OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 7 — Apr. 7, 2014
  • pp: 7598–7606
« Show journal navigation

Spiral autofocusing Airy beams carrying power-exponent-phase vortices

Peng Li, Sheng Liu, Tao Peng, Gaofeng Xie, Xuetao Gan, and Jianlin Zhao  »View Author Affiliations


Optics Express, Vol. 22, Issue 7, pp. 7598-7606 (2014)
http://dx.doi.org/10.1364/OE.22.007598


View Full Text Article

Acrobat PDF (5024 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose a new type of noncanonical optical vortex, named “power-exponent-phase vortex (PEPV)”. The spiral focusing of the autofocusing Airy beams carrying PEPVs are experimentally demonstrated, and the physical mechanism is theoretically analyzed by using the energy flow and far field mapping. In addition, the influences of the parameters of PEPVs on the focal fields and orbital angular momenta are also discussed. It is expected that the proposed PEPVs and the corresponding conclusions can be useful for the extension applications of optical vortices, especially for particle trapping and rotating.

© 2014 Optical Society of America

1. Introduction

Autofocusing beams, of which the abruptly autofocusing property may exhibit greatly potential applications in biomedical treatment and optical micromanipulation, have been an attractive theme for both theoretical and applied research in recent years [1

1. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010). [CrossRef] [PubMed]

9

9. J. A. Davis, D. M. Cottrell, and D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012). [CrossRef] [PubMed]

]. A typical autofocusing beams is often referred to autofocusing Airy beam (AAB), which is described by the radially symmetric or circular Airy function. It has been shown that an AAB undergoes abrupt autofocusing in free space, where the energy suddenly increases right before the focal point [1

1. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010). [CrossRef] [PubMed]

3

3. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011). [CrossRef] [PubMed]

]. Based on this property, many basic researches, such as abrupt polarization transitions [7

7. S. Liu, P. Li, M. Wang, P. Zhang, and J. Zhao, “Observation of abrupt polarization transitions associated with spin-orbit interaction of vector autofocusing Airy beams,” in Frontiers in Optics (2013).

, 8

8. S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013). [CrossRef] [PubMed]

] and non-linear intense light bullets [10

10. P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013). [CrossRef] [PubMed]

], have been reported, in addition to the applications on practical trapping [5

5. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011). [CrossRef] [PubMed]

, 11

11. Y. Jiang, K. Huang, and X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21(20), 24413–24421 (2013). [CrossRef] [PubMed]

]. In comparison with apparatus used in optical tweezers, the implementation of optical manipulations with AABs only need an objective lens with weaker magnification.

Another structured light beam, commonly known as optical vortex (OV), is characterized by helical phase structures, hollow-core intensity distributions and intriguing orbital angular momenta fractional (OAM) [12

12. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]

15

15. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef] [PubMed]

], which therefore promise plentiful applications in particle trappings [16

16. M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011). [CrossRef]

18

18. K. T. Gahagan and G. A. Swartzlander Jr., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996). [CrossRef] [PubMed]

]. Moreover, relying on their topological structures, interesting linear and nonlinear evolution dynamics of OVs have been demonstrated [19

19. X. Gan, J. Zhao, S. Liu, and L. Fang, “Generation and motion control of optical multi-vortex,” Chin. Opt. Lett. 7(12), 1142–1145 (2009). [CrossRef]

21

21. isX. Gan, P. Zhang, S. Liu, F. Xiao, and J. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89(1), 013844 (2014). [CrossRef]

]. Generally, a canonical OV carries a spiral phase varying uniformly with azimuthal angle. To exploring novel features and applications of OAM, many variational OVs, such as nonsymmetric OVs [22

22. G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001). [CrossRef] [PubMed]

, 23

23. G.-H. Kim, H. J. Lee, J.-U. Kim, and H. Suk, “Propagation dynamics of optical vortices with anisotropic phase profiles,” J. Opt. Soc. Am. B 20(2), 351–360 (2003). [CrossRef]

