Abstract

Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

© 2014 Optical Society of America

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2014 (1)

2013 (1)

2012 (1)

2011 (1)

F. Lenzini, S. Residori, F. T. Arecchi, U. Bortolozzo, “Optical vortex interaction and generation via nonlinear wave mixing,” Phys. Rev. A 84, 61801 (2011).
[CrossRef]

2010 (3)

2009 (2)

T. Brunet, J. L. Thomas, R. Marchiano, F. Coulouvrat, “Experimental observation of azimuthal shock waves on nonlinear acoustical vortices,” New J. Phys. 11, 13002 (2009).
[CrossRef]

Y. Ueno, Y. Toda, S. Adachi, R. Morita, T. Tawara, “Coherent transfer of orbital angular momentum to excitons by optical four-wave mixing,” Opt. Express 17, 20567–20574 (2009).
[CrossRef] [PubMed]

2008 (2)

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, K. Molmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 15401 (2008).
[CrossRef]

A. Börzsönyi, Z. Heiner, “Dispersion measurement of inert gases and gas mixtures at 800 nm,” Appl. Opt. 47, 4856–4863 (2008).
[CrossRef] [PubMed]

2007 (4)

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

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

A. V. Gorbach, D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98, 243601 (2007).
[CrossRef] [PubMed]

I. Zeylikovich, H. I. Sztul, V. Kartazaev, T. Le, R. R. Alfano, “Ultrashort Laguerre-Gaussian pulses with angular and group velocity dispersion compensation,” Opt. Lett. 32, 2025–2027 (2007).
[CrossRef] [PubMed]

2006 (4)

G. A. Swartzlander, “Achromatic optical vortex lens,” Opt. Lett. 31, 2042–2044 (2006).
[CrossRef] [PubMed]

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

W. Jiang, Q.-F. Chen, Y.-S. Zhang, G.-C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A 74, 1–4 (2006).

2005 (4)

A. S. Desyatnikov, Y. S. Kivshar, L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

A. Vinçotte, L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef] [PubMed]

I. G. Mariyenko, J. Strohaber, C. J. Uiterwaal, “Creation of optical vortices in femtosecond pulses,” Opt. Express 13, 7599–7608 (2005).
[CrossRef] [PubMed]

G. Foo, D. M. Palacios, G. A. Swartzlander, “Optical vortex coronagraph,” Opt. Lett. 30, 3308–3310 (2005).
[CrossRef]

2004 (1)

2003 (2)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef] [PubMed]

J. L. Thomas, R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett. 91, 244302 (2003).
[CrossRef] [PubMed]

2002 (3)

E. H. Brandt, J. Vanacken, V. V. Moshchalkov, “Vortices in physics,” Physica C: Superconductivity 369, 1–9 (2002).
[CrossRef]

S. L. Rolston, W. D. Phillips, “Nonlinear and quantum atom optics,” Nature 416, 219–224 (2002).
[CrossRef] [PubMed]

H. Saito, M. Ueda, “Split instability of a vortex in an attractive Bose-Einstein condensate,” Phys. Rev. Lett. 89, 190402 (2002).
[CrossRef] [PubMed]

2001 (1)

2000 (1)

K. W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, “Vortex formation in a stirred Bose-Einstein condensate,” Phys. Rev. Lett. 84, 806–809 (2000).
[CrossRef] [PubMed]

1999 (4)

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

J. E. Williams, M. J. Holland, “Preparing topological states of a Bose-Einstein condensate,” Nature 401, 568–572 (1999).
[CrossRef]

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

1997 (2)

W. J. Firth, D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79, 2450–2453 (1997).
[CrossRef]

M. Quiroga-Teixeiro, “Stable azimuthal stationary state in quintic nonlinear optical media,” J. Opt. Soc. Am. B 14, 2004–2009 (1997).
[CrossRef]

1996 (1)

K. Dholakia, N. B. Simpson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, 3742–3745 (1996).
[CrossRef]

1995 (2)

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, 826–829 (1995).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, B. Luther-Daves, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12, 2046–2052 (1995).
[CrossRef]

1974 (1)

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336, 165–190 (1974).
[CrossRef]

’t Hooft, G. W.

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

Adachi, S.

Alfano, R. R.

Allen, L.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, 3742–3745 (1996).
[CrossRef]

Andersen, M. F.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Anderson, B. P.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Arecchi, F. T.

F. Lenzini, S. Residori, F. T. Arecchi, U. Bortolozzo, “Optical vortex interaction and generation via nonlinear wave mixing,” Phys. Rev. A 84, 61801 (2011).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

Band, Y.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Bergé, L.

