Abstract

Optical trapping of airborne particles is emerging as an essential tool in applications ranging from online characterization of living cells and aerosols to particle transport and delivery. However, existing optical trapping techniques using a single laser beam can trap only transparent particles (via the radiative pressure force) or absorbing particles (via the photophoretic force), but not particles of either type—limiting the utility of trapping-enabled aerosol characterization techniques. Here, we present the first optical trapping technique capable of trapping both transparent and absorbing particles with arbitrary morphology using a single shaped laser beam. Such a general-purpose optical trapping mechanism could enable new applications such as trapping-enabled aerosol characterization with high specificity.

© 2015 Optical Society of America

The field of optical trapping developed rapidly from its first demonstration by Ashkin in the 1970s [1,2], becoming an integral tool in biological research, cold atom physics, and genetics, etc. [3,4]. Despite its widespread adoption, the first demonstration of optical trapping of an airborne particle using a single-beam gradient-force (i.e., not simply levitation) did not occur until 1997 [5], and most laser tweezer setups today are still used to trap relatively transparent particles in liquid. Trapping a particle in air using a single laser beam is more difficult than in liquid since the optical trap must overcome gravity and air turbulence. In addition, a particle in air has a higher relative refractive index than a particle in a liquid medium, which leads to a strong scattering force that tends to destabilize the trap [6]. Nonetheless, the ability to trap airborne particles is crucial for particle transport and delivery applications [710] as well as emerging aerosol characterization systems that combine optical trapping with interrogation techniques such as Raman spectroscopy [6,11,12]. As a result, there has been a surge of research in recent years developing new techniques to trap airborne particles using either the radiative pressure force or the photophoretic force.

The radiative pressure force generated by a single laser beam, including the gradient force and the scattering force, results from the transfer of momentum from photons to a particle. Despite the success of optical tweezers in manipulating particles in liquid, radiative pressure-based optical traps using a single laser beam are poorly suited for trapping airborne particles. The challenge involved can be understood by considering the radiative pressure force as a combination of a gradient force and a scattering force. If we consider a particle near the focus of a laser beam, the gradient force will pull the particle toward the high-intensity region at the focus, providing the restoring force required to trap a particle. On the other hand, the scattering force tends to push the particle in the direction of light propagation and does not provide the required restoring force. Roughly speaking, optical trapping is possible when the gradient force overcomes the scattering force [5,13]. The challenge when trapping airborne particles arises because the high refractive-index of a particle in air relative to the surrounding medium leads to a strong scattering force. As a result, high numerical aperture (NA) optics (typically >0.9) are required to produce a strong enough gradient force to trap airborne particles [5,13]. Although the scattering force can in principle be canceled out by using a counter-propagating beam configuration [1315], this requires precise alignment and is impractical in many applications.

Trapping absorbing airborne particles is possible using the photophoretic force. If a laser beam impinges on an absorbing particle, some of the light will be absorbed and converted to heat. The photophoretic force then results from the interaction between a nonuniformly heated or nonuniformly heat-emitting particle and the surrounding gas molecules. For example, if a strongly absorbing particle is illuminated from one side, then gas molecules on the higher temperature side of the particle will have higher velocities due to collisions with the hot side of the particle, imposing a net force pushing the particle toward its cold side. For a strongly absorbing particle, this photophoretic force can be 4 to 5 orders of magnitude stronger than the gradient force typically used in optical tweezers [16]. Recently, several methods have been proposed to enable optical trapping of absorbing airborne particles using the photophoretic force, including vortex beams [9,17], hollow cones formed by a single beam [12,18], or two counter-propagating beams [19], tapered rings [20], optical lattices [21], bottle beams [22], and even speckle fields [23]. In each of these techniques, the particles are trapped in a low intensity region—the opposite of what occurs in laser tweezers where the gradient force is used to trap particles near the high-intensity focal spot of a laser beam.

As a result of these distinct trapping mechanisms, existing optical traps are designed for either absorbing or transparent particles, but a single trap capable of capturing particles of either type has not been demonstrated to our knowledge. The particle morphology introduces additional complications, since many photophoretic traps work only for particles with a given geometry [7,24,25]. However, many applications require the ability to trap particles regardless of their morphology and absorptivity. In this work, we present a technique that enables absorbing or transparent particles to be trapped using a fixed optical geometry. The key to our technique is the use of a single shaped laser beam to produce a low-light-intensity region for photophoretic trapping of absorbing particles while simultaneously reducing the scattering force near the focal spot, thereby enabling radiative pressure-based trapping of transparent particles. In addition, this reduced scattering force enables radiative pressure-based trapping of airborne particles using relatively low NA optics (0.55 for a particle with a refractive index of 1.5). A similar approach was recently proposed to enable optical trapping of nonabsorbing particles with a high relative refractive index and applied to trap droplets in air [26,27]. However, to our knowledge, this approach has not been used to experimentally trap high refractive index solid particles in air, or shown to operate simultaneously as a photophoretic trap. Below, we present numerical modeling to illustrate the advantage of the proposed optical trap and then experimentally demonstrate trapping of both absorbing and transparent particles with either spherical or spatially irregular morphologies.

