11, 158-166 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-158.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-2-158.</a> [CrossRef] [PubMed]
  18. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, et al., "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002). [CrossRef] [PubMed]

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