A. Vinçotte, L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef] [PubMed]

Berry, M. V.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336, 165–190 (1974).
[CrossRef]

Bezuhanov, K.

Bortolozzo, U.

F. Lenzini, S. Residori, F. T. Arecchi, U. Bortolozzo, “Optical vortex interaction and generation via nonlinear wave mixing,” Phys. Rev. A 84, 61801 (2011).
[CrossRef]

Börzsönyi, A.

Brandt, E. H.

E. H. Brandt, J. Vanacken, V. V. Moshchalkov, “Vortices in physics,” Physica C: Superconductivity 369, 1–9 (2002).
[CrossRef]

Brunet, T.

T. Brunet, J. L. Thomas, R. Marchiano, F. Coulouvrat, “Experimental observation of azimuthal shock waves on nonlinear acoustical vortices,” New J. Phys. 11, 13002 (2009).
[CrossRef]

Chen, Q.-F.

W. Jiang, Q.-F. Chen, Y.-S. Zhang, G.-C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A 74, 1–4 (2006).

Chevy, F.

K. W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, “Vortex formation in a stirred Bose-Einstein condensate,” Phys. Rev. Lett. 84, 806–809 (2000).
[CrossRef] [PubMed]

Christou, J.

Clade, P.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Collins, L. A.

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, K. Molmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 15401 (2008).
[CrossRef]

Cornell, E. A.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Coulouvrat, F.

T. Brunet, J. L. Thomas, R. Marchiano, F. Coulouvrat, “Experimental observation of azimuthal shock waves on nonlinear acoustical vortices,” New J. Phys. 11, 13002 (2009).
[CrossRef]

Dalibard, J.

K. W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, “Vortex formation in a stirred Bose-Einstein condensate,” Phys. Rev. Lett. 84, 806–809 (2000).
[CrossRef] [PubMed]

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Deng, L.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Dennis, M. R.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, Y. S. Kivshar, L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, 3742–3745 (1996).
[CrossRef]

Dreischuh, A.

Eliel, E. R.

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

Fibich, G.

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

Firth, W. J.

W. J. Firth, D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79, 2450–2453 (1997).
[CrossRef]

Foo, G.

Friese, M. E. J.

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, 826–829 (1995).
[CrossRef] [PubMed]

Gaeta, A. L.

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

Gorbach, A. V.

A. V. Gorbach, D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98, 243601 (2007).
[CrossRef] [PubMed]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef] [PubMed]

Grow, T.

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

Guo, G.-C.

W. Jiang, Q.-F. Chen, Y.-S. Zhang, G.-C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A 74, 1–4 (2006).

Hagley, E. W.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Haljan, P. C.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Hall, D. S.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

He, H.

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, 826–829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

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, 826–829 (1995).
[CrossRef] [PubMed]

Heiner, Z.

Helmerson, K.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Holland, M. J.

J. E. Williams, M. J. Holland, “Preparing topological states of a Bose-Einstein condensate,” Nature 401, 568–572 (1999).
[CrossRef]

Holzwarth, R.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Hsu, C.-C.

Hu, S. X.

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, K. Molmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 15401 (2008).
[CrossRef]

Hua, X.

Ishaaya, A.

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

Jack, B.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

Jiang, W.

W. Jiang, Q.-F. Chen, Y.-S. Zhang, G.-C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A 74, 1–4 (2006).

Julienne, P. S.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Kartazaev, V.

King, R. P.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

Kippenberg, T. J.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Kivshar, Y. S.

Kolomenskii, A. A.

Kung, A. H.

Le, T.

Lenzini, F.

F. Lenzini, S. Residori, F. T. Arecchi, U. Bortolozzo, “Optical vortex interaction and generation via nonlinear wave mixing,” Phys. Rev. A 84, 61801 (2011).
[CrossRef]

Li, C.

Lu, C.-H.

Luther-Daves, B.

Madison, K. W.

K. W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, “Vortex formation in a stirred Bose-Einstein condensate,” Phys. Rev. Lett. 84, 806–809 (2000).
[CrossRef] [PubMed]

Maier, M.

Maleshkov, G.

Marchiano, R.

T. Brunet, J. L. Thomas, R. Marchiano, F. Coulouvrat, “Experimental observation of azimuthal shock waves on nonlinear acoustical vortices,” New J. Phys. 11, 13002 (2009).
[CrossRef]

J. L. Thomas, R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett. 91, 244302 (2003).
[CrossRef] [PubMed]

Mariyenko, I. G.

