Integrated optomechanical microelements

doi:10.1364/OE.15.005521

Integrated optomechanical microelements

Gregor Knöner, Simon Parkin, Timo A. Nieminen, Vincent L. Y. Loke, Norman R. Heckenberg, and Halina Rubinsztein-Dunlop »View Author Affiliations

Optics Express, Vol. 15, Issue 9, pp. 5521-5530 (2007)
http://dx.doi.org/10.1364/OE.15.005521

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▸ Article Outline
– Abstract
1. Introduction
2. Optical rotation
3. Microscopic diffractive optical element (MDOE)
4. Integrated device with MDOE and rotor
5. Applications
– References and links

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Abstract

We integrate the optical elements required to generate optical orbital angular momentum into a microdevice. This allows the rotation of either naturally occuring microparticles or specially fabricated optical rotors. We use a two photon photopolymerization process to create microscopic diffractive optical elements, customized to a wavelength of choice, which are integrated with micromachines in microfluidic devices. This enables the application of high optical torques with off-the-shelf optical tweezers systems.

1. Introduction

Integrated devices consisting of optically-driven microrotors combined with microscopic diffractive optical elements (MDOEs) are a promising candidate for deployment in microfluidic and lab-on-a-chip applications. Novel lab-on-a-chip devices can perform a variety of tasks ranging from mixing microscopic amounts of reagents to natural selection on a single enzyme level [1

A. Aharoni, A. D. Griffiths, and D. S. Tawfik, “High-throughput screens and selections of enzyme-encoding genes,” Curr. Opin. Chem. Biol. 9, 210–216 (2005). [CrossRef] [PubMed]

]. Such developments require the ability to move and sort microscopic particles or droplets, mix fluids and pump small amounts of liquid. Actuation by optical means [2

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]

] can provide the required control and finesse to perform these tasks [3

S. Kulin, R. Kishore, K. Helmerson, and L. Locascio, “Optical manipulation and fusion of liposomes as microreactors,” Langmuir 19, 8206–8210 (2003). [CrossRef]

]. Of particular interest is optical rotation of particles [4

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998). [CrossRef]

], which is not only suitable for initiating mixing [5

H. Ukita and M. Kanehira, “A shuttlecock optical rotator—its design, fabrication and evaluation for a microfluidic mixer,” IEEE J. Sel. Topics Quantum Electron. 8, 111–117 (2002). [CrossRef]

] and pumping [6

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006). [CrossRef] [PubMed]

], but also for measuring optical torques [7–9

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical measurement of microscopic torques,” J. Mod. Opt. 48, 405–413 (2001).

]. However, the application of optical rotation is at present limited, on one hand, by the availability of appropriate particles for rotation, and on the other hand, by the difficulty of creating beams with the high optical angular momentum required to drive these particles. Here, we present the construction, fabrication and application of MDOEs, and their integration in devices. These elements imprint orbital angular momentum [10

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef] [PubMed]

, 11

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,”. Am. J. Phys. 64, 77–82 (1996). [CrossRef]

] on a Gaussian laser beam, and so enable the rotation of any non-absorbing non-spherical particle in even the most basic optical tweezers system. High torques are applied while 3D trapping capability is maintained. We demonstrate these features by means of a microfabricated symmetric rotor. The MDOE can easily be integrated into lab-on-a-chip devices. Since no additional optical elements are required, MDOEs will greatly facilitate the use of orbital angular momentum and make optical rotation accessible to a wider community of researchers. The implementation of MDOEs will greatly enhance the range of operations that lab-on-a-chip devices can perform.

2. Optical rotation

The application of optical rotation is still an emerging field with high potential. Regular optical tweezers systems were first primarily used to manipulate microscopic objects, but later developed into highly sensitive measuring devices elucidating basic biophysical processes, such as forces acting in molecular motors. Similarly, optical rotation is at present mainly used for actuation, but biophysical applications [12

G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Characterization of optically driven fluid stress fields with optical tweezers,” Phys. Rev. E 72, 031507 (2005). [CrossRef]

, 13

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006). [CrossRef] [PubMed]

] based on optical torque measurements [7–9

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical measurement of microscopic torques,” J. Mod. Opt. 48, 405–413 (2001).