], Helico-conical optical beams [24

24. N. Hermosa, C. Rosales-Guzmán, and J. P. Torres, “Helico-conical optical beams self-heal,” Opt. Lett. 38(3), 383–385 (2013). [CrossRef] [PubMed]

26

26. N. P. Hermosa II and C. O. Manaois, “Phase structure of helicon-conical optical beams,” Opt. Commun. 271(1), 178–183 (2007). [CrossRef]

], fractional OVs [27

27. J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16(2), 993–1006 (2008). [CrossRef] [PubMed]

, 28

28. S. H. Tao, X.-C. Yuan, J. Lin, X. Peng, and H. B. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005). [CrossRef] [PubMed]

], Mathieu OVs [29

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

], modulated OVs [30

30. J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003). [CrossRef] [PubMed]

] and so on, have been proposed. On the other hand, introducing canonical OVs into AABs has been reported to present new optical properties [6

6. Y. Jiang, K. Huang, and X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012). [CrossRef] [PubMed]

9

9. J. A. Davis, D. M. Cottrell, and D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012). [CrossRef] [PubMed]

]. For example, two opposite OVs can collide and annihilate when nested in an AAB [6

6. Y. Jiang, K. Huang, and X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012). [CrossRef] [PubMed]

]. Furthermore, we recently have demonstrated that canonical OVs can also change the polarization states of the vector AABs [7

7. S. Liu, P. Li, M. Wang, P. Zhang, and J. Zhao, “Observation of abrupt polarization transitions associated with spin-orbit interaction of vector autofocusing Airy beams,” in Frontiers in Optics (2013).

, 8

8. S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013). [CrossRef] [PubMed]

]. However, the focusing properties of AAB carrying a noncanonical OV, as we have known, have not been reported yet.

In this paper, we propose a new type of noncanonical OV, characterized with power-exponent-phase, so we name it power-exponent-phase vortex (PEPV). The spiral autofocusing of the AABs carrying PEPVs is experimentally demonstrated, and the physical mechanism is theoretically analyzed with the energy flow and the far field mapping.

2. Power-exponent-phase vortex (PEPV)

In general, a canonical OV has a complex exponential term, exp(iψ), where the phase function is expressed by
ψ=lθ,
(1)
where, θ is the azimuthal angle, ranging from 0 to 2π; l is the topological charge, which determines the number of 2π-phase shifts that occurs across one revolution of θ, and the sign of l determines the handedness of helix.

Equation (1) can describe the general spiral phase distribution of OV, which changes uniformly with θ, as shown in Fig. 1(a)
Fig. 1 Spiral phase distributions of (a) OV (l = 7) and (b) PEPV with l = 7, n = 4.
. Now we construct a new type of noncanonical OV by writing the phase function as
ψ=2πl(θ2π)n,
(2)
where, l still denotes the topological charge of the vortex, and n determines the power order of the spiral phase, which can be either an integer or a fraction. Such an OV can be named as PEPV. Figure 1(b) shows a PEPV with l = 7 and n = 4. In contrast to the canonical vortex, the phase variation of PEPV with θ is gradually intensified due to the power-exponent phase term. To introduce PEPV to the incident beam, the most convenient way is to imprint the phase directly by using a phase spatial light modulator (PSLM) to form a helical phase plate, the same way as that has been done for noncanonical OVs [24

24. N. Hermosa, C. Rosales-Guzmán, and J. P. Torres, “Helico-conical optical beams self-heal,” Opt. Lett. 38(3), 383–385 (2013). [CrossRef] [PubMed]

, 25

25. C.-A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13(5), 1749–1760 (2005). [CrossRef] [PubMed]

].

3. AABs carrying PEPVs

Now we analyze the dynamics of AABs carrying PEPVs. The electric fields of AAB superimposed by a PEPV in cylindrical coordinates can be expressed as
u(r,θ,z=0)=Ai(r0rω)exp(r0rω)exp(iψ),
(3)
where, Ai denotes the Airy function, (r,θ) denote the polar coordinates, a is the decaying parameter, r0 and ω are the radius and width of the main lobe of AABs, respectively; ψ denotes the phase function given by Eq. (2).

To experimentally generate the AABs with the desired phase function, we utilize computer-generated holography similar to that used in the prior demonstrations [7

7. S. Liu, P. Li, M. Wang, P. Zhang, and J. Zhao, “Observation of abrupt polarization transitions associated with spin-orbit interaction of vector autofocusing Airy beams,” in Frontiers in Optics (2013).

,8

8. S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013). [CrossRef] [PubMed]

,19

19. X. Gan, J. Zhao, S. Liu, and L. Fang, “Generation and motion control of optical multi-vortex,” Chin. Opt. Lett. 7(12), 1142–1145 (2009). [CrossRef]

], as also shown in Fig. 2
Fig. 2 Experimental setup for generation of AABs carrying PEPV. RT = reversed telescope (5x, NA = 0.1); PSLM = phase spatial light modulator (Holoeye pluto, effective area: 15.36 mm × 8.64 mm); L = lens (focal length = 10 cm). A spatial filter and 4f system are used for generation desired AABs and AABs carrying PEPV. The insets depict the computer-generated hologram (CGH, top right) and the corresponding output intensity distribution at the focal region (bottom left).
. Here, a computer-generated hologram (CGH) is displayed on a PSLM, with its intensity profile computed as the interference field between the AABs and a plane wave, i.e. |u(r,θ) + exp(ifx)|2, where f determines the spatial frequency of the CGH. After passing through the PSLM, the expanded beam is filtered via a 4f system consisting of lenses L1 and L2 and forms the desired AABs. Placing the CCD at different distances, we observe the propagation characteristics of AABs carrying PEPVs.

Figure 3
Fig. 3 Propagation characteristics of AABs with different phase distributions. (a) Intensity profile of the generated AAB (10 cm away from the L2), where the top-right inset depicts the CGH used to generate AAB; (b),(c),(e) Intensity distributions near the focal points, where the top-right insets depict the corresponding initial phase distributions of AABs (30 cm away from the L2); (d) side view of the beam propagation from numerical simulation corresponding to (e). (b) l = n = 0; (c) l = n = 1; (e) l = 8, n = 2.
depicts the experimental results of the intensity distribution near the focal points of AABs carrying different phases. Where, Fig. 3(a) shows the intensity profile of the generated AAB, and Fig. 3(b) represents the focal field of the AABs without any additional phase (l = n = 0), which consists of a bright spot similar to the zero-order Bessel-like pattern [5

5. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011). [CrossRef] [PubMed]

] formed via the abrupt autofocusing of the AABs. For the case of study, where l = n = 1, as shown in Fig. 3(c), the AABs are nested with a single charged vortex, and evolved into a hollow spot [6

6. Y. Jiang, K. Huang, and X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012). [CrossRef] [PubMed]

8

8. S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013). [CrossRef] [PubMed]

]. When the AABs carry a PEPV [as indicated in Fig. 3(e), when l = 8, n = 2], the autofocusing process will be totally changed, and it forms the spiral spot. This resembles to an Archimedes spiral at the focal region, which is much similar to the focal field of Helico-conical optical beams [24

24. N. Hermosa, C. Rosales-Guzmán, and J. P. Torres, “Helico-conical optical beams self-heal,” Opt. Lett. 38(3), 383–385 (2013). [CrossRef] [PubMed]

, 25

25. C.-A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13(5), 1749–1760 (2005). [CrossRef] [PubMed]

]. To show evolution of the AABs with PEPV, the beam propagation method (BPM) is utilized to numerically simulate the propagation process. Figure 3(d) represents the simulation result of the side view of the AAB propagation at y-z plane. It can be seen that the light energy gradually converged and the intensity presents a bit oscillation when closing to the focal point. This can reveal the spiral focusing to some extent. Actually, the formed spiral focal spot will rotate during propagating at the focal region, resembling the cork-screw path. To demonstrate clearly this phenomenon, we simulate the propagation process of the AAB carrying a PEPV near the focal point (the parameters are selected as l = 12, and n = 2), as shown in Fig. 4
Fig. 4 Numerical results of the intensity profiles of the AABs with a PEPV (l = 12, n = 2) at different propagation distances near the focal point. (a)-(d) Corresponding to z = 19.52 cm, 20.50 cm, 21.48 cm, 22.45 cm, respectively. The white arrow head denotes the rotating direction.
, where Figs. 4(a)4(d) correspond to the intensity profiles at different propagation distances. The rotation direction is indicated by the white arrow head in Fig. 4(a). It can be clearly seen that the intensity profile of AAB follows the cork-screw path, and evolves into a spiral spot.

