Abstract

Perfect optical vortices (POVs) provide a solution to address the challenge induced by strong dependence of classical optical vortices on their carried topological charges. However, traditional POVs are all shaped into bright rings with a single main lobe along the radial direction. Here we propose a method for enhanced control on the ring profile (the radial intensity profile of circular rings) of POVs based on modulated circular sine/cosine radial functions, which is realized by a circular Dammann grating embedded with a spiral phase. Specifically, a type of “absolute” dark POVs surrounded by two bright lobe rings in each side is presented, which provides a perfect annular potential well along those dark impulse rings for trapping low-index particles, cells, or quantum gases. In addition, several POVs with different ring profiles, including conventional POVs with bright rings, the dark POVs mentioned above, and also POVs with tunable ring profiles, are demonstrated. This work opens up new possibilities to controllably tune the ring profile of perfect vortices, and this type of generalized POVs will enrich the content of singular optics and expand the application scope of perfect vortices in a range of areas including optical manipulation, both quantum and classical optical communications, enhanced optical imaging, and also novel structured pumping lasers.

© 2020 Chinese Laser Press

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2019 (5)

2018 (8)

K. Rong, F. Gan, K. Shi, S. Chu, and J. Chen, “Configurable integration of on-chip quantum dot lasers and subwavelength plasmonic waveguides,” Adv. Mater. 30, 1706546 (2018).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

M. Kamper, H. Ta, N. A. Jensen, S. W. Hell, and S. Jakobs, “Near-infrared STED nanoscopy with an engineered bacterial phytochrome,” Nat. Commun. 9, 4762 (2018).
[Crossref]

A. E. Willner, “Vector-mode multiplexing brings an additional approach for capacity growth in optical fibers,” Light Sci. Appl. 7, 18002 (2018).
[Crossref]

2017 (6)

T. Yuan, Y. Cheng, H. Wang, Y. Qin, and B. Fan, “Radar imaging using electromagnetic wave carrying orbital angular momentum,” J. Electron. Imaging 26, 023016 (2017).
[Crossref]

D. Gauthier, P. Ribič, G. Adhikary, A. Camper, C. Chappuis, R. Cucini, L. F. DiMauro, G. Dovillaire, F. Frassetto, R. Géneaux, P. Miotti, L. Poletto, B. Ressel, C. Spezzani, M. Stupar, T. Ruchon, and G. De Ninno, “Tunable orbital angular momentum in high-harmonic generation,” Nat. Commun. 8, 14971 (2017).
[Crossref]

A. Denoeud, L. Chopineau, A. Leblanc, and F. Quere, “Interaction of ultraintense laser vortices with plasma mirrors,” Phys. Rev. Lett. 118, 033902 (2017).
[Crossref]

A. J. Silenko, P. Zhang, and L. Zou, “Manipulating twisted electron beams,” Phys. Rev. Lett. 119, 243903 (2017).
[Crossref]

Y. Liu, Y. Ke, J. Zhou, Y. Liu, H. Luo, S. Wen, and D. Fan, “Generation of perfect vortex and vector beams based on Pancharatnam-Berry phase elements,” Sci. Rep. 7, 44096 (2017).
[Crossref]

A. A. Kovalev, V. V. Kotlyar, and A. P. Porfirev, “A highly efficient element for generating elliptic perfect optical vortices,” Appl. Phys. Lett. 110, 261102 (2017).
[Crossref]

2016 (9)

R. Paez-Lopez, U. Ruiz, V. Arrizon, and R. Ramos-Garcia, “Optical manipulation using optimal annular vortices,” Opt. Lett. 41, 4138–4141 (2016).
[Crossref]

S. G. Reddy, P. Chithrabhanu, P. Vaity, A. Aadhi, S. Prabhakar, and R. P. Singh, “Non-diffracting speckles of a perfect vortex beam,” J. Opt. 18, 055602 (2016).
[Crossref]

C. Zhang, C. Min, L. Du, and X. C. Yuan, “Perfect optical vortex enhanced surface plasmon excitation for plasmonic structured illumination microscopy imaging,” Appl. Phys. Lett. 108, 201601 (2016).
[Crossref]

N. A. Chaitanya, M. V. Jabir, and G. K. Samanta, “Efficient nonlinear generation of high power, higher order, ultrafast ‘perfect’ vortices in green,” Opt. Lett. 41, 1348–1351 (2016).
[Crossref]

M. V. Jabir, N. A. Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of ‘perfect’ vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6, 21877 (2016).
[Crossref]

A. Banerji, R. P. Singh, D. Banerjee, and A. Bandyopadhyay, “Generating a perfect quantum optical vortex,” Phys. Rev. A 94, 053838 (2016).
[Crossref]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41, 2205–2208 (2016).
[Crossref]

