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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 1, Iss. 5 — May. 5, 2006
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Visualization of optical binding of microparticles using a femtosecond fiber optical trap

N. K. Metzger, E. M. Wright, W. Sibbett, and K. Dholakia  »View Author Affiliations


Optics Express, Vol. 14, Issue 8, pp. 3677-3687 (2006)
http://dx.doi.org/10.1364/OE.14.003677


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Abstract

At the microscopic level, light-matter interactions can organize colloidal matter via a process known as optical binding. Optical binding refers to the creation of arrays of microparticles formed in the presence of laser fields, the inter-particle spacing being determined by the refocusing and/or scattering of the laser fields by the microparticles. In this paper we investigate one-dimensional optically bound arrays of microparticles using a femtosecond dual-beam optical fiber trap, and develop a means to visualize the field intensity distributions responsible for the optical binding using two-photon fluoresence imaging from fluorescein added to the host medium. The experimental intensity distributions are shown to be in good agreement with numerical simulations, thereby validating our new approach to visualizing the fields responsible for optical binding, and the physical model of optical binding as due to refocusing of the fields by the microparticles.

© 2006 Optical Society of America

1. Introduction

The dipole or gradient force of light is at the heart of the field of optical micromanipulation. The most important manifestation of this force is in the single beam optical trap, known commonly as “optical tweezers” [1–3

1. 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]

], which is now an established tool across a wide range of sciences [4

4. K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nano Today , 1, 18 (2006). [CrossRef]

]. It has permitted innovative studies in the biosciences, particularly in molecular motors [5

5. K. C. Neuman and S. M. Block, “Optical Trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004). [CrossRef]

]. Optical traps may be multiplexed using interferometric, acousto-optic or holographic methods to create many trap sites simultaneously [6–10

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

]. In such extended arrays of traps one typically ignores the light redistribution by the individual trapped microparticles (e.g. by scattering and/or refocusing) and the consequences for other microparticles in close proximity. However, this very interaction can lead to the phenomena of ‘optical binding’ whereby this light redistribution actually dictates the equilibrium position of each sphere in the array. Two versions of this phenomena have been observed, namely backscattering of an incident laser leading to very close (1 micron or less) arrangements of microparticles [11

11. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: Crystallization and binding in intense optical fields,” Science 249, 749–754 (1990). [CrossRef] [PubMed]

], and forward scattering of light in a counter-propagating (CP) beam geometry has resulted in another form of binding where particles are held up to ten times their diameter away from one another [12

12. S. Tatarkova, A. E. Carruthers, and K. Dholakia, “One dimensional optical bound arrays of microscopic particles,” Phys. Rev. Lett. 89, 283901 (2002). [CrossRef]

]. To date this has been backed up with qualitative modeling [13–15

13. D. McGloin, A. E. Carruthers, K. Dholakia, and E.M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004). [CrossRef]

] and an observation of bistability in the trap positions [14

14. 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]

]. In particular, this form of binding has implications for the creation of small optically trapped crystals and for co-operative studies in colloidal matter. It also presents an interesting and key challenge both from a theoretical and experimental standpoint in optical micromanipulation.

In this paper, we present data on one-dimensional arrays of microparticles in a dual-beam fiber optical trap. Our primary goal in this work is to perform an in situ visualization and analysis of the optical binding phenomena. We achieve this with the development of the first ever dual-beam fiber trap operating with a femtosecond pulse laser. The trap operates in an environment with a fluorescent dye added to the host medium. Two-photon excitation of the dye by the ultrashort pulsed trapping laser [16

16. K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, “Imaging in optical micromanipulation using two-photon excitation,” New J. Physics 6, 13 (2004). [CrossRef]

] permits us to map the light redistribution of around each trapped microparticle. We can thus observe the binding process in real time and a comparison with a numerical model is presented. To proceed, we first discuss our physical model that underpins our subsequent experimental observations.

