Abstract

We study the conditions under which a particle, laser-guided in a vertically-oriented hollow-core photonic crystal fiber filled with liquid, can be kept stationary against a microfluidic counter-flow. An immobility parameter—the fluid flow rate required to immobilize a particle against the radiation force produced by unit guided optical power—is introduced to quantify the conditions under which this occurs, including radiation, viscous and gravity forces. Measurements show that this parameter depends strongly on the ratio of particle radius a to core radius R, peaking at an intermediate value of a/R. The results follow fairly well the theoretical estimates of the optical (calculated approximately using a ray optics approach) and numerically simulated drag forces. We suggest that the system has potential applications in, e.g., measurement of the diameter, refractive index and density of particles, synthesis and biomedical research.

© 2011 OSA

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References

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  1. S. Kawata and T. Sugiura, “Movement of micrometer-sized particles in the evanescent field of a laser beam,” Opt. Lett. 17(11), 772–774 (1992).
    [CrossRef] [PubMed]
  2. S. Mandal and D. Erickson, “Optofluidic transport in liquid core waveguiding structures,” Appl. Phys. Lett. 90(18), 184103 (2007).
    [CrossRef]
  3. A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
    [CrossRef] [PubMed]
  4. T. G. Euser, M. K. Garbos, J. S. Y. Chen, and P. St. J. Russell, “Precise balancing of viscous and radiation forces on a particle in liquid-filled photonic bandgap fiber,” Opt. Lett. 34(23), 3674–3676 (2009).
    [CrossRef] [PubMed]
  5. T. G. Euser, M. K. Garbos, J. S. Y. Chen, and P. St. J. Russell, “Precise balancing of viscous and radiation forces on a particle in liquid-filled photonic bandgap fiber: erratum,” Opt. Lett. 35(13), 2142 (2010).
    [CrossRef]
  6. M. K. Garbos, T. G. Euser, O. A. Schmidt, S. Unterkofler, and P. St. J. Russell, “Doppler velocimetry on microparticles trapped and propelled by laser light in liquid-filled photonic crystal fiber,” Opt. Lett. 36(11), 2020–2022 (2011).
    [CrossRef] [PubMed]
  7. The hydraulic radius R = 2A/Lp is the radius of a circular channel with the same area A and wetted perimeter Lp as the slightly non-circular hollow core. From measurements of a high resolution scanning electron micrograph we find R = 8.7 μm.
  8. T. A. Birks, D. M. Bird, T. D. Hedley, J. M. Pottage, and P. St. J. Russell, “Scaling laws and vector effects in bandgap-guiding fibres,” Opt. Express 12(1), 69–74 (2004).
    [CrossRef] [PubMed]
  9. G. Antonopoulos, F. Benabid, T. A. Birks, D. M. Bird, J. C. Knight, and P. St. J. Russell, “Experimental demonstration of the frequency shift of bandgaps in photonic crystal fibers due to refractive index scaling,” Opt. Express 14(7), 3000–3006 (2006).
    [CrossRef] [PubMed]
  10. 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(5), 288–290 (1986).
    [CrossRef] [PubMed]
  11. N. Al Quddus, W. A. Moussa, and S. Bhattacharjee, “Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method,” J. Colloid Interface Sci. 317(2), 620–630 (2008).
    [CrossRef] [PubMed]
  12. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
    [CrossRef] [PubMed]
  13. W. L. Moreira, A. A. R. Neves, M. K. Garbos, T. G. Euser, P. St, J. Russell, and C. Lenz Cesar, “Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions,” arXiv.org, arXiv:1003.2392v2 (2010).
  14. T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, “Optical chromatography,” Anal. Chem. 67(11), 1763–1765 (1995).
    [CrossRef]
  15. S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83(25), 5316–5318 (2003).
    [CrossRef]
  16. P. C. Ashok, R. F. Marchington, P. Mthunzi, T. F. Krauss, and K. Dholakia, “Optical chromatography using a photonic crystal fiber with on-chip fluorescence excitation,” Opt. Express 18(6), 6396–6407 (2010).
    [CrossRef] [PubMed]
  17. P. Domachuk, N. Wolchover, M. Cronin-Golomb, and F. G. Omenetto, “Effect of hollow-core photonic crystal fiber microstructure on transverse optical trapping,” Appl. Phys. Lett. 94(14), 141101 (2009).
    [CrossRef]
  18. J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
    [CrossRef] [PubMed]
  19. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
    [CrossRef]

