Digitally tunable holographic lithography using a spatial light modulator as a programmable phase mask

J. Lutkenhaus; D. George; M. Moazzezi; U. Philipose; Y. Lin

doi:10.1364/OE.21.026227

Digitally tunable holographic lithography using a spatial light modulator as a programmable phase mask

J. Lutkenhaus, D. George, M. Moazzezi, U. Philipose, and Y. Lin

Optics Express
Vol. 21,
Issue 22,
pp. 26227-26235
(2013)
•https://doi.org/10.1364/OE.21.026227

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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, 26227-26235 (2013)

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Related Topics
Table of Contents Category
- Holography
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diffractive optics (090.1970)
- Photonic crystals (160.5298)
- Lithography (220.3740)
- Microstructure fabrication (220.4000)
- Diffraction theory (260.1960)

About this Article
History
- Original Manuscript: August 5, 2013
- Revised Manuscript: September 18, 2013
- Manuscript Accepted: October 8, 2013
- Published: October 25, 2013

Accessible

Open Access

Abstract

In this paper, we study tunable holographic lithography using an electrically addressable spatial light modulator as a programmable phase mask. We control the phases of interfering beams diffracted from the phase pattern displayed in the spatial light modulator. We present a calculation method for the assignment of phases in the laser beams and validate the phases of the interfering beams in phase-sensitive, dual-lattice, and two-dimensional patterns formed by a rotationally non-symmetrical configuration. A good agreement has been observed between fabricated holographic structures and simulated interference patterns. The presented method can potentially help design a gradient phase mask for the fabrication of graded photonic crystals or metamaterials.

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References

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Year
|
Author
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Publication

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]
E. Yablonovitch, “Inhibited spontaneous emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]
K. P. Chen, P. R. Herman, and R. Tam, “Strong fiber Bragg grating fabrication by hybrid 157- and 248-nm laser exposure,” IEEE Photon. Technol. Lett. 14(2), 170–172 (2002).
[Crossref]
S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293(5532), 1123–1125 (2001).
[Crossref] [PubMed]
Y. Liu, F. Qin, Z.-M. Meng, F. Zhou, Q.-H. Mao, and Z.-Y. Li, “All-optical logic gates based on two-dimensional low-refractive-index nonlinear photonic crystal slabs,” Opt. Express 19(3), 1945–1953 (2011).
[Crossref] [PubMed]
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]
K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89(5), 413–416 (1994).
[Crossref]
A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, A. Geoffrey, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[Crossref] [PubMed]
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(7), 444–447 (2004).
[Crossref] [PubMed]
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]
S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mater. 14(7), 2831–2833 (2002).
[Crossref]
I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, “Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography,” Appl. Phys. Lett. 82(11), 1667–1669 (2003).
[Crossref]
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]
K. Ohlinger, H. Zhang, Y. Lin, D. Xu, and K. P. Chen, “A tunable three layer phase mask for single laser exposure 3D photonic crystal generations: bandgap simulation and holographic fabrication,” Opt. Mater. Express 1(5), 1034–1039 (2011).
[Crossref]
D. Xu, K. P. Chen, A. Harb, D. Rodriguez, K. Lozano, and Y. Lin, “Phase tunable holographic fabrication for three-dimensional photonic crystal templates by using a single optical element,” Appl. Phys. Lett. 94(23), 231116 (2009).
T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046610 (2006).
[Crossref] [PubMed]
G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, “Two-dimensional photonic quasicrystals by single beam computer-generated holography,” Opt. Express 16(8), 5164–5170 (2008).
[Crossref] [PubMed]
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(3), 356–360 (2010).
[Crossref] [PubMed]
V. Arrizón, D. S. 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(11), 10553–10562 (2011).
[Crossref] [PubMed]
J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
[Crossref]
J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36(3), 403–405 (2011).
[Crossref] [PubMed]
M. Kumar and J. Joseph, “Embedding a nondiffracting defect site in helical lattice wave-field by optical phase engineering,” Appl. Opt. 52(23), 5653–5658 (2013).
[Crossref] [PubMed]
M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20(24), 27331–27343 (2012).
[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]
B. Arigong, K. Ohlinger, H. S. Kim, Y. Lin, and H. Zhang, “Transformation optics designed general optical luneburg lens with flattened shapes,” Proc. SPIE 8376, 83760R–1, 83760R-6 (2012).
[Crossref]
K. Ohlinger, J. Lutkenhaus, H. Zhang, and Y. Lin, “Spatially addressable design of Luneburg lens through spatial light modulator based holographic lithography,” J. Appl. Phys.submitted.
J. Lutkenhaus, D. George, D. Garrett, K. Ohlinger, H. Zhang, and Y. Lin, “Holographic formation of compound photonic crystal and nano-antenna templates through laser interference,” J. Appl. Phys. 113(10), 103103 (2013).
[Crossref]
R. C. Rumpf and J. Pazos, “Synthesis of spatially variant lattices,” Opt. Express 20(14), 15263–15274 (2012).
[Crossref] [PubMed]

