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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 24 — Nov. 22, 2010
  • pp: 25299–25305
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All-silica fiber Bessel-like beam generator and its applications in longitudinal optical trapping and transport of multiple dielectric particles

Sung Rae Lee, Jongki Kim, Sejin Lee, Yongmin Jung, Jun Ki Kim, and K. Oh  »View Author Affiliations


Optics Express, Vol. 18, Issue 24, pp. 25299-25305 (2010)
http://dx.doi.org/10.1364/OE.18.025299


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Abstract

A Bessel-like beam was generated in a novel all-fiber integrated structure. A concentric ring intensity pattern was achieved by the multimode interference along the coreless silica fiber, which was then focused by the integrated micro-lens to result in a Bessel-like beam. The average beam diameter of 7.5 μm maintained over 500 μm axial length for a continuous wave Yb-doped fiber laser input oscillating at the wavelength of 1.08 μm. The generated beam was successfully applied to two-dimension optical trapping and longitudinal transport of multiple dielectric particles confirming its unique non-diffracting and self-reconstructing nature. Physical principle of operation, fabrication, and experimental results are discussed.

© 2010 OSA

1. Introduction

Recently novel attempts have been reported using fiber optics for BBG [10

10. S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008). [CrossRef] [PubMed]

,11

11. J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]

] to provide an integrated micro-solution, which is inherently compatible to rapidly developing rare earth ion doped fiber lasers [12

12. J. F. Michel, Digonnet, Rare-earth-doped fiber lasers and amplifiers (Marcel Dekker, 2001).

]. A single mode fiber end has been chemically etched to form a conical-shaped axicon at the fiber tip [10

10. S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008). [CrossRef] [PubMed]

], but its non-diverging length was very limited in comparison to bulk counterpart. Recently the authors have reported a novel composite optical fiber BBG device in the visible lasers with a non-diffracting length over 1 mm comparable to bulk axicons [11

11. J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]

]. The device structure was fiber optic analogue of Durnin's method [7

7. J. Durnin, J. J. Miceli Jr, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]

,11

11. J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]

] showing a strong potential for compact and integrated micro BBG device, but it required a special hollow optical fiber [13

13. S. K. Oh, Choi, Y. Jung, and J. W. Lee, “Novel Hollow Optical Fibers and Their Applications in Photonic Devices for Optical Communications,” J. Lightwave Technol. 23(2), 524–532 (2005). [CrossRef]

] along with optimized splice conditions, and a separate post-process to form a polymeric lens.

In this study we report a new type of novel all-fiber BBG device fully compatible to Yb-doped fiber laser at the wavelength of 1.08 μm providing an integrated all-fiber micro-solution for laser beam shaping, for the first time. We successfully demonstrated two-dimensional optical trapping and transport of multiple dielectric particles along the axial direction to confirm both non-diffracting and self-reconstructing natures of the Bessel-like beam.

2. Theoretical base and fabrication of all-fiber BBG

Bessel beam is a particular solution of Helmholtz wave equation for a monochromatic wave as in Eq. (1). Its propagation along the axial direction, z, is decoupled from the extension of the wave in the transverse plane as in Eq. (2) [3

3. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005). [CrossRef]

,7

7. J. Durnin, J. J. Miceli Jr, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]

].

(2+k2)Φ(x,y,z;κ)=0.
(1)
ΦB(x,y,z;κ)=J0(αρ)eiβz.
(2)

The solution includes J0(x), zeroth-order Bessel function, where α2+β2=κ2, x2+y2=ρ2. The Bessel function results in a concentric ring intensity pattern and its central peak plays the major role to provide the gradient force for optical trapping of dielectric particles [4

4. J. Arlt, V. Garces-chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001). [CrossRef]

]. Bessel-like beams generated by bulk axicons maintain the focused central spots along the axial direction over several milimeters, which is dependent upon the cone angle, radius, and the refractive index of the axicon [14

14. S. Monk, J. Arlt, and M. J. Padgett, “The generation of Bessel beams at millimeter-wave frequencies by use of an axicon,” Opt. Commun. 170(4-6), 213–215 (1999). [CrossRef]

]. Alignment of the incident laser beam along the axicon axis, whose diameter is 50~100 mm [14

14. S. Monk, J. Arlt, and M. J. Padgett, “The generation of Bessel beams at millimeter-wave frequencies by use of an axicon,” Opt. Commun. 170(4-6), 213–215 (1999). [CrossRef]

], has been a critical issue and highly stabilized beam steering systems have been required.