For better understanding the formation of spiral focal fields, we analyzed the energy flow [31

31. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008). [CrossRef] [PubMed]

, 32

32. H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008). [CrossRef] [PubMed]

] of AABs. Figure 5
Fig. 5 Numerical simulation results of energy flow of the AABs at the input planes (top, z = 0 cm) and before the focal points (bottom, z = 20 cm). (a) l = n = 0; (b) l = n = 1; (c) l = 12, n = 2; (d) l = 12, n = 3.
depicts the energy flow of AABs at the input planes (top) and before the focal points (bottom). As shown in Fig. 5(a), for the AAB without any additional phase (l = n = 0), the light energy flow to the central region whether at the initial position or just before the focal point, behaving as focusing. For the AAB with a single charged vortex (l = n = 1), as shown in Fig. 5(b), the light energy circulates along a ring while shrinks gradually during propagation. This illustrates that the light spirals around the propagation axis while focusing. Due to the balanced energy cycle, the light intensity distribution keeps axisymmetric, i.e. a donut-shaped spot. For the AABs with a PEPV, the cycle of the energy flow is broken, and the energy will concentratedly flow to the certain region [see the regions with weak energy flow in the top of Figs. 5(c) and 5(d)]. On the other hand, it can be seen that the energy flow tends to shrink into the center because of the focusing effect. These lead to that the energy behaviors a spiral-like flow. Due to the spiral energy flow of PEPV, the light gradually evolves to a spiral-shape spot.

It is worth mentioning that during the propagations of AABs, although the intensity profiles vary a lot, the phase distributions keep unchanged essentially. Figure 6
Fig. 6 Numerical results of the phase distributions near the focal point (z = 20 cm). (a) l = n = 0; (b) l = n = 1; (c) l = 12, n = 2; (d) l = 12, n = 3.
illustrates four examples of the phase distributions near the focal points of the AABs with different initial phase. It reveals that besides the additional spherical phase, the phase distributions near the focal points are roughly identical to the initial ones.

4. Theoretical explanation

To theoretically explain the spiral focal fields, we look into the far-field propagation of AABs, which can be described by Fraunhofer diffraction integral. For the AAB with a PEPV, the far-field envelope is described by
E(x,y)u(x,y)exp[ikz(xx+yy)]dxdy,
(4)
where, (x, y) and (x', y') are the Cartesian coordinates, k is the wave number, z is the coordinate along the propagation direction, and u(x', y') corresponds to the light field given by Eq. (3), of which the phase term is ψ(r,θ) described by Eq. (2). Equation (4) can be considered as the Fourier transform of u(x', y') if the propagation distance is far enough [25

25. C.-A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13(5), 1749–1760 (2005). [CrossRef] [PubMed]

].

Under the approximation of slow-varying amplitude and phase, the field mapping can be provided by the local spatial frequencies, which can be achieved with the method of stationary phase and is defined as [25

25. C.-A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13(5), 1749–1760 (2005). [CrossRef] [PubMed]

, 30

30. J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003). [CrossRef] [PubMed]

]
fx=12πxψ(r,θ),fy=12πyψ(r,θ),
(5)
where (fx, fy) is the orthogonal coordinates in frequency domain. Applying this theory to Eq. (2), we obtain

fx=nlθn1sinθ()nr,fynlθn1cosθ()nr.
(6)

According to Eq. (6), the frequency mapping (fx, fy) to far field can be plotted, as shown in Fig. 7(a)
Fig. 7 (a) Spatial frequency mapping to the focal field; (b) focal field (30 cm away from L2) of the AAB with a PEPV.
, where the parameters are selected as n = 3, l = 7, and r = 1. The curve represents an Archimede spiral, which meets the shape of the corresponding focal field of AABs with PEPV [see Fig. 7(b)].

