Abstract

We present a method to combine two periodic lattice wave fields to generate a complex dual-lattice wave field which could be employed for microfabrication of corresponding two-dimensional dual-lattice structures. Since the addition of two periodic lattice wave fields is coherent in nature, the resultant dual-lattice structure is highly dependent on the relative phase difference between constituent wave fields. We show that it is possible to have control over the dual-lattice pattern by precisely controlling this relative phase difference. This control is enabled by making use of digitally addressable phase-only spatial light modulator (SLM). We provide the computational method for calculation of the corresponding phase mask to be displayed on the SLM and also verify the results experimentally by employing a simple 4f Fourier filter-based geometry. The method is completely scalable and reconfigurable in terms of the choice of periodic lattice wave fields and has the potential to form gradient phase masks which could be useful for fabrication of graded-index optical components.

© 2014 Optical Society of America

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  1. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).
  2. A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef]
  3. O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [CrossRef]
  4. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
    [CrossRef]
  5. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
    [CrossRef]
  6. C. Luo, S. G. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
    [CrossRef]
  7. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
    [CrossRef]
  8. M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013

2012

2011

J. L. Stay, G. M. Burrow, and T. Gaylord, “Three-beam interference lithography methodology,” Rev. Sci. Instrum. 82, 023115 (2011).
[CrossRef]

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

2009

2008

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
[CrossRef]

2004

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

2002

C. Luo, S. G. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

2001

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[CrossRef]

2000

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[CrossRef]

1999

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

1998

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

1996

A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

1994

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Arrizón, V.

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
[CrossRef]

Biswas, R.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Bo, X.-Z.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[CrossRef]

Boguslawski, M.

Burrow, G. M.

J. L. Stay, G. M. Burrow, and T. Gaylord, “Three-beam interference lithography methodology,” Rev. Sci. Instrum. 82, 023115 (2011).
[CrossRef]

Busch, K.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Campbell, M.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[CrossRef]

Chan, C.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Chen, J.

A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Dapkus, P.

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Denning, R.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[CrossRef]

Denz, C.

Deubel, M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Fan, S.

A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Gaylord, T.

J. L. Stay, G. M. Burrow, and T. Gaylord, “Three-beam interference lithography methodology,” Rev. Sci. Instrum. 82, 023115 (2011).
[CrossRef]

George, D.

Harrison, M.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[CrossRef]

Ho, K.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Joannopoulos, J.

C. Luo, S. G. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

Johnson, S. G.

C. Luo, S. G. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

Joseph, J.

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Kelberer, A.

Kim, I.

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Kumar, M.

Kurland, I.

A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Lee, R.

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Lin, Y.

Luo, C.

C. Luo, S. G. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Lutkenhaus, J.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

Mekis, A.

A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Méndez, G.

Moazzezi, M.

Norris, D. J.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

O’Brien, J.

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Painter, O.

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Pazos, J.

Pendry, J.

C. Luo, S. G. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

Pereira, S.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Philipose, U.

Rose, P.

Rumpf, R. C.

Sánchez-de-la-Llave, D.

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Scherer, A.

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Sharp, D.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[CrossRef]

Sigalas, M.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Soukoulis, C.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Soukoulis, C. M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Stay, J. L.

J. L. Stay, G. M. Burrow, and T. Gaylord, “Three-beam interference lithography methodology,” Rev. Sci. Instrum. 82, 023115 (2011).
[CrossRef]

Sturm, J. C.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Terhalle, B.

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Turberfield, A.

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[CrossRef]

Villeneuve, P. R.

A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Vlasov, Y. A.

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[CrossRef]

Von Freymann, G.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Wegener, M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

Xavier, J.

Yariv, A.

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

Nat. Mater.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Nat. Photonics

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
[CrossRef]

Nature

Y. A. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris, “On-chip natural assembly of silicon photonic bandgap crystals,” Nature 414, 289–293 (2001).
[CrossRef]

M. Campbell, D. Sharp, M. Harrison, R. Denning, and A. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404, 53–56 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

C. Luo, S. G. Johnson, J. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096 (1998).
[CrossRef]

Phys. Rev. Lett.

A. Mekis, J. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Rev. Sci. Instrum.

J. L. Stay, G. M. Burrow, and T. Gaylord, “Three-beam interference lithography methodology,” Rev. Sci. Instrum. 82, 023115 (2011).
[CrossRef]

Science

O. Painter, R. Lee, A. Scherer, A. Yariv, J. O’Brien, P. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef]

Solid State Commun.

K. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413–416 (1994).
[CrossRef]

Other

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2011).

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