2011

2010

2009

T. G. Euser, M. K. Garbos, J. S. Y. Chen, and P. St. J. Russell, “Precise balancing of viscous and radiation forces on a particle in liquid-filled photonic bandgap fiber,” Opt. Lett. 34(23), 3674–3676 (2009).
[CrossRef] [PubMed]

A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

P. Domachuk, N. Wolchover, M. Cronin-Golomb, and F. G. Omenetto, “Effect of hollow-core photonic crystal fiber microstructure on transverse optical trapping,” Appl. Phys. Lett. 94(14), 141101 (2009).
[CrossRef]

2008

N. Al Quddus, W. A. Moussa, and S. Bhattacharjee, “Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method,” J. Colloid Interface Sci. 317(2), 620–630 (2008).
[CrossRef] [PubMed]

2007

S. Mandal and D. Erickson, “Optofluidic transport in liquid core waveguiding structures,” Appl. Phys. Lett. 90(18), 184103 (2007).
[CrossRef]

2006

2005

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

2004

2003

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83(25), 5316–5318 (2003).
[CrossRef]

1995

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, “Optical chromatography,” Anal. Chem. 67(11), 1763–1765 (1995).
[CrossRef]

1992

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[CrossRef] [PubMed]

S. Kawata and T. Sugiura, “Movement of micrometer-sized particles in the evanescent field of a laser beam,” Opt. Lett. 17(11), 772–774 (1992).
[CrossRef] [PubMed]

1986

1970

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Al Quddus, N.

N. Al Quddus, W. A. Moussa, and S. Bhattacharjee, “Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method,” J. Colloid Interface Sci. 317(2), 620–630 (2008).
[CrossRef] [PubMed]

Ananthakrishnan, R.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Antonopoulos, G.

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[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(5), 288–290 (1986).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Ashok, P. C.

Benabid, F.

Bhattacharjee, S.

N. Al Quddus, W. A. Moussa, and S. Bhattacharjee, “Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method,” J. Colloid Interface Sci. 317(2), 620–630 (2008).
[CrossRef] [PubMed]

Bilby, C.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Bird, D. M.

Birks, T. A.

Bjorkholm, J. E.

Chen, J. S. Y.

Chu, S.

Cronin-Golomb, M.

P. Domachuk, N. Wolchover, M. Cronin-Golomb, and F. G. Omenetto, “Effect of hollow-core photonic crystal fiber microstructure on transverse optical trapping,” Appl. Phys. Lett. 94(14), 141101 (2009).
[CrossRef]

Dholakia, K.

Domachuk, P.

P. Domachuk, N. Wolchover, M. Cronin-Golomb, and F. G. Omenetto, “Effect of hollow-core photonic crystal fiber microstructure on transverse optical trapping,” Appl. Phys. Lett. 94(14), 141101 (2009).
[CrossRef]

Dziedzic, J. M.

Ebert, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Erickson, D.

A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

S. Mandal and D. Erickson, “Optofluidic transport in liquid core waveguiding structures,” Appl. Phys. Lett. 90(18), 184103 (2007).
[CrossRef]

Erickson, H. M.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Euser, T. G.

Garbos, M. K.

Guck, J.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Hart, S. J.

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83(25), 5316–5318 (2003).
[CrossRef]

Hedley, T. D.

Imasaka, T.

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, “Optical chromatography,” Anal. Chem. 67(11), 1763–1765 (1995).
[CrossRef]

Ishidzu, Y.

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, “Optical chromatography,” Anal. Chem. 67(11), 1763–1765 (1995).
[CrossRef]

Kaneta, T.

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, “Optical chromatography,” Anal. Chem. 67(11), 1763–1765 (1995).
[CrossRef]

Käs, J.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Kawabata, Y.

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, “Optical chromatography,” Anal. Chem. 67(11), 1763–1765 (1995).
[CrossRef]

Kawata, S.

Klug, M.

A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Knight, J. C.

Krauss, T. F.

Lenz, D.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Lincoln, B.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Lipson, M.

A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Mandal, S.

S. Mandal and D. Erickson, “Optofluidic transport in liquid core waveguiding structures,” Appl. Phys. Lett. 90(18), 184103 (2007).
[CrossRef]

Marchington, R. F.

