Abstract

As three-plane waves are the minimum number required for the formation of vortex-embedded lattice structures by plane wave interference, we present our experimental investigation on the formation of complex 3D photonic vortex lattice structures by a designed superposition of multiples of phase-engineered three-plane waves. The unfolding of the generated complex photonic lattice structures with higher order helical phase is realized by perturbing the superposition of a relatively phase-encoded, axially equidistant multiple of three noncoplanar plane waves. Through a programmable spatial light modulator assisted single step fabrication approach, the unfolded 3D vortex lattice structures are experimentally realized, well matched to our computer simulations. The formation of higher order intertwined helices embedded in these 3D spiraling vortex lattice structures by the superposition of the multiples of phase-engineered three-plane waves interference is also studied.

© 2012 Optical Society of America

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  1. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
    [CrossRef]
  2. V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
    [CrossRef]
  3. I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
    [CrossRef]
  4. M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
    [CrossRef]
  5. D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic, 2008).
  6. 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, 3039–3044 (2006).
    [CrossRef]
  7. G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75, 066613 (2007).
    [CrossRef]
  8. J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
    [CrossRef]
  9. L. G. Wang, L. Q. Wang, and S. Y. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282, 1088–1094 (2009).
    [CrossRef]
  10. A. Dreischuh, S. Chervenkov, D. Neshev, G. G. Paulus, and H. Walther, “Generation of lattice structures of optical vortices,” J. Opt. Soc. Am. B 19, 550–556 (2002).
    [CrossRef]
  11. S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007).
    [CrossRef]
  12. G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
    [CrossRef]
  13. V. Arrizón, D. Sánchez de-la-Llave, G. Méndez, and U. Ruiz, “Efficient generation of periodic and quasi-periodic non-diffractive optical fields with phase holograms,” Opt. Express 19, 10553–10562 (2011).
    [CrossRef]
  14. Y. F. Chen, H. C. Liang, Y. C. Lin, Y. S. Tzeng, K. W. Su, and K. F. Huang, “Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity,” Phys. Rev. A 83, 053813 (2011).
    [CrossRef]
  15. J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36, 403–405 (2011).
    [CrossRef]
  16. J. Xavier, S. Vyas, P. Senthilkumaran, C. Denz, and J. Joseph, “Sculptured 3D twister superlattices embedded with tunable vortex spirals,” Opt. Lett. 36, 3512–3514 (2011).
    [CrossRef]
  17. K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Stable structures with high topological charge in nonlinear photonic quasicrystals,” Phys. Rev. A 82, 035802 (2010).
    [CrossRef]
  18. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198–200 (2008).
    [CrossRef]
  19. J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34, 2625–2627 (2009).
    [CrossRef]
  20. C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photon. Rev. 4, 568–580 (2010).
    [CrossRef]
  21. J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
    [CrossRef]
  22. E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beam widths from a star,” Nature 464, 1018–1020 (2010).
    [CrossRef]
  23. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
    [CrossRef]
  24. M. Wegener and S. Linden, “Shaping optical space with metamaterials,” Phys. Today 63, 32–36 (2010).
    [CrossRef]
  25. G. Indbetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
    [CrossRef]
  26. P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).
    [CrossRef]
  27. J. Xavier, S. Vyas, P. Senthilkumaran, and J. Joseph, “Complex 3D vortex lattice formation by phase-engineered multiple beam interference,” Int. J. Opt. 2012, 863875 (2012).

2012

J. Xavier, S. Vyas, P. Senthilkumaran, and J. Joseph, “Complex 3D vortex lattice formation by phase-engineered multiple beam interference,” Int. J. Opt. 2012, 863875 (2012).

2011

2010

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Stable structures with high topological charge in nonlinear photonic quasicrystals,” Phys. Rev. A 82, 035802 (2010).
[CrossRef]

M. Wegener and S. Linden, “Shaping optical space with metamaterials,” Phys. Today 63, 32–36 (2010).
[CrossRef]

C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photon. Rev. 4, 568–580 (2010).
[CrossRef]

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[CrossRef]

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beam widths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef]

2009

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[CrossRef]

L. G. Wang, L. Q. Wang, and S. Y. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282, 1088–1094 (2009).
[CrossRef]

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34, 2625–2627 (2009).
[CrossRef]

2008

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198–200 (2008).
[CrossRef]

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

2007

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75, 066613 (2007).
[CrossRef]

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

2006

2005

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).
[CrossRef]

2002

2001

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef]

1994

I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[CrossRef]

1993

G. Indbetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

1992

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

1974

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

Andrews, D. L.

D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic, 2008).

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef]

Arrizón, V.

Bazhenov, V. Yu.

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

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[CrossRef]

Berry, M. V.

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

Bishop, A. R.