] are emerging. Rotational actuation itself is of great interest, in particular for applications in microfluidic devices. Rotational motion can mix fluids [5

H. Ukita and M. Kanehira, “A shuttlecock optical rotator—its design, fabrication and evaluation for a microfluidic mixer,” IEEE J. Sel. Topics Quantum Electron. 8, 111–117 (2002). [CrossRef]

], pump liquids [6

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006). [CrossRef] [PubMed]

], and can potentially be used for sorting applications by redirecting particles in flows.

Optical rotation can be achieved by a variety of techniques, but most of them have serious drawbacks. The most intuitive technique is the transfer of photon spin angular momentum, corresponding to circular polarization in the wave picture. If the circular polarization is reversed (e.g. from left to right handed) by an object, the maximum possible spin angular momentum of 2h¯ per photon is transferred. Apart from this upper limit to the torque, the object has to be birefringent in order to change the beam’s polarization. Microscopic spherical birefringent vaterite particles, which can be produced in a controlled manner have already proved useful in practice [8

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004). [CrossRef] [PubMed]

]. Unfortunately, these are prone to dissolving in slightly acidic environments, which greatly limits their applicability. An alternative is to microfabricate structurally stable form-birefringent objects [14

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nature Mat. 4, 530–533 (2005). [CrossRef]

]. However, although their orientation can be precisely controlled by the polarization of the trapping beam, their use is very limited since the applied torques are at least an order of magnitude lower compared to vaterite particles, and 3D trapping of these objects is not possible. Therefore, an alternative method of applying optical torques to such particles is highly desirable—the use of orbital angular momentum (OAM) allows rotation of any non-spherical object and application of high torques. Beams with Laguerre-Gauss LG_0ℓ mode components carry ℓ h¯ per photon angular momentum and can be created by phase holograms [15

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef]

] or spatial light modulators. However, both of these methods are specialized and only see wide use in a limited community of researchers. Furthermore, the 3D trapping capability of optical tweezers is lost when higher order modes are used (e.g., ℓ = 4), limiting the applicability of such OAM-carrying beams.

3. Microscopic diffractive optical element (MDOE)

The microscopic diffractive optical element that we introduce in this paper overcomes most of these drawbacks. It operates by generating OAM in an incident beam and is thus capable of applying high torques to a wide range of objects. Even when high order modes are created, 3D trapping capability is maintained. Furthermore, the elements can be produced with standard lithography techniques and integrated into microfluidic lab-on-a-chip devices. In this way, MDOEs can be used in combination with any basic or commercial optical tweezers system to drive optical rotation.

Similar to a standard phase hologram, the MDOE induces a phase shift in an incident laser beam which is proportional to the MDOE’s thickness. The MDOE used here consists of 8 phase ramps (Fig. 1). The phase difference between rays transmitted through the top and the bottom of each ramp is 2π. Therefore, there is a total phase shift around the beam axis of 8 × 2π and LG₀₈ mode components with 8h¨ angular momentum per photon are generated. The segmentation of a 16π phase ramp into 8 × 2π phase ramps is based on the same principle as employed by the well known Fresnel lenses. Even higher order modes can be generated by increasing the number of phase ramps.

Fig. 1. Microscopic diffractive optical element produced with two-photon photopolymerization. (a) A three dimensional model of an MDOE designed to produce orbital angular momentum carrying LG₀₈ mode components when illuminated with a Gaussian laser beam. The model is the input to the automated optical system that performs the two-photon polymerization. (b) Photopolymerized MDOE immersed in water and imaged using bright-field microscopy. The diameter of the MDOE is 9μm. The phase ramps that induce the helical wave fronts of the LG₀₈ mode are clearly visible.

