Abstract

For the first time, to the authors’ best knowledge, this paper demonstrates the digital, holographic fabrication of graded, super-basis photonic lattices with dual periodicity, dual basis, and dual symmetry. Pixel-by-pixel phase engineering of the laser beam generates the highest resolution in a programmable spatial light modulator (SLM) for the direct imaging of graded photonic super-lattices. This technique grants flexibility in designing 2-D lattices with size-graded features, differing periodicities, and differing symmetries, as well as lattices having simultaneously two periodicities and two symmetries in high resolutions. By tuning the diffraction efficiency ratio from the SLM, photonic cavities can also be generated in the graded super-lattice simultaneously through a one-exposure process. A high quality factor of over 1.56 × 106 for a cavity mode in the graded photonic lattice with a large super-cell is predicted by simulations.

© 2017 Optical Society of America

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    [Crossref]

2016 (3)

2015 (1)

2014 (5)

2013 (2)

2011 (1)

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

2010 (3)

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[Crossref] [PubMed]

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[Crossref] [PubMed]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

2009 (3)

W. S. Kim, L. Jia, and E. L. Thomas, “Hierarchically ordered topographic patterns via plasmonic mask photolithography,” Adv. Mater. 21(19), 1921–1926 (2009).
[Crossref]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

2008 (2)

2006 (4)

L. Wu, Y. Zhong, K. S. Wong, G. P. Wang, and L. Yuan, “Fabrication of heterobinary and honeycomb photonic crystals by one-step holographic lithography,” Appl. Phys. Lett. 88(9), 091115 (2006).
[Crossref]

Y. K. Pang, J. C. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9113–9119 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

2005 (1)

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86(7), 071117 (2005).
[Crossref]

2004 (1)

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

2001 (1)

2000 (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

1997 (2)

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[Crossref]

Abolghasemi, L. E.

Adewole, M.

Arakawa, Y.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Arigong, B.

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Behera, S.

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Boreman, G. D.

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[Crossref] [PubMed]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

Celanovic, I.

Chanda, D.

Chen, K. P.

Chiles, J.

D’Archangel, J.

Darmawikarta, K.

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86(7), 071117 (2005).
[Crossref]

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Digaum, J. L.

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[Crossref] [PubMed]

Fan, S. H.

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

Fathpour, S.

Fu, Y. Q.

Gabrielli, L. H.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

Gajic, R.

Geil, R. D.

George, D.

Guimard, D.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Haque, M.

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Herman, P. R.

L. L. Yuan and P. R. Herman, “Laser scanning holographic lithography for flexible 3D fabrication of multi-scale integrated nano-structures and optical biosensors,” Sci. Rep. 6(1), 22294 (2016).
[Crossref] [PubMed]

D. Chanda, L. E. Abolghasemi, M. Haque, M. L. Ng, and P. R. Herman, “Multi-level diffractive optics for single laser exposure fabrication of telecom-band diamond-like 3-dimensional photonic crystals,” Opt. Express 16(20), 15402–15414 (2008).
[Crossref] [PubMed]

Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86(7), 071117 (2005).
[Crossref]

Hingerl, K.

Ho, C. T.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Ippen, E. P.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Ishida, S.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Isic, G.

Iwamoto, S.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Jacobs, D.

Jia, L.

W. S. Kim, L. Jia, and E. L. Thomas, “Hierarchically ordered topographic patterns via plasmonic mask photolithography,” Adv. Mater. 21(19), 1921–1926 (2009).
[Crossref]

Joannopoulos, J.

Joannopoulos, J. D.

V. Rinnerbauer, E. Lausecker, F. Schäffler, P. Reininger, G. Strasser, R. D. Geil, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Nanoimprinted superlattice metallic photonic crystal as ultraselective solar absorber,” Optica 2(8), 743–746 (2015).
[Crossref]

V. Rinnerbauer, Y. Shen, J. D. Joannopoulos, M. Soljačić, F. Schäffler, and I. Celanovic, “Superlattice photonic crystal as broadband solar absorber for high temperature operation,” Opt. Express 22(7), A1895–A1906 (2014).
[Crossref] [PubMed]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

Johnson, S.