2. Theory

Our model comprises two monochromatic laser fields of frequency ω counter-propagating along the z-axis which interact with a system of N transparent dielectric spheres of refractive-index ns , radius R , and which are immersed in a host medium of refractive-index nh . The monochromatic electric field is expressed as a sum of positive and negative frequency components as

Ert=x̂2[(ε+(r)eikz+ε(r)eikz)eiωt+c.c],
(1)

where is the unit polarization vector of the field, ε±(r⃗) are the slowly varying electric field amplitudes of the right or forward propagating (+) and left or backward propagating (-) fields, and k = nhω/c is the wave-vector of the field in the host medium. The incident fields are assumed to be collimated Gaussians at longitudinal coordinates z = 0 for the forward field and z = Df for the backward field

ε+xyz=0=εxyz=Df=4P0nhcε0πer2/w02,
(2)

where r 2 = x 2 + y 2, w 0 is the initial Gaussian spot size, P 0 is the input power in each beam, and Df is the distance between the fiber ends. It is assumed that all the spheres are contained between the beam waists within the length DfR. For the case of a single field we choose the forward propagating field envelope ε+(r⃗).

In the present work we assume that the dielectric spheres, representing the trapped microparticles, are held at fixed positions {r⃗j }, j = 1,2,...N. The dielectric spheres then provide a spatially inhomogeneous refractive-index distribution, which is of the form

n2(r)=nh2+(ns2nh2)j=1Nθ(Rrrj),
(3)

where θ(R-|r⃗ - r⃗j |) is the Heaviside step function which is unity within the sphere of radius R centered on r⃗ = r⃗j , and zero outside. Then following standard procedures [13

13. D. McGloin, A. E. Carruthers, K. Dholakia, and E.M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004). [CrossRef]

] the CP fields are found to obey the paraxial wave equations

±ε±z=i2k2ε±+ik0(n2(r)nh2)2nhε±,
(4)

where 2 = ∂2/∂x 2 + ∂2/∂y 2 is the transverse Laplacian describing beam diffraction. The paraxial wave equations (4) are to be solved subject to the boundary conditions (2), and we have done this using the split-step beam propagation method. We remark that our equations are valid in the Mie size regime where the sphere diameter is larger than the wavelength 2R > λ [1

1. 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]

]. Furthermore, in keeping with the experimental conditions considered here the refractive-index difference between the sphere and host medium is small, Δn = (ns-nh) <0.1, meaning that there is negligible backscatter from the spheres, and the scattering is dominantly in the forward direction, the so-called Mie effect [17

17. M. Born and E. Wolf, “Diffraction by a conducting sphere,” in Principles of Optics, (Cambridge University Press, Cambridge, UK, 2003). pp. 759–789.

]. More specifically, the focal length for a sphere in the small-angle approximation neglecting higher-order aberrations is f = R/ (2Δn) [18

18. J. W. Goodman, “Wave-Optics Analysis of Coherent Optical Systems,” in Introduction to Fourier Optics, (McGraw-Hill, 1996), pp. 96–125.

], and since the sphere only focuses rays that pass through it within the sphere radius R away from the axis we can introduce an effective numerical aperture for the sphere NA = sin (θmax) = R/f = 2Δn, with θmax the maximum ray deflection angle due to the sphere. Since Δn < 0.1 for the experiments and simulations presented here, the spheres act as low NA < 0.2 focusing elements that can be well treated using scalar paraxial theory. This is true since the maximum deflection angle θmax ≪ 1 due to the sphere is small, so that initial paraxial rays will remain paraxial and the incident polarization state of the field will be mainly unchanged.

In this paper, our main interest is in the field distributions involved in optical binding as opposed to the self-consistent determination of the micro particle spacing, so the positions of the sphere centers zj , j = 1,2,...N are taken as input parameters from the experiment for the cases of both optical binding or by a ‘helper’ optical tweezers with its axis aligned orthogonal to the z-axis. Since the CP fields are assumed incoherent, the total field intensity is Ifield (x,y,z) = |ε +(x,y,z)|2 + |ε -(x,y,z)|2. In the experiment the detected quantity is the two-photon fluorescence signal from the fluorescein as imaged and collected along the x-axis. The experimentally detected two-photon fluorescence signal, adapted from [19

19. J. Liu, H. Schroeder, S L. Chin, R. Li, and Z. Xu, “Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation,” Opt. Express 13, 10248–10259 (2005), http://www.opticsexpress.org/abstract.cfm?id=86467 [CrossRef] [PubMed]

], is then proportional to

Stwophoton(y,z)Ifield2xyzdx
(5)

and we use this to compare the predicted fluorescence profiles from the numerical simulations with the experimental measurements. Although our model cannot predict the absolute magnitude of the fluorescence signal, comparing the observed and numerical spatial profiles of the fluorescence provides information of the beam profiles. In what follows the calculated fluorescence intensity distributions in the (y-z) plane are shown as false color images with the maximum field strength being normalized to the color red.

