## Design and optimization of a reflection-based fiber-optic tweezers

Optics Express, Vol. 16, Issue 22, pp. 17647-17653 (2008)

http://dx.doi.org/10.1364/OE.16.017647

Acrobat PDF (279 KB)

### Abstract

We present the numerical modelling of a novel all-fiber optical tweezers, whose efficacy has been recently demonstrated. The device, realized by properly shaping the end-face of a fiber bundle, exploits total internal reflection to enhance the trapping efficiency. In order to allow the optimization of the performance, the trapping efficiency is evaluated as a function of different geometrical parameters of the structure. Given the peculiar spatial and angular distribution of the optical field, a new figure of merit is adopted to assess tweezers performance.

© 2008 Optical Society of America

## 1. Introduction

1. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. **75**, 2787–2809 (2004). [CrossRef]

2. V. Emiliani, D. Cojoc, E. Ferrari, V. Garbin, C. Durieux, M. Coppey-Moisan, and E. Di Fabrizio “Wave front engineering for microscopy of living cells,” Opt. Express **13**, 1395–1405 (2005). [CrossRef] [PubMed]

5. J. Chan, H. Winhold, S. Lane, and T. Huser “Optical Trapping and Coherent Anti-Stokes Raman Scattering (CARS) Spectroscopy of submicron-size particles,” IEEE J. Sel. Top. Quantum Electron. **11**, 858–863 (2005). [CrossRef]

6. K. Taguchi, H. Ueno, T. Hiramatsu, and M. Ikeda, “Optical trapping of dielectric particle and biological cell using optical fibre,” Electron. Lett. **33**, 1413–1414 (1997). [CrossRef]

7. Z. Liu, C. Guo, J. Yang, and L. Yuan “Tapered fiber optical tweezer for microscopic particle trapping: fabrication and application,” Opt. Express **14**, 12511–12516 (2006). [CrossRef]

8. C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fiber probe for three dimensional optical trapping, manipulation and analysis,” Nat. Photonics **1**, 723–727 (2007). [CrossRef]

## 2. Numerical analysis of the proposed fiber OT structure

8. C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fiber probe for three dimensional optical trapping, manipulation and analysis,” Nat. Photonics **1**, 723–727 (2007). [CrossRef]

*θ*in the region corresponding to the fiber cores so that the light propagating through the fibers experiences total internal reflection at the interface with the surrounding medium. Hence optical beams are first deflected into the cladding and then transmitted out of the fibers converging all in the same point, at an angle

*φ*with respect to the fiber axis. It’s worth noticing that if the cut is not exactly perpendicular with respect to the

*y*-

*z*plane, the beams will not converge exactly in the same point. Anyway, as the fabrication error in the cut rotation is < 0.5°, the maximum offset of the beam centre from the “ideal” trapping position is less than 1 µm. This effect is not particularly critical, as the beam size in the trapping position is significantly larger than the maximum error in beam position.

11. N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. **43**, 2485–2491 (1996). [CrossRef]

12. A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of Laguerre-Gaussian modes in optical tweezers,” Opt. Commun. **193**, 45–50 (2001). [CrossRef]

10. P. Minzioni, F. Bragheri, C. Liberale, E. Di Fabrizio, and I. Cristiani, “A Novel Approach to Fiber-Optic Tweezers: Numerical Analysis of the Trapping Efficiency,” IEEE J. Sel. Top. Quantum Electron. **14**, 151–157 (2008). [CrossRef]

*z*) are completely neglected. However this decomposition works correctly in the case of standard OT, where the strong focusing leads to a focal depth much smaller than the particle radius (

_{R}*R*). In such a case, as the momentum transfer between the photons and the particle is produced on the particle surface, which lies in the far field (being

_{p}*R*≫

_{p}*z*), the forces are reliably described.

_{R}**2**~10) and the corresponding Rayleigh range can be much larger than the distance between the fiber-end and the trapping position. Hence, the particle surfaces cannot be considered as being always in the far-field, and the traditional ray optics description (reliable only when the distance between the fiber end-face and the particle surfaces is much larger than

*z*) cannot be applied.

