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  • Vol. 36, Iss. 17 — Sep. 1, 2011
  • pp: 3347–3349
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Waveguide trapping of hollow glass spheres

Balpreet Singh Ahluwalia, Pål Løvhaugen, and Olav Gaute Hellesø  »View Author Affiliations


Optics Letters, Vol. 36, Issue 17, pp. 3347-3349 (2011)
http://dx.doi.org/10.1364/OL.36.003347


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Abstract

Microparticles can be trapped and propelled by the evanescent field of optical waveguides. As the evanescent field only stretches 100 200 nm from the surface of the waveguide, only the lower caps of the microparticles interact directly with the field. This is taken advantage of by trapping hollow glass spheres on waveguides in the same way as solid glass spheres. For the chosen waveguide, numerical simulations show that hollow microspheres with a shell thickness above 60 nm can be stably trapped, while spheres with thinner shells are repelled. The average refractive index of the sphere–field intersection volume is used to explain the result in a qualitative way.

© 2011 Optical Society of America

The calculated optical forces (gradient and propagation forces) on a hollow sphere for a guided power of 1W are shown in Fig. 2 for a radius r=1.5μm as a function of the shell thickness t [13

13. P. Løvhaugen, B. S. Ahluwalia, and O. G. Hellesø, Proc. SPIE 7950, 79500P (2011). [CrossRef]

]. For spheres with t>60nm, the gradient force (Fx) is negative, pulling the spheres toward the waveguide. The propagation force (Fz) propels the hollow sphere along the waveguide. Thus, spheres where t>60nm are trapped and propelled in the same way as solid spheres. The propagation force increases gradually with the shell thickness and is maximum for solid spheres. For spheres where 500nm<t<1500nm, Fz increases very slowly, as the cap volume interacting with the evanescent field remains constant. For spheres where t<60nm, Fx is positive, repelling spheres vertically away from the waveguide surface. Consequently, spheres with t<60nm cannot be trapped on the waveguide.

A simple analytical model can be used to explain the simulated gradient force results. The average refractive index of the hollow sphere (nhollow) depends on the refractive indices of glass (nglass) and air (nair) and the volumes of the sphere (Vsphere) and the encapsulated air (Vair):
nhollow=nglassVsphereVairVsphere+nairVairVsphere.
(1)
The average refractive index is seen to be linearly dependent on the void fraction, Vair/Vsphere. Likewise, the average specific density of the hollow sphere (ρhollow) is a linear function of Vair/Vsphere. The interaction between the sphere and the field is approximated using a constant field of height h. For radii r<h/2, the whole sphere interacts with the field. For rh/2, the volume Vcap of the field–sphere intersection is
Vcap=πh2(3rh)3.
(2)
We can now define the average refractive index of the cap (ncap):
ncap=nglassVcapVcap:airVcap+nairVcap:airVcap,
(3)
where Vcap:air is found by replacing r by rt and h by ht in Eq. (2):
Vcap:air=π(ht)2(3(rt)(ht))3.
(4)
Our hypothesis is that waveguides will attract hollow spheres for all ncap>nw (refractive index of water), independently of nhollow. For ncap<nw, a hollow sphere should be repelled away from the waveguide surface. Gaussian beams, which interact with the whole sphere, will trap the sphere for which nhollow>nw. For the transition where nhollow=nw=1.33, the gradient force Fx=0. This condition is used in Eq. (1) to study how Gaussian beam traps depend on r and t. Similarly, by letting ncap=nw=1.33 in Eq. (3), the waveguide trap transition points, where Fx is zero, are found. Finally, ρhollow=ρwater determines the transition points between floating and sinking spheres. Figures 3a, 3b show how the transitions depend on r and t and show the simulated waveguide trapping transition points by FEM (Fx=0) for three different radii. The simulation results are seen to be consistent with the analytical model. Figure 3a visualizes four hollow sphere trapping regimes. I) t0.23r (nhollownw and ρhollowρwater): spheres are trapped by both Gaussian beams and waveguides. II) 0.16rt0.23r (nhollownwncap and ρhollowρwater): spheres are trapped by a waveguide, but not by Gaussian beams. III) 60nmt0.16r (nwncap and ρhollowρwater): spheres float but can be trapped by the attractive forces from the waveguide and not by Gaussian beams. IV) t<60nm (nwncap and ρhollowρwater): spheres float and are repelled away from waveguides. Spheres in regimes I, II, and III are trapped by the waveguide, but a Gaussian beam can only trap spheres in regime I. Spheres in regimes I, II, V, and VI sink (ρhollowρwater) and in regimes III and IV float (ρhollowρwater). Figure 3b shows the plot close to the transition region. Interestingly, Fig. 3b shows two small regimes. In regime V spheres are trapped by Gaussian beams and not by waveguides (ncapnwnhollow). In regime VI (nhollownw and ncapnw), spheres cannot be trapped by both Gaussian beams and waveguide traps, which is similar to regime IV. However, spheres in regime VI sink, whereas they float in regime IV. Regimes V and VI are small and occur only for 75nm<r<350nm and 20nm<t<60nm for the chosen waveguide parameters.

