Abstract

We present a technique to optically induce a defect site in helical lattice wave-field where the combined wave-field continues to maintain its nondiffracting (ND) nature. This is done by coherently superposing a helical lattice wave-field and a Bessel beam by method of phase engineering. The results are confirmed by numerical simulations and experimentally as well by generating the ND defect beam by displaying the numerically calculated phase pattern on a phase-only spatial light modulator. This technique is wavelength independent, completely scalable, and can easily be used to generate or transfer these structures in any photosensitive medium.

© 2013 Optical Society of America

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  1. J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36, 403–405 (2011).
    [CrossRef]
  2. J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. Kumar Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100, 121101 (2012).
    [CrossRef]
  3. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
    [CrossRef]
  4. H.-B. Sun, S. Matsuo, and H. Misawa, “Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin,” Appl. Phys. Lett. 74, 786 (1999).
    [CrossRef]
  5. O. Toader and S. John, “Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002).
    [CrossRef]
  6. Y. K. Pang, J. Lee, H. Lee, W. Y. Tam, C. Chan, and P. Sheng, “Chiral microstructures (spirals) fabrication by holographic lithography,” Opt. Express 13, 7615–7620 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Controlled formation and manipulation of colloidal lattices by dynamically reconfigurable three dimensional interferometric optical traps,” Appl. Phys. Lett. 101, 201101 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. Kumar Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100, 121101 (2012).
[CrossRef]

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Controlled formation and manipulation of colloidal lattices by dynamically reconfigurable three dimensional interferometric optical traps,” Appl. Phys. Lett. 101, 201101 (2012).
[CrossRef]

A. Y. Okulov, “Cold matter trapping via slowly rotating helical potential,” Phys. Lett. A 376, 650–655 (2012).
[CrossRef]

V. Arrizón, D. Sánchez-de-la-Llave, and G. Méndez, “Holographic generation of a class of nondiffracting fields with optimum efficiency,” Opt. Lett. 37, 2154–2156 (2012).
[CrossRef]

A. Kelberer, M. Boguslawski, P. Rose, and C. Denz, “Embedding defect sites into hexagonal nondiffracting wave fields,” Opt. Lett. 37, 5009–5011 (2012).
[CrossRef]

2011

2009

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

2008

A. H. Gevorgyan, “Chiral photonic crystals with an anisotropic defect layer: Oblique incidence,” Opt. Commun. 281, 5097–5103 (2008).
[CrossRef]

A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Near-perfect hologram reconstruction with a spatial light modulator,” Opt. Express 16, 2597–2603 (2008).
[CrossRef]

2007

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng. 46, 070501 (2007).
[CrossRef]

2005

2003

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

2002

O. Toader and S. John, “Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002).
[CrossRef]

1999

H.-B. Sun, S. Matsuo, and H. Misawa, “Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin,” Appl. Phys. Lett. 74, 786 (1999).
[CrossRef]

A. Scherer, O. Painter, and J. Vuckovic, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

1987

J. Durnin and J. J. Miceli, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

1985

1984

Ahlawat, S.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. Kumar Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100, 121101 (2012).
[CrossRef]

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Controlled formation and manipulation of colloidal lattices by dynamically reconfigurable three dimensional interferometric optical traps,” Appl. Phys. Lett. 101, 201101 (2012).
[CrossRef]

Arrizón, V.

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Bartelt, H.

Bartelt, H. O.

Bernet, S.

Boguslawski, M.

Chan, C.

Chen, M.-L.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng. 46, 070501 (2007).
[CrossRef]

Cheng, C.-J.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng. 46, 070501 (2007).
[CrossRef]

Dasgupta, R.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Controlled formation and manipulation of colloidal lattices by dynamically reconfigurable three dimensional interferometric optical traps,” Appl. Phys. Lett. 101, 201101 (2012).
[CrossRef]

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. Kumar Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100, 121101 (2012).
[CrossRef]

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

de-la-Llave, D. S.

Denz, C.

Durnin, J.

J. Durnin and J. J. Miceli, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Gevorgyan, A. H.

A. H. Gevorgyan and K. B. Oganesyan, “Defect modes of chiral photonic crystals with an isotropic defect,” Opt. Spectra 110, 952–960 (2011).
[CrossRef]

A. H. Gevorgyan, “Chiral photonic crystals with an anisotropic defect layer: Oblique incidence,” Opt. Commun. 281, 5097–5103 (2008).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).

Grier, D. G.

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

Gupta, P. K.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Controlled formation and manipulation of colloidal lattices by dynamically reconfigurable three dimensional interferometric optical traps,” Appl. Phys. Lett. 101, 201101 (2012).
[CrossRef]

Hsieh, M.-L.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng. 46, 070501 (2007).
[CrossRef]

Jesacher, A.

John, S.

O. Toader and S. John, “Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002).
[CrossRef]

Joseph, J.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. Kumar Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100, 121101 (2012).
[CrossRef]

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Controlled formation and manipulation of colloidal lattices by dynamically reconfigurable three dimensional interferometric optical traps,” Appl. Phys. Lett. 101, 201101 (2012).
[CrossRef]

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

Kelberer, A.

Kumar Gupta, P.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. Kumar Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100, 121101 (2012).
[CrossRef]

Lee, H.

Lee, J.

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Matsuo, S.

H.-B. Sun, S. Matsuo, and H. Misawa, “Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin,” Appl. Phys. Lett. 74, 786 (1999).
[CrossRef]

Maurer, C.

Méndez, G.

Miceli, J. J.

J. Durnin and J. J. Miceli, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Misawa, H.

H.-B. Sun, S. Matsuo, and H. Misawa, “Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin,” Appl. Phys. Lett. 74, 786 (1999).
[CrossRef]

Oganesyan, K. B.