3. Experiment

A dual-beam fiber optical trap was used for all experimental studies [20

20. A. Constable, J. Kim, J. Mervis, F. Zarinetchi, and M. Prentiss, “Demonstration of a fiber-optical light force trap,” Opt. Lett. 18, 1867–1869 (1993). [CrossRef] [PubMed]

]. A Titanium-Sapphire (Ti:Sa) femtosecond laser at a central wavelength of λ = 800 nm (p-polarized) with 95 fs output pulses at a repetition rate of 80 Mhz, average power ∼1 W (pulse energy of 12.5 nJ, 131 kW peak power), was used to operate the fiber trap. The light was coupled into two single mode fibers (Thorlabs 780HP for 780 to 970 nm; mode field diameter 5.0±0.5μm at 850 nm; Numerical Aperture 0.13; Attenuation <3.5 dB/km at 850nm) via a λ/2 plate and a polarizing beam splitter. The optical power emerging from each fiber could be adjusted with the neutral density filters to ensure equal field distribution of 40 mW (see Fig. 1).

Fig. 1. Fiber optical trap setup: Light at 800 nm from a Ti:Sa femtosecond laser is coupled via ND filters into fiber F1 and F2 to ensure equal power distribution. Inset shows fiber trap side view: The array is formed in the gap between the two fibers (F1 and F2) with D being the separation of the spheres and Df the fiber separation. A second helper tweezers is coupled into the observation microscope via dichroic beam splitter to hold a sphere in the beam or to initiate the array. Images were taken through the microscope via the CCD camera in front of which a lens could be flipped to achieve varying image magnification.

By choosing the optical path difference (5 cm) of the CP beams larger than the laser coherence length (calculated pulsed laser coherence length < 50 μm), standing wave effects [21

21. T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron particles,” Appl. Phys. Lett. 86, 174101 (2005). [CrossRef]

] were avoided. One fiber (F1) was mounted on a cover slip which was in a fixed positioned above the imaging setup, the second fiber (F2) was mounted on a XYZ stage and could be aligned with F1 much like in a fiber to fiber pig tailing setup of a distance between the two fiber ends (Df) of about 50 to 100 μm. A separate ytterbium fiber laser (IPG Photonics) at λ = 1070 nm was introduced into the sample chamber orthogonal to the beams creating the fiber trap. This beam was tightly focused via a microscope objective and additionally created a separate “helper” optical tweezers that permitted loading of the optically bound array [22

22. W. Singer, M. Frick, T. Haller, P. Dietl, S. Bernet, and M. Ritsch-Marte, “Combined optical tweezers and stretcher in microscopy,” in Hybrid and novel imaging and new optical instrumentation for Biomedical application,A.-C. Boccara and A. A. Oraevsky, eds., Proc. SPIE Vol. 4434, 227 (2001). [CrossRef]

].

The imaging system consisted out of a 100× long working distance microscope objective (Mitutoyo) or alternatively a 60× microscope (Newport) and a CCD camera (Watec WAT 902DM2S), which was connected to a computer with frame grabber card to capture the images. In the data presented the microscopic field of view for the 100× objective was, however, not always sufficient to get an image showing the field distribution in the array and both fiber ends at the same time. To ensure experimental data was acquired when the array center was at Df/2, and thereby assuring a centro-symmetric intensity distribution, a lens was flipped in front of the CCD camera and the power distribution readjusted via the λ/2 plate when necessary. A short pass filter was used to block out both trapping and tweezing wavelengths and solely pass the two-photon excitation light. The experiment was illuminated from above the cover slip and could be switched off to capture the two-photon images. Data analysis of these images was performed by utilizing a Lab VIEW script to determine the positions of the beads with an error of better than ±0.5 μm within a frame [14

14. 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]

]. A similar script was used obtain the line profile of the fluorescence intensity distribution as well as the experimental false color images from the grey scale two-photon image which are shown in the following graphs but are not to scale.