Hollow and solid spheres were trapped and propelled experimentally on a waveguide surface. The solid and hollow glass spheres were bought from Polysciences Inc. The solid spheres have specified diameters of 215μm and a density of ~2.5g/cm3. The hollow spheres have specified diameters of 220μm with a mean of 8μm and a nominal density of 1.1g/cm3. We used optical microscopy to measure the shell thickness (t) and diameter (2r) and estimate the density for a batch of spheres. Hollow spheres were dried on a substrate and imaged with a 100× objective lens for measuring 2r and t. For particles with r=18μm, the thickness was in the range t=4001400nm, with an estimated measurement error of 250nm. Figure 4 shows the distribution of the effective refractive index of spheres calculated from the measured values of 2r and t. A scanning electron microscope was also used to confirm the shell thickness variation of the crushed hollow spheres. For spheres with r<2μm, t was 300600nm, and for r>3μm, we measured t>500nm.

Both types of spheres were trapped and propelled on the waveguide surface. For the chosen waveguide width (3μm), both the hollow and the solid spheres of 46μm diameter are propelled faster than smaller and larger spheres of corresponding type. The lower velocities can be explained by the smaller spheres (2r<4μm) not interacting with the entire width of the waveguide field and by the larger spheres (2r>4μm) experiencing larger drag forces. Solid spheres were propelled faster than hollow spheres of similar diameters. The propulsion velocities of solid and hollow spheres of r=1.5μm are 15μm/s and 5μm/s, respectively (Fig. 5), giving a velocity ratio of 3. Simulations of solid spheres of r=1.5μm give Fz=13pN and of hollow spheres with t=350nm give Fz=7.5pN (Fig. 3), giving a force ratio of 1.7. Viscous drag forces are equal for hollow and solid spheres of the same diameter, and the velocity is proportional to Fz and to the power in the waveguide. The higher ratio of the measured velocities compared to the simulations can be due to the experimental spheres having thinner shells than the simulated spheres. The small amount of surfactant necessary for hollow sphere propulsion also gives reason to believe the hollow spheres have higher surface adhesion. The hollow spheres trapped experimentally (Fig. 5) belong to regimes I and II (ρ>1). To trap floating particles (regime III), the particles either have to be pushed onto the waveguide by applying an external force, or the waveguide has to be turned upside down.

Trapping of hollow and solid glass spheres in the evanescent field of an optical waveguide has been studied. The average refractive index of the sphere–field intersection volume is calculated with an analytical expression. A hollow sphere is attracted to the waveguide if the average index of the sphere–field intersection volume is higher than that of the surrounding medium. The attractive or repelling optical forces are dependent on the shell thickness. Stable lift by an optical beam has recently been demonstrated [14

14. G. A. Swartzlander Jr., T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photon. 5, 48 (2011). [CrossRef]

]. Future work will show if attractive and repulsive forces of an evanescent field can be balanced to create a stable lift.

The authors wish to thank J. S. Wilkinson, A. Subramanian, S. Gétin, and D. Néel for their help. This work is supported by the Research Council of Norway.

Fig. 1 Waveguide trapping of a hollow sphere together with the simulated optical field.
Fig. 2 Gradient (Fx) and propagation (Fz) optical forces on a hollow sphere of 1.5μm radius for different shell thicknesses (t). The power guided in the waveguide is kept constant at 1W.
Fig. 3 Optical trapping regimes of hollow spheres as a function of radius (r) and shell thickness (t).
Fig. 4 Refractive index and specific density of a batch of hollow spheres used in the experiment.
Fig. 5 Optical propulsion of hollow and solid spheres of different diameters on a waveguide of width=3μm and for an input power=1500mW.
1.

A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett. 24, 586 (1974). [CrossRef]

2.

K. T. Gahagan and G. A. Swartzlander, J. Opt. Soc. Am. B 15, 524 (1998). [CrossRef]

3.

