Abstract

We develop a novel method of creating optical vortex array by the conversion of a standing-wave Laguerre-Gaussian (LG) mode. Theoretically, by employing the transformational relation, the standing-wave LG mode is verified to be transformed from a pair of crisscrossed Hermite-Gaussian (HG) modes, embedded with optical vortex array, consists of a TEMn,m mode and a TEMm,n mode. Due to close correspondence between the transformational relation and the mode conversion of astigmatic lenses, we successfully generate the optical vortex array by transforming a standing-wave LG mode into the crisscrossed HG modes via a π/2 cylindrical lens mode converter. The investigation may provide useful insight in the study of the vortex light beam and its further applications.

© 2011 OSA

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2010 (2)

Y. F. Chen, Y. C. Lin, K. F. Huang, and T. H. Lu, “Spatial transformation of coherent optical waves with orbital morphologies,” Phys. Rev. A 82(4), 043801 (2010).
[CrossRef]

M. P. Thirugnanasambandam, Yu. Senatsky, and K. Ueda, “Generation of very-high order Laguerre-Gaussian modes in Yb:YAG ceramic laser,” Laser Phys. Lett. 7(9), 637–643 (2010).
[CrossRef]

2009 (1)

2007 (2)

S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46(15), 2893–2898 (2007).
[CrossRef] [PubMed]

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

2006 (2)

Y. F. Chen, T. H. Lu, and K. F. Huang, “Hyperboloid structures formed by polarization singularities in coherent vector fields with longitudinal-transverse coupling,” Phys. Rev. Lett. 97(23), 233903 (2006).
[CrossRef]

K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14(7), 3039–3044 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (5)

2003 (1)

2001 (3)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM*0,1 mode in a solid-state laser,” Phys. Rev. A 63(6), 063807 (2001).
[CrossRef]

1999 (1)

1998 (2)

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73(16), 2239 (1998).
[CrossRef]

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

1997 (1)

1996 (2)

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[CrossRef] [PubMed]

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

1994 (2)

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72(15), 2379–2382 (1994).
[CrossRef] [PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[CrossRef]

1993 (2)

G. Nienhuis and L. Allen, “Paraxial wave optics and harmonic oscillators,” Phys. Rev. A 48(1), 656–665 (1993).
[CrossRef] [PubMed]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

1992 (3)

1991 (1)

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun. 83(1-2), 123–135 (1991).
[CrossRef]

1990 (1)

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Abramochkin, E.

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun. 83(1-2), 123–135 (1991).
[CrossRef]

Adachi, H.

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

Akahoshi, S.

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

Allen, L.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[CrossRef] [PubMed]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[CrossRef] [PubMed]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

G. Nienhuis and L. Allen, “Paraxial wave optics and harmonic oscillators,” Phys. Rev. A 48(1), 656–665 (1993).
[CrossRef] [PubMed]

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]

Barnett, S.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

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]

Chang, J. S.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

Chen, Y. F.

Y. F. Chen, Y. C. Lin, K. F. Huang, and T. H. Lu, “Spatial transformation of coherent optical waves with orbital morphologies,” Phys. Rev. A 82(4), 043801 (2010).
[CrossRef]

Y. F. Chen, T. H. Lu, and K. F. Huang, “Hyperboloid structures formed by polarization singularities in coherent vector fields with longitudinal-transverse coupling,” Phys. Rev. Lett. 97(23), 233903 (2006).
[CrossRef]

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM*0,1 mode in a solid-state laser,” Phys. Rev. A 63(6), 063807 (2001).
[CrossRef]

Chu, S. C.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[CrossRef]

Courtial, J.

Crabtree, K.

D’Angelo, E. J.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Dai, G.

M. D. Levenson, T. J. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3(2), 293–304 (2004).
[CrossRef]

Davis, J. A.

Dennis, M. R.

Dholakia, K.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[CrossRef] [PubMed]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[CrossRef] [PubMed]

Ebihara, T. J.

M. D. Levenson, T. J. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3(2), 293–304 (2004).
[CrossRef]

Franke-Arnold, S.

Gahagan, K. T.

Gibson, G.

Green, C.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Grier, D. G.

Grynberg, G.

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72(15), 2379–2382 (1994).
[CrossRef] [PubMed]

Hayashi, N.

M. D. Levenson, T. J. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3(2), 293–304 (2004).
[CrossRef]

Heckenberg, N. R.

Huang, K. F.

Y. F. Chen, Y. C. Lin, K. F. Huang, and T. H. Lu, “Spatial transformation of coherent optical waves with orbital morphologies,” Phys. Rev. A 82(4), 043801 (2010).
[CrossRef]

Y. F. Chen, T. H. Lu, and K. F. Huang, “Hyperboloid structures formed by polarization singularities in coherent vector fields with longitudinal-transverse coupling,” Phys. Rev. Lett. 97(23), 233903 (2006).
[CrossRef]

Izdebskaya, Y.

Jeon, J. H.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

Kim, G. H.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

Ko, K. H.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[CrossRef]

Ladavac, K.

Lan, Y. P.