_{R}13. E. Sidick, S. D. Collins, and A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt **36**, 6423–6433 (1997). [CrossRef]

*z*, provided that the considered beams are not tightly focused and that the propagation can be described through paraxial approximation. After each propagation step

_{R}*Δz*’ along the fiber axis (

*z*’ in Fig. 2a) a new set of optical rays is defined by calculating the amplitude and the wave-front curvature of the Gaussian beam:

*A*(

*ρ*,

*z*’) and

*r*(

*ρ*,

*z*’) respectively. The amplitude is used to assess the optical power associated to each ray, while the curvature radius is used to determine their propagation direction, which is perpendicular to the wave-fronts. It is worth noticing that the procedure to calculate the optical field is an approximation since the resulting rays’ directions depend on the propagation coordinate

*z*. Anyway the obtained field profile introduces the proper correction for the finite beam dimension in the focal point.

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

10. P. Minzioni, F. Bragheri, C. Liberale, E. Di Fabrizio, and I. Cristiani, “A Novel Approach to Fiber-Optic Tweezers: Numerical Analysis of the Trapping Efficiency,” IEEE J. Sel. Top. Quantum Electron. **14**, 151–157 (2008). [CrossRef]

*x*,

*y*,

*z*) shown also in Fig. 1, where

*z*is the probe axis, and the fiber cores lie on the

*x*or

*y*axis. As the propagation direction of the beams coming out from the fibers is tilted with respect to the bundle axis by a known angle

*φ*, a simple change of the frame of reference is needed. For each possible position of the particle in the (

*x*,

*y*,

*z*) space, we determine its position in the cylindrical frame of reference associated to each fiber (

*ρ*,

*z*’), we calculate the corresponding force and then we simply sum the contributions of all the four fibers.

*Q*, defined as a function of the total force (

*F*), the total optical power (

_{T}*P*), the medium refractive index (

*n*), and the speed of light in vacuum (

_{M}*c*):

*Q*(

*x*,

*y*,

*z*)=

*c*

*F*(

_{T}*x*,

*y*,

*z*)/

*n*. Figure 3(a) shows the

_{M}P*Q*distribution obtained by illuminating a sphere whose radius and index of refraction are 5 µm and 1.59 respectively. The BB-TOFT has the structure shown in Fig. 1: the radius of the annulus along which the fibers’ cores are disposed is

*R*=55 µm, the fibers have a MFD=8 µm and the cutting angle is

*θ*=66°. It can be seen that the optical trap is formed at a distance of about 27 µm from the bundle end-face. The

*Q*parameter is shown in the

*yz*plane; due to the symmetric arrangement of the four fibers, identical results can be obtained in the

*xz*plane.

*ε*), which is the minimum energy necessary to a particle in order to escape from the trap [10

_{esc}10. P. Minzioni, F. Bragheri, C. Liberale, E. Di Fabrizio, and I. Cristiani, “A Novel Approach to Fiber-Optic Tweezers: Numerical Analysis of the Trapping Efficiency,” IEEE J. Sel. Top. Quantum Electron. **14**, 151–157 (2008). [CrossRef]

*ε*a two-stage computation is performed. At first we calculate the work per unit power (

_{esc}*ε*) that has to be done against the optical forces to move a particle along a straight-line connecting the centre of the trap to any possible target point in the surrounding space. As a second step, we evaluate, for any possible linear escape trajectory, the maximum value of

_{TP}*ε*, thus identifying the energy required to move a particle along the corresponding path. The minimum among these values is defined as

_{TP}*ε*and the corresponding trajectory is the most energetically favoured escape path. Hence it is easy to figure

_{esc}*ε*as the “trap-depth” and it is also evident that the highest and lowest values of

_{esc}*ε*can be found along the beam propagation directions. In particular, the most favoured escape path is along the propagation directions of the slanted rays coming from the fibers (

_{TP}*ε*≈ 2.53 fJ/W), whereas the less likely path is along the same direction, but in the opposite heading. It is worth noticing that the resulting

_{esc}*ε*value is similar to those obtained considering a strongly focused Gaussian beam, as used in standard OT. Figure 3(b) shows a colormap of

_{esc}*ε*obtained by integrating the forces of Fig. 3(a). The attached movie shows the three dimensional shape of the quantity

_{TP}*ε*, where the optical trap clearly resembles a potential well.

_{TP}## 3. BB-TOFT optimization

*ε*as a figure of merit we can evaluate the BB-TOFT trapping efficiency in order to optimize its design. We consider three fundamental parameters: the radius (

_{esc}*R*) of the annulus along which the fibers’ cores are disposed, the fiber MFD and the cutting angle

*θ*. The values of

*R*and MFD affect essentially the conformation of the trap: as shown in Fig. 4(a), 4(b) for a fixed value of

*θ*(

*θ*=68°) the distance between the probe-end and the optical trap becomes larger, while

*ε*decreases by increasing

_{esc}*R*.