5. Influences of the parameters on the focal fields

Now we examine the influences of the parameters l and n on the focal fields of the AABs carrying PEPVs. Figure 8
Fig. 8 Focal fields of AABs carrying PEPVs (l = 8, 30 cm away from L2). (a)-(h) Corresponding to n = 2, 3, 4, …, 9, respectively. The inserted white lines depict the corresponding spatial frequency mappings.
demonstrates the experimental results of the focal fields (the intensity distributions at the plane 30 cm away from the lens L2) of AABs carrying PEPVs (l = 8), where Figs. 8(a)8(h) correspond to n = 2, 3, 4, …, 9, respectively, with the corresponding spatial frequency mappings inserted as white lines. It reveals that as the power order n increases, the focal spot shrinks with the tail shortened and the curved line stretches itself gradually. This phenomenon can be also seen from Eq. (2): with the increase of n, the phase gradients concentrate to the interval of θ near 2π, leading to the locally high gradient of phase. As a result, the light energy flow more quickly to the certain region. With increasing the parameters n, the light concentrates faster, and the focal spot became more shrinked. The experimental results are coincident with the corresponding frequency maps calculated from Eq. (6).

Figure 9
Fig. 9 Focal fields of AABs carrying PEPVs (n = 2, 30 cm away from L2). (a)-(h) Corresponding to l = 3, 4, 5, …, 10, respectively. The inserted white lines depict the corresponding spatial frequency mappings.
demonstrates the experimental results of the focal fields of AABs with PEPVs (n = 2), where Figs. 9(a)9(h) correspond to l = 3, 4, 5, …, 10, respectively, with the corresponding spatial frequency mappings inserted as white lines. It can be seen that with the increase of the topological charge l, the spiral focal spot is wholly enlarged, but the shape remains the same. From Eq. (2), it can be also seen that the topological charge l never influences the distribution of the phase function, but changes the whole phase gradient. Thus, the energy flow distribution keeps wholly unchanged. While the rotating flow is speeded up with increasing l, and the focusing flow is accordingly reduced. These result in the wholly enlarged spiral focal spot. The conclusions of PEPVs are same as that of the canonical vortices [33

33. J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003). [CrossRef] [PubMed]

]. Moreover, Eq. (6) also reveals that the frequency mapping is proportional to l. It means that l merely changes the size of the frequency mapping, as also shown in Fig. 9.

6. OAM of AABs carrying PEPVs

It is known that some light fields can carry OAM, which are associated with the spiral wavefronts. Actually, the proposed PEPV is a type of light wave with spiral wavefront. Thus, it also carries OAM [34

34. S. A. C. Baluyot and N. P. Hermosa 2nd, “Intensity profiles and propagation of optical beams with bored helical phase,” Opt. Express 17(18), 16244–16254 (2009). [CrossRef] [PubMed]

].

The OAM density of light field about the z axis in spatial space can be expressed as
Jz=(r×E×H)z=xSyySx,
(7)
where, E and H are the electric and magnetic fields, respectively; r = (x2 + y2)1/2; Sx and Sy are the components along the x and y axes of the Poynting vector (S = E × H), respectively.

7. Conclusions

Acknowledgments

This work was supported by the 973 Program (2012CB921900), the National Natural Science Foundation of China (61205001 and 61377035), Natural Science Basic Research Plan in Shaanxi Province of China (2012JQ1017), the Northwestern Polytechnical University (NPU) Foundation for Fundamental Research (JC20120251).

References and links

1.

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010). [CrossRef] [PubMed]

2.

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36(10), 1890–1892 (2011). [CrossRef] [PubMed]

3.

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011). [CrossRef] [PubMed]

4.

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36(18), 3675–3677 (2011). [CrossRef] [PubMed]

5.

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011). [CrossRef] [PubMed]

6.

Y. Jiang, K. Huang, and X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012). [CrossRef] [PubMed]

7.

S. Liu, P. Li, M. Wang, P. Zhang, and J. Zhao, “Observation of abrupt polarization transitions associated with spin-orbit interaction of vector autofocusing Airy beams,” in Frontiers in Optics (2013).

8.

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013). [CrossRef] [PubMed]

9.

J. A. Davis, D. M. Cottrell, and D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012). [CrossRef] [PubMed]

10.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013). [CrossRef] [PubMed]

11.

Y. Jiang, K. Huang, and X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21(20), 24413–24421 (2013). [CrossRef] [PubMed]

12.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]

13.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002). [CrossRef] [PubMed]

14.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007). [CrossRef]

15.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef] [PubMed]

16.

M. J. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011). [CrossRef]

17.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995). [CrossRef] [PubMed]

18.

K. T. Gahagan and G. A. Swartzlander Jr., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996). [CrossRef] [PubMed]

19.

X. Gan, J. Zhao, S. Liu, and L. Fang, “Generation and motion control of optical multi-vortex,” Chin. Opt. Lett. 7(12), 1142–1145 (2009). [CrossRef]

20.

W. Zhang, S. Liu, P. Li, X. Jiao, and J. Zhao, “Controlling the polarization singularities of the focused azimuthally polarized beams,” Opt. Express 21(1), 974–983 (2013). [CrossRef] [PubMed]

21.

isX. Gan, P. Zhang, S. Liu, F. Xiao, and J. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89(1), 013844 (2014). [CrossRef]

22.

G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001). [CrossRef] [PubMed]

23.

G.-H. Kim, H. J. Lee, J.-U. Kim, and H. Suk, “Propagation dynamics of optical vortices with anisotropic phase profiles,” J. Opt. Soc. Am. B 20(2), 351–360 (2003). [CrossRef]

24.

N. Hermosa, C. Rosales-Guzmán, and J. P. Torres, “Helico-conical optical beams self-heal,” Opt. Lett. 38(3), 383–385 (2013). [CrossRef] [PubMed]

25.

C.-A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13(5), 1749–1760 (2005). [CrossRef] [PubMed]

26.

N. P. Hermosa II and C. O. Manaois, “Phase structure of helicon-conical optical beams,” Opt. Commun. 271(1), 178–183 (2007). [CrossRef]

27.

J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16(2), 993–1006 (2008). [CrossRef] [PubMed]

28.

S. H. Tao, X.-C. Yuan, J. Lin, X. Peng, and H. B. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005). [CrossRef] [PubMed]

29.

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

30.

J. E. Curtis and D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003). [CrossRef] [PubMed]

31.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008). [CrossRef] [PubMed]

32.

H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008). [CrossRef] [PubMed]

33.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003). [CrossRef] [PubMed]

34.

S. A. C. Baluyot and N. P. Hermosa 2nd, “Intensity profiles and propagation of optical beams with bored helical phase,” Opt. Express 17(18), 16244–16254 (2009). [CrossRef] [PubMed]

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(350.5500) Other areas of optics : Propagation
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Physical Optics

History
Original Manuscript: January 20, 2014
Revised Manuscript: March 2, 2014
Manuscript Accepted: March 6, 2014
Published: March 25, 2014

Citation
Peng Li, Sheng Liu, Tao Peng, Gaofeng Xie, Xuetao Gan, and Jianlin Zhao, "Spiral autofocusing Airy beams carrying power-exponent-phase vortices," Opt. Express 22, 7598-7606 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-7-7598