A. H. Gevorgyan and K. B. Oganesyan, “Defect modes of chiral photonic crystals with an isotropic defect,” Opt. Spectra 110, 952–960 (2011).
[CrossRef]

Okulov, A. Y.

A. Y. Okulov, “Cold matter trapping via slowly rotating helical potential,” Phys. Lett. A 376, 650–655 (2012).
[CrossRef]

Painter, O.

Pang, Y. K.

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Ritsch-Marte, M.

Rose, P.

Ruiz, U.

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Sánchez-de-la-Llave, D.

Scherer, A.

Schwaighofer, A.

Sheng, P.

Sun, H.-B.

H.-B. Sun, S. Matsuo, and H. Misawa, “Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin,” Appl. Phys. Lett. 74, 786 (1999).
[CrossRef]

Tam, W. Y.

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Toader, O.

O. Toader and S. John, “Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002).
[CrossRef]

von Freymann, G.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Vuckovic, J.

Wegener, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Xavier, J.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. Kumar Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100, 121101 (2012).
[CrossRef]

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Controlled formation and manipulation of colloidal lattices by dynamically reconfigurable three dimensional interferometric optical traps,” Appl. Phys. Lett. 101, 201101 (2012).
[CrossRef]

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

Appl. Opt.

Appl. Phys. Lett.

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. Kumar Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100, 121101 (2012).
[CrossRef]

H.-B. Sun, S. Matsuo, and H. Misawa, “Three-dimensional photonic crystal structures achieved with two-photon-absorption photopolymerization of resin,” Appl. Phys. Lett. 74, 786 (1999).
[CrossRef]

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Controlled formation and manipulation of colloidal lattices by dynamically reconfigurable three dimensional interferometric optical traps,” Appl. Phys. Lett. 101, 201101 (2012).
[CrossRef]

J. Opt. Soc. Am. B

Nature

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

Opt. Commun.

A. H. Gevorgyan, “Chiral photonic crystals with an anisotropic defect layer: Oblique incidence,” Opt. Commun. 281, 5097–5103 (2008).
[CrossRef]

Opt. Eng.

M.-L. Hsieh, M.-L. Chen, and C.-J. Cheng, “Improvement of the complex modulated characteristic of cascaded liquid crystal spatial light modulators by using a novel amplitude compensated technique,” Opt. Eng. 46, 070501 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectra

A. H. Gevorgyan and K. B. Oganesyan, “Defect modes of chiral photonic crystals with an isotropic defect,” Opt. Spectra 110, 952–960 (2011).
[CrossRef]

Phys. Lett. A

A. Y. Okulov, “Cold matter trapping via slowly rotating helical potential,” Phys. Lett. A 376, 650–655 (2012).
[CrossRef]

Phys. Rev. E

O. Toader and S. John, “Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002).
[CrossRef]

Phys. Rev. Lett.

J. Durnin and J. J. Miceli, “Diffraction free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]

Science

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325, 1513–1515 (2009).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2005).

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Figures (6)

Fig. 1.
Fig. 1.

Numerical simulation results showing amplitude (left column) and phase (right column). (a) and (b) show amplitude and phase of six beam interference field ES (with all beams having designed initial phase offset); (c) and (d) show amplitude and phase of synthesized Bessel beam EB; (e) and (f) show amplitude and phase of resultant field ERes. The inset images show the irradiance profile at the FT plane due to each of the complex fields (amplitude and phase part together), and the color bar serves the twin purpose of representing the normalized amplitude from 0 (low) to 1 (high) and phase levels from 0 to 2π. This color bar does not apply to inset images.

Fig. 2.
Fig. 2.

(a)–(c) show numerically calculated irradiance profile at the Fourier plane for the phase-only component of ES, EB, and ERes wave-fields, respectively. (d) FF function (white=unity transmission and black=zero transmission) to discard unwanted terms from the FT of (a)–(c) to match them to corresponding FT of original complex wave-fields. (e) Numerically calculated FT of phase-only component of ERes+carrier wave-field to give rise to a zero-order term. (f) FF to discard unwanted terms from (e) to get the desired wave-field.

Fig. 3.
Fig. 3.

Irradiance profile at the imaging plane after proper Fourier filtering and experimental diagram. Numerically calculated results are shown in panels (a)–(c) for the case of six side+central beam interference, Bessel+central beam interference, and six+Bessel+central beam interference obtained according to our methods, respectively. Experimentally obtained result for six+Bessel+central beam interference leading to defect-embedded helical lattice wave-field is shown in (d), while the schematic for our experimental setup is shown in (e).

Fig. 4.
Fig. 4.

Top view (in left column), side view (in middle column), and perspective view (in right column) of various interference profiles (after thresholding) in space for the case of ES+on axis plane wave in (a)–(c), EB+on axis plane wave in (d)–(f), and ERes+on axis plane wave in (g)–(i). All the plots are obtained by applying a threshold level to actual intensity in each layer. The red line in each of the panels in left column identifies the side that is plotted in the middle column.

Fig. 5.
Fig. 5.

Experimentally recorded irradiance profiles in the image plane due to the display of phase-only components of (a) ES, (b) EB, and (c) ERes on phase SLM.

Fig. 6.
Fig. 6.

Irradiance profiles along an xy plane for different depths of z=0, p/4, 2p/4, and 3p/4, respectively where p is the pitch of the spirals. (a)–(d) show numerically simulated results and, (e)–(h) show experimentally recorded images by CMOS camera in the final imaging plane. p=1.72cm in our case. Slow rotation of helix along with ND defect is quite evident.

Equations (2)

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

ERes=ES+a·eiπEB,
I(r)=i=0n|Ei|2+i=0nj=0jinEiEj*·exp[i(kikj)·r+iψij],

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