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Stable structures with high topological charge in nonlinear photonic quasicrystals,” Phys. Rev. A 82, 035802 (2010).
[CrossRef]

Boguslawski, M.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[CrossRef]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef]

Buccoliero, D.

Burruss, R.

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beam widths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef]

Chen, Y. F.

Y. F. Chen, H. C. Liang, Y. C. Lin, Y. S. Tzeng, K. W. Su, and K. F. Huang, “Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity,” Phys. Rev. A 83, 053813 (2011).
[CrossRef]

Chervenkov, S.

de-la-Llave, D. Sánchez

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[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, 3039–3044 (2006).
[CrossRef]

Denz, C.

Desyatnikov, A. S.

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef]

Dreischuh, A.

Dubik, B.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

Freund, I.

I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[CrossRef]

Huang, K. F.

Y. F. Chen, H. C. Liang, Y. C. Lin, Y. S. Tzeng, K. W. Su, and K. F. Huang, “Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity,” Phys. Rev. A 83, 053813 (2011).
[CrossRef]

Indbetouw, G.

G. Indbetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

Joseph, J.

J. Xavier, S. Vyas, P. Senthilkumaran, and J. Joseph, “Complex 3D vortex lattice formation by phase-engineered multiple beam interference,” Int. J. Opt. 2012, 863875 (2012).

J. Xavier, S. Vyas, P. Senthilkumaran, C. Denz, and J. Joseph, “Sculptured 3D twister superlattices embedded with tunable vortex spirals,” Opt. Lett. 36, 3512–3514 (2011).
[CrossRef]

J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36, 403–405 (2011).
[CrossRef]

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[CrossRef]

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34, 2625–2627 (2009).
[CrossRef]

Kevrekidis, P. G.

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Stable structures with high topological charge in nonlinear photonic quasicrystals,” Phys. Rev. A 82, 035802 (2010).
[CrossRef]

Kivshar, Y. S.

Krolikowski, W.

Law, K. J. H.

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Stable structures with high topological charge in nonlinear photonic quasicrystals,” Phys. Rev. A 82, 035802 (2010).
[CrossRef]

Liang, H. C.

Y. F. Chen, H. C. Liang, Y. C. Lin, Y. S. Tzeng, K. W. Su, and K. F. Huang, “Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity,” Phys. Rev. A 83, 053813 (2011).
[CrossRef]

Lin, Y. C.

Y. F. Chen, H. C. Liang, Y. C. Lin, Y. S. Tzeng, K. W. Su, and K. F. Huang, “Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity,” Phys. Rev. A 83, 053813 (2011).
[CrossRef]

Linden, S.

M. Wegener and S. Linden, “Shaping optical space with metamaterials,” Phys. Today 63, 32–36 (2010).
[CrossRef]

Lipson, R. H.

C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photon. Rev. 4, 568–580 (2010).
[CrossRef]

Lu, C.

C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photon. Rev. 4, 568–580 (2010).
[CrossRef]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef]

Masajada, J.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

Mawet, D.

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beam widths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef]

Méndez, G.

Neshev, D.

Nye, J. F.

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

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[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, 3039–3044 (2006).
[CrossRef]

Padgett, M. J.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, “Singular optics: optical vortices and polarization singularities,” Prog. Opt. 53, 293–363 (2009).
[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, 3039–3044 (2006).
[CrossRef]

Paganin, D. M.

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75, 066613 (2007).
[CrossRef]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef]

Paulus, G. G.

Rose, P.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[CrossRef]

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34, 2625–2627 (2009).
[CrossRef]

Ruben, G.

G. Ruben and D. M. Paganin, “Phase vortices from a Young’s three-pinhole interferometer,” Phys. Rev. E 75, 066613 (2007).
[CrossRef]

Ruiz, U.

Saxena, A.

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Stable structures with high topological charge in nonlinear photonic quasicrystals,” Phys. Rev. A 82, 035802 (2010).
[CrossRef]

Schimmel, H.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).
[CrossRef]

Senthilkumaran, P.

J. Xavier, S. Vyas, P. Senthilkumaran, and J. Joseph, “Complex 3D vortex lattice formation by phase-engineered multiple beam interference,” Int. J. Opt. 2012, 863875 (2012).

J. Xavier, S. Vyas, P. Senthilkumaran, C. Denz, and J. Joseph, “Sculptured 3D twister superlattices embedded with tunable vortex spirals,” Opt. Lett. 36, 3512–3514 (2011).
[CrossRef]

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

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).
[CrossRef]

Serabyn, E.

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beam widths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef]

Shvartsman, N.

I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[CrossRef]

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef]

Soskin, M. S.

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

Su, K. W.