Matthews, M. R.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Molina-Terriza, G.

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

Molmer, K.

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, K. Molmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 15401 (2008).
[CrossRef]

Morita, R.

Moshchalkov, V. V.

E. H. Brandt, J. Vanacken, V. V. Moshchalkov, “Vortices in physics,” Physica C: Superconductivity 369, 1–9 (2002).
[CrossRef]

Natarajan, V.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Neshev, D. N.

Nie, Z.

Nye, J. F.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336, 165–190 (1974).
[CrossRef]

Nygaard, N.

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, K. Molmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 15401 (2008).
[CrossRef]

O’Holleran, K.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

Padgett, M. J.

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

K. Dholakia, N. B. Simpson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, 3742–3745 (1996).
[CrossRef]

Palacios, D. M.

Paulus, G. G.

Phillips, W. D.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

S. L. Rolston, W. D. Phillips, “Nonlinear and quantum atom optics,” Nature 416, 219–224 (2002).
[CrossRef] [PubMed]

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Quiroga-Teixeiro, M.

Residori, S.

F. Lenzini, S. Residori, F. T. Arecchi, U. Bortolozzo, “Optical vortex interaction and generation via nonlinear wave mixing,” Phys. Rev. A 84, 61801 (2011).
[CrossRef]

Rolston, S. L.

S. L. Rolston, W. D. Phillips, “Nonlinear and quantum atom optics,” Nature 416, 219–224 (2002).
[CrossRef] [PubMed]

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Rubinsztein-Dunlop, H.

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, 826–829 (1995).
[CrossRef] [PubMed]

Ryu, C.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Saito, H.

H. Saito, M. Ueda, “Split instability of a vortex in an attractive Bose-Einstein condensate,” Phys. Rev. Lett. 89, 190402 (2002).
[CrossRef] [PubMed]

Samoc, M.

Schatzel, M. G.

Schliesser, A.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Schneider, B. I.

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, K. Molmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 15401 (2008).
[CrossRef]

Schuessler, H.

Schuessler, H. A.

Schwarz, U. T.

Si, J.

Simpson, N. B.

K. Dholakia, N. B. Simpson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, 3742–3745 (1996).
[CrossRef]

Simsarian, J. E.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Simula, T. P.

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, K. Molmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 15401 (2008).
[CrossRef]

Skryabin, D. V.

A. V. Gorbach, D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98, 243601 (2007).
[CrossRef] [PubMed]

W. J. Firth, D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79, 2450–2453 (1997).
[CrossRef]

Sogomonian, S.

Sokolov, A. V.

Strohaber, J.

Swartzlander, G. A.

Sztul, H. I.

Tawara, T.

Thomas, J. L.

T. Brunet, J. L. Thomas, R. Marchiano, F. Coulouvrat, “Experimental observation of azimuthal shock waves on nonlinear acoustical vortices,” New J. Phys. 11, 13002 (2009).
[CrossRef]

J. L. Thomas, R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett. 91, 244302 (2003).
[CrossRef] [PubMed]

Tikhonenko, V.

Toda, Y.

Torner, L.

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

A. S. Desyatnikov, Y. S. Kivshar, L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Torres, J. P.

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

Trippenbach, M.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Ueda, M.

H. Saito, M. Ueda, “Split instability of a vortex in an attractive Bose-Einstein condensate,” Phys. Rev. Lett. 89, 190402 (2002).
[CrossRef] [PubMed]

Ueno, Y.

Uiterwaal, C. J.

Vanacken, J.

E. H. Brandt, J. Vanacken, V. V. Moshchalkov, “Vortices in physics,” Physica C: Superconductivity 369, 1–9 (2002).
[CrossRef]

Vaziri, A.

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Vinçotte, A.

A. Vinçotte, L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef] [PubMed]

Vuong, L. T.

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

Walther, H.

Wang, K.

Wang, R.

Wen, J.

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

Wieman, C. E.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Williams, J. E.

J. E. Williams, M. J. Holland, “Preparing topological states of a Bose-Einstein condensate,” Nature 401, 568–572 (1999).
[CrossRef]

Wohlleben, W.

K. W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, “Vortex formation in a stirred Bose-Einstein condensate,” Phys. Rev. Lett. 84, 806–809 (2000).
[CrossRef] [PubMed]

Xiao, M.

Yang, L.-F.

Yang, S.-D.

Zeylikovich, I.

Zhang, Y.

Zhang, Y.-S.