The optical trapping geometry is shown schematically in Fig. 1(a). We used a continuous wave (CW) Ar-ion laser operating at λ=488nm with an output power 750mW. A tunable iris is used to adjust the diameter of an expanded laser beam, which then passes through two axicon lenses to form a hollow beam with a ring-shaped transverse cross-section. The axicon lenses were chosen such that the outer diameter of the hollow beam matches the diameter of the focusing aspheric lens (diameter=24mm, focal length=18mm). As indicated by the light blue rays in Fig. 1(a), the inner diameter of the ring can be controlled by adjusting the iris diameter: as the iris is closed, the ring width becomes narrower. The hollow beam is then focused to a spot after passing through an aspheric lens with NA=0.55. The focal spot is formed within a glass containment cell to minimize air turbulence near the trapping region. The optical trapping geometry can then be described by the outer NA (NAo=nsinαo), which is fixed by the aspheric lens at 0.55, and the inner NA (NAi=nsinαi), which can be continuously adjusted using the iris. The importance of adjusting the inner NA will be discussed below. The numerically calculated intensity profile near the focal position is shown in Fig. 1(b) on a log-scale for NAo=0.6 and NAi=0.55 at λ=488nm. Figure 1(c) contains a photograph of the hollow optical cone obtained using a long exposure time while introducing a large quantity of Johnson Smut Grass Spores into the glass containment cell. After the particles settle, a single spore remains trapped near the focal spot, as shown in Fig. 1(d). The spores are strongly absorbing and thus the dominant force is photophoretic, and the particle is trapped in the low-intensity region just above the focal point, similar to the photophoretic trap presented in Refs. [19,25]. Although the hollow cone does not provide a full 3D optical potential to trap particles via the photophoretic force, a stable trap is formed in combination with the gravitational force that pushes the particles back toward the focal point of the cone [25]. We also note that photophoretic trapping has been reported in the high-intensity region of a single focused beam [10,28]. This type of trap was explained to rely on the accommodation force that is highly particle dependent; nonetheless, some absorbing particles could be trapped in the high-intensity region of the hollow beam used here.

 figure: Fig. 1.

Fig. 1. (a) Schematic of the optical trapping apparatus. The diameter of an expanded laser beam is controlled with a tunable iris before passing through two axicons to form a collimated hollow beam. The aspheric lens forms a hollow conical focus within a glass chamber where airborne particles are trapped. By adjusting the beam size before the axicon lenses with the iris, the size of the hollow region can be adjusted, as indicated by the light blue regions. (b) Calculated intensity profile near the focal spot plotted on a log-scale. (c) Image of the conical focal region produced inside the chamber obtained by introducing Johnson Smut Grass Spores and recording a long exposure time image. (d) Image of a spore trapped in air near the focal point.

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The trapping geometry shown in Fig. 1 can also be used to trap transparent particles. To optimize the trap for transparent particles, we performed numerical simulations of the trapping force acting on a particle in the hollow cone geometry. The simulations were performed using the Optical Tweezers Toolbox [29,30] assuming spherical particles in air with a diameter of 10λ. In Fig. 2(a), we first present the optical trapping force along the optical axis experienced by a particle with refractive index of 1.5. The trapping efficiency is expressed by the dimensionless quantity Qz, which is related to the actual force acting on the particle as Fz=QzPn/c, where P is the incident laser power, n is the refractive index of the particle, and c is the speed of light [30]. The blue dotted line shows the force experienced using the full lens as in a standard single-beam gradient trap [5] (i.e., without the axicons shown in Fig. 1), and the solid red line shows the force experienced using the ring illumination geometry shown in Fig. 1. In both cases, the outer NA is set to 0.6, while for the ring geometry the inner NA is set to 0.55. The trapping force is presented as a function of position along the optical axis z, and the focus is set at z=0. In both cases, a positive force acts on the particles at negative z positions (i.e., before the focus), which will push a particle that drifts in the negative z direction toward the focus. In order to achieve optical trapping, a negative restoring force is also required at positive values of z to pull particles that drift in the positive z direction back toward the focus. Without a negative Qz, optical levitation may still be possible by balancing the gravitational force, but levitation-based traps are typically less stable [13] and are strongly dependent on the particle size and optical power [26]. As shown in Fig. 2(a), a negative Qz is achieved using the ring geometry, but not using the full lens. This can be understood as a trade-off between the scattering force and the gradient force. In a single beam geometry, a very high NA is required to obtain a gradient force that is stronger than the scattering force. For this reason, single-beam optical trapping geometries typically require very high NA (>0.9) optics. In the ring geometry, we removed the center of the beam where the direction of propagation is most aligned with the z axis, thus reducing the momentum of incident light along the z direction. This effectively reduces the scattering force along the optical axis such that the gradient force is sufficient to achieve optical trapping at a much lower outer NA.

