OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19643–19652
« Show journal navigation

Optofluidic immobility of particles trapped in liquid-filled hollow-core photonic crystal fiber

M. K. Garbos, T. G. Euser, and P. St. J. Russell  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 19643-19652 (2011)
http://dx.doi.org/10.1364/OE.19.019643


View Full Text Article

Acrobat PDF (1457 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

1. Introduction

2. Experiments

A scanning electron micrograph (SEM) of the hollow-core photonic crystal fiber (HC-PCF) used in the experiments is shown in Fig. 1(a)
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.
. The cladding pitch is Λ = 4.7 µm and the hydraulic radius of the core is R = 8.7 µm [7

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.

]. The fiber was designed to guide a single-mode at 1064 nm when all core and cladding holes are filled with D2O (refractive index nfl = 1.33) [8

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

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]

]. D2O is chosen for its low absorption (4 dB.m−1) at 1064 nm. Launch efficiencies as high as 89% were achieved using an objective lens (4 × 0.1 NA) that matched the numerical aperture (NA) of the guided mode. Figure 1(b) shows the near-field intensity profile at the output face of a 1 m long piece of D2O-filled fiber at 1064 nm. Its shape agrees well with a J0 2 function that goes to its first zero at the core boundaries, showing that only the fundamental mode is excited. Indeed, robust single-mode guidance was obtained over the whole wavelength range 970 to 1140 nm. The loss spectrum was determined using the cut-back technique (Fig. 1(c)). At 1064 nm the loss was 5 dB.m−1, dominated not by intrinsic waveguide loss but by absorption in the D2O (dashed curve). Bend loss in the 970-1090 nm range was measured to be less than 0.2 dB per turn around a mandrel of radius of 7 mm. These characteristics make HC-PCFs highly suitable as low loss, flexible and reconfigurable single-mode liquid waveguides.

The pressure head p H necessary to keep the particle stationary in the vertical fiber section divided by the fiber length L is plotted in 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.
as a function of guided optical power P opt, estimated by measuring the power at the fiber output and extrapolating back to the particle position using the measured value of fiber loss (Fig. 1(c)). The results were reproducible to within 2% over a time periods of an hour or more and were repeated for 14 different particle radii from 1 µm to 6.25 µm. In all cases the value of p H needed to achieve immobility increased approximately linearly with optical power.

3. Microfluidic forces

Fdrag=6πηa(K1(ζ)vp+K2(ζ)vm)
(1)

where ζ = a/R and K 1 and K 2 are wall correction factors that are accurately approximated (for ζ < 0.9) by the polynomials:

K1 = (12.0711 ζ + 0.37088 ζ2+3.6478 ζ32.8946 ζ4 + 0.68845 ζ5)1K2 = (12.0413 ζ + 0.16226 ζ2+2.2368 ζ31.8409 ζ4 + 0.48511 ζ5)1.
(2)

Note that the values of K 1 and K 2, and thus the drag force, increase rapidly as ζ → 1, when the particle almost completely fills the channel.

4. Relating pressure head to flow rate

The fluid flow rate will in principle be constrained by the presence of the particle, particularly when ζ → 1. To estimate the particle sizes and fiber lengths at which this becomes significant, we modeled the liquid flow field in the vicinity of the particle numerically using a finite element approach (Comsol Multiphysics). Figures 4(a-c)
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).
show the results for a liquid-filled tube with length L = 5R and a fixed pressure difference p H between both ends. Note that we have normalized v m to the new parameter v m0 – the center-tube flow speed in the absence of a particle. It may be seen that in this very short fiber the effect on the flow is quite substantial.