4. Two-photon excitation

5. Visualization of the light redistribution in optical binding

We now move on to discuss the visualization of the optical binding and its accompanying light intensity redistribution. As a first step we permitted light to solely enter one of the fibers and used the helper tweezers to hold a single microsphere (N = 1) in the path of the single laser field. We scanned this 5.17 μm silica sphere through the emerging field and compared the observed light pattern with a simulation. The movie (left side of Fig. 2) shows good agreement with the experiment and similar simulations conducted in Ref. [29

29. P. Domachuk, M. Cronin-Golomb, B. Eggleton, S. Mutzenich, G. Rosengarten, and A. Mitchell, “Application of optical trapping to beam manipulation in optofluidics,” Opt. Express 13, 7265–7275 (2005), http://www.opticsexpress.org/abstract.cfm?id=85429 [CrossRef] [PubMed]

]. When the bead is not fully centered light is diffracted away from the beam path creating a cone of low intensity light emerging from the rim of the bead, which is shown in a transverse line profile plot from a to b along the y-axis in Fig. 2 (right).

Fig. 2. [1.38MB] Diffraction pattern of a 5.17 μm silica sphere being scanned along the y-axis by an optical tweezers. The sphere position (overlaid white circle) is at approximately 50±1 μm from the beam waist. The movie shows the experimental images and the theoretical simulation. The insert on the right shows the intensity distribution along the y-axis from a to b at 8±1 μm after the sphere which has an offset from the beam axis of 3±0.5 μm (experiment: blue dots; theory: red line). Light is diffracted away from the beam path creating a valley of low intensity light.

To elucidate the influence of the refractive-index difference between the sphere and the host medium on our results we present in Fig. 3 a comparison of a single 5.17 μm diameter sphere diffracting the fiber output beam path at a distance of 54±1 μm from the beam waist for (A) Δn = ns - nh = 0.07, and (B) Δn = 0.05. (Note that for 3 μm and 5.17 μm diameter silica spheres in water and a free space wavelength of 0.8 μm, the sphere diameter is almost five and nine times the wavelength in the host medium, so we are well in the Mie size regime per our usage.)

Fig. 3. Diffraction pattern of a 5.17 μm silica sphere which is held by optical tweezers at 54±1 μm from the beam waist in a single beam, originating from the left side of images. Comparison between different refractive index mismatches Δn:
  1. Δn = 0.07. 1) On-axis intensity distribution (blue – experimental data; red – theoretical prediction). 2) Theoretical simulation of diffraction pattern, and 3) False color images of two-photon fluorescence.
  2. Δn = 0.05. 1) On-axis intensity, 2) Theoretical simulation, and 3) False color images of two-photon fluorescence.

For each example plot 1 shows a comparison of the experimental and numerical on-axis fluorescence signals (y = 0), whereas plots 2 and 3 show the numerical and experimental fluorescence profiles over the (y-z) plane, respectively (This numerical labeling of the plots is used in all subsequent plots). These results show that the higher the refractive-index difference the more the light is refocused after the sphere, as expected intuitively, and this observation is at the heart of the interpretation of how optical binding works, at least in the Mie size regime considered here. More specifically, the focusing length of the sphere in the small-angle approximation (measured from the sphere center) is f = R/(2Δn) which yields f ≈ 18 microns, in reasonable agreement with the results in Fig. 3 where a focus appears at around 70 microns (note that the slight inaccuracy of the small-angle approximation to the focal length does not imply failure of the scalar paraxial wave theory used here which accurately captures the higher-order aberrations for low NA optical elements.)

5.1 Optically bound arrays

Optical binding with CP fields arises from the fact that the net force acting on each sphere has two components deriving from the force exerted from each laser field. Considering the case of two spheres for illustration, a give sphere will experience a direct force from the field emanating from the closest laser fiber end, and a second oppositely directed force from the refocused laser field emanating from the other fiber. Balancing of these two forces is the usual explanation of how optical binding can arise, and the extension to more particles follows. Fig. 4(a) is for the example of an optically bound array of two spheres (N=2), and shows the intensity distribution profile for two 3 μm spheres with a separation of 8 μm, and very good agreement is obtained between the numerical and experimental profiles.