 figure: Fig. 2.

Fig. 2. (a) The trapping efficiency, Qz, experienced by a particle along the optical axis using either a full lens of NA=0.6 or the ring geometry shown in Fig. 1. Optical trapping is possible if Qz becomes negative at some position, providing the required restoring force. Due to the relatively high index of the particle, the standard laser tweezers approach (“full lens”) is not able to trap the particle, whereas the ring geometry provides the required negative restoring force. (b) The minimum of Qz is shown for the ring geometry as a function of the inner and outer NA. The black line corresponds to Qz=0, and trapping is possible for combinations of inner and outer NA to the right of the line. (c), (d) The minimum of Qz is shown using a full lens (c) or the ring geometry (d) as a function of the refractive index of the particle and the outer NA. The white contour lines correspond to Qz=0, and trapping is possible when the minimum force is negative. Experimentally, we trapped particles with index 1.5 using an outer NA of 0.55 in the ring geometry, corresponding to the position indicated by the black “×.”

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To optimize the optical trapping geometry, we then calculated the minimum value of Qz, experienced by a particle with a diameter of 10λ and refractive index of 1.5 using the ring geometry as a function of the inner and outer NA, as shown in Fig. 2(b). Optical trapping is possible when the minimum of Qz is negative. The black contour line indicates Qz=0 and combinations of outer and inner NA that allow for optical trapping are indicated as the “trapping regime.” We found that for a relatively narrow ring (i.e., where the inner NA is only slightly less than the outer NA), optical trapping is possible for an outer NA as low as 0.55. To illustrate the advantage of using the ring geometry as opposed to the “full lens” approach taken in standard laser tweezers, we then simulated the minimum trapping force as a function of the outer NA and the refractive index of the particle. Figure 2(c) shows the minimum trapping force obtained using the full lens and Fig. 2(d) shows the minimum trapping force obtained using the ring geometry with NAi=NAo0.05. In both cases, the solid white contour line indicates Qz=0, and trapping is possible to the right of the contour line. The oscillations as a function of refractive index are due to Mie resonances [27]. Nonetheless, Figs. 2(c) and 2(d) clearly show that optical trapping is possible using a much lower NA with the ring geometry, an advantage that is particularly pronounced when trapping relatively high index particles. The parameters of the particles trapped experimentally are indicated by a black “×” in Figs. 2(c) and 2(d), showing that trapping particles with index 1.5 using a lens with NA=0.55 is only possible using the ring geometry.

Based on the numerical simulations presented in Fig. 2(b), we experimentally adjusted the iris to provide the optimal inner NA of 0.5 given the 0.55 outer NA of our aspheric lens. We then experimentally demonstrated optical trapping of four classes of airborne particles: absorbing and nonabsorbing particles as well as particles with spherical and spatially irregular morphology. We used 3–9 μm diameter glass beads as an example of a nonabsorbing, spherical particle; 1–10 μm diameter bovine albumin particles as an example of a nonabsorbing, spatially irregular particle; 6-μm-diameter fluorescent polymer spheres as an example of an absorbing, spherical particle; and 6.2–9.8 μm diameter Johnson smut grass spores as an example of an absorbing, spatially irregular particle. The camera position and trapping optics were fixed while particles of each type were trapped and imaged. Representative images of a trapped particle of each type are shown in Fig. 3. The transparent yellow lines overlaid on the images in Fig. 3 were extracted from a long exposure time image [similar to the image shown in Fig. 1(c)], which we used to identify the focal position of the hollow cone. However, since the glass chamber was removed and cleaned after testing each particle type, the precise position of the focal spot changed slightly, and the yellow lines provide only an approximation of the focal position. Nonetheless, particles of each type were found to be trapped near the focal spot. The absorbing particles (the spores in particular) were also trapped in additional positions along the cone walls, similar to the observation in Ref. [31]. Moreover, the precise height (z-position) of the trapped particles varied slightly depending on the size, shape, and absorptivity of the particle and the laser power. Nonetheless, since particles of each type were trapped along the optical axis, this trapping technique could be combined with interrogation techniques such as Raman or fluorescence spectroscopy by imaging the optical axis to the entrance slit of a spectrometer and integrating the spectrum along the z-axis [11].

 figure: Fig. 3.

Fig. 3. Optical trapping is demonstrated for four classes of particles, described by the particle shape (spherical or spatially irregular) and material type (absorbing or nonabsorbing). The images show an example of a trapped particle of each type. The yellow lines indicate the approximate position of the focal cone, extracted from an image similar to the one shown in Fig. 1(c). Particles of each type are trapped along the optical axis near the focal position.

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In summary, a general purpose optical trapping technique was presented. The optical trap consists of a single hollow cone focused with relatively low NA optics from a single shaped laser beam. The use of a single beam enables simple alignment, while the ability to use relatively low NA optics will allow easy integration with additional optical characterization components. Numerical simulations were used to guide the design of the hollow cone in order to enable efficient trapping of nonabsorbing (transparent) particles. We experimentally demonstrated stable optical trapping of four types of particles: absorbing and nonabsorbing particles with either spherical or spatially irregular shapes using the fixed optical geometry. Such a general purpose optical trapping scheme could improve the versatility of laser trapping systems designed for airborne particles, and enable extensive online characterization of aerosols when coupled with particle interrogation techniques.

FUNDING INFORMATION

Defense Threat Reduction Agency (DTRA) (HDTRA1310184, HDTRA1514122); US Army Research Laboratory (W911NF-12-2-0019).

We thank Steven Hill, Chuji Wang, Yongqing Li, and Yaron Bromberg for useful discussions.

References

1. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970). [CrossRef]  

2. A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971). [CrossRef]  

3. A. Ashkin and J. M. Dziedzic, Science 235, 1517 (1987). [CrossRef]  

4. K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004). [CrossRef]  

5. R. Omori, T. Kobayashi, and A. Suzuki, Opt. Lett. 22, 816 (1997). [CrossRef]  

6. J. B. Wills, K. J. Knox, and J. P. Reid, Chem. Phys. Lett. 481, 153 (2009). [CrossRef]  

7. V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, Nat. Photonics 8, 846 (2014). [CrossRef]  

8. V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010). [CrossRef]  

9. V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, Opt. Express 17, 5743 (2009). [CrossRef]  

10. J. Lin and Y. Li, Appl. Phys. Lett. 104, 101909 (2014). [CrossRef]  

11. Y.-L. Pan, S. C. Hill, and M. Coleman, Opt. Express 20, 5325 (2012). [CrossRef]  

12. C. Wang, Y.-L. Pan, S. C. Hill, and B. Redding, J. Quant. Spectrosc. Radiat. Transfer 153, 4 (2015). [CrossRef]  

13. T. Li, Fundamental Tests of Physics with Optically Trapped Microspheres (Springer, 2013).

14. G. Roosen and C. Imbert, Phys. Lett. A 59, 6 (1976). [CrossRef]  

15. M. Guillon, O. Moine, and B. Stout, Phys. Rev. Lett. 96, 143902 (2006). [CrossRef]  

16. M. Lewittes, S. Arnold, and G. Oster, Appl. Phys. Lett. 40, 455 (1982). [CrossRef]  

17. A. S. Desyatnikov, V. G. Shvedov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, Opt. Express 17, 8201 (2009). [CrossRef]  

18. K. T. Gahagan and G. a. Swartzlander, Opt. Lett. 21, 827 (1996). [CrossRef]  

19. Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014). [CrossRef]  

20. F. Liu, Z. Zhang, Y. Wei, Q. Zhang, T. Cheng, and X. Wu, Opt. Express 22, 23716 (2014). [CrossRef]  

21. V. G. Shvedov, C. Hnatovsky, N. Shostka, A. V. Rode, and W. Krolikowski, Opt. Lett. 37, 1934 (2012). [CrossRef]  

22. P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 1491 (2011). [CrossRef]  

23. V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 18, 3137 (2010). [CrossRef]  

24. J. Lin, A. G. Hart, and Y.-Q. Li, Appl. Phys. Lett. 106, 171906 (2015). [CrossRef]  

25. B. Redding, S. C. Hill, D. Alexson, C. Wang, and Y.-L. Pan, Opt. Express 23, 3630 (2015). [CrossRef]  

26. D. R. Burnham and D. McGloin, J. Opt. Soc. Am. B 28, 2856 (2011). [CrossRef]  

27. R. D. Dear, D. R. Burnham, M. D. Summers, D. McGloin, and G. A. D. Ritchie, Phys. Chem. Chem. Phys. 14, 15826 (2012). [CrossRef]  