The total pressure difference between both fiber ends p H may be approximated as:

pH=Δpp+dpdz(L2a)=CFdrag/πR2+4ηvm(L2a)/R2=vm(6CaK2(ζ)+4(L2a))η/R2
(3)

where dp/dz is the pressure gradient far from the particle and Δp p is the pressure drop across it, taken to be proportional to the drag force divided by the core cross-sectional area, i.e., Δp p = C.F dragR 2 where C is a correction factor (to be determined). Equation (3) can be used to show that:

vmvm0=112a/L+3CaK2(ζ)/2L.
(4)

Comparing Eq. (4) with the results of finite element simulations for different particle sizes yields a best fit for C = 1.7, as shown in Fig. 4(d). The results show that if L > 1000 × R the reduction in v m is less than 5% for ζ < 0.75. For the experiments reported here L ~105 × R so that the flow speed is practically unaffected by the presence of a particle. For short fiber lengths L < 100R, or for ζ ~1, an optically propelled particle could even be used to drive a small fluid flow.

5. Optical forces

The optical forces acting on a spherical particle can be estimated using the ray-optics approach developed by Ashkin [12

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]

], assuming that the optical mode can be represented by a bundle of rays travelling parallel to the fiber axis. The momentum transferred to the particle is obtained via ray tracing, the contributions of all rays being integrated, taking into account the J0 2(j01 r / R) mode intensity profile for the fundamental mode, where j01 is the first zero of a J0 Bessel function and r the radial position. The resulting axial (q z) and radial (q r) forces per Watt of optical power acting on borosilicate glass particles with a = 1 and 2 µm, plotted versus radial displacement from the axis, are shown in 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.
.

Propulsive force

When it is on-axis the larger particle experiences a propulsive force of 84 pN/W, some 3.7 times larger than for the smaller particle and roughly proportional to the particle area intercepting the optical mode. For comparison, the value for a perfectly absorbing sphere of the same size as the particle, taking account of the J0 2 intensity profile, is 841 pN/W. Thus, for the 2 µm radius sphere only 10% of the incoming momentum is transferred to the particle. The axial propulsive force on a centrally-placed particle is plotted in Fig. 6(a)
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.
versus radius a for different values of particle index n p. The maximum value occurs at a particle radius of ~5 µm, almost independently of the value of n p. In Fig. 6(b) the wall correction factor K 2 is plotted versus a/R; note how strongly it increases as a/R → 1.

Trap stiffness

6. Immobility parameter

The forces acting on a particle in a vertically-oriented fiber are shown in 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'.
. We define the immobility parameter μ i as the center-channel flow velocity far from the particle needed to immobilize it (in the laboratory frame) when it is propelled by unit guided optical power, i.e.,

μi=vmPopt,     vp=0.
(5)

For a particle to be held stationary against a fluid flow in a vertically oriented fiber, the optical force must equal the sum of the microfluidic drag force and gravity:

Fopt=qzPopt=Fdrag+m'g=6πaηK2(ζ)vm+4πa3(ρpρfl)g/3,
(6)

where ρ p is the particle density. Assuming that the particle does not significantly constrain the flow, i.e., v m = v m0, the immobility parameter can be written:

μi=vmPopt=16πaηK2(ζ)(qz4πa3(ρpρfl)g3Popt).
(7)

As expected, μ i is zero when the propulsive optical force exactly balances gravity, i.e., when P opt = 4πa 3(ρ pρ fl)g/3q z. Note that in the limit of large optical powers, gravity can be ignored, leading to the simpler expression:

μi=qz6πaηK2(ζ),   Popt.
(8)

In this limit, experimental (symbols) and theoretical values (curves) for μi are plotted in 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).
against particle radius for a range of different values of n p. Experimentally, μi is obtained by extrapolating the curves in Fig. 3 to 1 W of optical power and calculating the flow speed v m from the pressure gradient p H/L. In the experiment μi increases with particle radius, reaching a maximum value of 1.7 mm.s−1.W−1 at a = 2.8 µm and then decreasing again for larger values. The calculated immobility for n p = 1.55 (the borosilicate glass index) underestimates the experimental data slightly for smaller particles (a < 2 μm), the error being a factor of two in the worst case for larger particles. This we attribute to underestimation of the optical forces by the simplistic ray model that does not take into account the waveguide properties. Preliminary results of a separate theoretical study (in preparation) show that a rigorous scattering approach gives better agreement [13

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).