Mitchell, D.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Moore, S. D.

A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Moussa, W. A.

N. Al Quddus, W. A. Moussa, and S. Bhattacharjee, “Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method,” J. Colloid Interface Sci. 317(2), 620–630 (2008).
[CrossRef] [PubMed]

Mthunzi, P.

Omenetto, F. G.

P. Domachuk, N. Wolchover, M. Cronin-Golomb, and F. G. Omenetto, “Effect of hollow-core photonic crystal fiber microstructure on transverse optical trapping,” Appl. Phys. Lett. 94(14), 141101 (2009).
[CrossRef]

Pottage, J. M.

Romeyke, M.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Russell, P. St. J.

Schinkinger, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Schmidt, B. S.

A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Schmidt, O. A.

Sugiura, T.

Terray, A. V.

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83(25), 5316–5318 (2003).
[CrossRef]

Ulvick, S.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Unterkofler, S.

Wolchover, N.

P. Domachuk, N. Wolchover, M. Cronin-Golomb, and F. G. Omenetto, “Effect of hollow-core photonic crystal fiber microstructure on transverse optical trapping,” Appl. Phys. Lett. 94(14), 141101 (2009).
[CrossRef]

Wottawah, F.

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

Yang, A. H.

A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Anal. Chem.

T. Imasaka, Y. Kawabata, T. Kaneta, and Y. Ishidzu, “Optical chromatography,” Anal. Chem. 67(11), 1763–1765 (1995).
[CrossRef]

Appl. Phys. Lett.

S. J. Hart and A. V. Terray, “Refractive-index-driven separation of colloidal polymer particles using optical chromatography,” Appl. Phys. Lett. 83(25), 5316–5318 (2003).
[CrossRef]

P. Domachuk, N. Wolchover, M. Cronin-Golomb, and F. G. Omenetto, “Effect of hollow-core photonic crystal fiber microstructure on transverse optical trapping,” Appl. Phys. Lett. 94(14), 141101 (2009).
[CrossRef]

S. Mandal and D. Erickson, “Optofluidic transport in liquid core waveguiding structures,” Appl. Phys. Lett. 90(18), 184103 (2007).
[CrossRef]

Biophys. J.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61(2), 569–582 (1992).
[CrossRef] [PubMed]

J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke, D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Käs, S. Ulvick, and C. Bilby, “Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence,” Biophys. J. 88(5), 3689–3698 (2005).
[CrossRef] [PubMed]

J. Colloid Interface Sci.

N. Al Quddus, W. A. Moussa, and S. Bhattacharjee, “Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method,” J. Colloid Interface Sci. 317(2), 620–630 (2008).
[CrossRef] [PubMed]

Nature

A. H. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Other

The hydraulic radius R = 2A/Lp is the radius of a circular channel with the same area A and wetted perimeter Lp as the slightly non-circular hollow core. From measurements of a high resolution scanning electron micrograph we find R = 8.7 μm.

W. L. Moreira, A. A. R. Neves, M. K. Garbos, T. G. Euser, P. St, J. Russell, and C. Lenz Cesar, “Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions,” arXiv.org, arXiv:1003.2392v2 (2010).

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Figures (9)

Fig. 1
Fig. 1

(a) SEM of the HC-PCF structure, inter-hole spacing Λ = 4.7μm and hydraulic radius R = 8.7 μm; (b) Mode intensity profile measured at the output of a D2O-filled fiber at 1064 nm. Cross-sections along central horizontal and vertical axes are shown above and to the right. The measured profiles (symbols) are fitted to a J0 2(j 01 r/R) shape expected for the fundamental mode, where j 01 is the first zero of the J0 Bessel function (red curves); (c) Loss spectra for bulk D2O, the liquid-filled PCF and the excess loss introduced by the fiber. The shaded region indicates where light is guided in a low-loss single-lobed fundamental mode, the loss being dominated by D2O absorption.