For rapid prototyping, we produce MDOEs by two-photon photopolymerization. MDOEs were polymerized from photo-curable resin (NOA63, Norland). Laser pulses of length < 80 fs at a wavelength of 780 nm are used to induce two photon processes to polymerize the resin, which cures at wavelengths below 400 nm with one-photon photopolymerization. The photopolymerization is carried out under an inverted microscope with a 100× 1.3 numerical aperture objective lens and a computer controlled nano-positioning stage. The control program uses bitmap stacks as an input and exposes the resin at the specified locations using a high speed shutter (Uniblitz). Unexposed resin is removed by washing in acetone. This process allows us to construct any 3D structure up to a size of 18 × 18 × 18 μm with a lateral resolution of 0.3 μm, corresponding to the smallest exposable region (voxel). The 3D model (Fig. 1(a)) used to control the photopolymerization apparatus has ramp height of 4.7 μm to create the 2π phase shift when immersed in water (n _H₂O = 1.33, n _MDOE = 1.56, wavelength λ = 1070 nm in air). The element is 8.5 μm wide and has a base for firm attachment to the cover slip on which it is fabricated. The polymerized and fixed MDOE (Fig. 1(b)) is slightly bigger and has more rounded features than the model due to the finite voxel size of the polymerization process. Even so, the difference in thickness of the phase ramps is maintained.

4. Integrated device with MDOE and rotor

We verified the functionality of the MDOE by integrating it into a closed sample chamber filled with a suspension of 2 μm polystyrene microspheres.

Three microspheres were trapped with upright optical tweezers. The Gaussian linearly polarized beam of a Nd:YAG laser (λ = 1064 nm) was focussed with a 100× 1.3 numerical aperture objective lens. The sample chamber containing the microhologram and the microsphere suspension was mounted on a nano-positioning stage. Forward scattered light was collected with a photodetector. The spheres were slightly pushed against the microscope slide so that they arranged themselves next to each other (Fig. 2(a)).

This cluster of microspheres provides an ideal test system since the simple geometry allows calculation of the viscous drag. Only 2D trapping can be used in order to maintain the arrangement of the cluster, but, as we show below, this is not a limitation of the MDOE-rotor system. This microsphere structure has enough rotational symmetry to enable smooth rotation, yet is non-spherical enough to enable OAM transfer. The structure does not rotate in a Gaussian linearly polarized laser beam. Moving the microhologram into the laser beam path immediately causes the microsphere structure to rotate (Fig. 2, supplementary movie 1). This clearly demonstrates the creation of OAM carrying mode components in the incident laser beam by the MDOE and the subsequent transfer of OAM to the microsphere structure. The experiment also demonstrates that MDOE aided optical rotation can be achieved with very simple means, i.e. by using standard microspheres and a Gaussian laser beam.

The optically applied torque and the frictional Stokes drag determine the rotation frequency of the microsphere structure. An advantage of using such a simple structure is that it can be modeled hydrodynamically. By measuring the rotation frequency and modeling the drag coefficient, the applied optical torque can be estimated. We use the finite element method to solve the Navier-Stokes equations in the low Reynolds number regime for the fluid velocities (Fig. 3). The viscous force per unit area P_i acting on the surface of the structure in coordinate direction i can be calculated from the viscous drag tensor

P_{i} = - η \sum_{k} {(\frac{\partial v_{i}}{\partial x_{k}} + \frac{\partial v_{k}}{\partial x_{i}})}_{surf} ∙ n_{k}

(1)

where v_i are the fluid velocities, x_i the coordinates, n_k the surface normals and η is the fluid viscosity. The viscous drag torque acting on the structure is obtained by integrating the force contributions over the surface of the structure. An accuracy of 0.1% in the drag torque was achieved for a single rotating sphere, for which the analytical solution is known. Further consideration was given to the increase in drag torque due to the proximity of the structure to the microscope slide. The wall effect was quantified by measuring the roll-off frequency of the thermal position fluctuations of a trapped microsphere as a function of distance to the slide. This frequency is inversely proportional to the drag coefficient at constant trap stiffness. The drag coefficient increased by a factor of 3.9 ± 1 when the sphere was touching the slide.

Fig. 2. Rotation of a microsphere structure in a beam passing through the MDOE. (a) The microsphere structure, consisting of three 2.09 μm diameter polystyrene spheres, is stationary when trapped in a linearly polarized Gaussian beam that carries no angular momentum. (b) The microsphere structure immediately starts to rotate when the MDOE is moved into the beam path. The MDOE imprints orbital angular momentum on the beam that is subsequently transferred to the microsphere structure. The position of the MDOE is marked by the black circle. (c) Rotation signal of the microsphere structure rotating at 3.3 Hz. One rotation period (marked in green) corresponds to three spikes that are very similar due to the equal size of the microspheres. Full movie (656 KB) from which (a) and (b) are taken is available in the supplementary material.

With a laser power of P = 175mW, a rotation rate of 3.3 Hz, as seen in Fig. 2(c), was achieved. From the simulated drag model and the wall correction factor, a total drag torque of (13.8 ± 3.5) × 10^-18Nm acts on the structure at this rotation rate. This must equal the optical torque τ _opt applied by the beam that passed through the MDOE. The fraction of angular momentum transferred per photon, or torque efficiency, is [8

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004). [CrossRef] [PubMed]

]

Δ σ = \frac{τ_{opt} ω}{P}

(2)

where ω is the optical frequency. It follows that we transfer an angular momentum of 0.14 h¯ per photon to the microsphere structure. The transfer efficiency of orbital angular momentum from LG modes to microsphere structures has been shown to be smaller than 10% [9

S. J. Parkin, G. Knöner, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the total optical angular momentum transfer in optical tweezers,” Opt. Express 14, 6963–6970 (2006). [CrossRef] [PubMed]

]. The MDOE generated beam must thus have carried at least 1.4h¯ per photon orbital angular momentum. This already exceeds the spin angular momentum carried by a circularly polarized beam (1 h¯ per photon), yet is still below the angular momentum of 8h¯ per photon carried by a perfect LG₀₈ mode.

Fig. 3. Finite element simulation of the fluid flow generated by the rotating microsphere structure. (a) Three dimensional representation of the finite element grid. The domain of the final simulation was larger (60μm diameter) to prevent any wall effects and the mesh structure was much finer. Simulation of the drag torque on a single sphere agreed to within 0.1% with the analytical result. (b) Equal speed contours of the fluid flow near the microsphere structure rotating at 3.3 Hz. The hydrodynamic stress tensor on the microsphere surface was calculated from the fluid velocities and the viscous drag force per unit area was found.

The MDOE used here is smaller than the beam where the beam passes through it—at present only 50% of the beam passes through it. Increasing the size of the MDOE to the width of the beam would double the angular momentum content to more than 2.8 h¯ per photon. The phase ramps of the MDOE were also of uniform height. Since the light passing through is converging, an optimised MDOE would have lower phase ramps at the edges, so that both low-angle rays in the center of the beam and high-angle rays at the edges experience the same phase change. Increased size would also allow an increase in the number of phase ramps. Doubling the size and the number of phase ramps would, if the efficiency of the MDOE remains the same, would double the angular momentum per photon, so we estimate that at least 5h¯ angular momentum per photon is achievable.

The torque of 0.14h¯ per photon on the microsphere structure is comparable to torques exerted on birefringent vaterite particles [8

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004). [CrossRef] [PubMed]

] and considerably larger than torques on form-birefringent objects (1 Hz rotation at 1 W laser power) [14

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nature Mat. 4, 530–533 (2005). [CrossRef]

]. The torques applied can be substantially increased by trapping structures that couple more efficiently to high order LG modes.

The microsphere structure was trapped two dimensionally to demonstrate that the rotation of very simple objects can be driven by the MDOE. However, unlike some other schemes, beams generated with the MDOE still maintain their 3D trapping capability while applying high torques. We show this by three dimensionally trapping a photopolymerized microrotor using a custom built inverted microscope. The Gaussian linearly polarized beam of a fiber laser (λ = 1070 nm) was again focussed with a 100× 1.3 numerical aperture objective lens. A short focal length lens was used instead of a condenser to provide access for a micromanipulator which was used to detach the photopolymerized microrotor from the substrate. Images obtained from that system show more diffraction broadening and less z-sectioning as a result.

The rotor consists of a stalk and a symmetric cross structure (Fig. 4). When trapped in a linearly polarized Gaussian beam, the stalk aligns with the beam axis and one of the cross bars aligns with the direction of polarization due to form birefringence (Fig. 4(a)). Moving the MDOE into the beam path immediately causes the rotor to rotate, as can be seen in the supplementary information movie 2. Although the trapping beam now carries high orbital angular momentum, 3D trapping is maintained and the rotor remains in the trap. The rotation signal (Fig. 4(b)) obtained by partially intersecting the forward scattered trapping light with a photodetector shows rotation at 2.6 Hz. The signature of all four arms of the rotor is visible. The rotation at that rate clearly shows that the torque due to OAM transfer exceeds the alignment torque due to form birefringence.

Finally, we have integrated the MDOE into a microchannel. The microchannel was produced with a standard soft lithography technique. A template for producing the microchannels was created by spin coating silicon wafers with SU8 photoresist. The wafers were exposed using a printed high resolution mask (20000 dots per inch) and a mask aligner. After developing the template, a PDMS cast of the microchannel structure was produced. The PDMS mold was peeled off the master wafer and access holes for the microfluidic connections were punched. The cover slip containing the microhologram was immediately attached to the mold. The geometry of the MDOE within the microfluidic device is shown in figure 5 This demonstrates the feasibility of using MDOEs in lab-on-a-chip devices to drive optical rotation.

Fig. 4. Rotation of a 3D trapped microfabricated rotor in the beam created by the MDOE. (a) Bright-field microscopy image of the trapped microrotor and the MDOE. The rotor (diameter 5.6μm) is trapped above the focal plane and is stationary whereas the MDOE is located below the focal plane. The diffraction broadening of the image is stronger since the condenser was removed to gain access for detaching the microrotor from the substrate. Full movie (601 KB) is available in the supplementary material. (b) Rotation signal of the microrotor after the MDOE was moved into the beam path. Again, rotation is driven by the orbital angular momentum that the MDOE transfers to the trapping beam. (c) Schematic representation of the microrotor trapped in a microchannel and rotating above the MDOE. MDOEs can easily be integrated into microfluidic devices where they could be used to actuate fluids for pumping and mixing or to apply optical torques for biophysical studies.

Fig. 5. The geometry of the microfluidic device into which we incorporated the MDOE is shown. The depth of the channel was approximately 0.1 mm. Other dimensions are given in the figure. The MDOE was positioned at the bottom of the channel.

5. Applications

The MDOE can be used to optically rotate non-spherical particles in a basic optical tweezers system. We have demonstrated the rotation of two very different types of objects. Rotation of biological objects, such as chloroplasts [16

S. Bayoudh, M. Mehta, H. Rubinsztein-Dunlop, N. R. Heckenberg, and C. Critchley, “Micromanipulation of chloroplasts using optical tweezers,” J. Microsc. 203, 214–222 (2001). [CrossRef] [PubMed]

] or red blood cells should easily be achievable. We believe that the MDOE offers a number of advantages over externally generating a beam carrying orbital angular momentum.