Despite very successful implementation of bulk axicon in BBG, its large form factor and tight alignment tolerance has become a major bottleneck for further micro-nano scale applications such as in-vivo investigations of nano-bio particles. Therefore, alignment-free micron-scale integrated BBG device would open a new avenue of optical trapping applications in the emerging nano-bio science.

The schematic structure of the proposed BBG is shown in Fig. 1
Fig. 1 (a) Schematic diagram of the principle of Bessel-like beam generation in the proposed all-fiber BBG device by multi-mode interference. (b) Photographic image of the fabricated all-fiber BBG and its geometrical parameters.
. It is composed of three fiber segments serially concatenated: single mode fiber (SMF, Corning HI-1060), coreless silica fiber (CSF) drawn from a pure silica glass rod, and micro-lens formed at the end-facet of CSF. As in Fig. 1(a), the fundamental LP 01 mode from the input SMF excites LP 0m higher order modes in CSF. In the multi-mode interference (MMI) theory, these excited modes can form a basis set to form an arbitrary field distribution Eoutas they propagate [15

15. X. Zhu, A. Schülzgen, H. Li, H. Wei, J. V. Moloney, and N. Peyghambarian, “Coherent beam transformations using multimode waveguides,” Opt. Express 18(7), 7506–7520 (2010). [CrossRef] [PubMed]

].

Eout(r,φ,l)=m=1Cmem(r,φ)eiβml
(3)

Here em(r,φ)is the electric field of the LP 0m modes excited along CSF, with their amplitudes of Cm and the propagation constants of βm. l is the length of CSF. In this study, we used CSF whose diameter was 125 μm and the surrounding air served as the cladding to allow significantly larger number of excited modes enough to obtain Bessel-like field distribution in comparison to conventional multimode fibers whose core diameter are in the range of 50~62.5 μm. The excited symmetric modes propagate along the CSF accumulating the phase differences to form a concentric intensity distribution similar to Bessel function by MMI at an optimal propagation length l of CSF. This concentric ring MMI pattern is then focused by integrated fiber lens formed at the end facet of the CSF to subsequently generate a Bessel-like beam. Note that the proposed device is based on MMI along the fiber and its imaging, in contrast to prior Fourier transformation techniques used in the ring apertures [7

7. J. Durnin, J. J. Miceli Jr, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]

,11

11. J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]

] and axicons [9

9. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6(1), 150–152 (1989). [CrossRef]

].

A photograph of the fabricated device is shown in Fig. 1(b). The SMF provided the fundamental LP 01 mode guidance for the incident Yb-doped fiber laser at the wavelength of 1.08 μm with the the mode field diameter of ~4.3 μm. The SMF had the LP 01 mode cut-off near 920 nm and the relative core-cladding refractive index, Δ, was 1%. CSF was drawn from a fused silica rod to the cladding diameter of 125 μm. The SMF and CSF were seamlessly connected by electric arc fusion splices. The fiber lens at the end of CSF was fabricated by applying an electric arc over the vertically cleaved end-facet of CSF. The high temperature of the electrical arc melted the CSF, which flew over the CSF cross-section to form a convex lens. Note that all the constituents of the proposed device are centered along the fiber axis obviating tedious alignment efforts required in the conventional bulk axicons. It is also noteworthy that the device thickness is reduced to 125 μm, which can provide flexible and efficient maneuvering capability for in-vivo optical trapping applications.

3. Simulation based on MMI theory

The evolution of the light intensity pattern from the incident LP 01 mode in the SMF along the CSF, and through the fiber lens was numerically investigated using a beam propagation method (BPM) package. The most critical parameters for Bessel-like beam generation were: the radius of the fiber lens, rlens, the CSF diameter, dcsf, and the CSF length, l c, which directly affected the non-diffracting length, Zmax, central beam intensity, and central peak diameter of the output beam. After manipulating all these parameters, we discovered geometric optimization for Bessel-like beam generation, where rlens is near 80 μm and dcsf is 125 μm.

4. Experiment results

-Beam intensity distribution of transverse and longitudinal plane

Based upon numerical analysis, we fabricated proposed BBG devices with three different CSF lengths, l c=400, 1600, and 2400 μm. The radius of curvature of the fiber lens was set to 82 μm by optimizing the arc-conditions. A picture of the fabricated device is shown in Fig. 1(b) along with its geometrical parameters. A continuous wave (CW) Yb-doped fiber laser (λin =1.08 μm) was used as a light source, whose laser cavity was closed by fiber Bragg grating and pumped by fiber coupled 910 nm laser diodes. The input optical power of the laser was 89.52 mW and the output power of the device was 81.13 mW, which corresponds to a low insertion loss of 0.42 dB.

In order to confirm the Bessel-like beam pattern, we measured the cross-sectional intensity distributions of the output beam using an infrared CCD camera (Edmund eo1312) at every 50 μm along the z axis. For precise measurements, the proposed device was mounted on an electro-mechanical translation system with the position control accuracy of 0.1 μm. The measured intensity patterns are summarized in Fig. 3
Fig. 3 Intensity distributions for the beam from the fabricated all-fiber BBG device, measured by CCD camera. The CSF length was l c=1600 μm and the axial position was (a) z=150 μm, (b) 450 μm, (c) 550 μm.
for the axial distances of 100, 450, and 550 μm. The images in the upper row of Fig. 3 clearly show Bessel-like beam characteristics with the central spike surrounded by concentric ring intensity patterns, which showed a good agreement with numerical analysis in Fig. 2(c) for l c=1600 μm. The line profiles of the measured intensity distributions are shown in the lower row of Fig. 3, which also confirmed that the output beam can be well approximated to the zero-th order Bessel function. It was also noted that this Bessel-like beam intensity distribution remained over the axial distance of 500 μm as predicted by BPM in Fig. 2(c).

To confirm the non-diffractive nature of the Bessel-like beam from the proposed device, we further measured the variations in the intensity at the central peak and its full width at half maximum (FWHM) diameter along the axial direction. The experimental measurements are summarized in Fig. 4
Fig. 4 (a) The central peak intensity profile along the longitudinal direction for the propose device (red line) and vertically cleaved SMF (black line). The right axis is the FWHM diameter, dFWHM. Red squares are for the proposed device and black circles are for SMF. (b) longitudinal intensity distribution for the proposed devices with various CSF lengths.
.

The output beam of the proposed device, the red line, maintained its peak intensity over the axial distance of 500 μm in Fig. 4(a). In contrast, the axial power from the cleaved conventional SMF rapidly decreased due to its diffracting nature as in black line. Within the non-diffracting length, the proposed device shows the average FWHM beam diameter, dFWHM of 6.44 μm ranging from the minimum of 3.89 μm at the focal plane of fiber lens around z = 250 μm to the maximum of 8.57 μm at z = 600 μm. See the red squares in Fig. 4(a). The axial intensity distributions of the fabricated devices with various CSF lengths are shown in Fig. 4(b). For the CSF length of l c = 400 μm, the device showed a shorter non-diffracting length of ~400 μm. In the case of 2400 μm long CSF, the axial intensity showed a large fluctuation with an abrupt decrease over the axial position of 500 μm. The device with the optimal CSF length near 1600 μm showed the most stable and longest non-diffracting length, which is in a good agreement with the numerical prediction in Fig. 3.

-Optical trapping and transport of multiple dielectric particles

As a final step to validate the self re-construction nature of the Bessel-like beam from the proposed device, we carried out optical trapping experiments using polystyrene dielectric beads. A micro channel with 200 μm width 200 μm height for was devised for the fiber BBG device and the channel was connected to a circular reservoir that contained a milk-water suspension [11

11. J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]

] and 10 μm diameter polystyrene beads with the refractive index nb = 1.55. The non-diffracting beam silhouette from the proposed device was clearly observed by the scattering in the colloidal solution as in Fig. 5(a)
Fig. 5 (a) The image of Bessel-like beam propagation out of the proposed device in a colloidal solution. (b) Optical trapping of multiple dielectric particles(marked as white arrows) and subsequent optical transport along the axial direction.
. Using a CCD camera mounted on an inverted microscope, we could successfully observe optical trapping and subsequent transport of the dielectric beads along the axial direction in a real-time video (25 frame per second). Particles near the edge of the beam were trapped toward the center by the gradient force and transported along the axial direction by radiation scattering force. It is also observed that two beads marked by white arrows were simultaneously trapped along z axis as shown in Fig. 5(b), which directly confirms the self-reconstructing nature of the beam from the proposed device.