Fig. 2
Fig. 2

Experimental set-up. (a) A CW laser beam (Nd:YAG, 1064 nm) is divided between an optical tweezers trap and a particle guidance beam. The split ratio is controlled with a λ/2 plate and a polarizing beam splitter (PBS). A 100 × 1.1 NA water immersion objective forms a conventional optical trap [10] that is used to tweezer a selected particle up to the entrance of the HC-PCF core. Two cameras (CCD1 and CCD2) monitor the launching process in three dimensions. (b) Close-up of the open sample cell arrangement for loading and launching particles (to scale). The output facet is enclosed in a custom designed liquid cell (LC). The mode intensity profile is monitored by CCD4. The pressure head can be varied by moving the D2O reservoir up and down. (c) Image of an optically guided particle taken by CCD3. The vertical stripes represent the liquid-filled cladding holes that run along the fiber. P: polarizer; EOM: electro-optic modulator; CM: cold mirror.

Fig. 3
Fig. 3

Pressure head p H divided by fiber length L required for particle immobility, plotted against optical power for 4 different particle radii.

Fig. 4
Fig. 4

(a-c): Flow velocity field around spherical particles of different sizes, normalized to the on-axis velocity in an unobstructed tube, for L = 5R (images clipped) at a fixed pressure difference. (d) Normalized on-axis flow velocity v m/v m0 in the obstructed core, at an axial distance 2.5R from the particle position, plotted versus L/R. The numerical calculations (solid lines) are compared to the predictions of the analytical model in Eq. (4) (symbols).

Fig. 5
Fig. 5

Calculated axial (q z) and radial (q r) forces per W of guided power on particles of 1 µm (dashed curves) and 2 µm radius (solid curves) as a function of radial position. R = 8.7 µm, n p = 1. 55, n fl = 1.33.

Fig. 6
Fig. 6

Calculated axial optical force parameter q z versus a/R. The particle refractive index n p ranges from 1.45 to 1.60 while keeping the fluid index constant (n fl = 1.33). The points indicate the different borosilicate glass spheres studied experimentally. (b) Wall correction factor K2 as function of a/R for a stationary particle. As expected the drag force increases dramatically when a/R → 1. (c) Calculated trap stiffness at 1 W optical power for particles guided in a D2O-filled fiber. (d) Lateral displacement of the particles in a horizontally placed fiber under the influence of gravity. The density ρ p of the particles was taken to be 2500 kg/m3.

Fig. 7
Fig. 7

Schematic illustrating the forces acting on a particle inside a vertically oriented fluid-filled HC-PCF. The Poynting vector distribution of the guided optical mode (propagating upwards) and the velocity distribution of the fluid flow (moving downwards) are shown. The effective mass of the particle, including buoyancy, is m'.

Fig. 8
Fig. 8

Immobility parameter at high optical power, μi , versus particle radius; theory (solid curves) and experimental data (circles). Reasonable agreement is found if the theoretical curve for n p = 1.55 is multiplied by 1.7 (dashed curve).

Fig. 9
Fig. 9

Measured (symbols) and calculated (curves) immobility parameter versus (low) optical power for three particle radii. A correction factor of 1.7 was used for the optical force (see Fig. 8). The estimated experimental errors (represented by the error bars) Δp H/p H = ±% and ΔP opt/P opt = ±0.1. The shaded regions show the spread of calculated µ i values, assuming uncertainties of Δn p/n p = ± 0.01 and Δa = ±0.3 µm in particle parameters.

Equations (8)

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F drag = 6 π η a ( K 1 ( ζ ) v p + K 2 ( ζ ) v m )
K 1  =  ( 1 2.0711   ζ   +   0.37088   ζ 2 + 3.6478   ζ 3 2.8946   ζ 4   +   0.68845   ζ 5 ) 1 K 2  =  ( 1 2.0413   ζ   +   0.16226   ζ 2 + 2.2368   ζ 3 1.8409   ζ 4   +   0.48511   ζ 5 ) 1 .
p H = Δ p p + d p d z ( L 2 a ) = C F drag / π R 2 + 4 η v m ( L 2 a ) / R 2 = v m ( 6 C a K 2 ( ζ ) + 4 ( L 2 a ) ) η / R 2
v m v m0 = 1 1 2 a / L + 3 C a K 2 ( ζ ) / 2 L .
μ i = v m P opt ,       v p = 0
F opt = q z P opt = F drag + m ' g = 6 π a η K 2 ( ζ ) v m + 4 π a 3 ( ρ p ρ fl ) g / 3 ,
μ i = v m P opt = 1 6 π a η K 2 ( ζ ) ( q z 4 π a 3 ( ρ p ρ fl ) g 3 P opt ) .
μ i = q z 6 π a η K 2 ( ζ ) ,     P opt .

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