Abstract

We present a new, single-step approach for generating a hexagonal lattice wave field with a gradient local basis structure. We incorporate this by coherently superposing two (or more) hexagonal lattice wave fields, which differ in their basis structures. The basis of the resultant lattice wave field is highly dependent on the relative strengths of constituent wave fields, and a desired spatial modulation of basis structure is thus obtained by controlling the spatial modulation of relative strengths of constituent wave fields. The experimental realization of gradient lattice is achieved by using a phase-only spatial light modulator (SLM) in an optical 4f Fourier filter setup where the SLM is displayed with a numerically calculated gradient phase mask. The presented method is wavelength independent and is completely scalable, making it promising for microfabrication of corresponding structures.

© 2014 Optical Society of America

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2014 (2)

M. Kumar and J. Joseph, J. Nanophoton. 8, 083894 (2014).
[CrossRef]

M. Kumar and J. Joseph, Appl. Opt. 53, 1333 (2014).
[CrossRef]

2013 (2)

M. Kumar and J. Joseph, Appl. Opt. 52, 5653 (2013).
[CrossRef]

K. Ohlinger, J. Lutkenhaus, B. Arigong, H. Zhang, and Y. Lin, J. Appl. Phys. 114, 213102 (2013).
[CrossRef]

2012 (3)

2011 (1)

2010 (1)

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, Adv. Mater. 22, 356 (2010).
[CrossRef]

2009 (1)

2007 (1)

2004 (1)

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

2003 (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

2000 (1)

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, Nature 404, 53 (2000).
[CrossRef]

1999 (1)

1994 (1)

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

1987 (1)

J. Durnin, J. J. Miceli, and J. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Arigong, B.

K. Ohlinger, J. Lutkenhaus, B. Arigong, H. Zhang, and Y. Lin, J. Appl. Phys. 114, 213102 (2013).
[CrossRef]

Arrizón, V.

Biswas, R.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Boguslawski, M.

A. Kelberer, M. Boguslawski, P. Rose, and C. Denz, Opt. Lett. 37, 5009 (2012).
[CrossRef]

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, Adv. Mater. 22, 356 (2010).
[CrossRef]

Busch, K.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Campbell, M.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, Nature 404, 53 (2000).
[CrossRef]

Campos, J.

Chan, C.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Citrin, D. S.

Cottrell, D. M.

Davis, J. A.

de-la-Llave, D. S.

Denning, R.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, Nature 404, 53 (2000).
[CrossRef]

Denz, C.

Deubel, M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J.

J. Durnin, J. J. Miceli, and J. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Grier, D. G.

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

Harrison, M.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, Nature 404, 53 (2000).
[CrossRef]

Ho, K.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Joseph, J.

Kelberer, A.

Kittel, C.

C. Kittel and P. McEuen, Introduction to Solid State Physics (Wiley, 1996).

Kumar, M.

Kurt, H.

Lin, Y.

K. Ohlinger, J. Lutkenhaus, B. Arigong, H. Zhang, and Y. Lin, J. Appl. Phys. 114, 213102 (2013).
[CrossRef]

Lutkenhaus, J.

K. Ohlinger, J. Lutkenhaus, B. Arigong, H. Zhang, and Y. Lin, J. Appl. Phys. 114, 213102 (2013).
[CrossRef]

McEuen, P.

C. Kittel and P. McEuen, Introduction to Solid State Physics (Wiley, 1996).

Méndez, G.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Moreno, I.

Ohlinger, K.

K. Ohlinger, J. Lutkenhaus, B. Arigong, H. Zhang, and Y. Lin, J. Appl. Phys. 114, 213102 (2013).
[CrossRef]

Pazos, J.

Pereira, S.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Rose, P.

Ruiz, U.

Rumpf, R. C.

Sánchez-de-la-Llave, D.

Sharp, D.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, Nature 404, 53 (2000).
[CrossRef]

Sigalas, M.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Soukoulis, C.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Soukoulis, C. M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Terhalle, B.

Turberfield, A.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, Nature 404, 53 (2000).
[CrossRef]

Von Freymann, G.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Wegener, M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Xavier, J.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, Adv. Mater. 22, 356 (2010).
[CrossRef]

J. Xavier, P. Rose, B. Terhalle, J. Joseph, and C. Denz, Opt. Lett. 34, 2625 (2009).
[CrossRef]

Yzuel, M. J.

Zhang, H.

K. Ohlinger, J. Lutkenhaus, B. Arigong, H. Zhang, and Y. Lin, J. Appl. Phys. 114, 213102 (2013).
[CrossRef]

Adv. Mater. (1)

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, Adv. Mater. 22, 356 (2010).
[CrossRef]

Appl. Opt. (3)

J. Appl. Phys. (1)

K. Ohlinger, J. Lutkenhaus, B. Arigong, H. Zhang, and Y. Lin, J. Appl. Phys. 114, 213102 (2013).
[CrossRef]

J. Nanophoton. (1)

M. Kumar and J. Joseph, J. Nanophoton. 8, 083894 (2014).
[CrossRef]

Nat. Mater. (1)

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, Nat. Mater. 3, 444 (2004).
[CrossRef]

Nature (2)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef]

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, Nature 404, 53 (2000).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Solid State Commun. (1)

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, Solid State Commun. 89, 413 (1994).
[CrossRef]

Other (1)

C. Kittel and P. McEuen, Introduction to Solid State Physics (Wiley, 1996).

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Figures (6)

Fig. 1.
Fig. 1.

Numerically calculated normalized complex wave field and corresponding intensity pattern for: E6Ph in (a1) and (a2); for E3Ph in (b1) and (b2); and for (E6PhE3Ph) in (c1) and (c2), respectively. The inset images are numerically calculated FT of corresponding complex wave fields.

Fig. 2.
Fig. 2.

Effect of varying strength of a on resultant wave field. a=0, 0.5 and 1 for row number 1, 2, and 3, respectively. Phase profile of ERes in (a1)–(a3); numerically calculated FT of corresponding phase profile of first column in (b1)–(b3); numerically simulated interference pattern in (c1)–(c3); experimentally recorded FT intensity profile in (d1)–(d3); and experimentally obtained interference pattern in (e1)–(e3).

Fig. 3.
Fig. 3.

Schematic diagram of the experimental setup. MO, microscope objective.

Fig. 4.
Fig. 4.

Numerically calculated normalized complex wave fields and corresponding phase profiles for E6 in (a1) and (a2); E3 in (b1) and (b2); E6E3 in (c1) and (c2); and (E6E3)E6/2 in (d1) and (d2), respectively.

Fig. 5.
Fig. 5.

Variation of parameters a and b along x axis in order to achieve a gradual linear variation of basis structure.

Fig. 6.
Fig. 6.

Realization of hexagonal lattice wave field with gradient basis structure. (a) Numerically synthesized gradient phase profile. (b) Simulated interference profile. (c) Experimentally obtained FT pattern. (d) Experimentally obtained interference profile.

Tables (2)

Tables Icon

Table 1. Synthesis of Various Periodic Lattice Wave Fields

Tables Icon

Table 2. Parameters for Obtaining Specific Lattice Wave Fields

Equations (4)

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

En\_beam(r)=j=1nEjei(kj·r+φj),
kj=k×[cos(qjπ)×sinθ,sin(qjπ)×sinθ,cosθ].
ERes=E6Ph+a×E3Ph×eiπ.
ERes=E6Ph+a×E3Ph×eiπ+b×E6S×eiπ.

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