*ε*is larger for

_{esc}*R*< 50µm, since the propagation distance outside the fiber is short, showing a maximum value of 4.2 fJ/W for the case

*R*=35 µm and MFD=8 µm. By further increasing the MFD (12 < MFD < 16 µm) we observe that the slope of the curves reported in Fig. 4(a) strongly decreases; this can be explained by considering that diffraction becomes less relevant as the beams have a larger MFD and a longer propagation doesn’t sensibly modify the trapping efficiency.

*ε*is lowered by increasing the MFD; this happens because the optical intensity is distributed on a larger region, and the beam’s intensity gradient is thus lower. The third fundamental parameter is the cutting angle

_{esc}*θ*that affects both the BB-TOFT’s NA and its trapping distance. Figure 4(c) and 4d show that, considering a fixed value of

*R*(

*R*=55 µm)

*ε*decreases when the angle

_{esc}*θ*increases, while the trapping distance increases almost linearly. Also in this case it is possible to explain the behaviour by geometrical consideration. Indeed an increase of

*θ*corresponds to a decrease of the

*NA*, thus thrusting the rays to propagate with a smaller angle

*φ*with respect to the beam axis and increasing the scattering component of the forces. As in the previous case, the analysis has been performed for different values of MFD: as expected due to a lower impact of diffraction we find that an increase of MFD results in a higher trapping efficiency.

*ε*gets higher for MFD increasing from

_{esc}**2**to 10 µm, while a further increase of the size doesn’t result in any improvement (diffraction is no more limiting the trapping performance), and

*ε*is instead reduced because of the reduction in the beam intensity gradient. It is worth underlining that in the performances’ evaluation, reported in [10

_{esc}**14**, 151–157 (2008). [CrossRef]

_{R}from the fiber-end were not properly taken into account. Such a fact yielded to correct results in the case of OT realized with the annular-core fiber, but it caused an overestimation of the escape energy for the 4-fibers bundle structure. Indeed, at the same conditions (

*R*=55 µm, MFD=6 µm and cut angle

*θ*=70°) which yielded to an escape energy estimation of 1.75 fJ/W, a much lower value (0.31 fJ/W) is now obtained, thus confirming the need for an accurate description of the beam propagation features as they have a relevant impact on the trap formation.

*θ*and of the bundle dimension

*R*results in a more efficient optical trap, while the trapping position gets closer to the fiber end-facet. The experimental verification of the trapping distance, carried out as shown in [8

8. C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fiber probe for three dimensional optical trapping, manipulation and analysis,” Nat. Photonics **1**, 723–727 (2007). [CrossRef]

*R*, must be identified as a trade off between the impact of diffraction and the reduction of the intensity gradient produced using a larger MFD.

## 4. Conclusion

*ε*. Our study shows that in order to optimize the performance of the proposed fiber-optic tweezers the fiber MFD should range from 8 to 10 µm. Moreover we find out that once the beam size is chosen a further improvement is obtained by keeping the radius of the annulus and the cut angle as small as possible. It is worth noticing that the critical value of the angle for total reflection is

_{esc}*θ*=66.5°; anyway, if a metallic coating is deposited on the cut surfaces, the angle can be lowered down, increasing the value of

_{c}*ε*, while avoiding total internal reflection at the second interface between the fiber and the outer medium.

_{esc}## Acknowledgments

## References and links

1. | K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. |

2. | V. Emiliani, D. Cojoc, E. Ferrari, V. Garbin, C. Durieux, M. Coppey-Moisan, and E. Di Fabrizio “Wave front engineering for microscopy of living cells,” Opt. Express |

3. | M. Goksor, J. Enger, and D. Hanstorp “Optical manipulation in combination with multiphoton microscopy for single-cell studies,” Appl. Opt. |

4. | C.M. Creely, G. Volpe, G.P. Singh, M. Soler, and D.V. Petrov, “Raman imaging of floating cells,” Opt. Express |

5. | J. Chan, H. Winhold, S. Lane, and T. Huser “Optical Trapping and Coherent Anti-Stokes Raman Scattering (CARS) Spectroscopy of submicron-size particles,” IEEE J. Sel. Top. Quantum Electron. |

6. | K. Taguchi, H. Ueno, T. Hiramatsu, and M. Ikeda, “Optical trapping of dielectric particle and biological cell using optical fibre,” Electron. Lett. |

7. | Z. Liu, C. Guo, J. Yang, and L. Yuan “Tapered fiber optical tweezer for microscopic particle trapping: fabrication and application,” Opt. Express |