The 3D trapping capability of optical tweezers is generally lost when relatively pure LG modes of higher order are used for trapping. The reason is that high order modes have a considerable width in the focal plane with a dark spot in the center caused by the phase singularity. The resulting lower field gradient in the axial direction prevents stable 3D trapping. Two effects enable us to maintain 3D trapping in the beam created by the MDOE. First, the beam still has Gaussian mode components that come to a diffraction limited spot and support 3D trapping. Second, the trapped rotor is located in the near field of the beam diffracted by the MDOE so that the dark spot in the beam’s center has not yet fully developed.

The MDOE also provides the capability to switch rotation on and off quickly, by moving the MDOE into and out of the beam path, by normal operation of the microscope stage, without risking release of the trapped particle. Different MDOEs with opposite handedness could be used to allow rotation in either direction. For externally generated beams, such switching is possible by, for example, moving the dislocation in an off-axis phase hologram [15

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef]

] into or out of the beam, which requires the operator to leave the microscope, or by using a spatial modulator to vary the beam mode, which necessitates the availability of a spatial light modulator.

In particular, an MDOE offers a simple and low-cost method of adding rotational manipulation to essentially any optical tweezers system, including off-the-shelf system, and does not require any addition of external optical elements to the beam path.

The torques applied by MDOE generated beams are relatively high, already surpassing torques generated by form birefringence. Matching of the MDOE to the symmetry of the trapped object could increase the applied torque manifold by enhancing the coupling between the generated LG modes and the trapped object.

The chief limitation of the MDOE used in this manner is that rotation is only possible at certain positions within the sample chamber. If one is seeking to rotate particles that can be freely moved within the sample chamber by the optical trap, this is of little consequence. If, however, one wishes to rotate a probe particle near some structure or specimen that is fixed to the microscope slide, the MDOE may be of little use.

We have also shown that it possible to integrate the MDOE into, for example, a microfluidic device. This can simplify the operation of optically-driven mechanical elements in lab-on-a-chip devices. For example, Maruo and Inoue [17

S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Appl. Phys. Lett. 89, 144101 (2006). [CrossRef]

] demonstrated a micropump driven by a scanned laser beam. A similar pump could be driven by an MDOE positioned above it, using a stationary beam that could be turned on and off to switch the pump on and off. In a device such as this, the pump is in a fixed position within the device, and no disadvantage results from the fixed nature of the MDOE. A number of rotating elements could be driven, in different directions, with a single time-shared Gaussian beam being used to illuminate them in sequence. The beam could be used to trap a microparticle in the device at the same time. This ability to generate beams with either handedness of angular momentum, and at the same time have a beam with no angular momentum with a single time-shared Gaussian beam as input can add a great increase in flexibility to such an opto-mechanical-fluidic device, with little added complexity.

Finally, although beams carrying large angular momentum fluxes can be generated by an MDOE, it should be kept in mind that the transfer of angular momentum to a particle is limited by the shape and size of the particle [18

J. Courtial and M. J. Padgett, “Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle,” Opt. Commun. 173, 269–274 (2000). [CrossRef]

,19

T. A. Nieminen, S. J. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque and symmetry,” Proc. SPIE 5514, 254–263 (2004). [CrossRef]

