Abstract

A modification of the helical phase profile obtained by eliminating the on-axis screw-dislocation is presented. Beams with this phase possess a variety of interesting properties different from optical vortex beams. Numerical simulations verify analytic predictions and reveal that beams with this phase have intensity patterns which vary as a function of the phase parameters, as well as the propagation distance. Calculations of the Poynting vector and orbital angular momentum are also performed. Experiments verify the intensity profiles obtained in simulation.

© 2009 Optical Society of America

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2008 (1)

2007 (3)

2006 (1)

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

2005 (1)

2004 (3)

M. V. Berry, "Optical Vortices Evolving from helicoidal integer and fractional phase steps," J. Opt. A 6, 259 - 268 (2004).
[CrossRef]

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Synthesis and analysis of optical vortices with fractional topological charges," J. Opt. A 6, S166 - S169 (2004).
[CrossRef]

W.M. Lee, X.-C. Yuan, K. Dholakia, "Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step," Opt. Commun. 239, 129-135 (2004).
[CrossRef]

2003 (1)

G. V. Borgatiryova and M. S. Soskin, "Detection and metrology of optical vortex helical wavefronts," SPQEO 6, 254 - 258 (2003).

2002 (2)

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241 - 258 (2002).
[CrossRef]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

2000 (2)

1997 (3)

M. J. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35 - 38 (1997).

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 - 4075 (1997).
[CrossRef]

G.-H. Kim, J.-H. Jeon, K.-H. Ko, H.-J. Moon, J.-H. Lee, and J.-S. Chang, "Optical vortices produced with a nonspiral phase plate," Appl. Opt. 36, 8614 - 8621 (1997).
[CrossRef]

1995 (2)

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604 - 612 (1995).
[CrossRef]

M. J. Padgett, and L. Allen, "The Poynting vector in Laguerre-Gaussian laser modes," Opt. Commun. 121, 36 - 40 (1995).
[CrossRef]

1994 (1)

S. M. Barnett, and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670 - 678 (1994).
[CrossRef]

1993 (2)

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422 - 428 (1993).
[CrossRef]

G. Indebetouw, "Optical vortices and their propagation," J. Mod. Opt. 40, 73 - 87 (1993).
[CrossRef]

1992 (2)

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985 - 990 (1992).
[CrossRef]

K. Staliunas, "Dynamics of optical vortices in a laser beam," Opt. Commun. 90, 123 - 127 (1992).
[CrossRef]

Ahluwalia, B. S.

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Allen, L.

M. J. Padgett and L. Allen, "Optical tweezers and spanners," Phys. World 10, 35 - 38 (1997).

M. J. Padgett, and L. Allen, "The Poynting vector in Laguerre-Gaussian laser modes," Opt. Commun. 121, 36 - 40 (1995).
[CrossRef]

S. M. Barnett, and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670 - 678 (1994).
[CrossRef]

Alonzo, C. A.

Arlt, J.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

Arnold, A. S.

Barnett, S. M.

Basistiy, I. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Synthesis and analysis of optical vortices with fractional topological charges," J. Opt. A 6, S166 - S169 (2004).
[CrossRef]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604 - 612 (1995).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422 - 428 (1993).
[CrossRef]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422 - 428 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985 - 990 (1992).
[CrossRef]

Berry, M. V.

M. V. Berry, "Optical Vortices Evolving from helicoidal integer and fractional phase steps," J. Opt. A 6, 259 - 268 (2004).
[CrossRef]

Borgatiryova, G. V.

G. V. Borgatiryova and M. S. Soskin, "Detection and metrology of optical vortex helical wavefronts," SPQEO 6, 254 - 258 (2003).

Bu, J.

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Chang, J.-S.

Chavez-Cerda, S.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

Cheong, W. C.

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Dholakia, K.

W.M. Lee, X.-C. Yuan, K. Dholakia, "Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step," Opt. Commun. 239, 129-135 (2004).
[CrossRef]

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

Dreischuh, A.

Ellinas, D.

Flossmann, F.

Franke-Arnold, S.

Garces-Chavez, V.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

Girkin, J. M.

Gluckstad, P.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 - 4075 (1997).
[CrossRef]

Gotte, J. B.

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 - 4075 (1997).
[CrossRef]

Hermosa, N. P.

N. P. HermosaII and C. O. Manaois, "Phase structure of Helico-conical optical beams," Opt. Commun. 271, 178 - 183 (2007).
[CrossRef]

Indebetouw, G.

G. Indebetouw, "Optical vortices and their propagation," J. Mod. Opt. 40, 73 - 87 (1993).
[CrossRef]

Jeon, J.-H.

Kelemen, L.