Y. F. Chen, H. C. Liang, Y. C. Lin, Y. S. Tzeng, K. W. Su, and K. F. Huang, “Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity,” Phys. Rev. A 83, 053813 (2011).
[CrossRef]

Terhalle, B.

Tzeng, Y. S.

Y. F. Chen, H. C. Liang, Y. C. Lin, Y. S. Tzeng, K. W. Su, and K. F. Huang, “Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity,” Phys. Rev. A 83, 053813 (2011).
[CrossRef]

Vasnetsov, M. V.

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

Vyas, S.

Walther, H.

Wang, L. G.

L. G. Wang, L. Q. Wang, and S. Y. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282, 1088–1094 (2009).
[CrossRef]

Wang, L. Q.

L. G. Wang, L. Q. Wang, and S. Y. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282, 1088–1094 (2009).
[CrossRef]

Wegener, M.

M. Wegener and S. Linden, “Shaping optical space with metamaterials,” Phys. Today 63, 32–36 (2010).
[CrossRef]

Wyrowski, F.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).
[CrossRef]

Xavier, J.

J. Xavier, S. Vyas, P. Senthilkumaran, and J. Joseph, “Complex 3D vortex lattice formation by phase-engineered multiple beam interference,” Int. J. Opt. 2012, 863875 (2012).

J. Xavier, S. Vyas, P. Senthilkumaran, C. Denz, and J. Joseph, “Sculptured 3D twister superlattices embedded with tunable vortex spirals,” Opt. Lett. 36, 3512–3514 (2011).
[CrossRef]

J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36, 403–405 (2011).
[CrossRef]

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[CrossRef]

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, “Three-dimensional optically induced reconfigurable photorefractive nonlinear photonic lattices,” Opt. Lett. 34, 2625–2627 (2009).
[CrossRef]

Zhu, S. Y.

L. G. Wang, L. Q. Wang, and S. Y. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282, 1088–1094 (2009).
[CrossRef]

Adv. Mater.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[CrossRef]

Appl. Opt.

Int. J. Opt.

J. Xavier, S. Vyas, P. Senthilkumaran, and J. Joseph, “Complex 3D vortex lattice formation by phase-engineered multiple beam interference,” Int. J. Opt. 2012, 863875 (2012).

J. Mod. Opt.

G. Indbetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (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]

J. Opt. Soc. Am. B

Laser Photon. Rev.

C. Lu and R. H. Lipson, “Interference lithography: a powerful tool for fabricating periodic structures,” Laser Photon. Rev. 4, 568–580 (2010).
[CrossRef]

Nature

E. Serabyn, D. Mawet, and R. Burruss, “An image of an exoplanet separated by two diffraction beam widths from a star,” Nature 464, 1018–1020 (2010).
[CrossRef]

Opt. Commun.

J. Masajada and B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–27 (2001).
[CrossRef]

L. G. Wang, L. Q. Wang, and S. Y. Zhu, “Formation of optical vortices using coherent laser beam arrays,” Opt. Commun. 282, 1088–1094 (2009).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005).
[CrossRef]

Opt. Lett.

Phys. Rev. A

Y. F. Chen, H. C. Liang, Y. C. Lin, Y. S. Tzeng, K. W. Su, and K. F. Huang, “Generation of optical crystals and quasicrystal beams: Kaleidoscopic patterns and phase singularity,” Phys. Rev. A 83, 053813 (2011).
[CrossRef]

K. J. H. Law, A. Saxena, P. G. Kevrekidis, and A. R. Bishop, “Stable structures with high topological charge in nonlinear photonic quasicrystals,” Phys. Rev. A 82, 035802 (2010).
[CrossRef]

I. Freund and N. Shvartsman, “Wave-field phase singularities: the sign principle,” Phys. Rev. A 50, 5164–5172 (1994).
[CrossRef]

Phys. Rev. E

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Supplementary Material (1)

» Media 1: MPG (853 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

(a) Schematic representation of three-plane wave interference. k 1 , k 2 , and k 3 are the wave vectors and θ is the angle subtended by them with the central axis. ξ is the angle between the projection of wave vector on the k x k y plane and the k x axis. (b)–(c) Analysis of vortices in 2D photonic lattice formation by 3 noncoplanar plane wave interference. (d)–(e) Analysis of vortices in 3D photonic lattice formation by 3 + 1 noncoplanar plane wave interference ( n = 3 , p = 1 ). (b) and (d) Transverse intensity distribution in x - y plane. (c) and (e) Zero crossing plots (blue line: Re E ( r ) , green line: Im E ( r ) ). [Insets: Phase profiles].

Fig. 2.
Fig. 2.