Fig. 4. Optically bound arrays:
  1. Array of two 3 μm spheres with a separation of 8 μm with Δn = 0.06. 1) On-axis intensity distribution showing the full waist separation of 72 μm (blue – experimental data; red – theoretical prediction). 2) Theoretical simulation of diffraction pattern in a 2 sphere array, 3) False color image of two-photon fluorescence.
  2. Same array as in A) with left propagating field blocked, and for a time such that the sphere separation is 9 μm. 2) Theoretical simulation of the diffraction pattern, 3) false color image of two-photon fluorescence beam coming from left side of picture.
  3. Array of three 3 μm spheres with a separation of 5 μm with Δn = 0.05 and a waist separation of 100 μm. 1) On-axis intensity comparison between theory and experiment which is being cut off at 60 μm. 2) and 3) theoretical and experimental images of diffraction pattern.
  4. Array of four 3 μm sphere array with a separation of 12 μm with Δn = 0.01 with a waist separation of 85 μm. 1) On-axis intensity plot, 2) Theoretical image matching, 3) experimental false color image of two-photon fluorescence with right and left hand side of beam being partly cut off.

In particular, the profiles clearly show that the intensity is refocused after the spheres, in keeping with the physical picture of optical binding. 4(b) is the same as Fig. 4(a) except the left propagating laser field has been turned off causing the particles to be propelled to the right due to imbalance of the optical forces now acting on the spheres, and for an elapsed time such that the particle spacing had increased to 9 μm. Once again, very good agreement is obtained between theory and experiment, and this example further shows that two-photon fluorescence can be used as a tool to obtain real-time monitoring of the dynamics of optically bound arrays.

To obtain binding for larger arrays the refractive-index difference needed to be lowered in order to inhibit the collapse of the array into a closed chain [12

12. S. Tatarkova, A. E. Carruthers, and K. Dholakia, “One dimensional optical bound arrays of microscopic particles,” Phys. Rev. Lett. 89, 283901 (2002). [CrossRef]

, 15

15. W. Singer, M. Frick, S. Bernet, and M. Ritsch-Marte, “Self-organized array of regularly spaced microbeads in a fiber-optical trap,” J. Opt. Soc. Am. B 20, 1568–1574 (2001). [CrossRef]

]. Qualitatively we may explain this as follows: a lower refractive-index difference subsequently causes less light being refocused by a sphere (as was shown in Fig. 3) onto its nearest neighbor in the array. For the case of 3 μm sized spheres this means that by decreasing the refocusing effect of each individual sphere, the balance of the forces from both CP fields is still maintained for a higher number of spheres N. The results in Figs. 4 (c) and 4(d) are for optically bound arrays with N=3 and N=4 particles, with excellent overall agreement seen in all cases. Fig. 4(c) shows three spheres bound in an array, and when Δn is changed to 0.05. The separation of the spheres decreased to 5 μm and did not permit the optical field to emerge further between the spheres. With a refractive-index difference of 0.01, N=4 spheres can be bound in an array whilst having a very large spacing of 12 μm, as shown in Fig. 4(d). Here the reduced refocusing effect can be clearly seen at each end of the array, where the on-axis intensity peak has significantly decreased in comparison to Figs. 4(a) or 4(c). These examples amply demonstrate that imaging of two-photon fluorescence is a reliable tool for visualizing the redistribution of intensity in optical binding of arrays, and that our model for the field propagation is valid in the Mie size regime considered here.

5.2 Optical bistability in bound matter

We have recently shown that optically bound arrays can also exhibit the phenomena of bistability due to feedback. As the sphere position influences the diffractive refocusing of the field and vice versa, this may result in more than one stable sphere separation [14

14. 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]

]. In Fig. 5(a) and (b) two such stable positions for 2.3 μm spheres are shown. Comparing both graphs shows that with a small separation the intensity peak after the light exits the array is very pronounced which indicates a high intensity and a strong optical gradient. For the large separation, those peaks have significantly decreased permitting the field intensity between the spheres to evolve.