Kim, G.-H.

Ko, K.-H.

Leach, J.

Lee, J.-H.

Lee, W.M.

W.M. Lee, X.-C. Yuan, K. Dholakia, "Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step," Opt. Commun. 239, 129-135 (2004).
[CrossRef]

Lembessis, V. E.

Lin, J.

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 - 4075 (1997).
[CrossRef]

Manaois, C. O.

N. P. HermosaII and C. O. Manaois, "Phase structure of Helico-conical optical beams," Opt. Commun. 271, 178 - 183 (2007).
[CrossRef]

Moh, K. J.

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Molloy, J. E.

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241 - 258 (2002).
[CrossRef]

Moon, H.-J.

Neshev, D.

Ohberg, P.

O'Holleran, K.

Ormos, P.

Padgett, M. J.

Pas’ko, V. A.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Synthesis and analysis of optical vortices with fractional topological charges," J. Opt. A 6, S166 - S169 (2004).
[CrossRef]

Paulus, G. G.

Preece, D.

Ramee, S.

Rodrigo, P. J.

Simon, R.

Slyusar, V. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Synthesis and analysis of optical vortices with fractional topological charges," J. Opt. A 6, S166 - S169 (2004).
[CrossRef]

Soskin, M. S.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Synthesis and analysis of optical vortices with fractional topological charges," J. Opt. A 6, S166 - S169 (2004).
[CrossRef]

G. V. Borgatiryova and M. S. Soskin, "Detection and metrology of optical vortex helical wavefronts," SPQEO 6, 254 - 258 (2003).

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 - 4075 (1997).
[CrossRef]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604 - 612 (1995).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422 - 428 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985 - 990 (1992).
[CrossRef]

Staliunas, K.

K. Staliunas, "Dynamics of optical vortices in a laser beam," Opt. Commun. 90, 123 - 127 (1992).
[CrossRef]

Tao, S.

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Valkai, S.

Vasnetsov, M. V.

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Synthesis and analysis of optical vortices with fractional topological charges," J. Opt. A 6, S166 - S169 (2004).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 - 4075 (1997).
[CrossRef]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604 - 612 (1995).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422 - 428 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985 - 990 (1992).
[CrossRef]

Volke-Sepulveda, K.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

Walther, H.

Wright, A. J.

Yuan, X.

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Yuan, X.-C.

W.M. Lee, X.-C. Yuan, K. Dholakia, "Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step," Opt. Commun. 239, 129-135 (2004).
[CrossRef]

Zhang, L.

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Appl. Opt. (1)

Contemp. Phys. (1)

J. E. Molloy and M. J. Padgett, "Lights, action: optical tweezers," Contemp. Phys. 43, 241 - 258 (2002).
[CrossRef]

J. Mod. Opt. (2)

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985 - 990 (1992).
[CrossRef]

G. Indebetouw, "Optical vortices and their propagation," J. Mod. Opt. 40, 73 - 87 (1993).
[CrossRef]

J. Opt. A (2)

I. V. Basistiy, V. A. Pas’ko, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Synthesis and analysis of optical vortices with fractional topological charges," J. Opt. A 6, S166 - S169 (2004).
[CrossRef]

M. V. Berry, "Optical Vortices Evolving from helicoidal integer and fractional phase steps," J. Opt. A 6, 259 - 268 (2004).
[CrossRef]

J. Opt. B (1)

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, "Orbital angular momentum of a high-order Bessel light beam," J. Opt. B 4, S82-S89 (2002).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (7)

W.M. Lee, X.-C. Yuan, K. Dholakia, "Experimental observation of optical vortex evolution in a Gaussian beam with an embedded fractional phase step," Opt. Commun. 239, 129-135 (2004).
[CrossRef]

M. J. Padgett, and L. Allen, "The Poynting vector in Laguerre-Gaussian laser modes," Opt. Commun. 121, 36 - 40 (1995).
[CrossRef]

K. Staliunas, "Dynamics of optical vortices in a laser beam," Opt. Commun. 90, 123 - 127 (1992).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Optics of light beams with screw dislocations," Opt. Commun. 103, 422 - 428 (1993).
[CrossRef]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604 - 612 (1995).
[CrossRef]

S. M. Barnett, and L. Allen, "Orbital angular momentum and nonparaxial light beams," Opt. Commun. 110, 670 - 678 (1994).
[CrossRef]

N. P. HermosaII and C. O. Manaois, "Phase structure of Helico-conical optical beams," Opt. Commun. 271, 178 - 183 (2007).
[CrossRef]

Opt. Express (4)

Opt. Photon. News (1)

X. Yuan, B. S. Ahluwalia, W. C. Cheong, L. Zhang, J. Bu, S. Tao, K. J. Moh, and J. Lin, "Micro-optical elements for optical manipulation," Opt. Photon. News 17, 36 - 41 (2006).
[CrossRef]

Phys. Rev. A (1)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064 - 4075 (1997).
[CrossRef]

Phys. World (1)

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Supplementary Material (1)

» Media 1: MPG (1689 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Comparison of (a) Helical and (b) Bored Helical (BH) Phases. While BH phases retain its helical profile in the region O\I, it is zero within the bore region I.