W. Jiang, Q.-F. Chen, Y.-S. Zhang, G.-C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A 74, 1–4 (2006).

Zhao, Y.

Zhi, M.

Appl. Opt. (1)

J. Opt. Soc. Am. B (3)

Nat. Phys. (2)

M. R. Dennis, R. P. King, B. Jack, K. O’Holleran, M. J. Padgett, “Isolated optical vortex knots,” Nat. Phys. 6, 118–121 (2010).
[CrossRef]

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

Nature (5)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[CrossRef] [PubMed]

S. L. Rolston, W. D. Phillips, “Nonlinear and quantum atom optics,” Nature 416, 219–224 (2002).
[CrossRef] [PubMed]

L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, W. D. Phillips, “Four-wave mixing with matter waves,” Nature 398, 218–220 (1999).
[CrossRef]

J. E. Williams, M. J. Holland, “Preparing topological states of a Bose-Einstein condensate,” Nature 401, 568–572 (1999).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

New J. Phys. (1)

T. Brunet, J. L. Thomas, R. Marchiano, F. Coulouvrat, “Experimental observation of azimuthal shock waves on nonlinear acoustical vortices,” New J. Phys. 11, 13002 (2009).
[CrossRef]

Opt. Express (6)

Opt. Lett. (5)

Phys. Rev. A (5)

T. P. Simula, N. Nygaard, S. X. Hu, L. A. Collins, B. I. Schneider, K. Molmer, “Angular momentum exchange between coherent light and matter fields,” Phys. Rev. A 77, 15401 (2008).
[CrossRef]

F. Lenzini, S. Residori, F. T. Arecchi, U. Bortolozzo, “Optical vortex interaction and generation via nonlinear wave mixing,” Phys. Rev. A 84, 61801 (2011).
[CrossRef]

W. Jiang, Q.-F. Chen, Y.-S. Zhang, G.-C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A 74, 1–4 (2006).

K. Dholakia, N. B. Simpson, M. J. Padgett, L. Allen, “Second-harmonic generation and the orbital angular momentum of light,” Phys. Rev. A 54, 3742–3745 (1996).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, M. J. Padgett, “Parametric down-conversion for light beams possessing orbital angular momentum,” Phys. Rev. A 59, 3950–3952 (1999).
[CrossRef]

Phys. Rev. Lett. (10)

A. Vinçotte, L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett. 95, 193901 (2005).
[CrossRef] [PubMed]

L. T. Vuong, T. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96, 2–5 (2006).
[CrossRef]

A. V. Gorbach, D. V. Skryabin, “Cascaded generation of multiply charged optical vortices and spatiotemporal helical beams in a Raman medium,” Phys. Rev. Lett. 98, 243601 (2007).
[CrossRef] [PubMed]

H. Saito, M. Ueda, “Split instability of a vortex in an attractive Bose-Einstein condensate,” Phys. Rev. Lett. 89, 190402 (2002).
[CrossRef] [PubMed]

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, 826–829 (1995).
[CrossRef] [PubMed]

W. J. Firth, D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79, 2450–2453 (1997).
[CrossRef]

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, E. A. Cornell, “Vortices in a Bose-Einstein condensate,” Phys. Rev. Lett. 83, 2498–2501 (1999).
[CrossRef]

J. L. Thomas, R. Marchiano, “Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices,” Phys. Rev. Lett. 91, 244302 (2003).
[CrossRef] [PubMed]

K. W. Madison, F. Chevy, W. Wohlleben, J. Dalibard, “Vortex formation in a stirred Bose-Einstein condensate,” Phys. Rev. Lett. 84, 806–809 (2000).
[CrossRef] [PubMed]

M. F. Andersen, C. Ryu, P. Clade, V. Natarajan, A. Vaziri, K. Helmerson, W. D. Phillips, “Quantized rotation of atoms from photons with orbital angular momentum,” Phys. Rev. Lett. 97, 170406 (2006).
[CrossRef] [PubMed]

Physica C: Superconductivity (1)

E. H. Brandt, J. Vanacken, V. V. Moshchalkov, “Vortices in physics,” Physica C: Superconductivity 369, 1–9 (2002).
[CrossRef]

Proc. R. Soc. London A Math. Phys. Sci. (1)

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London A Math. Phys. Sci. 336, 165–190 (1974).
[CrossRef]

Prog. Opt. (1)

A. S. Desyatnikov, Y. S. Kivshar, L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Algebra of vortex beams with increasing topological charge (TC) due to cascaded four-wave mixing. The experimental double-peak input spectrum is shown in red, together with simulated intensity (top) and phase (bottom) profiles after nonlinear propagation for the mixing of a Gaussian beam with a vortex of unit TC. The magnitude of the TC changes by 1 with the order of the cascading process, which can be seen in the steeper phase spirals further away from the pump beams. The intensity profile in 3rd order already shows distortion due to strong intensity dependence.