(a)–(b) Computational analysis of 3D photonic vortex lattice with a quasi-crystallographic fivefold transverse rotational symmetry for n = 5 , p = 1 (c)–(d) (a)–(b) Computational analysis of periodic hexagonal 3D photonic vortex lattice for n = 6 , p = 1 (a) and (c) Transverse intensity distribution in x - y plane. [Inset: Folded lattice structure prior to perturbation] (b) and (d) Zero crossing plots (blue line: Re E ( r ) , green line: Im E ( r ) ). [Inset: For folded lattice structure prior to perturbation].

Fig. 3.
Fig. 3.

Computer simulations of intensity distributions of complex 3D photonic vortex lattice structures. Taking the multiples of relatively phase shifted three adjacent plane waves, where the number of interfering beams involved are respectively (a)  6 + 1 beams, (b)  9 + 1 beams, and (c)  15 + 1 beams. Transverse plane projection of their k vectors onto a circle is shown below the respective vortex lattice structures. The initial offset phase of adjacent beams is depicted in three different colors.

Fig. 4.
Fig. 4.

Computational analysis of complex 3D PVL structures. Taking the multiples of phase-engineered three beams, where the number of interfering beams involved are respectively (a)–(b)  6 + 1 plane waves, (c)–(d)  9 + 1 plane waves. (a) and (c) Transverse intensity distribution in x - y plane. [Inset: Folded lattice structure prior to perturbation] (b) and (d) Zero crossing plots [blue line: Re E ( r ) , green line: Im E ( r ) ]. [Inset: For folded lattice structure prior to perturbation.]

Fig. 5.
Fig. 5.

Computational analysis of the distribution of vortices by 15 + 1 noncoplanar plane wave interference. (a)–(b) 3D PVL for n = 15 , p = 1 . (c)–(d) Unfolded 3D PVL by multiples of three phase-engineered plane wave interference for n = 3 , p = 5 . (a) and (c) Transverse intensity distribution in x y plane. [Inset: Folded lattice structure prior to perturbation] (b) and (d) Zero crossing plots [blue line: Re E ( r ) , green line: Im E ( r ) ]. [Inset: For folded lattice structure prior to perturbation].

Fig. 6.
Fig. 6.

Schematic representation of the experimental setup for the generation of diverse 3D PVL structures. HWP, half-wave plate; PBS, polarizing beam splitter; MO, microscope objective; PH, pin hole; L, lens; BS, beam splitter; FF, Fourier filter. Region of recording is indicated in dotted line.

Fig. 7.
Fig. 7.

Experimentally recorded transverse intensity ( x y plane) distribution of 3D PVL structures involving multiples of relatively phase-shifted three noncoplanar beams. In the insets the recorded 2D lattice structures are given. (a) For a 3 + 1 beam geometry ( n = 3 , p = 1 ). (b) Complex PVL by a 6 + 1 beam geometry ( n = 3 , p = 2 ).[In the inset 2D lattice structure embedded with vortex of charge 2 is given] (c) Complex PVL by a 6 + 1 beam geometry ( n = 3 , p = 2 ).[In the inset 2D lattice structure embedded with a vortex of charge 3 is given]. All scale bars = 15 μm .

Fig. 8.
Fig. 8.

Experimental results of transverse intensity recorded images of complex PVL by relatively phase-engineered 15 + 1 plane wave interference (a) and (c) Folded structures (15 plane waves). (b) and (d) Unfolded structures ( 15 + 1 plane waves). (a)–(b) For g = 15 , n = 3 and p = 5 . (c)–(d) For g = 15 , n = 15 and p = 1 . Inset: Experimentally realized fork formation while the lattice forming beams are superposed with a plane wave launched at a large angle from the axis. The direction and the number of forks indicate the sign and the topological charge of the formed vortex. All scale bars = 20 μm .

Fig. 9.
Fig. 9.

Computational and experimental results of transverse intensity distributions of spiraling complex 3D PVL structures formed in the presence of a perturbing beam and a fivefold multiple of relatively phase-shifted three beams leading to 15 + 1 noncoplanar multiple beam interference. (a) Computed transverse intensity distributions of x y planes of spiraling complex 3D PVL while z is varied (in steps of Δ z 30 μm ) along the longitudinal direction of propagation (Media 1). (b) Computed fivefolded bright intertwined helices at the center (computed with higher threshold value of intensity). (c) Experimentally recorded transverse intensity distributions. The circled region (red) visualizes the position of spiraling vortex distribution and the circled region (yellow) depicts how the energy gets coupled to the adjacent region while the complex vortex lattice structure makes a helical movement along the direction of propagation. All scale bars = 20 μm .

Equations (2)

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I ( r ) = i = 0 q | E i | 2 + i = 0 q j = 0 q j i E i E j * · exp [ i ( k i k j ) · r + i ϕ i j ] ,
k s = k 0 { cos [ 2 ( s 1 ) π / q ] × sin θ i , sin [ 2 ( s 1 ) π / q ] × sin θ i , cos θ i } ,

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