S. Fu, C. Gao, T. Wang, S. Zhang, and Y. Zhai, “Simultaneous generation of multiple perfect polarization vortices with selective spatial states in various diffraction orders,” Opt. Lett. 41, 5454–5457 (2016).
[Crossref]

R. Géneaux, A. Camper, T. Auguste, O. Gobert, J. Caillat, R. Taieb, and T. Ruchon, “Synthesis and characterization of attosecond light vortices in the extreme ultraviolet,” Nat. Commun. 7, 12583 (2016).
[Crossref]

2015 (2)

2014 (3)

2013 (4)

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photon. Rev. 7, 839–854 (2013).
[Crossref]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

M. Chen, M. Mazilu, Y. Arita, E. M. Wright, and K. Dholakia, “Dynamics of microparticles trapped in a perfect vortex beam,” Opt. Lett. 38, 4919–4922 (2013).
[Crossref]

A. S. Ostrovsky, C. Rickenstorff-Parrao, and V. Arrizón, “Generation of the ‘perfect’ optical vortex using a liquid-crystal spatial light modulator,” Opt. Lett. 38, 534–536 (2013).
[Crossref]

2012 (1)

M. Zuerch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8, 743–746 (2012).
[Crossref]

2011 (2)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011).
[Crossref]

L. Zhang and P. L. Marston, “Angular momentum flux of nonparaxial acoustic vortex beams and torques on axisymmetric objects,” Phys. Rev. E 84, 065601 (2011).
[Crossref]

2010 (2)

2008 (2)

S. Sasaki and I. McNulty, “Proposal for generating brilliant x-ray beams carrying orbital angular momentum,” Phys. Rev. Lett. 100, 124801 (2008).
[Crossref]

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[Crossref]

2006 (1)

2005 (2)

2004 (1)

G. Molina-Terriza, A. Vaziri, J. Řeháček, Z. Hradil, and A. Zeilinger, “Triggered qutrits for quantum communication protocols,” Phys. Rev. Lett. 92, 167903 (2004).
[Crossref]

2003 (1)

1999 (1)

I. Amidror, “Fourier spectra of radially periodic images with a non-symmetric radial period,” J. Opt. A 1, 621–625 (1999).
[Crossref]

1998 (1)

I. Amidror, “The Fourier-spectrum of circular sine and cosine gratings with arbitrary radial phase,” Opt. Commun. 149, 127–134 (1998).
[Crossref]

1997 (2)

1996 (1)

1995 (1)

1994 (1)

1992 (1)

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, 8185–8189 (1992).
[Crossref]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974).
[Crossref]

Aadhi, A.

M. V. Jabir, N. A. Chaitanya, A. Aadhi, and G. K. Samanta, “Generation of ‘perfect’ vortex of variable size and its effect in angular spectrum of the down-converted photons,” Sci. Rep. 6, 21877 (2016).
[Crossref]

S. G. Reddy, P. Chithrabhanu, P. Vaity, A. Aadhi, S. Prabhakar, and R. P. Singh, “Non-diffracting speckles of a perfect vortex beam,” J. Opt. 18, 055602 (2016).
[Crossref]

Adhikary, G.

D. Gauthier, P. Ribič, G. Adhikary, A. Camper, C. Chappuis, R. Cucini, L. F. DiMauro, G. Dovillaire, F. Frassetto, R. Géneaux, P. Miotti, L. Poletto, B. Ressel, C. Spezzani, M. Stupar, T. Ruchon, and G. De Ninno, “Tunable orbital angular momentum in high-harmonic generation,” Nat. Commun. 8, 14971 (2017).
[Crossref]

Allen, L.

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, 8185–8189 (1992).
[Crossref]

Alpmann, C.

M. Woerdemann, C. Alpmann, M. Esseling, and C. Denz, “Advanced optical trapping by complex beam shaping,” Laser Photon. Rev. 7, 839–854 (2013).
[Crossref]

Amato-Grill, J.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, “Optical forces arising from phase gradients,” Phys. Rev. Lett. 100, 013602 (2008).
[Crossref]

Amidror, I.

I. Amidror, “Fourier spectra of radially periodic images with a non-symmetric radial period,” J. Opt. A 1, 621–625 (1999).
[Crossref]

I. Amidror, “The Fourier-spectrum of circular sine and cosine gratings with arbitrary radial phase,” Opt. Commun. 149, 127–134 (1998).
[Crossref]

I. Amidror, “Fourier spectrum of radially periodic images,” J. Opt. Soc. Am. A 14, 816–826 (1997).
[Crossref]

Arita, Y.

Arrizon, V.

Arrizón, V.

Auguste, T.