]. Reasonable agreement is obtained, however, if the optical force calculated from the ray-optics model is multiplied by a fixed correction factor of 1.7 (see dashed curve for n p = 1.55).

Figure 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.
shows µ i against optical power for 3 different particle radii. At higher optical powers gravity can be ignored and μ i asymptotically approaches μ i . At optical powers small enough so that gravity forces dominate, μ i goes negative, i.e., the propulsive optical force is insufficient to balance against gravity and the flow has to be reversed to achieve particle immobility. The theoretical curves were calculated using Eq. (7), using the correction factor (1.7) for the optical force. There is reasonable agreement with the experimental data.

7. Discussion and conclusions

Micron-sized dielectric particles trapped in the liquid-filled hollow core of a single-mode photonic crystal fiber can be held stably against a fluidic counterflow using radiation pressure. The trap stiffness is large enough to keep the particles close to the center of the guided optical mode even in the presence of gravity, resulting in highly reproducible radiation forces. An immobility parameter μ i gives the flow rate needed to keep a particle stationary for unit optical power level.

By fitting the theory (including a more accurate model for the optical forces [13

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).

]) to precise experimental measurements, it should be possible to determine the diameter, refractive index and density of an unknown particle. For small (a << R) and large (a/R close to 1) particles the immobility parameter varies strongly with particle radius, allowing accurate size measurements. In the intermediate region it depends strongly on the particle refractive index, while it is less sensitive to variations in particle size. For borosilicate spheres (n p = 1.55) it is 2.5 times larger than that of a silica sphere (n p = 1.45) of the same size.

Our system has three major advantages of over existing optical chromatography methods [14

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

16

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]

]. Firstly, the microfluidic drag depends strongly on the exact particle radius, due to confinement effects. Secondly, the approximately circular symmetry of the core causes particles to self-align in the center of both the flow profile and the optical mode. Thirdly, the immobility measurement does not require a precise measurement of particle position.

The system offers fresh possibilities for studying the forces acting on particles in microfluidic channels. For example, if a trapped particle is pushed sideways using a laterally focused laser beam (which could be delivered through the cladding [17

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]

]), the imbalance of viscous drag on opposite sides will cause it to spin, enhancing chemical reactions at the particle surface. Such spinning has already been observed while the particle is being launched into the fiber [4

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

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]

].

In biomedical research, the system could be used to study optically induced deformations of cells [18

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]

]. In particular for large a/R values, small deformations would cause large changes in the immobility parameter. In addition, small concentrations of biochemicals could be applied to a cell optically held against a fluidic counterflow. Small changes in cell volume and refractive index could be observed through changes in the immobility. This would allow the study of the effectiveness of chemical therapy at the single cell level.

A useful extension to the existing setup would be to launch two counter-propagating beams into the fiber. In such a system the radial optical force can be changed independently of the axial force, as in Ashkin’s earliest optical trapping work [19

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

]. By adjusting the intensity ratio between the two beams, particles could be moved to and fro in a stationary liquid.

Acknowledgments

We are grateful to Silke Rammler, Michael Scharrer, Amir Abdolvand, Johannes Nold and Jocelyn Chen for help in designing and fabricating the fiber, and thank Sarah Unterkofler for experimental assistance. The work was partly funded by the Koerber Foundation.

References and links

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]

OCIS Codes
(350.4855) Other areas of optics : Optical tweezers or optical manipulation
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: August 4, 2011
Revised Manuscript: September 12, 2011
Manuscript Accepted: September 15, 2011
Published: September 22, 2011

Virtual Issues
Vol. 6, Iss. 10 Virtual Journal for Biomedical Optics

Citation
M. K. Garbos, T. G. Euser, and P. St. J. Russell, "Optofluidic immobility of particles trapped in liquid-filled hollow-core photonic crystal fiber," Opt. Express 19, 19643-19652 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19643


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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,” Nature457(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. Express12(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. Express14(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. Express18(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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited