Abstract

We report on the generation of vector vortex beams using a 10-μm core multimode liquid core optical fiber (LCOF) filled with CS2. The first higher-order modes including radially, azimuthally and hybrid polarized vector modes, as well as the higher-order modes such as LP21 mode and LP31 mode are selectively excited by adjusting the incidence angle of the linearly polarized input Gaussian beam with respect to the fiber axis. The interferograms with single forklet verify the phase singularity of the vector beams generated. Compared to silica optical fibers, the vector vortex beams from the LCOFs have higher excitation efficiency and larger bending tolerance.

© 2014 Optical Society of America

1. Introduction

The vortex beam with the phase singularity is characterized by a doughnut-shaped spatial profile and spiral phase term of exp(i) (l: topological charge; θ: azimuthal angle). That makes it carry an orbital angular momentum of lper photon. Such beam can be potentially applied to atom trapping and guiding, material processing, free space optical communication, and so on [18]. The vector beams with the radial, azimuthal and hybrid polarizations have attracted great interest due to their peculiar focusing properties [9,10]. These beams possess polarization singularities at the center, similar to phase vortices, leading to doughnut intensity distributions. The vector vortex beam (VVB) with phase and polarization singularities has been demonstrated a sharper focal spot than common vector beams [1113], which is useful in super-resolution microscopy, lithographic optics and atom lenses. The VVB was obtained by using a linearly polarized beam propagating through a radial or azimuthal polarization converter and then a vortex phase plate or spiral phase hologram.

The VVB can also be generated conveniently by utilizing the mode conversion inside the optical fiber. The first higher-order vector modes including TM01 mode (radial polarization), TE01 mode (azimuthal polarization) and HE21 (hybrid polarization) inside the fiber waveguide can be directly excited by adjusting the launch condition or the input beam polarization. The phase singularities of these vector modes have been verified [1416]. Viswanathan et al. reported first the generation of a radially polarized LG01 beam, linearly polarized HG10 and HG01 beams by changing the direction of the linear input polarization at a fixed off-axis coupling orientation using a two-mode fiber [14]. Furthermore, the different vector vortex modes can be excited and switched depending on the handiness of circular-polarization of the input Gaussian light beam and its launch angle with respect to the fiber axis [15]. Recently, Fang et al. investigated the impact of the polarization states of Gaussian incident beam and off-axis conditions on the excitation of vector vortex modes in a few-mode fiber, and concluded that only linearly polarized incident beam could excite the inhomogeneous polarizations at different off-axis conditions [16]. Experiments have demonstrated that this method of off-axis coupling has advantages of simple structure, convenient operation and low cost. However, the refractive index difference between the core and cladding in two- or few-mode fibers is relatively low. As a result, the excited modes are sensitive to the fiber bending, and the off-axis coupling efficiency is also very low (i.e., 7%).

Another method of exciting the vector vortex modes in the fiber is on-axially injecting a Hermit-Gaussian (HG) beam or first-order Laguerre-Gaussian (LG) beam into the fiber and stressing the fiber using a polarization controller or other stress providing devices [1719]. The method has excitation efficiency of 50%. Nevertheless, additional devices for generating HG or LG beam and controlling stress are required.

In this paper, we present a method for generating vector vortex beams by off-axis coupling a linearly polarized Gaussian beam into a small core multimode liquid core optical fiber (LCOF). In the LCOF, the refractive index of the core can be varied flexibly by selecting different liquids, resulting in the change of the modal number. It has been verified the LCOF has tunable and low bending loss [20]. And also, the LCOF has been developed a novel platform for photonic devices and has bright prospects [2124]. In our experiment, CS2 is chosen as core liquid owing to its high refractive index (1.62 at 632.8nm) and low absorption [25,26]. The LP11 mode and higher-order modes are excited at different off-axis orientations. Compared with few-mode silica fiber, the VVBs generated by the multimode LCOF are insensitive to the bending, and have higher coupling efficiencies because of larger numerical aperture (NA).