Fig. 2
Fig. 2

Experimental setup. i) Vortex generation and FWM, ii) reference beam generation, iii) output characterization. D: Iris, DBS: dichroic beamsplitter, VL: vortex lens, SP: short-pass filter, LP: long-pass filter, BS: beamsplitter, FM1: focusing mirror f=2m, GC: gas cell, FM2: collimating mirror f=3m, FM3: collimating mirror f=4m, ND: ND filter, CCD: CCD-camera, SM: spectrometer, HCF: hollow-core fiber (filled with Ne gas), FM4: collimating mirror f=1m, DLY: delay stage.

Fig. 3
Fig. 3

Experimental interferograms and beam profiles for different vortex pump beams after nonlinear four-wave mixing. The pump beams are highlighted in grey. The respective central frequencies and wavelengths of the spectral satellite/pump beam along with the cascading order of the FWM process are denoted on top. a) Two vortices of equal TC m0 = m1 = +1, b) Vortex and Gaussian TCs m0 = +1 and m1 = 0, c) corresponding intensity profiles for case b), d) Two vortices of opposite TCs m0 = −m1 = +1. Contrast has been enhanced slightly for the −3rd order interferograms. The number in each box indicates TCs of the generated vortices.

Fig. 4
Fig. 4

tanh-vortex simulations: Intensity (odd rows) and phase (even rows) of the pump waves at 770nm and 800nm and of 6 of the newly generated waves in the observation plane (one diffraction length L D 0 away from the exit of the nonlinear medium of length L D 0). The outermost spectral components are left out due to already too strong diffraction. Case a/ - pump vortices with identical charges; Case b/ - pump vortex and Gaussian beams; Case c/ - pump vortices of opposite charges. Separators - central wavelengths of the simulated waves and estimated conversion efficiencies. Some 16% of the total computational window is shown in each frame. See text for further details.

Fig. 5
Fig. 5

r-vortex simulations: Intensity (odd rows) and phase (even rows) of the pump waves at 770nm and 800nm and of the newly generated waves in the observation plane (one diffraction length L D 0 away from the exit of the nonlinear medium of length 0.5 L D 0). Case a/ - pump vortices with identical charges; Case b/ - pump vortex and Gaussian beams; Case c/ - pump vortices of opposite charges. Separators - central wavelengths of the simulated waves and estimated conversion efficiencies. Some 16% of the total computational window is shown in each frame. See text for further details.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

i A n z + L D 0 k n A n + k 0 2 k n Δ A n + γ ( | A n | 2 A n + 2 n m | A m | 2 A n + H n ) = 0 .
H + 2 = 2 A 1 * A 0 A + 1 exp ( i Δ k 1 z L D 0 ) + A 0 * A + 1 2 exp ( i Δ k 2 z L D 0 ) , H + 1 = 2 A 1 A 0 * A + 2 exp ( i Δ k 1 z L D 0 ) + 2 A 0 A + 1 * A + 2 exp ( i Δ k 2 z L D 0 ) + A 1 * A 0 2 exp ( i Δ k 3 z L D 0 ) , H 0 = 2 A 1 A + 1 * A + 2 exp ( i Δ k 1 z L D 0 ) + 2 A 1 A 0 * A + 1 exp ( i Δ k 3 z L D 0 ) + A + 1 2 A + 2 * exp ( i Δ k 2 z L D 0 ) , H 1 = 2 A 0 A + 1 A + 2 * exp ( i Δ k 1 z L D 0 ) + A 0 2 A + 1 * exp ( i Δ k 3 z L D 0 ) ,
Δ k 1 = k 0 k 1 + k + 1 k + 2 , Δ k 2 = 2 k + 1 k 0 k + 2 , Δ k 3 = 2 k 0 k 1 k + 1 .
A ( r , ϕ ) = A 0 ( r / r 0 ) | m | exp ( r 2 / r 0 2 ) exp ( i m ϕ ) ,
A ( r , ϕ ) = A 0 exp ( r 2 / r B G 2 ) tanh ( r / r 0 ) exp { i × m × ( 2 π × 16 ) × int [ 16 ϕ / ( 2 π ) ] } .

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