28. Z. Zhang, D. Cannan, J. Liu, P. Zhang, D. N. Christodoulides, and Z. Chen, Opt. Express 20, 16212 (2012). [CrossRef]  

29. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007). [CrossRef]  

30. T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014). [CrossRef]  

31. C. Wang, Y.-L. Pan, and M. Coleman, Opt. Lett. 39, 2767 (2014). [CrossRef]  

References

  • View by:

  1. A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
    [Crossref]
  2. A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
    [Crossref]
  3. A. Ashkin and J. M. Dziedzic, Science 235, 1517 (1987).
    [Crossref]
  4. K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
    [Crossref]
  5. R. Omori, T. Kobayashi, and A. Suzuki, Opt. Lett. 22, 816 (1997).
    [Crossref]
  6. J. B. Wills, K. J. Knox, and J. P. Reid, Chem. Phys. Lett. 481, 153 (2009).
    [Crossref]
  7. V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, Nat. Photonics 8, 846 (2014).
    [Crossref]
  8. V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
    [Crossref]
  9. V. G. Shvedov, A. S. Desyatnikov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, Opt. Express 17, 5743 (2009).
    [Crossref]
  10. J. Lin and Y. Li, Appl. Phys. Lett. 104, 101909 (2014).
    [Crossref]
  11. Y.-L. Pan, S. C. Hill, and M. Coleman, Opt. Express 20, 5325 (2012).
    [Crossref]
  12. C. Wang, Y.-L. Pan, S. C. Hill, and B. Redding, J. Quant. Spectrosc. Radiat. Transfer 153, 4 (2015).
    [Crossref]
  13. T. Li, Fundamental Tests of Physics with Optically Trapped Microspheres (Springer, 2013).
  14. G. Roosen and C. Imbert, Phys. Lett. A 59, 6 (1976).
    [Crossref]
  15. M. Guillon, O. Moine, and B. Stout, Phys. Rev. Lett. 96, 143902 (2006).
    [Crossref]
  16. M. Lewittes, S. Arnold, and G. Oster, Appl. Phys. Lett. 40, 455 (1982).
    [Crossref]
  17. A. S. Desyatnikov, V. G. Shvedov, A. V. Rode, W. Krolikowski, and Y. S. Kivshar, Opt. Express 17, 8201 (2009).
    [Crossref]
  18. K. T. Gahagan and G. a. Swartzlander, Opt. Lett. 21, 827 (1996).
    [Crossref]
  19. Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014).
    [Crossref]
  20. F. Liu, Z. Zhang, Y. Wei, Q. Zhang, T. Cheng, and X. Wu, Opt. Express 22, 23716 (2014).
    [Crossref]
  21. V. G. Shvedov, C. Hnatovsky, N. Shostka, A. V. Rode, and W. Krolikowski, Opt. Lett. 37, 1934 (2012).
    [Crossref]
  22. P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 1491 (2011).
    [Crossref]
  23. V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 18, 3137 (2010).
    [Crossref]
  24. J. Lin, A. G. Hart, and Y.-Q. Li, Appl. Phys. Lett. 106, 171906 (2015).
    [Crossref]
  25. B. Redding, S. C. Hill, D. Alexson, C. Wang, and Y.-L. Pan, Opt. Express 23, 3630 (2015).
    [Crossref]
  26. D. R. Burnham and D. McGloin, J. Opt. Soc. Am. B 28, 2856 (2011).
    [Crossref]
  27. R. D. Dear, D. R. Burnham, M. D. Summers, D. McGloin, and G. A. D. Ritchie, Phys. Chem. Chem. Phys. 14, 15826 (2012).
    [Crossref]
  28. Z. Zhang, D. Cannan, J. Liu, P. Zhang, D. N. Christodoulides, and Z. Chen, Opt. Express 20, 16212 (2012).
    [Crossref]
  29. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
    [Crossref]
  30. T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
    [Crossref]
  31. C. Wang, Y.-L. Pan, and M. Coleman, Opt. Lett. 39, 2767 (2014).
    [Crossref]

2015 (3)

C. Wang, Y.-L. Pan, S. C. Hill, and B. Redding, J. Quant. Spectrosc. Radiat. Transfer 153, 4 (2015).
[Crossref]

J. Lin, A. G. Hart, and Y.-Q. Li, Appl. Phys. Lett. 106, 171906 (2015).
[Crossref]

B. Redding, S. C. Hill, D. Alexson, C. Wang, and Y.-L. Pan, Opt. Express 23, 3630 (2015).
[Crossref]

2014 (6)

Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014).
[Crossref]

F. Liu, Z. Zhang, Y. Wei, Q. Zhang, T. Cheng, and X. Wu, Opt. Express 22, 23716 (2014).
[Crossref]

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
[Crossref]

C. Wang, Y.-L. Pan, and M. Coleman, Opt. Lett. 39, 2767 (2014).
[Crossref]

J. Lin and Y. Li, Appl. Phys. Lett. 104, 101909 (2014).
[Crossref]

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, Nat. Photonics 8, 846 (2014).
[Crossref]

2012 (4)

2011 (2)

2010 (2)

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 18, 3137 (2010).
[Crossref]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[Crossref]

2009 (3)

2007 (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[Crossref]

2006 (1)

M. Guillon, O. Moine, and B. Stout, Phys. Rev. Lett. 96, 143902 (2006).
[Crossref]

2004 (1)

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[Crossref]

1997 (1)

1996 (1)

1987 (1)

A. Ashkin and J. M. Dziedzic, Science 235, 1517 (1987).
[Crossref]

1982 (1)

M. Lewittes, S. Arnold, and G. Oster, Appl. Phys. Lett. 40, 455 (1982).
[Crossref]

1976 (1)

G. Roosen and C. Imbert, Phys. Lett. A 59, 6 (1976).
[Crossref]

1971 (1)

A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
[Crossref]

1970 (1)

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Alexson, D.

Arnold, S.

M. Lewittes, S. Arnold, and G. Oster, Appl. Phys. Lett. 40, 455 (1982).
[Crossref]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, Science 235, 1517 (1987).
[Crossref]

A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
[Crossref]

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

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K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
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T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
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Bui, A. A. M.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
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R. D. Dear, D. R. Burnham, M. D. Summers, D. McGloin, and G. A. D. Ritchie, Phys. Chem. Chem. Phys. 14, 15826 (2012).
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D. R. Burnham and D. McGloin, J. Opt. Soc. Am. B 28, 2856 (2011).
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C. Wang, Y.-L. Pan, and M. Coleman, Opt. Lett. 39, 2767 (2014).
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Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014).
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Y.-L. Pan, S. C. Hill, and M. Coleman, Opt. Express 20, 5325 (2012).
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V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, Nat. Photonics 8, 846 (2014).
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Dear, R. D.

R. D. Dear, D. R. Burnham, M. D. Summers, D. McGloin, and G. A. D. Ritchie, Phys. Chem. Chem. Phys. 14, 15826 (2012).
[Crossref]

Desyatnikov, A. S.

du Preez-Wilkinson, N.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
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Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, Science 235, 1517 (1987).
[Crossref]

A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
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V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, Nat. Photonics 8, 846 (2014).
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Gahagan, K. T.

Guillon, M.

M. Guillon, O. Moine, and B. Stout, Phys. Rev. Lett. 96, 143902 (2006).
[Crossref]

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J. Lin, A. G. Hart, and Y.-Q. Li, Appl. Phys. Lett. 106, 171906 (2015).
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Heckenberg, N. R.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
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Hernandez, D.

Hill, S. C.

B. Redding, S. C. Hill, D. Alexson, C. Wang, and Y.-L. Pan, Opt. Express 23, 3630 (2015).
[Crossref]

C. Wang, Y.-L. Pan, S. C. Hill, and B. Redding, J. Quant. Spectrosc. Radiat. Transfer 153, 4 (2015).
[Crossref]

Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014).
[Crossref]

Y.-L. Pan, S. C. Hill, and M. Coleman, Opt. Express 20, 5325 (2012).
[Crossref]

Hnatovsky, C.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, Nat. Photonics 8, 846 (2014).
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V. G. Shvedov, C. Hnatovsky, N. Shostka, A. V. Rode, and W. Krolikowski, Opt. Lett. 37, 1934 (2012).
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Huang, S.

Imbert, C.

G. Roosen and C. Imbert, Phys. Lett. A 59, 6 (1976).
[Crossref]

Izdebskaya, Y. V.

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
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Kivshar, Y. S.

Knöner, G.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
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J. B. Wills, K. J. Knox, and J. P. Reid, Chem. Phys. Lett. 481, 153 (2009).
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Krolikowski, W.

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M. Lewittes, S. Arnold, and G. Oster, Appl. Phys. Lett. 40, 455 (1982).
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Li, T.

T. Li, Fundamental Tests of Physics with Optically Trapped Microspheres (Springer, 2013).

Li, Y.