Fig. 2.
Fig. 2.

vs ρREL phase plot at z=1.33×105 λ. Intensity profiles of BH beams are observed to vary with the topological charge and cavity radius ρi .

Fig. 3.
Fig. 3.

Modeled =5, ρREL =0.4 BH beam as a function of propagation distance z. Transverse intensity patterns of BH beams vary as viewed on different z-planes. Rotation of the beam patterns is observed as the beam propagates.

Fig. 4.
Fig. 4.

Angular displacement α (deg) as a function of propagation distance z of a charge 6 BH beam. Rotation angles are measured by tracking distinctive zeroes in the intensity profile as the beam propagates. In spite of rotation, distinct OV’s embedded in the profile remain uniformly distributed.

Fig. 5.
Fig. 5.

Variation of rotation angle α (deg) with distance z of a BH beam with ρREL =0.6.

Fig. 6.
Fig. 6.

Setup used to experimentally verify BH beams. (a) The expanded and collimated He-Ne (λ=632.8nm) laser beam is imprinted with the bored helical phase via a computer-generated hologram (CGH). The BH beam is then diffracted using a lens of f=f1 . The 1st-order diffraction is isolated by blocking other orders. The transverse intensity profile of the 1st-order beam is then imaged into a CCD camera using a lens of f=f2 . (b) Computer-generated hologram illustrating the (calculated) interference of a BH beam with a plane reference wave.

Fig. 7.
Fig. 7.

Transverse intensity profiles of ρREL =0.2 BH beams of charge 1 (a), 2 (b), and 3 (c) captured using a CCD camera. Images shown are scaled.

Fig. 8.
Fig. 8.

Experimentally obtained intensity patterns of charge 3 BH beams with ρREL =0 (a), 0.2 (b), and 0.4 (c).

Fig. 9.
Fig. 9.

(a) Simulated and (b) reconstructed BH beams of charge 3 and ρREL =0.64 shown in pseudo-color.

Fig. 10.
Fig. 10.

(Media 1) Propagation of the zeroth-(right) and first-order (center) diffraction beams emerging from a CGH denoting a =3, ρREL =0.6 BH beam beginning from the focal plane. The sequence of images were taken at constant intervals of z.

Equations (19)

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Φ (ρ,φ)=φ.
ΦBH (ρ,φ,z=0)={φ;ρiρ<ρo0;otherwise=χoI(ρ)φ,
χA (x){1;xA0;xA,
I {ρ+{0}:ρ<ρi};ρi+{0},
O {ρ+{0}:ρ<ρo};ρo+;ρi<ρo.
O I = O Ic = {ρ+{0}:ρiρ<ρo}.
H (fx,fy;z) = exp [ikzλz(fx2+fy2)] .
η = 1 + cos [2πxΛ+ΦBH(ρ,φ,z=0)],
uBH (ρ,φ,z=0)Cχo(ρ)exp(ρ2σ2)exp[iΦBH(ρ,φ,z=0)],
uBH (ρ,φ,z)=Ckexp(ikz)iz exp (ik2zρ2){0+χ1(ρ)exp[(1σ2+ik2z)ρ2]J0(zρ)ρdρ
+ i exp (iφ) 0+χoI(ρ)exp[(1σ2+ik2z)ρ2]J(zρ)ρdρ}
= Iu(ρ,z)+Ou(ρ,φ,z) .
S·φ̂=ωμ01ρ{Ou2+12[IuOu*+u*Ou]},
S·ẑ=ωkμ0uBH2.
j · ẑ = ρ p · φ̂ = ρc2 S · φ̂ .
JzΞ = ε0ω02π0+Ou(ρ,φ,z)2ρdρdφε0ω202π0+uBH(ρ,φ,z)2ρdρdφ
= ε0ω02π0+Ou(ρ,φ,z=0)2ρdρdφε0ω202π0+uBH(ρ,φ,z=0)2ρdρdφ
= ω 02π0+Ou(ρ,φ,z=0)2ρdρdφ,
02π0+Ou(ρ,φ,z=0)2ρdρdφ02π0+uBH(ρ,φ,z=0)2ρdρdφ=1,

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