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Joseph, J.

S. Behera and J. Joseph, “Single-step optical realization of bio-inspired dual-periodic motheye and gradient-index-array photonic structures,” Opt. Lett. 41(15), 3579–3582 (2016).
[Crossref] [PubMed]

M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105(5), 051102 (2014).
[Crossref]

Kim, W. S.

W. S. Kim, L. Jia, and E. L. Thomas, “Hierarchically ordered topographic patterns via plasmonic mask photolithography,” Adv. Mater. 21(19), 1921–1926 (2009).
[Crossref]

Kuebler, S. M.

Kumar, M.

M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105(5), 051102 (2014).
[Crossref]

Kurizki, G.

Kurt, H.

Lausecker, E.

Lee, J. C.

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Li, J.

Li, Y. H.

Liang, B.

Lidorikis, E.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Lin, Y.

Lipson, M.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

Liu, Y.

Lowell, D.

Lutkenhaus, J.

Mandelshtam, V. A.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[Crossref]

Minin, I. V.

Minin, O. V.

Moazzezi, M.

Ng, M. L.

Nomura, M.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Oner, B. B.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Padilla, G.

Pang, Y. K.

Pazos, J. J.

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Philipose, U.

Poitras, C. B.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

Poole, Z. L.

Qi, M.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Rakich, P. T.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Reininger, P.

Rinnerbauer, V.

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Rumpf, R. C.

Schäffler, F.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Shen, Y.

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Smith, H. I.

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

Soljacic, M.

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
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Strasser, G.

Tam, W. Y.

Tandaechanurat, A.

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Tatulian, A.

Taylor, H. S.

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[Crossref]

Thomas, E. L.

W. S. Kim, L. Jia, and E. L. Thomas, “Hierarchically ordered topographic patterns via plasmonic mask photolithography,” Adv. Mater. 21(19), 1921–1926 (2009).
[Crossref]

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Turduev, M.

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Vasic, B.

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

Wang, G. P.

L. Wu, Y. Zhong, K. S. Wong, G. P. Wang, and L. Yuan, “Fabrication of heterobinary and honeycomb photonic crystals by one-step holographic lithography,” Appl. Phys. Lett. 88(9), 091115 (2006).
[Crossref]

Wegener, M.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[Crossref] [PubMed]

Wong, K. S.

J. Li, Y. Liu, X. Xie, P. Zhang, B. Liang, L. Yan, J. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008).
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L. Wu, Y. Zhong, K. S. Wong, G. P. Wang, and L. Yuan, “Fabrication of heterobinary and honeycomb photonic crystals by one-step holographic lithography,” Appl. Phys. Lett. 88(9), 091115 (2006).
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L. Wu, Y. Zhong, K. S. Wong, G. P. Wang, and L. Yuan, “Fabrication of heterobinary and honeycomb photonic crystals by one-step holographic lithography,” Appl. Phys. Lett. 88(9), 091115 (2006).
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Xie, X.

Yan, L.

Yuan, L.

L. Wu, Y. Zhong, K. S. Wong, G. P. Wang, and L. Yuan, “Fabrication of heterobinary and honeycomb photonic crystals by one-step holographic lithography,” Appl. Phys. Lett. 88(9), 091115 (2006).
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Yuan, L. L.

L. L. Yuan and P. R. Herman, “Laser scanning holographic lithography for flexible 3D fabrication of multi-scale integrated nano-structures and optical biosensors,” Sci. Rep. 6(1), 22294 (2016).
[Crossref] [PubMed]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Zhang, H.

Zhang, P.

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[Crossref] [PubMed]

Zhong, Y.