References and links

1.	A. Aharoni, A. D. Griffiths, and D. S. Tawfik, “High-throughput screens and selections of enzyme-encoding genes,” Curr. Opin. Chem. Biol. 9, 210–216 (2005). [CrossRef] [PubMed]
2.	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]
3.	S. Kulin, R. Kishore, K. Helmerson, and L. Locascio, “Optical manipulation and fusion of liposomes as microreactors,” Langmuir 19, 8206–8210 (2003). [CrossRef]
4.	M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998). [CrossRef]
5.	H. Ukita and M. Kanehira, “A shuttlecock optical rotator—its design, fabrication and evaluation for a microfluidic mixer,” IEEE J. Sel. Topics Quantum Electron. 8, 111–117 (2002). [CrossRef]
6.	J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, “An optically driven pump for microfluidics,” Lab Chip 6, 735–739 (2006). [CrossRef] [PubMed]
7.	T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical measurement of microscopic torques,” J. Mod. Opt. 48, 405–413 (2001).
8.	A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004). [CrossRef] [PubMed]
9.	S. J. Parkin, G. Knöner, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the total optical angular momentum transfer in optical tweezers,” Opt. Express 14, 6963–6970 (2006). [CrossRef] [PubMed]
10.	L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef] [PubMed]
11.	M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,”. Am. J. Phys. 64, 77–82 (1996). [CrossRef]
12.	G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Characterization of optically driven fluid stress fields with optical tweezers,” Phys. Rev. E 72, 031507 (2005). [CrossRef]
13.	L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006). [CrossRef] [PubMed]
14.	S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, “All-optical control of microfluidic components using form birefringence,” Nature Mat. 4, 530–533 (2005). [CrossRef]
15.	N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef]
16.	S. Bayoudh, M. Mehta, H. Rubinsztein-Dunlop, N. R. Heckenberg, and C. Critchley, “Micromanipulation of chloroplasts using optical tweezers,” J. Microsc. 203, 214–222 (2001). [CrossRef] [PubMed]
17.	S. Maruo and H. Inoue, “Optically driven micropump produced by three-dimensional two-photon microfabrication,” Appl. Phys. Lett. 89, 144101 (2006). [CrossRef]
18.	J. Courtial and M. J. Padgett, “Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle,” Opt. Commun. 173, 269–274 (2000). [CrossRef]
19.	T. A. Nieminen, S. J. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque and symmetry,” Proc. SPIE 5514, 254–263 (2004). [CrossRef]

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(140.7010) Lasers and laser optics : Laser trapping
(230.3990) Optical devices : Micro-optical devices
(230.4000) Optical devices : Microstructure fabrication

ToC Category:
Trapping

History
Original Manuscript: March 9, 2007
Revised Manuscript: April 16, 2007
Manuscript Accepted: April 16, 2007
Published: April 20, 2007

Virtual Issues
Vol. 2, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Gregor Knöner, Simon Parkin, Timo A. Nieminen, Vincent L. Y. Loke, Norman R. Heckenberg, and Halina Rubinsztein-Dunlop, "Integrated optomechanical microelements," Opt. Express 15, 5521-5530 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-9-5521

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References

A. Aharoni, A. D. Griffiths, and D. S. Tawfik, "High-throughput screens and selections of enzyme-encoding genes," Curr. Opin. Chem. Biol. 9, 210-216 (2005). [CrossRef] [PubMed]
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]
S. Kulin, R. Kishore, K. Helmerson, and L. Locascio, "Optical manipulation and fusion of liposomes as microreactors," Langmuir 19, 8206-8210 (2003). [CrossRef]
M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998). [CrossRef]
H. Ukita and M. Kanehira, "A shuttlecock optical rotator—its design, fabrication and evaluation for a microfluidic mixer," IEEE J. Sel. Topics Quantum Electron. 8, 111-117 (2002). [CrossRef]
J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, "An optically driven pump for microfluidics," Lab Chip 6, 735-739 (2006). [CrossRef] [PubMed]
T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of microscopic torques," J. Mod. Opt. 48, 405-413 (2001).
A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical microrheology using rotating laser-trapped particles," Phys. Rev. Lett. 92, 198104 (2004). [CrossRef] [PubMed]
S. J. Parkin, G. Knoner, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the total optical angular momentum transfer in optical tweezers," Opt. Express 14, 6963-6970 (2006). [CrossRef] [PubMed]
L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992). [CrossRef] [PubMed]
M. Padgett, J. Arlt, N. Simpson, and L. Allen, "An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes," Am. J. Phys. 64, 77-82 (1996). [CrossRef]
G. Knoner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72, 031507 (2005). [CrossRef]
L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, "Direct measurement of torque in an optical trap and its application to double-strand DNA," Phys. Rev. Lett. 97, 058301 (2006). [CrossRef] [PubMed]
S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, "All-optical control of microfluidic components using form birefringence," Nature Mat. 4, 530-533 (2005). [CrossRef]
N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, "Generation of optical phase singularities by computer-generated holograms," Opt. Lett. 17, 221-223 (1992). [CrossRef]
S. Bayoudh, M. Mehta, H. Rubinsztein-Dunlop, N. R. Heckenberg, and C. Critchley, "Micromanipulation of chloroplasts using optical tweezers," J. Microsc. 203, 214-222 (2001). [CrossRef] [PubMed]
S. Maruo and H. Inoue, "Optically driven micropump produced by three-dimensional two-photon microfabrication," Appl. Phys. Lett. 89, 144101 (2006). [CrossRef]
J. Courtial and M. J. Padgett, "Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle," Opt. Commun. 173, 269-274 (2000). [CrossRef]
T. A. Nieminen, S. J. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical torque and symmetry," Proc. SPIE 5514, 254-263 (2004). [CrossRef]