Fig. 5. [1.31MB] On-axis intensity distribution of two 2.3 μm sphere array exhibiting bistability with a separation of a) 5 μm, and B) 16 μm with Δn = 0.065 and a waist separation of 90 μm. The respective on-axis intensity plots show a slight disagreement for a separation of 16 μm in B1) which is caused by sphere size variation within the sample batch. Respective intensity planes are shown in A2) and B2) for the simulations and A3) and B3) from the experiment. The movie shows an array of two 2.3 μm spheres having a separation of 16 μm, which are being guided to the right fiber facet. After the left propagating beam is reintroduced, they exhibit a separation of 5 μm. To get a clearer image of the spheres the microscope illumination was used, but the two-photon signal of the beam in the medium can still be observed.

6. Conclusion

In this paper, we have reported the development of a femtosecond fiber optical trap that permits the first direct visualization of the process of optical binding for micro particles, including the light distribution within an array and the light redistribution in optical guiding. A numerical model for diffraction and beam propagation has allowed a direct comparison between experiment and theory for the resultant light redistribution in these cases. It also permitted validation of the physical model and our numerical model in the Mie size regime. Visualization of the light distribution within an optically bound array confirms that diffractive refocusing of the incident light fields is the key issue for array formation. We anticipate that the two-photon imaging methods reported here will have broader use in the field of optical binding and diagnosing the physics of optical micromanipulation.

Acknowledgments

NKM would like to thank A.A. Lagatsky for his help with the autocorrelation measurement and B. Agate and D. McRobbie for their support with the Ti:Sa laser.

This work was supported by the European Commission Sixth Framework Programme - NEST ADVENTURE Activity -, through Project ATOM-3D (No. 508952) and the European Science Foundation EUROCORES Programme SONS (project NOMSAN) by funds from the UK Engineering and Physical Sciences Research Council and the EC Sixth Framework Program.

References and links

1.

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]

2.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992). [CrossRef] [PubMed]

3.

A. Ashkin, J.-M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987). [CrossRef] [PubMed]

4.

K. Dholakia and P. Reece, “Optical micromanipulation takes hold,” Nano Today , 1, 18 (2006). [CrossRef]

5.

K. C. Neuman and S. M. Block, “Optical Trapping,” Rev. Sci. Instrum. 75, 2787–2809 (2004). [CrossRef]

6.

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

7.

H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia, and D. McGloin,“Creation and manipulation of three-dimensional optically trapped structures,” Opt. Express 11, 3562 (2003), http://www.opticsexpress.org/abstract.cfm?id=78220 [CrossRef] [PubMed]

8.

J. Leach, G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. Laczik, “3D manipulation of particles into crystal structures using holographic optical tweezers,” Opt. Express 12, 220–226 (2004), http://www.opticsexpress.org/abstract.cfm?id=78450 [CrossRef] [PubMed]

9.

Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express 13, 5434–5439 (2005), http://www.opticsexpress.org/abstract.cfm?id=84909 [CrossRef] [PubMed]

10.

P. J. Rodrigo, V. R. Daria, and J. Glueckstad, “Four-dimensional optical manipulation of colloidal particles,” Appl. Phys. Lett. 86, 074103 (2005). [CrossRef]

11.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: Crystallization and binding in intense optical fields,” Science 249, 749–754 (1990). [CrossRef] [PubMed]

12.

S. Tatarkova, A. E. Carruthers, and K. Dholakia, “One dimensional optical bound arrays of microscopic particles,” Phys. Rev. Lett. 89, 283901 (2002). [CrossRef]

13.

D. McGloin, A. E. Carruthers, K. Dholakia, and E.M. Wright, “Optically bound microscopic particles in one dimension,” Phys. Rev. E 69, 021403 (2004). [CrossRef]

14.

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]

15.

W. Singer, M. Frick, S. Bernet, and M. Ritsch-Marte, “Self-organized array of regularly spaced microbeads in a fiber-optical trap,” J. Opt. Soc. Am. B 20, 1568–1574 (2001). [CrossRef]

16.