J. Lin and Y. Li, Appl. Phys. Lett. 104, 101909 (2014).
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Li, Y.-Q.

J. Lin, A. G. Hart, and Y.-Q. Li, Appl. Phys. Lett. 106, 171906 (2015).
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Lin, J.

J. Lin, A. G. Hart, and Y.-Q. Li, Appl. Phys. Lett. 106, 171906 (2015).
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J. Lin and Y. Li, Appl. Phys. Lett. 104, 101909 (2014).
[Crossref]

Liu, F.

Liu, J.

Loke, V. L. Y.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
[Crossref]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[Crossref]

McGloin, D.

R. D. Dear, D. R. Burnham, M. D. Summers, D. McGloin, and G. A. D. Ritchie, Phys. Chem. Chem. Phys. 14, 15826 (2012).
[Crossref]

D. R. Burnham and D. McGloin, J. Opt. Soc. Am. B 28, 2856 (2011).
[Crossref]

Moine, O.

M. Guillon, O. Moine, and B. Stout, Phys. Rev. Lett. 96, 143902 (2006).
[Crossref]

Neuman, K. C.

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[Crossref]

Nieminen, T. A.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
[Crossref]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[Crossref]

Omori, R.

Oster, G.

M. Lewittes, S. Arnold, and G. Oster, Appl. Phys. Lett. 40, 455 (1982).
[Crossref]

Pan, Y.-L.

C. Wang, Y.-L. Pan, S. C. Hill, and B. Redding, J. Quant. Spectrosc. Radiat. Transfer 153, 4 (2015).
[Crossref]

B. Redding, S. C. Hill, D. Alexson, C. Wang, and Y.-L. Pan, Opt. Express 23, 3630 (2015).
[Crossref]

C. Wang, Y.-L. Pan, and M. Coleman, Opt. Lett. 39, 2767 (2014).
[Crossref]

Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014).
[Crossref]

Y.-L. Pan, S. C. Hill, and M. Coleman, Opt. Express 20, 5325 (2012).
[Crossref]

Prakash, J.

Redding, B.

B. Redding, S. C. Hill, D. Alexson, C. Wang, and Y.-L. Pan, Opt. Express 23, 3630 (2015).
[Crossref]

C. Wang, Y.-L. Pan, S. C. Hill, and B. Redding, J. Quant. Spectrosc. Radiat. Transfer 153, 4 (2015).
[Crossref]

Reid, J. P.

J. B. Wills, K. J. Knox, and J. P. Reid, Chem. Phys. Lett. 481, 153 (2009).
[Crossref]

Ritchie, G. A. D.

R. D. Dear, D. R. Burnham, M. D. Summers, D. McGloin, and G. A. D. Ritchie, Phys. Chem. Chem. Phys. 14, 15826 (2012).
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Rode, A. V.

Roosen, G.

G. Roosen and C. Imbert, Phys. Lett. A 59, 6 (1976).
[Crossref]

Rubinsztein-Dunlop, H.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
[Crossref]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[Crossref]

Salazar, M.

Santarpia, J. L.

Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014).
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Shostka, N.

Shvedov, V.

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, Nat. Photonics 8, 846 (2014).
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Shvedov, V. G.

Stilgoe, A. B.

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
[Crossref]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[Crossref]

Stout, B.

M. Guillon, O. Moine, and B. Stout, Phys. Rev. Lett. 96, 143902 (2006).
[Crossref]

Summers, M. D.

R. D. Dear, D. R. Burnham, M. D. Summers, D. McGloin, and G. A. D. Ritchie, Phys. Chem. Chem. Phys. 14, 15826 (2012).
[Crossref]

Suzuki, A.

Swartzlander, G. a.

Wang, C.

C. Wang, Y.-L. Pan, S. C. Hill, and B. Redding, J. Quant. Spectrosc. Radiat. Transfer 153, 4 (2015).
[Crossref]

B. Redding, S. C. Hill, D. Alexson, C. Wang, and Y.-L. Pan, Opt. Express 23, 3630 (2015).
[Crossref]

C. Wang, Y.-L. Pan, and M. Coleman, Opt. Lett. 39, 2767 (2014).
[Crossref]

Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014).
[Crossref]

Wei, Y.

Wills, J. B.

J. B. Wills, K. J. Knox, and J. P. Reid, Chem. Phys. Lett. 481, 153 (2009).
[Crossref]

Wu, X.

Zhang, P.

Zhang, Q.

Zhang, Z.