In comparison to prior fiber axicons [10

10. S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008). [CrossRef] [PubMed]

], the proposed device can provide an order of magnitude longer non-diffracting length exceeding 500 μm, along which multiple particles can be trapped. Prior fiber axicons required optical power over 146mW [10

10. S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008). [CrossRef] [PubMed]

], yet the proposed device was operating normally at almost half of the power, 81.l3 mW, providing more efficient and faster 2D optical trapping of dielectric particles.

Recently pulsed laser Bessel beams have been reported to take advantage of broadband supercontinuum source [16

16. X. Tsampoula, K. Taguchi, T. Čižmár, V. Garces-Chavez, N. Ma, S. Mohanty, K. Mohanty, F. Guun-Moore, and K. Dholakia, “Fiber based cellular transfection,” Opt. Express 16(21), 17007–17013 (2008). [CrossRef] [PubMed]

]. The proposed device would also allow pulsed laser operation if the the average power of pulsed laser fairly corresponds to that of CW lasers used in the experiment and the center wavelength of pulsed laser will be near to that of CW laser.

5. Conclusion

In summary, we successfully proposed and demonstrated a novel all-fiber device to generate a Bessel-like beam based upon multimode interference along the coreless silica fiber segment and subsequent focusing its concentric ring pattern using a fiberized lens. Non-diffracting nature of the beam was predicted for an optimal coreless fiber length of 1600 μm and fiber lens radius of 82 μm. Experimentally the non-diffracting length over 500 μm with a low insertion loss of 0.42 dB was achieved for Yb-doped fiber laser at the wavelength of 1.08 μm, showing a good agreement with theoretical predictions. Self re-construction nature of the beam was also experimentally confirmed by trapping of multiple polystyrene beads of 10 μm diameter, and their transport along the axial direction. The proposed all-fiber device can be a very attractive alternative to conventional bulk optics to generate the Bessel-like beams opening new applications requiring an in situ compact integrated solution in optical manipulation of nano-meso-scopic particles can be readily applied in novel nano- and micro-pattern generation.

Acknowledgments

This work was supported in part by the NRF under Grant ROA-2008-000-20054-0, Grant R15-2004-024-00000-0, Grant 2009-8-2175, and Grant 2010-8-0939, Grant 2010-8-0037(the European Community's Seventh Framework Program [FP7/2007-2013] under Grant agreement no 219299, Gospel), Grant 2009-8-1339, Grant 2009-0093823, and in part by the Brain Korea 21 Project of the KRF.

References and links

1.

C. Scott, Holswade, and F. M. Dickey, Laser beam shaping (CRC, 2005).

2.

C. A. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a nondiffracting light beam,” Am. J. Phys. 67(10), 912–915 (1999). [CrossRef]

3.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005). [CrossRef]

4.

J. Arlt, V. Garces-chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001). [CrossRef]

5.

K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33(15), 1696–1698 (2008). [CrossRef] [PubMed]

6.

S. Juodkazis, H. Misawa, and I. Maksimov, “Thermal accumulation effect in three-dimensional recording by picoseconds pulses,” Appl. Phys. Lett. 85(22), 5239–5241 (2004). [CrossRef]

7.

J. Durnin, J. J. Miceli Jr, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]

8.

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31(15), 2708–2713 (1992). [CrossRef] [PubMed]

9.

G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6(1), 150–152 (1989). [CrossRef]

10.

S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008). [CrossRef] [PubMed]

11.

J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]

12.

J. F. Michel, Digonnet, Rare-earth-doped fiber lasers and amplifiers (Marcel Dekker, 2001).

13.