K. T. Gahagan and G. A. Swartzlander Jr., J. Opt. Soc. Am. B 16, 533 (1999). [CrossRef]

4.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002). [CrossRef]

5.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, J. Appl. Phys. 99, 113104 (2006). [CrossRef]

6.

K. Sasaki, H. Misawa, M. Koshioka, N. Kitamura, and H. Masuhara, Appl. Phys. Lett. 60, 807 (1992). [CrossRef]

7.

S. Kawata and T. Tani, Opt. Lett. 21, 1768 (1996). [CrossRef] [PubMed]

8.

S. Gaugiran, S. Gétin, G. Colas, A. Fuchs, F. Chatelain, J. Dérouard, and J. M. Fedeli, Opt. Express 13, 6956 (2005). [CrossRef] [PubMed]

9.

B. P. S. Ahluwalia, A. Z. Subramanian, O. G. Helleso, N. M. B. Perney, N. P. Sessions, and J. S. Wilkinson, IEEE Photon. Technol. Lett. 21, 1408 (2009). [CrossRef]

10.

B. P. S. Ahluwalia, P. McCourt, Thomas Huser, and O. G. Hellesø, Opt. Express 18, 21053 (2010). [CrossRef] [PubMed]

11.

H. Y. Jaising and O. G. Hellesø, Opt. Commun. 246, 373 (2005). [CrossRef]

12.

J. Ng and C. T. Chan, Appl. Phys. Lett. 92, 251109 (2008). [CrossRef]

13.

P. Løvhaugen, B. S. Ahluwalia, and O. G. Hellesø, Proc. SPIE 7950, 79500P (2011). [CrossRef]

14.

G. A. Swartzlander Jr., T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photon. 5, 48 (2011). [CrossRef]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(240.6690) Optics at surfaces : Surface waves
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: April 19, 2011
Revised Manuscript: July 19, 2011
Manuscript Accepted: July 28, 2011
Published: August 22, 2011

Virtual Issues
October 18, 2011 Spotlight on Optics

Citation
Balpreet Singh Ahluwalia, Pål Løvhaugen, and Olav Gaute Hellesø, "Waveguide trapping of hollow glass spheres," Opt. Lett. 36, 3347-3349 (2011)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-36-17-3347


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References

  1. A. Ashkin and J. M. Dziedzic, Appl. Phys. Lett. 24, 586 (1974). [CrossRef]
  2. K. T. Gahagan and G. A. Swartzlander, J. Opt. Soc. Am. B 15, 524 (1998). [CrossRef]
  3. K. T. Gahagan and G. A. Swartzlander, Jr., J. Opt. Soc. Am. B 16, 533 (1999). [CrossRef]
  4. V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, Phys. Rev. A 66, 063402 (2002). [CrossRef]
  5. B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, J. Appl. Phys. 99, 113104 (2006). [CrossRef]
  6. K. Sasaki, H. Misawa, M. Koshioka, N. Kitamura, and H. Masuhara, Appl. Phys. Lett. 60, 807 (1992). [CrossRef]
  7. S. Kawata and T. Tani, Opt. Lett. 21, 1768 (1996). [CrossRef] [PubMed]
  8. S. Gaugiran, S. Gétin, G. Colas, A. Fuchs, F. Chatelain, J. Dérouard, and J. M. Fedeli, Opt. Express 13, 6956 (2005). [CrossRef] [PubMed]
  9. B. P. S. Ahluwalia, A. Z. Subramanian, O. G. Helleso, N. M. B. Perney, N. P. Sessions, and J. S. Wilkinson, IEEE Photon. Technol. Lett. 21, 1408 (2009). [CrossRef]
  10. B. P. S. Ahluwalia, P. McCourt, Thomas Huser, and O. G. Hellesø, Opt. Express 18, 21053 (2010). [CrossRef] [PubMed]
  11. H. Y. Jaising and O. G. Hellesø, Opt. Commun. 246, 373 (2005). [CrossRef]
  12. J. Ng and C. T. Chan, Appl. Phys. Lett. 92, 251109 (2008). [CrossRef]
  13. P. Løvhaugen, B. S. Ahluwalia, and O. G. Hellesø, Proc. SPIE 7950, 79500P (2011). [CrossRef]
  14. G. A. Swartzlander, Jr., T. J. Peterson, A. B. Artusio-Glimpse, and A. D. Raisanen, Nat. Photon. 5, 48 (2011). [CrossRef]

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