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, “Imaging in optical micromanipulation using two-photon excitation,” New J. Physics 6, 13 (2004). [CrossRef]

17.

M. Born and E. Wolf, “Diffraction by a conducting sphere,” in Principles of Optics, (Cambridge University Press, Cambridge, UK, 2003). pp. 759–789.

18.

J. W. Goodman, “Wave-Optics Analysis of Coherent Optical Systems,” in Introduction to Fourier Optics, (McGraw-Hill, 1996), pp. 96–125.

19.

J. Liu, H. Schroeder, S L. Chin, R. Li, and Z. Xu, “Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation,” Opt. Express 13, 10248–10259 (2005), http://www.opticsexpress.org/abstract.cfm?id=86467 [CrossRef] [PubMed]

20.

A. Constable, J. Kim, J. Mervis, F. Zarinetchi, and M. Prentiss, “Demonstration of a fiber-optical light force trap,” Opt. Lett. 18, 1867–1869 (1993). [CrossRef] [PubMed]

21.

T. Cizmar, V. Garces-Chavez, K. Dholakia, and P. Zemanek, “Optical conveyor belt for delivery of submicron particles,” Appl. Phys. Lett. 86, 174101 (2005). [CrossRef]

22.

W. Singer, M. Frick, T. Haller, P. Dietl, S. Bernet, and M. Ritsch-Marte, “Combined optical tweezers and stretcher in microscopy,” in Hybrid and novel imaging and new optical instrumentation for Biomedical application,A.-C. Boccara and A. A. Oraevsky, eds., Proc. SPIE Vol. 4434, 227 (2001). [CrossRef]

23.

B. Agate, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Femtosecond optical tweezers for in-situ control of two-photon fluorescence,” Opt. Express 12, 3011–3017 (2004), http://www.opticsexpress.org/abstract.cfm?id=80322 [CrossRef] [PubMed]

24.

W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1, 139–149 (1984). [CrossRef]

25.

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, London, UK, 1995).

26.

J. B. Kelman, D. A. Greenhalgh, E. Ramsay, D. Xiao, and D. T. Reid, “Flow imaging by use of femtosecond-laser induced two-photon fluorescence,” Opt. Lett. 29, 1873–1875 (2004). [CrossRef] [PubMed]

27.

W. Kaiser and C. G. B. Garret, “Two-photon excitation in CaF2:Eu2+,” Phys. Rev. Lett. 7, 229–331 (1961). [CrossRef]

28.

A. Fischer, C. Cremer, and E. H. K. Stelzer, “Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titan-sapphire laser,” Appl. Opt. 34, 1989–2003 (1995). [CrossRef] [PubMed]

29.

P. Domachuk, M. Cronin-Golomb, B. Eggleton, S. Mutzenich, G. Rosengarten, and A. Mitchell, “Application of optical trapping to beam manipulation in optofluidics,” Opt. Express 13, 7265–7275 (2005), http://www.opticsexpress.org/abstract.cfm?id=85429 [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(140.7010) Lasers and laser optics : Laser trapping
(190.4180) Nonlinear optics : Multiphoton processes

ToC Category:
Trapping

History
Original Manuscript: February 14, 2006
Revised Manuscript: April 1, 2006
Manuscript Accepted: April 2, 2006
Published: April 17, 2006

Virtual Issues
Vol. 1, Iss. 5 Virtual Journal for Biomedical Optics

Citation
N. K. Metzger, E. M. Wright, W. Sibbett, and K. Dholakia, "Visualization of optical binding of microparticles using a femtosecond fiber optical trap," Opt. Express 14, 3677-3687 (2006)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-14-8-3677