S. K. Oh, Choi, Y. Jung, and J. W. Lee, “Novel Hollow Optical Fibers and Their Applications in Photonic Devices for Optical Communications,” J. Lightwave Technol. 23(2), 524–532 (2005). [CrossRef]

14.

S. Monk, J. Arlt, and M. J. Padgett, “The generation of Bessel beams at millimeter-wave frequencies by use of an axicon,” Opt. Commun. 170(4-6), 213–215 (1999). [CrossRef]

15.

X. Zhu, A. Schülzgen, H. Li, H. Wei, J. V. Moloney, and N. Peyghambarian, “Coherent beam transformations using multimode waveguides,” Opt. Express 18(7), 7506–7520 (2010). [CrossRef] [PubMed]

16.

X. Tsampoula, K. Taguchi, T. Čižmár, V. Garces-Chavez, N. Ma, S. Mohanty, K. Mohanty, F. Guun-Moore, and K. Dholakia, “Fiber based cellular transfection,” Opt. Express 16(21), 17007–17013 (2008). [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(140.3300) Lasers and laser optics : Laser beam shaping
(160.2290) Materials : Fiber materials
(220.4000) Optical design and fabrication : Microstructure fabrication
(100.3175) Image processing : Interferometric imaging

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: August 3, 2010
Revised Manuscript: November 5, 2010
Manuscript Accepted: November 11, 2010
Published: November 19, 2010

Citation
Sung Rae Lee, Jongki Kim, Sejin Lee, Yongmin Jung, Jun Ki Kim, and K. Oh, "All-silica fiber Bessel-like beam generator and its applications in longitudinal optical trapping and transport of multiple dielectric particles," Opt. Express 18, 25299-25305 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-24-25299


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References

  1. C. Scott, Holswade, and F. M. Dickey, Laser beam shaping (CRC, 2005).
  2. C. A. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a nondiffracting light beam,” Am. J. Phys. 67(10), 912–915 (1999). [CrossRef]
  3. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005). [CrossRef]
  4. J. Arlt, V. Garces-chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197(4-6), 239–245 (2001). [CrossRef]
  5. K. S. Lee and J. P. Rolland, “Bessel beam spectral-domain high-resolution optical coherence tomography with micro-optic axicon providing extended focusing range,” Opt. Lett. 33(15), 1696–1698 (2008). [CrossRef] [PubMed]
  6. S. Juodkazis, H. Misawa, and I. Maksimov, “Thermal accumulation effect in three-dimensional recording by picoseconds pulses,” Appl. Phys. Lett. 85(22), 5239–5241 (2004). [CrossRef]
  7. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]
  8. Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31(15), 2708–2713 (1992). [CrossRef] [PubMed]
  9. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6(1), 150–152 (1989). [CrossRef]
  10. S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008). [CrossRef] [PubMed]
  11. J. K. Kim, J. Kim, Y. Jung, W. Ha, Y. S. Jeong, S. Lee, A. Tünnermann, and K. Oh, “Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens,” Opt. Lett. 34(19), 2973–2975 (2009). [CrossRef] [PubMed]
  12. J. F. Michel, Digonnet, Rare-earth-doped fiber lasers and amplifiers (Marcel Dekker, 2001).
  13. S. K. Oh, Choi, Y. Jung, and J. W. Lee, “Novel Hollow Optical Fibers and Their Applications in Photonic Devices for Optical Communications,” J. Lightwave Technol. 23(2), 524–532 (2005). [CrossRef]
  14. S. Monk, J. Arlt, and M. J. Padgett, “The generation of Bessel beams at millimeter-wave frequencies by use of an axicon,” Opt. Commun. 170(4-6), 213–215 (1999). [CrossRef]
  15. X. Zhu, A. Schülzgen, H. Li, H. Wei, J. V. Moloney, and N. Peyghambarian, “Coherent beam transformations using multimode waveguides,” Opt. Express 18(7), 7506–7520 (2010). [CrossRef] [PubMed]
  16. X. Tsampoula, K. Taguchi, T. Čižmár, V. Garces-Chavez, N. Ma, S. Mohanty, K. Mohanty, F. Guun-Moore, and K. Dholakia, “Fiber based cellular transfection,” Opt. Express 16(21), 17007–17013 (2008). [CrossRef] [PubMed]

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