2. Experimental setup

A schematic of the experimental setup is shown in Fig. 1. The light source used is an internal-mirror He-Ne laser with the output of a partially polarized Gaussian beam. A polarizer (P1) is used to form a linearly polarized (LP) light. The LP beam passing through a beam splitter (BS1) is then focused by a microscope objective lens (L1, 0.25 NA 10 × ) into the CS2 filled LCOF, which is fixed on the five-dimension optical stage. The length and core diameter of the LCOF here are 75cm and 10μm, respectively. The refractive index of CS2 is 1.62 at 632nm, as a result, the NA of the filled fiber is around 0.68, indicating that the LCOF is highly multimode for the 10μm-core diameter (the V-parameter is equal to 33.7 at 632.8nm). The LCOF output intensity pattern is collimated using a lens L2, and imaged on the CCD after transmitting through a beam splitter (BS2). The interference pattern of the transmitted beam by the BS2 and the reflected plane beam by the BS1, M1, M2 and BS2 (dashed line in Fig. 1) can be recorded by the CCD to analyze the phase singularity of the output beam. A rotating polarizer (P2) can be placed between L2 and BS2 to analyze the polarization state of the output beam.

 figure: Fig. 1

Fig. 1 Experimental setup. P1,2, polarizers; BS1,2, beam splitters; L1,2, lenses; LCOF, liquid core optical fiber; M1,2, mirrors.

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In the experiment, we use a fused silica capillary to fabricate the LCOF. Both ends of the LCOF are held tightly by the entrance and exit cell that filled with the liquid (see the dotted box of Fig. 1). The filling is done from one end by capillary action. After the liquid reaches the opposite end of the capillary, the second cell is filled with the liquid. The two access ports are then sealed. In these processes, two points should be noted: one is that the capillary is properly filled without any air gaps or bubbles in it; two is that the end face of the capillary closes to the quartz window to obtain good coupling.

2. Experimental results and discussions

When fixing the polarization of the incident Gaussian beam, the fundamental mode and some higher-order waveguide modes can be selectively excited by adjusting the angle and position of the input beam relative to the LCOF axis, as shown in Fig. 2. The fundamental mode LP01 is selected at an on-axis input condition, corresponding to the coupling efficiency of about 50% [Fig. 2(a)]. For off-axis illumination, the first higher-order LP11 modes [Figs. 2(b) and 2(c)], as well as other higher-order modes such as LP21 [Fig. 2(d)] and LP31 (not shown) can be excited. The LP11 comprises several intrinsic vector modes (TM01, TE01 and HE21). The linear combination of these eigenmodes can generate different intensity patterns of the LP11 including the doughnut mode [Fig. 2(b)] and two-lobe mode [Fig. 2(c)] [27], whose excitation efficiencies are measured to be about 37%. This value is much larger than the efficiency of vector modal excitation in a few-mode silica fiber (7%) [16]. The reason is that the CS2 filled LCOF has relatively high NA, the slightly off-axis coupling has less effect on its efficiency. On the other hand, the high-order modes with large modal areas also find applications in high-power fiber lasers [28]. These high-order modes can be further amplified by stimulated Brillouin scatter [29] or stimulated Raman scattering [30] to meet the application requirements. Figure 3 depicts the interference pattern of the doughnut LP11 mode and reflected reference beam. It can be seen that a single forklet is situated in the middle of the pattern, indicating that the doughnut mode has the phase singularity, and confirms to be the optical vortex beam with single topological charge.

 figure: Fig. 2

Fig. 2 Near-field images of the intensity distribution of the fundamental mode and higher-order modes. (a) LP01 mode; (b) doughnut LP11 mode; (c) two-lobe LP11 mode; (d) LP21 mode.

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 figure: Fig. 3

Fig. 3 Interferogram generated by combining the doughnut LP11 mode with a plane reference beam.

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We also obtain various doughnut LP11 modes with the radial, azimuthal and hybrid polarization states using the LCOF based on the method of controlling the off-axis orientation [16]. Three types of polarizations can be distinguished by rotating the polarizer. When the dark line between the two lobes transmitted through the polarizer rotates in the opposite direction as the polarizer, the hybrid polarized HE21 mode is excited [Fig. 4(a)]; when the dark line rotates in the same direction, the radially polarized TM01 mode or azimuthally polarized TE01 mode is selected. The direction of the dark line is perpendicular to the direction of the polarizer for TM01 mode [Fig. 4(b)] and parallel to it for TE01 mode [Fig. 4(c)] [27]. Figures 3 and 4 show that the hollow beams generated by a small core multimode LCOF possess phase and polarization singularities, belonging to the VVBs.

 figure: Fig. 4

Fig. 4 Near-field images of the intensity distribution of the doughnut LP11 modes with different polarizations (Column 1), corresponding intensity profiles after passing a polarizer orientated in the direction of the arrow (Column 2-5) and corresponding polarization patterns (Column 6). (a) hybrid polarized HE21 mode; (b) radially polarized TM01 mode; (c) azimuthally polarized TE01 mode.

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The influence of bending on the intensity distribution of the vector vortex is also investigated. The LCOF is bent with a constant radius of curvature (R), varying from infinity (straight configuration) down to 3 cm. The experimental results reveal that the doughnut mode remains for varying bending radius (straight fiber, 7 cm, 5cm and 3 cm), though its intensity distribution slightly changes, as shown in Fig. 5. As a comparison, we repeat the above experiment using a 75-cm-long piece of standard Ge-doped silica optical fiber (Corning, SMF-28e). The fiber has a calculated V-number of 6.95 at 632.8nm. The doughnut mode excited at an off-axis orientation and two-beam interference pattern are plotted in Fig. 6. The forklet interference pattern verifies that the output beam from the silica fiber is also vortex beam with single topological charge. The silica fiber is bent with the same radius of curvature as the LCOF. Unfortunately, the output pattern is distorted seriously, as shown in Fig. 7, it sometimes appears in a two-lobe mode [Figs. 7(b) and 7(c)] and sometimes in other distorted mode [Fig. 7(d)]. The propagating mode field along the fiber is associated with the change of refractive indices of the fiber core and cladding. The equivalent refractive index profile of the bent fiber can be expressed as [31,32]

nR(x)=n(x)(1+xR)
where n(x) is the refractive index profile of the straight fiber, x stands for the distance from the central core in a fiber cross section. According to Eq. (1), nR increases with x for the same R. As a result, for the bent fiber the refractive index has a larger augment in the cladding than in the core with respect to the straight one, leading to the decreased index difference between the core and the cladding. In our experiment, the index difference of the silica fiber (Δn = 0.01) is much smaller than that of the LCOF (Δn = 0.14). Thereby, when bending the fiber, the propagating mode of the silica fiber can couple more easily to cladding modes, resulting in the mode conversion or distortion. By contrast, the LCOF has a greater bending tolerance and controllable mode number by selecting core liquid with appropriately high refractive index and smaller core diameter.

 figure: Fig. 5

Fig. 5 Near field patterns of the doughnut LP11 modes generated by the LCOF for different bending radius. (a) straight fiber; (b) 7cm; (c) 5cm; (d) 3cm.

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 figure: Fig. 6

Fig. 6 Near field patterns of (a) the doughnut LP11 modes generated by the silica optical fiber and (b) two-beam interferogram, (c) is locally linear amplification of the forklet interferogram.

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 figure: Fig. 7

Fig. 7 Near field patterns of the doughnut LP11 modes generated by the silica optical fiber for different bending radius. (a) straight fiber; (b) 7cm; (c) 5cm; (d) 3cm.

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5. Conclusion

We have demonstrated, to the best of our knowledge, the first VVB generation using a multimode LCOF filled with the liquids characterized by high refractive indices. We have investigated experimentally the polarization and the phase properties of the VVB generated, and the influence of the fiber bending on its intensity pattern. The results show that the vector vortex mode of inhomogeneous polarization and the higher-order mode outputs are achieved by changing off-axis launch orientations. This approach allows for obtaining high excitation efficiency and great bending tolerance by selecting suitable liquids. The purity of the VVB can be further improved by optimizing the LCOF length based on polarization corrected propagation constants. Therefore, the new platform for launching skew rays into the LCOF should be useful applications involving optical tweezers, high-power fiber laser and nonlinear optics.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61078004, 61378003), the China Postdoctoral Science Foundation (Grant No. 2012T50372).

References and links

1. P. F. Ding and J. X. Pu, “The cross correlation function of partially coherent vortex beam,” Opt. Express 22(2), 1350–1358 (2014). [CrossRef]   [PubMed]  

2. J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18(3), 2144–2151 (2010). [CrossRef]   [PubMed]  

3. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012). [CrossRef]   [PubMed]  

4. Z. Y. Wang, N. Zhang, and X. C. Yuan, “High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication,” Opt. Express 19(2), 482–492 (2011). [CrossRef]   [PubMed]  

5. H. R. Li and J. P. Yin, “Generation of a vectorial Mathieu-like hollow beam with a periodically rotated polarization property,” Opt. Lett. 36(10), 1755–1757 (2011). [CrossRef]   [PubMed]  

6. A. Lehmuskero, Y. M. Li, P. Johansson, and M. Käll, “Plasmonic particles set into fast orbital motion by an optical vortex beam,” Opt. Express 22(4), 4349–4356 (2014). [CrossRef]   [PubMed]  

7. Y. J. Yang, Y. Dong, C. L. Zhao, Y. D. Liu, and Y. J. Cai, “Autocorrelation properties of fully coherent beam with and without orbital angular momentum,” Opt. Express 22(3), 2925–2932 (2014). [CrossRef]   [PubMed]  

8. P. Schemmel, S. Maccalli, G. Pisano, B. Maffei, and M. W. Ng, “Three-dimensional measurements of a millimeter wave orbital angular momentum vortex,” Opt. Lett. 39(3), 626–629 (2014). [CrossRef]   [PubMed]  

9. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]  

10. Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002). [CrossRef]   [PubMed]  

11. X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010). [CrossRef]   [PubMed]  

12. K. Huang and Y. Li, “Realization of a subwavelength focused spot without a longitudinal field component in a solid immersion lens-based system,” Opt. Lett. 36(18), 3536–3538 (2011). [CrossRef]   [PubMed]  

13. G. H. Yuan, S. B. Wei, and X. C. Yuan, “Nondiffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011). [CrossRef]   [PubMed]  

14. N. K. Viswanathan and V. V. G. K. Inavalli, “Generation of optical vector beams using a two-mode fiber,” Opt. Lett. 34(8), 1189–1191 (2009). [CrossRef]   [PubMed]  

15. V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283(6), 861–864 (2010). [CrossRef]  

16. Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013). [CrossRef]  

17. N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37(13), 2451–2453 (2012). [CrossRef]   [PubMed]  

18. T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005). [CrossRef]  

19. M. Koyama, T. Hirose, M. Okida, K. Miyamoto, and T. Omatsu, “Nanosecond vortex laser pulses with millijoule pulse energies from a Yb-doped double-clad fiber power amplifier,” Opt. Express 19(15), 14420–14425 (2011). [CrossRef]   [PubMed]  

20. F. F. Dai, Y. H. Xu, and X. F. Chen, “Tunable and low bending loss of liquid-core fiber,” Chin. Opt. Lett. 8(1), 14–17 (2010). [CrossRef]  

21. K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse Raman scattering in liquid-core optical fibers,” Opt. Lett. 37(5), 942–944 (2012). [CrossRef]   [PubMed]  

22. K. Kieu, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics,” Opt. Express 20(7), 8148–8154 (2012). [CrossRef]   [PubMed]  

23. K. Kieu, D. Churin, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Brillouin lasing in integrated liquid-core optical fibers,” Opt. Lett. 38(4), 543–545 (2013). [CrossRef]   [PubMed]  

24. O. D. Herrera, L. Schneebeli, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Raman-induced frequency shift in CS2-filled integrated,” Opt. Commun. 318, 83–87 (2014). [CrossRef]  

25. S. Kedenburg, M. Vieweg, T. Gissibl, and H. Giessen, “Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region,” Opt. Mater. Express 2(11), 1588–1611 (2012). [CrossRef]  

26. A. I. Erokhin, V. I. Kovalev, and F. S. Faĭzullov, “Determination of the parameters of a nonlinear response of liquids in an acoustic response region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16(7), 872–877 (1986). [CrossRef]  

27. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

28. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31(12), 1797–1799 (2006). [CrossRef]   [PubMed]  

29. W. Gao, X. B. Hu, D. Sun, and J. Y. Li, “Simultaneous generation and Brillouin amplification of a dark hollow beam with a liquid-core optical fiber,” Opt. Express 20(18), 20715–20720 (2012). [CrossRef]   [PubMed]  

30. B. M. Trabold, A. Abdolvand, T. G. Euser, A. M. Walser, and P. St. J. Russell, “Amplification of higher-order modes by stimulated Raman scattering in H2-filled hollow-core photonic crystal fiber,” Opt. Lett. 38(5), 600–602 (2013). [CrossRef]   [PubMed]  

31. T. Murao, K. Saitoh, and M. Koshiba, “Detailed theoretical investigation of bending properties in solid-core photonic bandgap fibers,” Opt. Express 17(9), 7615–7629 (2009). [CrossRef]   [PubMed]  

32. K. Nagano, S. Kawakami, and S. Nishida, “Change of the refractive index in an optical fiber due to external forces,” Appl. Opt. 17(13), 2080–2085 (1978). [CrossRef]   [PubMed]  

References

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  • |

  1. P. F. Ding and J. X. Pu, “The cross correlation function of partially coherent vortex beam,” Opt. Express 22(2), 1350–1358 (2014).
    [Crossref] [PubMed]
  2. J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18(3), 2144–2151 (2010).
    [Crossref] [PubMed]
  3. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
    [Crossref] [PubMed]
  4. Z. Y. Wang, N. Zhang, and X. C. Yuan, “High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication,” Opt. Express 19(2), 482–492 (2011).
    [Crossref] [PubMed]
  5. H. R. Li and J. P. Yin, “Generation of a vectorial Mathieu-like hollow beam with a periodically rotated polarization property,” Opt. Lett. 36(10), 1755–1757 (2011).
    [Crossref] [PubMed]
  6. A. Lehmuskero, Y. M. Li, P. Johansson, and M. Käll, “Plasmonic particles set into fast orbital motion by an optical vortex beam,” Opt. Express 22(4), 4349–4356 (2014).
    [Crossref] [PubMed]
  7. Y. J. Yang, Y. Dong, C. L. Zhao, Y. D. Liu, and Y. J. Cai, “Autocorrelation properties of fully coherent beam with and without orbital angular momentum,” Opt. Express 22(3), 2925–2932 (2014).
    [Crossref] [PubMed]
  8. P. Schemmel, S. Maccalli, G. Pisano, B. Maffei, and M. W. Ng, “Three-dimensional measurements of a millimeter wave orbital angular momentum vortex,” Opt. Lett. 39(3), 626–629 (2014).
    [Crossref] [PubMed]
  9. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009).
    [Crossref]
  10. Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
    [Crossref] [PubMed]
  11. X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
    [Crossref] [PubMed]
  12. K. Huang and Y. Li, “Realization of a subwavelength focused spot without a longitudinal field component in a solid immersion lens-based system,” Opt. Lett. 36(18), 3536–3538 (2011).
    [Crossref] [PubMed]
  13. G. H. Yuan, S. B. Wei, and X. C. Yuan, “Nondiffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011).
    [Crossref] [PubMed]
  14. N. K. Viswanathan and V. V. G. K. Inavalli, “Generation of optical vector beams using a two-mode fiber,” Opt. Lett. 34(8), 1189–1191 (2009).
    [Crossref] [PubMed]
  15. V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283(6), 861–864 (2010).
    [Crossref]
  16. Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013).
    [Crossref]
  17. N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37(13), 2451–2453 (2012).
    [Crossref] [PubMed]
  18. T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
    [Crossref]
  19. M. Koyama, T. Hirose, M. Okida, K. Miyamoto, and T. Omatsu, “Nanosecond vortex laser pulses with millijoule pulse energies from a Yb-doped double-clad fiber power amplifier,” Opt. Express 19(15), 14420–14425 (2011).
    [Crossref] [PubMed]
  20. F. F. Dai, Y. H. Xu, and X. F. Chen, “Tunable and low bending loss of liquid-core fiber,” Chin. Opt. Lett. 8(1), 14–17 (2010).
    [Crossref]
  21. K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse Raman scattering in liquid-core optical fibers,” Opt. Lett. 37(5), 942–944 (2012).
    [Crossref] [PubMed]
  22. K. Kieu, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics,” Opt. Express 20(7), 8148–8154 (2012).
    [Crossref] [PubMed]
  23. K. Kieu, D. Churin, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Brillouin lasing in integrated liquid-core optical fibers,” Opt. Lett. 38(4), 543–545 (2013).
    [Crossref] [PubMed]
  24. O. D. Herrera, L. Schneebeli, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Raman-induced frequency shift in CS2-filled integrated,” Opt. Commun. 318, 83–87 (2014).
    [Crossref]
  25. S. Kedenburg, M. Vieweg, T. Gissibl, and H. Giessen, “Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region,” Opt. Mater. Express 2(11), 1588–1611 (2012).
    [Crossref]
  26. A. I. Erokhin, V. I. Kovalev, and F. S. Faĭzullov, “Determination of the parameters of a nonlinear response of liquids in an acoustic response region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16(7), 872–877 (1986).
    [Crossref]
  27. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  28. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31(12), 1797–1799 (2006).
    [Crossref] [PubMed]
  29. W. Gao, X. B. Hu, D. Sun, and J. Y. Li, “Simultaneous generation and Brillouin amplification of a dark hollow beam with a liquid-core optical fiber,” Opt. Express 20(18), 20715–20720 (2012).
    [Crossref] [PubMed]
  30. B. M. Trabold, A. Abdolvand, T. G. Euser, A. M. Walser, and P. St. J. Russell, “Amplification of higher-order modes by stimulated Raman scattering in H2-filled hollow-core photonic crystal fiber,” Opt. Lett. 38(5), 600–602 (2013).
    [Crossref] [PubMed]
  31. T. Murao, K. Saitoh, and M. Koshiba, “Detailed theoretical investigation of bending properties in solid-core photonic bandgap fibers,” Opt. Express 17(9), 7615–7629 (2009).
    [Crossref] [PubMed]
  32. K. Nagano, S. Kawakami, and S. Nishida, “Change of the refractive index in an optical fiber due to external forces,” Appl. Opt. 17(13), 2080–2085 (1978).
    [Crossref] [PubMed]

2014 (5)

2013 (3)

2012 (6)

2011 (5)

2010 (4)

2009 (3)

2006 (1)

2005 (1)

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[Crossref]

2002 (1)

1986 (1)

A. I. Erokhin, V. I. Kovalev, and F. S. Faĭzullov, “Determination of the parameters of a nonlinear response of liquids in an acoustic response region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16(7), 872–877 (1986).
[Crossref]

1978 (1)

Abdolvand, A.

Aoki, N.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Bozinovic, N.

Cai, Y. J.

Chen, X. F.

Chujo, K.

Churin, D.

Courjon, D.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[Crossref]

Dai, F. F.

DeSimone, A.

Dimarcello, F. V.

Ding, P. F.

Dong, Y.

Erokhin, A. I.

A. I. Erokhin, V. I. Kovalev, and F. S. Faĭzullov, “Determination of the parameters of a nonlinear response of liquids in an acoustic response region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16(7), 872–877 (1986).
[Crossref]

Euser, T. G.

Faizullov, F. S.

A. I. Erokhin, V. I. Kovalev, and F. S. Faĭzullov, “Determination of the parameters of a nonlinear response of liquids in an acoustic response region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16(7), 872–877 (1986).
[Crossref]

Fang, Z. Q.

Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013).
[Crossref]

Gao, W.

Ghalmi, S.

Giessen, H.

Gissibl, T.

Golowich, S.

Grosjean, T.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[Crossref]

Hales, J. M.

Hamazaki, J.

Hao, X.

Herrera, O. D.

O. D. Herrera, L. Schneebeli, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Raman-induced frequency shift in CS2-filled integrated,” Opt. Commun. 318, 83–87 (2014).
[Crossref]

Hirose, T.

Hu, X. B.

Huang, K.

Inavalli, V. V. G. K.

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283(6), 861–864 (2010).
[Crossref]

N. K. Viswanathan and V. V. G. K. Inavalli, “Generation of optical vector beams using a two-mode fiber,” Opt. Lett. 34(8), 1189–1191 (2009).
[Crossref] [PubMed]

Johansson, P.

Käll, M.

Kang, M. Q.

Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013).
[Crossref]

Kawakami, S.

Kedenburg, S.

Kieu, K.

Kobayashi, Y.

Koshiba, M.

Kovalev, V. I.

A. I. Erokhin, V. I. Kovalev, and F. S. Faĭzullov, “Determination of the parameters of a nonlinear response of liquids in an acoustic response region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16(7), 872–877 (1986).
[Crossref]

Koyama, M.

Kristensen, P.

Kuang, C. F.

Leger, J. R.

Lehmuskero, A.

Li, H. R.

Li, J. L.

Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013).
[Crossref]

Li, J. Y.

Li, Y.

Li, Y. M.

Liu, X.

Liu, Y. D.

Maccalli, S.

Maffei, B.

Merzlyak, E.

Miyamoto, K.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

M. Koyama, T. Hirose, M. Okida, K. Miyamoto, and T. Omatsu, “Nanosecond vortex laser pulses with millijoule pulse energies from a Yb-doped double-clad fiber power amplifier,” Opt. Express 19(15), 14420–14425 (2011).
[Crossref] [PubMed]

Monberg, E.

Morita, R.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18(3), 2144–2151 (2010).
[Crossref] [PubMed]

Murao, T.

Nagano, K.

Ng, M. W.

Nicholson, J. W.

Nishida, S.

Norwood, R. A.

Okida, M.