R. Géneaux, A. Camper, T. Auguste, O. Gobert, J. Caillat, R. Taieb, and T. Ruchon, “Synthesis and characterization of attosecond light vortices in the extreme ultraviolet,” Nat. Commun. 7, 12583 (2016).
[Crossref]

Bandyopadhyay, A.

A. Banerji, R. P. Singh, D. Banerjee, and A. Bandyopadhyay, “Generating a perfect quantum optical vortex,” Phys. Rev. A 94, 053838 (2016).
[Crossref]

Banerjee, D.

A. Banerji, R. P. Singh, D. Banerjee, and A. Bandyopadhyay, “Generating a perfect quantum optical vortex,” Phys. Rev. A 94, 053838 (2016).
[Crossref]

Banerji, A.

A. Banerji, R. P. Singh, D. Banerjee, and A. Bandyopadhyay, “Generating a perfect quantum optical vortex,” Phys. Rev. A 94, 053838 (2016).
[Crossref]

Bateman, H.

H. Bateman, Tables of Integral Transforms (McGraw-Hill, 1954).

Beijersbergen, M. W.

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, 8185–8189 (1992).
[Crossref]

Bernet, S.

Bernhard, C.

A. A. Sirenko, P. Marsik, C. Bernhard, T. N. Stanislavchuk, V. Kiryukhin, and S.-W. Cheong, “Terahertz vortex beam as a spectroscopic probe of magnetic excitations,” Phys. Rev. Lett. 122, 237401 (2019).
[Crossref]

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974).
[Crossref]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref]

Brunet, C.

Cai, Y.

Caillat, J.

R. Géneaux, A. Camper, T. Auguste, O. Gobert, J. Caillat, R. Taieb, and T. Ruchon, “Synthesis and characterization of attosecond light vortices in the extreme ultraviolet,” Nat. Commun. 7, 12583 (2016).
[Crossref]

Camarena, F.

N. Jiménez, V. Romero-García, L. M. García-Raffi, F. Camarena, and K. Staliunas, “Sharp acoustic vortex focusing by Fresnel-spiral zone plates,” Appl. Phys. Lett. 112, 204101 (2018).
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Supplementary Material (1)

NameDescription
» Visualization 1       A more subtle transition from a bright POV to a dark one and then again to a bright POV is demonstrated

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Figures (7)

Fig. 1.
Fig. 1. Schematic diagrams of the experimental scheme. (a) The proof-of-principle experimental setup. L12 are lenses for expanding and collimation. L3 and L4 are a confocal lens pair, and L5 is the focusing lens; PBS12 are polarizing beam splitter cubes; BS1 is a non-polarizing beam splitter; M is a reflective mirror; SLM denotes a spatial light modulator; P12 denote polarizers; λ/4 denotes a quarter-wave plate. CMOS denotes a complementary metal-oxide semiconductor camera. (b) Phase distributions of a typical binary CDG, (c) a spiral phase, and (d) the CDG embedded with the spiral phase. The insets in the bottom-right corner indicate the enlarged portions in those rectangular areas in (b) and (d), respectively.
Fig. 2.
Fig. 2. Simulation and experimental results of dark POVs generated by CDGs embedded with spiral phases with charges of (a) l=1, (b) 5, and (c) 15. In each box, the simulation results of the intensity distribution and interferograms are shown in the first and second rows; the experimental results of the intensity distribution and interferograms are shown in the third and fourth rows, respectively. The insets are enlarged portions of dark impulse rings in rectangular areas in those sub-images for intensity distribution. The scale bar denotes 300 μm.
Fig. 3.
Fig. 3. Simulation and experimental results of interferograms on defocused planes (with defocus distance Δd=10  mm) for dark POVs with charges of (a) l=10 and (b) 5. In each box, the simulation and experimental results are shown in the first and second rows, and the results on defocused planes before and after the focus are shown in the first and second columns, respectively. The scale bar denotes 300 μm.
Fig. 4.
Fig. 4. Simulation and experimental results of phase distributions on defocused planes (with defocus distance Δd=25  mm) for dark POVs with charges of (a) l=10 and (b) l=5. In each box, the simulation and the experimental results are shown in the first and second rows, and the results on defocused planes before and after the focus are shown in the first and second columns, respectively. The scale bar denotes 300 μm.
Fig. 5.
Fig. 5. Simulation and experimental results of bright POVs generated by CDGs embedded with spiral phases with charges of (a) l=1, (b) 5, and (c) 20. In each box, the simulation results of the intensity distributions and interferograms are shown in the first and second rows; the experimental results of the intensity distributions and interferograms are shown in the third and fourth rows, respectively. The insets are enlarged portions of bright impulse rings in rectangular areas in those sub-figures for intensity distribution. The scale bar denotes 300 μm.
Fig. 6.
Fig. 6. Simulation and experimental results of POVs with tunable ring profiles generated by CDGs (with period number of N=30 inside the aperture) embedded with spiral phase with charge of l=10. (a) The curve of the side-lobe ratio β as a function of the phase difference δϕ; a POV with side-lobe ratio of (b) 1/3 with a lobe ring outside, (c) 1/3 with a lobe ring inside, (d) 2/3 with a lobe ring inside, and (e) 2/3 with a lobe ring outside; (f) a POV with a bright ring profile (a bright POV with the smallest side-lobe ratio), and (g) denotes its interferogram on the focal plane; (h) a POV with a dark ring profile (a dark POV with unity side-lobe ratio), and (i) is its interferogram on the focal plane. The scale bar denotes 500 μm.
Fig. 7.
Fig. 7. Influences of topological charge and period number on performance parameters of POVs with bright and dark ring profiles generated by CDGs. (a) The ring radius, (b) the ring width, and (c) the side-lobe ratio as a function of the charge; (d) the ring radius, (e) the ring width, and (f) the side-lobe ratio versus the period number inside the aperture. In each sub-figure, the blue solid line denotes the simulation results of POVs with bright ring profiles (bright POVs) and the red broken line denotes the simulation results of POVs with dark ring profiles (dark POVs); the square denotes the experimental results of bright POVs, and the circle is the experimental results of dark POVs.