J. Li, Y. Liu, X. Xie, P. Zhang, B. Liang, L. Yan, J. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008).
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L. Wu, Y. Zhong, K. S. Wong, G. P. Wang, and L. Yuan, “Fabrication of heterobinary and honeycomb photonic crystals by one-step holographic lithography,” Appl. Phys. Lett. 88(9), 091115 (2006).
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Zhou, J.

Adv. Mater. (1)

W. S. Kim, L. Jia, and E. L. Thomas, “Hierarchically ordered topographic patterns via plasmonic mask photolithography,” Adv. Mater. 21(19), 1921–1926 (2009).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

L. Wu, Y. Zhong, K. S. Wong, G. P. Wang, and L. Yuan, “Fabrication of heterobinary and honeycomb photonic crystals by one-step holographic lithography,” Appl. Phys. Lett. 88(9), 091115 (2006).
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M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105(5), 051102 (2014).
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Y. Lin, P. R. Herman, and K. Darmawikarta, “Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals,” Appl. Phys. Lett. 86(7), 071117 (2005).
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Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

J. Chem. Phys. (1)

V. A. Mandelshtam and H. S. Taylor, “Harmonic inversion of time signals,” J. Chem. Phys. 107(17), 6756–6769 (1997).
[Crossref]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
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Nat. Photonics (2)

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3(8), 461–463 (2009).
[Crossref]

A. Tandaechanurat, S. Ishida, D. Guimard, M. Nomura, S. Iwamoto, and Y. Arakawa, “Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap,” Nat. Photonics 5(2), 91–94 (2011).
[Crossref]

Nature (3)

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429(6991), 538–542 (2004).
[Crossref] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Opt. Express (9)

J. Lutkenhaus, D. George, M. Moazzezi, U. Philipose, and Y. Lin, “Digitally tunable holographic lithography using a spatial light modulator as a programmable phase mask,” Opt. Express 21(22), 26227–26235 (2013).
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D. George, J. Lutkenhaus, D. Lowell, M. Moazzezi, M. Adewole, U. Philipose, H. Zhang, Z. L. Poole, K. P. Chen, and Y. Lin, “Holographic fabrication of 3D photonic crystals through interference of multi-beams with 4 + 1, 5 + 1 and 6 + 1 configurations,” Opt. Express 22(19), 22421–22431 (2014).
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S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
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Y. K. Pang, J. C. Lee, C. T. Ho, and W. Y. Tam, “Realization of woodpile structure using optical interference holography,” Opt. Express 14(20), 9113–9119 (2006).
[Crossref] [PubMed]

J. Li, Y. Liu, X. Xie, P. Zhang, B. Liang, L. Yan, J. Zhou, G. Kurizki, D. Jacobs, K. S. Wong, and Y. Zhong, “Fabrication of photonic crystals with functional defects by one-step holographic lithography,” Opt. Express 16(17), 12899–12904 (2008).
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B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
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J. L. Digaum, J. J. Pazos, J. Chiles, J. D’Archangel, G. Padilla, A. Tatulian, R. C. Rumpf, S. Fathpour, G. D. Boreman, and S. M. Kuebler, “Tight control of light beams in photonic crystals with spatially-variant lattice orientation,” Opt. Express 22(21), 25788–25804 (2014).
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V. Rinnerbauer, Y. Shen, J. D. Joannopoulos, M. Soljačić, F. Schäffler, and I. Celanovic, “Superlattice photonic crystal as broadband solar absorber for high temperature operation,” Opt. Express 22(7), A1895–A1906 (2014).
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D. Chanda, L. E. Abolghasemi, M. Haque, M. L. Ng, and P. R. Herman, “Multi-level diffractive optics for single laser exposure fabrication of telecom-band diamond-like 3-dimensional photonic crystals,” Opt. Express 16(20), 15402–15414 (2008).
[Crossref] [PubMed]

Opt. Lett. (2)

Opt. Mater. Express (1)

Optica (1)

Sci. Rep. (1)