Y. F. Chen and Y. P. Lan, “Dynamics of the Laguerre Gaussian TEM*0,1 mode in a solid-state laser,” Phys. Rev. A 63(6), 063807 (2001).
[CrossRef]

Lee, J. H.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

Levenson, M. D.

M. D. Levenson, T. J. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3(2), 293–304 (2004).
[CrossRef]

Lin, Y. C.

Y. F. Chen, Y. C. Lin, K. F. Huang, and T. H. Lu, “Spatial transformation of coherent optical waves with orbital morphologies,” Phys. Rev. A 82(4), 043801 (2010).
[CrossRef]

Lu, T. H.

Y. F. Chen, Y. C. Lin, K. F. Huang, and T. H. Lu, “Spatial transformation of coherent optical waves with orbital morphologies,” Phys. Rev. A 82(4), 043801 (2010).
[CrossRef]

Y. F. Chen, T. H. Lu, and K. F. Huang, “Hyperboloid structures formed by polarization singularities in coherent vector fields with longitudinal-transverse coupling,” Phys. Rev. Lett. 97(23), 233903 (2006).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Maître, A.

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72(15), 2379–2382 (1994).
[CrossRef] [PubMed]

Masajada, J.

J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun. 239(4-6), 373–381 (2004).
[CrossRef]

McDuff, R.

Mindlin, G. B.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Miyakawa, K.

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

Moon, H. J.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

Moreno, I.

Morikawa, Y.

M. D. Levenson, T. J. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3(2), 293–304 (2004).
[CrossRef]

Nienhuis, G.

G. Nienhuis and L. Allen, “Paraxial wave optics and harmonic oscillators,” Phys. Rev. A 48(1), 656–665 (1993).
[CrossRef] [PubMed]

Noh, Y. C.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

O’Holleran, K.

Otsuka, K.

Padgett, M. J.

Pas’ko, V.

Pereira, S. F.

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73(16), 2239 (1998).
[CrossRef]

Petrossian, A.

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72(15), 2379–2382 (1994).
[CrossRef] [PubMed]

Senatsky, Yu.

M. P. Thirugnanasambandam, Yu. Senatsky, and K. Ueda, “Generation of very-high order Laguerre-Gaussian modes in Yb:YAG ceramic laser,” Laser Phys. Lett. 7(9), 637–643 (2010).
[CrossRef]

Senthilkumaran, P.

Shvedov, V.

Simpson, N. B.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[CrossRef] [PubMed]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[CrossRef] [PubMed]

Smith, C. P.

Solari, H. G.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Soskin, M. S.

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

Spreeuw, R. J. C.

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]

Swartzlander, G. A.

Tan, S. M.

M. D. Levenson, T. J. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3(2), 293–304 (2004).
[CrossRef]

Thirugnanasambandam, M. P.

M. P. Thirugnanasambandam, Yu. Senatsky, and K. Ueda, “Generation of very-high order Laguerre-Gaussian modes in Yb:YAG ceramic laser,” Laser Phys. Lett. 7(9), 637–643 (2010).
[CrossRef]

Tredicce, J. R.

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Ueda, K.

M. P. Thirugnanasambandam, Yu. Senatsky, and K. Ueda, “Generation of very-high order Laguerre-Gaussian modes in Yb:YAG ceramic laser,” Laser Phys. Lett. 7(9), 637–643 (2010).
[CrossRef]

van Exter, M. P.

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73(16), 2239 (1998).
[CrossRef]

Vanderveen, H.

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

Vasnetsov, M.

Vasnetsov, M. V.

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Volostnikov, V.

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun. 83(1-2), 123–135 (1991).
[CrossRef]

Volyar, A.

Vyas, S.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

White, A. G.

Willemsen, M. B.

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73(16), 2239 (1998).
[CrossRef]

Woerdman, J. P.

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73(16), 2239 (1998).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

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]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, “Pinning of daisy modes in optically pumped vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 73(16), 2239 (1998).
[CrossRef]

J. Microlithogr. Microfabr. Microsyst. (1)

M. D. Levenson, T. J. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and S. M. Tan, “Optical vortex mask via levels,” J. Microlithogr. Microfabr. Microsyst. 3(2), 293–304 (2004).
[CrossRef]

Laser Phys. Lett. (1)

M. P. Thirugnanasambandam, Yu. Senatsky, and K. Ueda, “Generation of very-high order Laguerre-Gaussian modes in Yb:YAG ceramic laser,” Laser Phys. Lett. 7(9), 637–643 (2010).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Opt. Commun. (5)

M. W. Beijersbergen, L. Allen, H. Vanderveen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994).
[CrossRef]

E. Abramochkin and V. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun. 83(1-2), 123–135 (1991).
[CrossRef]

J. Masajada, “Small-angle rotations measurement using optical vortex interferometer,” Opt. Commun. 239(4-6), 373–381 (2004).
[CrossRef]

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147(1-3), 131–137 (1998).
[CrossRef]

Opt. Express (3)

Opt. Lett. (7)

Phys. Rev. A (6)

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Y. F. Chen, Y. C. Lin, K. F. Huang, and T. H. Lu, “Spatial transformation of coherent optical waves with orbital morphologies,” Phys. Rev. A 82(4), 043801 (2010).
[CrossRef]