Equations (22)

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T(r,θ)=T(r)exp(ilθ)=a02exp(ilθ)+m=1amcos(2πmrΛ)exp(ilθ),
am=0ΛT(r)cos(2πmrΛ)dr.
hm(r,θ)=amexp(ilθ)2[exp(i2πmrΛ)+exp(i2πmrΛ)].
am=cm+cm=|cm|exp(iΔϕm2)+|cm|exp(iΔϕm2),
hm(r,θ)=m=1|cm|cos(2πmrΛ+Δϕm/2)exp(ilθ),
cm=n=1N1rnrn+1exp{i[1+(1)n]π2}exp(i2πmrΛ)dr,
Hm(ρ,φ)=(i)l+1kfexp(ilφ)[umHmc(ρ)+vmHms(ρ)],
Hmc(ρ)=0Rcos(2πmr/Λ)Jl(kρr/f)rdr,
Hms(ρ)=0Rsin(2πmr/Λ)Jl(kρr/f)rdr.
β(Δϕm)={|Hmmin/Hmmax|2,if  |Hmmax||Hmmin||Hmmax/Hmmin|2,if  |Hmmax|<|Hmmin|,
cos(αr)Hα21(α/2+πρ)3/2δ(1/2)(α/2πρ),
sin(αr)Hα21(α/2+πρ)3/2δ(1/2)(ρα/2π),
cos(αr+Δϕ2)=ucos(αr)+vsin(αr),
sin(αr+Δϕ2)=vcos(αr)+usin(αr),
H{cos(αr+Δϕ2)}=α21(α/2+πρ)3/2×[uδ1/2(ρα2π)+vδ1/2(α2πρ)],
H{cos(αr+Δϕ2)eilθ}=2πeilφ0[ucos(αr)+vsin(αr)]Jl(2πρr)rdr=2πeilφ[uHc(ρ)+vHs(ρ)],
Hc(ρ)=0cos(αr)Jl(2πρr)rdr={(2πρ)lΓ(l+2)cos[π(l+2)/2]2lα(l+2)Γ(l+1)F12[1+l/2,3/2+l/2;l+1;(2πρ/α)2],0<ρ<α/2πΓ(l/2+1)2(πρ)2Γ(l/2)F12[1+l/2,1l/2;1/2;(α/2πρ)2],ρ>α/2π,
Hs(ρ)=0sin(αr)Jl(2πρr)rdr={(2πρ)lΓ(l+2)sin[π(l+2)/2]2lα(l+2)Γ(l+1)F12[3/2+l/2,1+l/2;l+1;(2πρ/α)2],0<ρ<α/2π2lαΓ(l/2+3/2)2(πρ)3Γ(l/21/2)F12[3/2+l/2,3/2l/2;3/2;(α/2πρ)2],ρ>α/2π,
I(x,y)=Ax22+Ay22+AxAycos[ϕ(x,y)+2θ],
ϕ(x,y)={arctan(y/x)π,x>0andy>0arctan(y/x),x>0andy<0arctan(y/x)+π/2,x<0,
x=I04I2+3I4,y=(3I14I3+I5),
In=Ax22+Ay22+AxAycos[ϕ(x,y)+2nΔθ],n=0,1,2,3,4,5,

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