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. N. K. Efremidis, D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010). [CrossRef] [PubMed]
  2. I. Chremmos, N. K. Efremidis, D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36(10), 1890–1892 (2011). [CrossRef] [PubMed]
  3. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011). [CrossRef] [PubMed]
  4. I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36(18), 3675–3677 (2011). [CrossRef] [PubMed]
  5. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36(15), 2883–2885 (2011). [CrossRef] [PubMed]
  6. Y. Jiang, K. Huang, X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012). [CrossRef] [PubMed]
  7. S. Liu, P. Li, M. Wang, P. Zhang, and J. Zhao, “Observation of abrupt polarization transitions associated with spin-orbit interaction of vector autofocusing Airy beams,” in Frontiers in Optics (2013).
  8. S. Liu, M. Wang, P. Li, P. Zhang, J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013). [CrossRef] [PubMed]
  9. J. A. Davis, D. M. Cottrell, D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012). [CrossRef] [PubMed]
  10. P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013). [CrossRef] [PubMed]
  11. Y. Jiang, K. Huang, X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21(20), 24413–24421 (2013). [CrossRef] [PubMed]
  12. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef] [PubMed]
  13. A. T. O’Neil, I. MacVicar, L. Allen, M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88(5), 053601 (2002). [CrossRef] [PubMed]
  14. G. Molina-Terriza, J. P. Torres, L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007). [CrossRef]
  15. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). [CrossRef] [PubMed]
  16. M. J. Padgett, R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011). [CrossRef]
  17. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995). [CrossRef] [PubMed]
  18. K. T. Gahagan, G. A. Swartzlander., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996). [CrossRef] [PubMed]
  19. X. Gan, J. Zhao, S. Liu, L. Fang, “Generation and motion control of optical multi-vortex,” Chin. Opt. Lett. 7(12), 1142–1145 (2009). [CrossRef]
  20. W. Zhang, S. Liu, P. Li, X. Jiao, J. Zhao, “Controlling the polarization singularities of the focused azimuthally polarized beams,” Opt. Express 21(1), 974–983 (2013). [CrossRef] [PubMed]
  21. isX. Gan, P. Zhang, S. Liu, F. Xiao, J. Zhao, “Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton,” Phys. Rev. A 89(1), 013844 (2014). [CrossRef]
  22. G. Molina-Terriza, E. M. Wright, L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26(3), 163–165 (2001). [CrossRef] [PubMed]
  23. G.-H. Kim, H. J. Lee, J.-U. Kim, H. Suk, “Propagation dynamics of optical vortices with anisotropic phase profiles,” J. Opt. Soc. Am. B 20(2), 351–360 (2003). [CrossRef]
  24. N. Hermosa, C. Rosales-Guzmán, J. P. Torres, “Helico-conical optical beams self-heal,” Opt. Lett. 38(3), 383–385 (2013). [CrossRef] [PubMed]
  25. C.-A. Alonzo, P. J. Rodrigo, J. Glückstad, “Helico-conical optical beams: a product of helical and conical phase fronts,” Opt. Express 13(5), 1749–1760 (2005). [CrossRef] [PubMed]
  26. N. P. Hermosa, C. O. Manaois, “Phase structure of helicon-conical optical beams,” Opt. Commun. 271(1), 178–183 (2007). [CrossRef]
  27. J. B. Götte, K. O’Holleran, D. Preece, F. Flossmann, S. Franke-Arnold, S. M. Barnett, M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16(2), 993–1006 (2008). [CrossRef] [PubMed]
  28. S. H. Tao, X.-C. Yuan, J. Lin, X. Peng, H. B. Niu, “Fractional optical vortex beam induced rotation of particles,” Opt. Express 13(20), 7726–7731 (2005). [CrossRef] [PubMed]
  29. H. Li, J. Yin, “Generation of a vectorial Mathieu-like hollow beam with a periodically rotated polarization property,” Opt. Lett. 36(10), 1755–1757 (2011). [CrossRef] [PubMed]
  30. J. E. Curtis, D. G. Grier, “Modulated optical vortices,” Opt. Lett. 28(11), 872–874 (2003). [CrossRef] [PubMed]
  31. J. Broky, G. A. Siviloglou, A. Dogariu, D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008). [CrossRef] [PubMed]
  32. H. I. Sztul, R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008). [CrossRef] [PubMed]
  33. J. E. Curtis, D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90(13), 133901 (2003). [CrossRef] [PubMed]
  34. S. A. C. Baluyot, N. P. Hermosa, “Intensity profiles and propagation of optical beams with bored helical phase,” Opt. Express 17(18), 16244–16254 (2009). [CrossRef] [PubMed]

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