Am. J. Phys.

M. Padgett, J. Arlt, N. Simpson, and L. Allen, "An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes," Am. J. Phys. 64, 77-82 (1996). [CrossRef]

Appl. Phys. Lett.

S. Maruo and H. Inoue, "Optically driven micropump produced by three-dimensional two-photon microfabrication," Appl. Phys. Lett. 89, 144101 (2006). [CrossRef]

Curr. Opin. Chem. Biol.

A. Aharoni, A. D. Griffiths, and D. S. Tawfik, "High-throughput screens and selections of enzyme-encoding genes," Curr. Opin. Chem. Biol. 9, 210-216 (2005). [CrossRef] [PubMed]

IEEE J. Sel. Topics Quantum Electron.

H. Ukita and M. Kanehira, "A shuttlecock optical rotator—its design, fabrication and evaluation for a microfluidic mixer," IEEE J. Sel. Topics Quantum Electron. 8, 111-117 (2002). [CrossRef]

J. Microsc.

S. Bayoudh, M. Mehta, H. Rubinsztein-Dunlop, N. R. Heckenberg, and C. Critchley, "Micromanipulation of chloroplasts using optical tweezers," J. Microsc. 203, 214-222 (2001). [CrossRef] [PubMed]

J. Mod. Opt.

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of microscopic torques," J. Mod. Opt. 48, 405-413 (2001).

Lab Chip

J. Leach, H. Mushfique, R. di Leonardo, M. Padgett, and J. Cooper, "An optically driven pump for microfluidics," Lab Chip 6, 735-739 (2006). [CrossRef] [PubMed]

Langmuir

S. Kulin, R. Kishore, K. Helmerson, and L. Locascio, "Optical manipulation and fusion of liposomes as microreactors," Langmuir 19, 8206-8210 (2003). [CrossRef]

Nature

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998). [CrossRef]

Nature Mat.

S. L. Neale, M. P. MacDonald, K. Dholakia, and T. F. Krauss, "All-optical control of microfluidic components using form birefringence," Nature Mat. 4, 530-533 (2005). [CrossRef]

Opt. Commun.

J. Courtial and M. J. Padgett, "Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle," Opt. Commun. 173, 269-274 (2000). [CrossRef]

Opt. Express

S. J. Parkin, G. Knoner, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Measurement of the total optical angular momentum transfer in optical tweezers," Opt. Express 14, 6963-6970 (2006). [CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992). [CrossRef] [PubMed]

Phys. Rev. E

G. Knoner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72, 031507 (2005). [CrossRef]

Phys. Rev. Lett.

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, "Direct measurement of torque in an optical trap and its application to double-strand DNA," Phys. Rev. Lett. 97, 058301 (2006). [CrossRef] [PubMed]
A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical microrheology using rotating laser-trapped particles," Phys. Rev. Lett. 92, 198104 (2004). [CrossRef] [PubMed]

Proc. SPIE

T. A. Nieminen, S. J. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical torque and symmetry," Proc. SPIE 5514, 254-263 (2004). [CrossRef]

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