L. L. Yuan and P. R. Herman, “Laser scanning holographic lithography for flexible 3D fabrication of multi-scale integrated nano-structures and optical biosensors,” Sci. Rep. 6(1), 22294 (2016).
[Crossref] [PubMed]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of experimental optics setup using the SLM for spatially specified phase engineering for interfering beams. Diffraction beams (green and yellow dots) from the SLM are passed through Lens 1 and are focused to points in the Fourier plane. The green and yellow dots are the outer and inner diffraction beams respectively. A filter is placed at the Fourier plane to block unwanted diffraction spots. The selected beams pass through Lens 2 to interfere at the 4f plane. (b) The 2 × 2 repeating unit in the SLM pattern, which produces the outer four diffraction spots in (e). (c) The 24 × 24 repeating unit in the SLM which produces the inner diffraction spots in (e). (d) The actual pattern consists a checkerboard pattern within the dark regions of the 24 × 24 pixel unit cell in (c) and a different colored checkerboard pattern in the light regions of the 24 × 24 unit cell in (c). (e) Image at the Fourier plane showing the eight diffracted beams from the actual SLM unit cell (e). (f) Diffraction efficiency of inner (blue curve) and outer (purple curve) beams from the square, supercell SLM pattern as well as their intensity ratio (red curve), plotted against the difference in gray level between the two checkerboard patterns.
Fig. 2
Fig. 2 (a) Supercell phase tiles assembled from 12 × 12 tiles of checkerboard phase patterns with gray levels of (158, 254) and (192, 254), respectively. (b) Enlarged view of (158, 254) and (192, 254) checkerboards patterns. (c) Simulated iso-intensity surface of the interference pattern. (d) A gradient lattice plus a super-basis can be combined to represent the interference structures in the red dashed square of (c). (e) SEM of fabricated sample showing large periodicity and square symmetry. The blue square indicates a supercell in the structure which corresponds to the supercell of the SLM phase pattern in blue square in (a) and simulated interference in (c). (f) Enlarged view of fabricated gradient superlattice structures showing d = 8 μm. (g) Diffraction pattern of fabricated sample from 532 nm laser.
Fig. 3
Fig. 3 (a) Rectangular supercell used to construct the SLM phase pattern for 10 beam interference. The supercell consists of triangularly alternating combinations of gray levels 158/254 and 192,254 in checkerboard patterns. (b) Simulated iso-intensity surface of the interference from the tiled SLM phase pattern in (a). (c) A large-area SEM of simultaneous square and hexagonal symmetry structures. The red square indicates a supercell in the structure which corresponds to the supercell of the SLM phase image in (a). The yellow hexagon is drawn for eye guidance of the hexagonal symmetry. (d) Enlarged view of structures in dashed red square in (c). The square symmetry and graded dual-basis are clearly visible. (e) Diffraction pattern of fabricated sample from 532 nm laser.
Fig. 4
Fig. 4 Binary dielectric/air supercells produced by setting threshold intensity to be 45% (a) and 60% (b) of maximum interference intensity with the ratio of diffraction efficiencies = 12.5. Computed photonic band structures up to over 200 bands with full photonic band gap in (c) and a cavity mode within the photonic band gap in (d) for the extremely large supercells in (a) and (b), respectively.
Fig. 5
Fig. 5 (a) Simulated electric field distributions of cavity modes in the 12a × 12a binary dielectric/air supercells produced with diffraction efficiency ratios of 12.5:1 (a) and 30:1 (b). (c) Simulated electric field in the 18a × 18a binary dielectric/air supercell produced with a diffraction efficiency ratio of 30:1.

Equations (5)

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I( r )= i=1 8 E i 2 (r,t)+ i<j 8 E i E j e i e j cos[ ( k j k i )r+( δ j δ i ) ].
( 2D )sin θ 1 =λ.
tan θ 2 = f 1 tan θ 1 ×( f 2 f 1 )× 2 f 2 . 
P= 2π ksin θ 2 = λ sin θ 2 =  λ 2 sin θ 1 = 2D 2 .
P= 2π ksin θ 2 = λ sin θ 2 =  λ 2 sin θ 1 = 2D 2 .

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