8. | C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, “Miniaturized all-fiber probe for three dimensional optical trapping, manipulation and analysis,” Nat. Photonics |

9. | A. Ashkin, “Forces of a single beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. |

10. | P. Minzioni, F. Bragheri, C. Liberale, E. Di Fabrizio, and I. Cristiani, “A Novel Approach to Fiber-Optic Tweezers: Numerical Analysis of the Trapping Efficiency,” IEEE J. Sel. Top. Quantum Electron. |

11. | N. B. Simpson, L. Allen, and M. J. Padgett, “Optical tweezers and optical spanners with Laguerre-Gaussian modes,” J. Mod. Opt. |

12. | A. T. O’Neil and M. J. Padgett, “Axial and lateral trapping efficiency of Laguerre-Gaussian modes in optical tweezers,” Opt. Commun. |

13. | E. Sidick, S. D. Collins, and A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt |

**OCIS Codes**

(060.2310) Fiber optics and optical communications : Fiber optics

(170.3890) Medical optics and biotechnology : Medical optics instrumentation

(170.4520) Medical optics and biotechnology : Optical confinement and manipulation

(230.1150) Optical devices : All-optical devices

**ToC Category:**

Optical Trapping and Manipulation

**History**

Original Manuscript: June 23, 2008

Revised Manuscript: August 28, 2008

Manuscript Accepted: August 28, 2008

Published: October 17, 2008

**Virtual Issues**

Vol. 3, Iss. 12 *Virtual Journal for Biomedical Optics*

**Citation**

F. Bragheri, P. Minzioni, C. Liberale, E. Di Fabrizio, and I. Cristiani, "Design and optimization of a reflection-based fiber-optic tweezers," Opt. Express **16**, 17647-17653 (2008)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-16-22-17647

Sort: Year | Journal | Reset

### References

- K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004). [CrossRef]
- V. Emiliani, D. Cojoc, E. Ferrari, V. Garbin, C. Durieux, M. Coppey-Moisan, and E. Di Fabrizio "Wave front engineering for microscopy of living cells," Opt. Express 13, 1395-1405 (2005). [CrossRef] [PubMed]
- M. Goksor, J. Enger, and D. Hanstorp "Optical manipulation in combination with multiphoton microscopy for single-cell studies," Appl. Opt. 43, 4831-4837 (2004). [CrossRef] [PubMed]
- C. M. Creely, G. Volpe, G. P. Singh, M. Soler, and D. V. Petrov, "Raman imaging of floating cells," Opt. Express 12, 6105-6110 (2005). [CrossRef]
- J. Chan, H. Winhold, S. Lane, and T. Huser "Optical Trapping and Coherent Anti-Stokes Raman Scattering (CARS) Spectroscopy of submicron-size particles," IEEE J. Sel. Top. Quantum Electron. 11, 858-863 (2005). [CrossRef]
- K. Taguchi, H. Ueno, T. Hiramatsu, and M. Ikeda, "Optical trapping of dielectric particle and biological cell using optical fibre," Electron. Lett. 33, 1413-1414 (1997). [CrossRef]
- Z. Liu, C. Guo, J. Yang, and L. Yuan "Tapered fiber optical tweezer for microscopic particle trapping: fabrication and application," Opt. Express 14, 12511-12516 (2006). [CrossRef]
- C. Liberale, P. Minzioni, F. Bragheri, F. De Angelis, E. Di Fabrizio, and I. Cristiani, "Miniaturized all-fiber probe for three dimensional optical trapping, manipulation and analysis," Nat. Photonics 1, 723-727 (2007). [CrossRef]
- A. Ashkin, "Forces of a single beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992). [CrossRef] [PubMed]
- P. Minzioni, F. Bragheri, C. Liberale, E. Di Fabrizio, and I. Cristiani, "A Novel Approach to Fiber-Optic Tweezers: Numerical Analysis of the Trapping Efficiency," IEEE J. Sel. Top. Quantum Electron. 14, 151-157 (2008). [CrossRef]
- N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. Mod. Opt. 43, 2485-2491 (1996). [CrossRef]
- A. T. O'Neil and M. J. Padgett, "Axial and lateral trapping efficiency of Laguerre-Gaussian modes in optical tweezers," Opt. Commun. 193, 45-50 (2001). [CrossRef]
- E. Sidick, S. D. Collins, and A. Knoesen, "Trapping forces in a multiple-beam fiber-optic trap," Appl. Opt 36, 6423-6433 (1997). [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.