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)

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]

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]

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)

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]

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]

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]

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]

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)

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

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]

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)

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

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]

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]

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]

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]

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)

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

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

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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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