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References

  1. 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]
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  7. H. Melville, G. F. Milne, G. C. Spalding, W. Sibbett, K. Dholakia and D. McGloin,"Creation and manipulation of three-dimensional optically trapped structures," Opt. Express 11, 3562 (2003), http://www.opticsexpress.org/abstract.cfm?id=78220 [CrossRef] [PubMed]
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  9. 9. Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005), http://www.opticsexpress.org/abstract.cfm?id=84909 [CrossRef] [PubMed]
  10. P. J. Rodrigo, V. R. Daria, J. Glueckstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005). [CrossRef]
  11. M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, "Optical matter: Crystallization and binding in intense optical fields," Science 249, 749-754 (1990). [CrossRef] [PubMed]
  12. S. Tatarkova, A. E. Carruthers and K. Dholakia, "One dimensional optical bound arrays of microscopic particles," Phys. Rev. Lett. 89, 283901 (2002). [CrossRef]
  13. D. McGloin, A. E. Carruthers, K. Dholakia and E.M. Wright, "Optically bound microscopic particles in one dimension," Phys. Rev. E 69, 021403 (2004). [CrossRef]
  14. 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]
  15. W. Singer, M. Frick, S. Bernet and M. Ritsch-Marte, "Self-organized array of regularly spaced microbeads in a fiber-optical trap," J. Opt. Soc. Am. B 20, 1568-1574 (2001). [CrossRef]
  16. K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D McGloin, L. Paterson, and W. Sibbett, "Imaging in optical micromanipulation using two-photon excitation," New J. Physics 6, 13 (2004). [CrossRef]
  17. M. Born and E. Wolf, "Diffraction by a conducting sphere," in Principles of Optics, (Cambridge University Press, Cambridge, UK, 2003). pp. 759-789.
  18. J. W. Goodman, "Wave-Optics Analysis of Coherent Optical Systems," in Introduction to Fourier Optics, (McGraw-Hill, 1996), pp. 96-125.
  19. J. Liu, H. Schroeder, S L. Chin, R. Li, and Z. Xu, "Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation," Opt. Express 13, 10248-10259 (2005), http://www.opticsexpress.org/abstract.cfm?id=86467 [CrossRef] [PubMed]
  20. A. Constable, J. Kim, J. Mervis, F. Zarinetchi, and M. Prentiss, "Demonstration of a fiber-optical light force trap," Opt. Lett. 18, 1867-1869 (1993). [CrossRef] [PubMed]
  21. T. Cizmar, V. Garces-Chavez, K. Dholakia and P. Zemanek, "Optical conveyor belt for delivery of submicron particles," Appl. Phys. Lett. 86, 174101 (2005). [CrossRef]
  22. W. Singer, M. Frick, T. Haller, P. Dietl, S. Bernet and M. Ritsch-Marte, "Combined optical tweezers and stretcher in microscopy," in Hybrid and novel imaging and new optical instrumentation for Biomedical application, A.-C. Boccara, A. A. Oraevsky, eds., Proc. SPIE Vol. 4434, 227 (2001). [CrossRef]
  23. B. Agate, C. T. A. Brown, W. Sibbett and K. Dholakia, "Femtosecond optical tweezers for in-situ control of two-photon fluorescence," Opt. Express 12, 3011-3017 (2004), http://www.opticsexpress.org/abstract.cfm?id=80322 [CrossRef] [PubMed]
  24. W. J. Tomlinson, R. H. Stolen and C. V. Shank, "Compression of optical pulses chirped by self-phase modulation in fibers," J. Opt. Soc. Am. B 1, 139-149 (1984). [CrossRef]
  25. G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, London, UK, 1995).
  26. J. B. Kelman, D. A. Greenhalgh, E. Ramsay, D. Xiao, and D. T. Reid, "Flow imaging by use of femtosecond-laser induced two-photon fluorescence," Opt. Lett. 29, 1873-1875 (2004). [CrossRef] [PubMed]
  27. W. Kaiser and C. G. B. Garret, "Two-photon excitation in CaF2:Eu2+," Phys. Rev. Lett. 7, 229-331 (1961). [CrossRef]
  28. A. Fischer, C. Cremer and E. H. K. Stelzer, Fluorescence of coumarins and xanthenes after two-photon absorption with a pulsed titan-sapphire laser," Appl. Opt. 34, 1989-2003 (1995). [CrossRef] [PubMed]
  29. P. Domachuk, M. Cronin-Golomb, B. Eggleton, S. Mutzenich, G. Rosengarten and A. Mitchell, "Application of optical trapping to beam manipulation in optofluidics, " Opt. Express 13, 7265-7275 (2005), http://www.opticsexpress.org/abstract.cfm?id=85429 [CrossRef] [PubMed]

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