G. Nienhuis and L. Allen, “Paraxial wave optics and harmonic oscillators,” Phys. Rev. A 48(1), 656–665 (1993).
[CrossRef] [PubMed]

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]

H. Adachi, S. Akahoshi, and K. Miyakawa, “Orbital motion of spherical microparticles trapped in diffraction patterns of circularly polarized light,” Phys. Rev. A 75(6), 063409 (2007).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54(5), R3742–R3745 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

G. Grynberg, A. Maître, and A. Petrossian, “Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror,” Phys. Rev. Lett. 72(15), 2379–2382 (1994).
[CrossRef] [PubMed]

C. Green, G. B. Mindlin, E. J. D’Angelo, H. G. Solari, and J. R. Tredicce, “Spontaneous symmetry breaking in a laser: The experimental side,” Phys. Rev. Lett. 65(25), 3124–3127 (1990).
[CrossRef] [PubMed]

Y. F. Chen, T. H. Lu, and K. F. Huang, “Hyperboloid structures formed by polarization singularities in coherent vector fields with longitudinal-transverse coupling,” Phys. Rev. Lett. 97(23), 233903 (2006).
[CrossRef]

Prog. Opt. (1)

M. S. Soskin and M. V. Vasnetsov, “Singular Optics,” Prog. Opt. 42, 219–276 (2001).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

A. E. Siegman, Lasers (University Science, 1986).

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Figures (8)

Fig. 1
Fig. 1

Theoretical demonstration of Eq. (1) for the superposition of ψ 0 , 11 ( H G ) and ψ 11 ,     0 ( H G ) modes with relative phase α = π / 2 .

Fig. 2
Fig. 2

Theoretical results of Ψ 0 ,     11 ( x , y , z , α ) of various relative phases.

Fig. 3
Fig. 3

(a) Theoretical results of Ψ 0 ,     11 ( x , y , z , π / 2 ) . (b) Phase distribution of (a). (c) Enlarged figure of the box region in (b). (d) linear momentum density p for the box region in (b) of Ψ 0 ,     11 ( x , y , z , π / 2 ) .

Fig. 4
Fig. 4

Theoretical results of superposed state Φ 0 , 11 ( r , ϕ , z , α ) of various relative phases.

Fig. 5
Fig. 5

Experimental setup utilized to transform the flower-like LG modes into the crisscrossed HG modes with the cylindrical lenses.

Fig. 6
Fig. 6

(a) Diagram for the transformational relation of a flower-like LG mode and the crisscrossed HG mode. (b) Operational scheme for the rotation of the mode converter.

Fig. 7
Fig. 7

Experimental results of an input LG mode with     ( n , m ) = ( 0 , 11 ) and the corresponding crisscrossed HG modes while rotating the CLMC.

Fig. 8
Fig. 8

Theoretical analysis: (a) LG modes with non-vanishing radial index n . (b) The resulting modes converted from the LG modes. (c) Phase distribution corresponding to (b).

Equations (10)

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ψ n , m ( H G ) ( x , y , z ) = ψ n , m ( H G ) ( x , y , z ) e i ( n + m + 1 ) θ G ( z )   e i ξ ( x , y , z ) ,
ψ n , m ( H G ) ( x , y , z ) = C n , m ( H G ) w ( z )     e ( x 2 + y 2 w ( z ) 2 ) H n ( 2 w ( z ) x ) H m ( 2 w ( z ) y ) ,
ψ p , l ( L G ) ( r , ϕ , z ) = ψ p , l ( L G ) ( r , ϕ , z ) e i ( 2 p + l + 1 ) θ G ( z ) e i ξ ( r , ϕ , z ) ,
ψ p , l ( L G ) ( r , ϕ , z ) = C p , l ( L G ) w ( z ) ( 1 ) p ( 2 r w ( z ) ) l L p l ( 2 r 2 w ( z ) 2 ) e r 2 w ( z ) 2     e i l ϕ ,
ψ p ,     l ( L G ) ( r , ϕ , z )     ψ n , m ( H G ) ( x , y , z ) ,
ψ p , l ( L G ) ( r , ϕ , z )     ψ m ,     n ( H G ) ( x , y , z ) ,
Ψ n ,     m ( x , y , z , α ) = ψ n , m ( H G ) ( x , y , z ) + e i α ψ m , n ( H G ) ( x , y , z ) ,
p = i ω ε 0 2 ( Ψ * Ψ Ψ Ψ * ) ,
Ψ n ,     m ( x , y , z , α )       Φ p ,     l ( r , ϕ , z , α ) = ψ p ,     l ( L G ) ( r , ϕ , z , α ) + e i α ψ p , l ( L G ) ( r , ϕ , z , α ) ,
Φ p , l ( r , ϕ , z , α ) = e i α 2 C p ,     l ( L G ) w ( z ) ( 1 ) p ( 2 r w ( z ) ) l L p l ( 2 r 2 w ( z ) 2 ) e r 2 w ( z ) 2 × 2 cos [ l ( ϕ + α 2 l ) ] .

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