Omatsu, T.

Perry, J. W.

Peyghambarian, N.

Pisano, G.

Pu, J. X.

Ramachandran, S.

Russell, P. St. J.

Sabac, A.

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[Crossref]

Saitoh, K.

Schemmel, P.

Schneebeli, L.

Sun, D.

Tanda, S.

Toyoda, K.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Trabold, B. M.

Ueda, K.

Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013).
[Crossref]

Vieweg, M.

Viswanathan, N. K.

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283(6), 861–864 (2010).
[Crossref]

N. K. Viswanathan and V. V. G. K. Inavalli, “Generation of optical vector beams using a two-mode fiber,” Opt. Lett. 34(8), 1189–1191 (2009).
[Crossref] [PubMed]

Walser, A. M.

Wang, T. T.

Wang, Z. Y.

Wei, S. B.

Wisk, P.

Xia, K. G.

Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013).
[Crossref]

Xu, Y. H.

Yan, M. F.

Yang, Y. J.

Yao, Y.

Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013).
[Crossref]

Yin, J. P.

Yuan, G. H.

Yuan, X. C.

Zhan, Q.

Zhang, N.

Zhao, C. L.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Chin. Opt. Lett. (1)

Nano Lett. (1)

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, “Using optical vortex to control the chirality of twisted metal nanostructures,” Nano Lett. 12(7), 3645–3649 (2012).
[Crossref] [PubMed]

Opt. Commun. (4)

T. Grosjean, A. Sabac, and D. Courjon, “A versatile and stable device allowing the efficient generation of beams with radial, azimuthal or hybrid polarizations,” Opt. Commun. 252(1-3), 12–21 (2005).
[Crossref]

V. V. G. K. Inavalli and N. K. Viswanathan, “Switchable vector vortex beam generation using an optical fiber,” Opt. Commun. 283(6), 861–864 (2010).
[Crossref]

Z. Q. Fang, Y. Yao, K. G. Xia, M. Q. Kang, K. Ueda, and J. L. Li, “Vector mode excitation in few-mode fiber by controlling incident polarization,” Opt. Commun. 294, 177–181 (2013).
[Crossref]

O. D. Herrera, L. Schneebeli, K. Kieu, R. A. Norwood, and N. Peyghambarian, “Raman-induced frequency shift in CS2-filled integrated,” Opt. Commun. 318, 83–87 (2014).
[Crossref]

Opt. Express (10)

K. Kieu, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Integrated liquid-core optical fibers for ultra-efficient nonlinear liquid photonics,” Opt. Express 20(7), 8148–8154 (2012).
[Crossref] [PubMed]

W. Gao, X. B. Hu, D. Sun, and J. Y. Li, “Simultaneous generation and Brillouin amplification of a dark hollow beam with a liquid-core optical fiber,” Opt. Express 20(18), 20715–20720 (2012).
[Crossref] [PubMed]

T. Murao, K. Saitoh, and M. Koshiba, “Detailed theoretical investigation of bending properties in solid-core photonic bandgap fibers,” Opt. Express 17(9), 7615–7629 (2009).
[Crossref] [PubMed]

A. Lehmuskero, Y. M. Li, P. Johansson, and M. Käll, “Plasmonic particles set into fast orbital motion by an optical vortex beam,” Opt. Express 22(4), 4349–4356 (2014).
[Crossref] [PubMed]

Y. J. Yang, Y. Dong, C. L. Zhao, Y. D. Liu, and Y. J. Cai, “Autocorrelation properties of fully coherent beam with and without orbital angular momentum,” Opt. Express 22(3), 2925–2932 (2014).
[Crossref] [PubMed]

M. Koyama, T. Hirose, M. Okida, K. Miyamoto, and T. Omatsu, “Nanosecond vortex laser pulses with millijoule pulse energies from a Yb-doped double-clad fiber power amplifier,” Opt. Express 19(15), 14420–14425 (2011).
[Crossref] [PubMed]

Z. Y. Wang, N. Zhang, and X. C. Yuan, “High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication,” Opt. Express 19(2), 482–492 (2011).
[Crossref] [PubMed]

P. F. Ding and J. X. Pu, “The cross correlation function of partially coherent vortex beam,” Opt. Express 22(2), 1350–1358 (2014).
[Crossref] [PubMed]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18(3), 2144–2151 (2010).
[Crossref] [PubMed]

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
[Crossref] [PubMed]

Opt. Lett. (11)

X. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Phase encoding for sharper focus of the azimuthally polarized beam,” Opt. Lett. 35(23), 3928–3930 (2010).
[Crossref] [PubMed]

K. Huang and Y. Li, “Realization of a subwavelength focused spot without a longitudinal field component in a solid immersion lens-based system,” Opt. Lett. 36(18), 3536–3538 (2011).
[Crossref] [PubMed]

G. H. Yuan, S. B. Wei, and X. C. Yuan, “Nondiffracting transversally polarized beam,” Opt. Lett. 36(17), 3479–3481 (2011).
[Crossref] [PubMed]

N. K. Viswanathan and V. V. G. K. Inavalli, “Generation of optical vector beams using a two-mode fiber,” Opt. Lett. 34(8), 1189–1191 (2009).
[Crossref] [PubMed]

H. R. Li and J. P. Yin, “Generation of a vectorial Mathieu-like hollow beam with a periodically rotated polarization property,” Opt. Lett. 36(10), 1755–1757 (2011).
[Crossref] [PubMed]

K. Kieu, L. Schneebeli, E. Merzlyak, J. M. Hales, A. DeSimone, J. W. Perry, R. A. Norwood, and N. Peyghambarian, “All-optical switching based on inverse Raman scattering in liquid-core optical fibers,” Opt. Lett. 37(5), 942–944 (2012).
[Crossref] [PubMed]

P. Schemmel, S. Maccalli, G. Pisano, B. Maffei, and M. W. Ng, “Three-dimensional measurements of a millimeter wave orbital angular momentum vortex,” Opt. Lett. 39(3), 626–629 (2014).
[Crossref] [PubMed]

N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37(13), 2451–2453 (2012).
[Crossref] [PubMed]

S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31(12), 1797–1799 (2006).
[Crossref] [PubMed]

B. M. Trabold, A. Abdolvand, T. G. Euser, A. M. Walser, and P. St. J. Russell, “Amplification of higher-order modes by stimulated Raman scattering in H2-filled hollow-core photonic crystal fiber,” Opt. Lett. 38(5), 600–602 (2013).
[Crossref] [PubMed]

K. Kieu, D. Churin, L. Schneebeli, R. A. Norwood, and N. Peyghambarian, “Brillouin lasing in integrated liquid-core optical fibers,” Opt. Lett. 38(4), 543–545 (2013).
[Crossref] [PubMed]

Opt. Mater. Express (1)

Sov. J. Quantum Electron. (1)

A. I. Erokhin, V. I. Kovalev, and F. S. Faĭzullov, “Determination of the parameters of a nonlinear response of liquids in an acoustic response region by the method of nondegenerate four-wave interaction,” Sov. J. Quantum Electron. 16(7), 872–877 (1986).
[Crossref]

Other (1)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

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Figures (7)

Fig. 1
Fig. 1 Experimental setup. P1,2, polarizers; BS1,2, beam splitters; L1,2, lenses; LCOF, liquid core optical fiber; M1,2, mirrors.
Fig. 2
Fig. 2 Near-field images of the intensity distribution of the fundamental mode and higher-order modes. (a) LP01 mode; (b) doughnut LP11 mode; (c) two-lobe LP11 mode; (d) LP21 mode.
Fig. 3
Fig. 3 Interferogram generated by combining the doughnut LP11 mode with a plane reference beam.
Fig. 4
Fig. 4 Near-field images of the intensity distribution of the doughnut LP11 modes with different polarizations (Column 1), corresponding intensity profiles after passing a polarizer orientated in the direction of the arrow (Column 2-5) and corresponding polarization patterns (Column 6). (a) hybrid polarized HE21 mode; (b) radially polarized TM01 mode; (c) azimuthally polarized TE01 mode.
Fig. 5
Fig. 5 Near field patterns of the doughnut LP11 modes generated by the LCOF for different bending radius. (a) straight fiber; (b) 7cm; (c) 5cm; (d) 3cm.
Fig. 6
Fig. 6 Near field patterns of (a) the doughnut LP11 modes generated by the silica optical fiber and (b) two-beam interferogram, (c) is locally linear amplification of the forklet interferogram.
Fig. 7
Fig. 7 Near field patterns of the doughnut LP11 modes generated by the silica optical fiber for different bending radius. (a) straight fiber; (b) 7cm; (c) 5cm; (d) 3cm.

Equations (1)

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n R (x)=n(x)( 1+ x R )

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