Appl. Phys. Lett. (5)

A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett. 19, 283 (1971).
[Crossref]

J. Lin and Y. Li, Appl. Phys. Lett. 104, 101909 (2014).
[Crossref]

M. Lewittes, S. Arnold, and G. Oster, Appl. Phys. Lett. 40, 455 (1982).
[Crossref]

Y.-L. Pan, C. Wang, S. C. Hill, M. Coleman, L. A. Beresnev, and J. L. Santarpia, Appl. Phys. Lett. 104, 113507 (2014).
[Crossref]

J. Lin, A. G. Hart, and Y.-Q. Li, Appl. Phys. Lett. 106, 171906 (2015).
[Crossref]

Chem. Phys. Lett. (1)

J. B. Wills, K. J. Knox, and J. P. Reid, Chem. Phys. Lett. 481, 153 (2009).
[Crossref]

J. Opt. A (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 9, S196 (2007).
[Crossref]

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

J. Quant. Spectrosc. Radiat. Transfer (2)

T. A. Nieminen, N. du Preez-Wilkinson, A. B. Stilgoe, V. L. Y. Loke, A. A. M. Bui, and H. Rubinsztein-Dunlop, J. Quant. Spectrosc. Radiat. Transfer 146, 59 (2014).
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C. Wang, Y.-L. Pan, S. C. Hill, and B. Redding, J. Quant. Spectrosc. Radiat. Transfer 153, 4 (2015).
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Nat. Photonics (1)

V. Shvedov, A. R. Davoyan, C. Hnatovsky, N. Engheta, and W. Krolikowski, Nat. Photonics 8, 846 (2014).
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Opt. Express (7)

Opt. Lett. (5)

Phys. Chem. Chem. Phys. (1)

R. D. Dear, D. R. Burnham, M. D. Summers, D. McGloin, and G. A. D. Ritchie, Phys. Chem. Chem. Phys. 14, 15826 (2012).
[Crossref]

Phys. Lett. A (1)

G. Roosen and C. Imbert, Phys. Lett. A 59, 6 (1976).
[Crossref]

Phys. Rev. Lett. (3)

M. Guillon, O. Moine, and B. Stout, Phys. Rev. Lett. 96, 143902 (2006).
[Crossref]

V. G. Shvedov, A. V. Rode, Y. V. Izdebskaya, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 105, 118103 (2010).
[Crossref]

A. Ashkin, Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, Rev. Sci. Instrum. 75, 2787 (2004).
[Crossref]

Science (1)

A. Ashkin and J. M. Dziedzic, Science 235, 1517 (1987).
[Crossref]

Other (1)

T. Li, Fundamental Tests of Physics with Optically Trapped Microspheres (Springer, 2013).

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Figures (3)

Fig. 1.
Fig. 1. (a) Schematic of the optical trapping apparatus. The diameter of an expanded laser beam is controlled with a tunable iris before passing through two axicons to form a collimated hollow beam. The aspheric lens forms a hollow conical focus within a glass chamber where airborne particles are trapped. By adjusting the beam size before the axicon lenses with the iris, the size of the hollow region can be adjusted, as indicated by the light blue regions. (b) Calculated intensity profile near the focal spot plotted on a log-scale. (c) Image of the conical focal region produced inside the chamber obtained by introducing Johnson Smut Grass Spores and recording a long exposure time image. (d) Image of a spore trapped in air near the focal point.
Fig. 2.
Fig. 2. (a) The trapping efficiency, Q z , experienced by a particle along the optical axis using either a full lens of NA = 0.6 or the ring geometry shown in Fig. 1. Optical trapping is possible if Q z becomes negative at some position, providing the required restoring force. Due to the relatively high index of the particle, the standard laser tweezers approach (“full lens”) is not able to trap the particle, whereas the ring geometry provides the required negative restoring force. (b) The minimum of Q z is shown for the ring geometry as a function of the inner and outer NA. The black line corresponds to Q z = 0 , and trapping is possible for combinations of inner and outer NA to the right of the line. (c), (d) The minimum of Q z is shown using a full lens (c) or the ring geometry (d) as a function of the refractive index of the particle and the outer NA. The white contour lines correspond to Q z = 0 , and trapping is possible when the minimum force is negative. Experimentally, we trapped particles with index 1.5 using an outer NA of 0.55 in the ring geometry, corresponding to the position indicated by the black “×.”
Fig. 3.
Fig. 3. Optical trapping is demonstrated for four classes of particles, described by the particle shape (spherical or spatially irregular) and material type (absorbing or nonabsorbing). The images show an example of a trapped particle of each type. The yellow lines indicate the approximate position of the focal cone, extracted from an image similar to the one shown in Fig. 1(c). Particles of each type are trapped along the optical axis near the focal position.

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