2013 (2)

J. Lutkenhaus, D. George, D. Garrett, K. Ohlinger, H. Zhang, and Y. Lin, “Holographic formation of compound photonic crystal and nano-antenna templates through laser interference,” J. Appl. Phys. 113(10), 103103 (2013).
[Crossref]

M. Kumar and J. Joseph, “Embedding a nondiffracting defect site in helical lattice wave-field by optical phase engineering,” Appl. Opt. 52(23), 5653–5658 (2013).
[Crossref] [PubMed]

2012 (4)

J. Xavier, R. Dasgupta, S. Ahlawat, J. Joseph, and P. K. Gupta, “Three dimensional optical twisters-driven helically stacked multi-layered microrotors,” Appl. Phys. Lett. 100(12), 121101 (2012).
[Crossref]

R. C. Rumpf and J. Pazos, “Synthesis of spatially variant lattices,” Opt. Express 20(14), 15263–15274 (2012).
[Crossref] [PubMed]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20(24), 27331–27343 (2012).
[Crossref] [PubMed]

B. Arigong, K. Ohlinger, H. S. Kim, Y. Lin, and H. Zhang, “Transformation optics designed general optical luneburg lens with flattened shapes,” Proc. SPIE 8376, 83760R–1, 83760R-6 (2012).
[Crossref]

2011 (5)

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]

Y. Liu, F. Qin, Z.-M. Meng, F. Zhou, Q.-H. Mao, and Z.-Y. Li, “All-optical logic gates based on two-dimensional low-refractive-index nonlinear photonic crystal slabs,” Opt. Express 19(3), 1945–1953 (2011).
[Crossref] [PubMed]

J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36(3), 403–405 (2011).
[Crossref] [PubMed]

V. Arrizón, D. S. 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(11), 10553–10562 (2011).
[Crossref] [PubMed]

K. Ohlinger, H. Zhang, Y. Lin, D. Xu, and K. P. Chen, “A tunable three layer phase mask for single laser exposure 3D photonic crystal generations: bandgap simulation and holographic fabrication,” Opt. Mater. Express 1(5), 1034–1039 (2011).
[Crossref]

2010 (1)

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(3), 356–360 (2010).
[Crossref] [PubMed]

2009 (1)

D. Xu, K. P. Chen, A. Harb, D. Rodriguez, K. Lozano, and Y. Lin, “Phase tunable holographic fabrication for three-dimensional photonic crystal templates by using a single optical element,” Appl. Phys. Lett. 94(23), 231116 (2009).

2008 (1)

G. Zito, B. Piccirillo, E. Santamato, A. Marino, V. Tkachenko, and G. Abbate, “Two-dimensional photonic quasicrystals by single beam computer-generated holography,” Opt. Express 16(8), 5164–5170 (2008).
[Crossref] [PubMed]

2006 (3)

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046610 (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. 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(7), 444–447 (2004).
[Crossref] [PubMed]

2003 (1)

I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, “Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography,” Appl. Phys. Lett. 82(11), 1667–1669 (2003).
[Crossref]

2002 (2)

K. P. Chen, P. R. Herman, and R. Tam, “Strong fiber Bragg grating fabrication by hybrid 157- and 248-nm laser exposure,” IEEE Photon. Technol. Lett. 14(2), 170–172 (2002).
[Crossref]

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, “Creating periodic three-dimensional structures by multibeam interference of visible laser,” Chem. Mater. 14(7), 2831–2833 (2002).
[Crossref]

2001 (1)

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, “Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design,” Science 293(5532), 1123–1125 (2001).
[Crossref] [PubMed]

2000 (2)

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, A. Geoffrey, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[Crossref] [PubMed]

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]

1994 (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89(5), 413–416 (1994).
[Crossref]

1987 (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]

Abbate, G.

Ahlawat, S.

Aizenberg, J.

Arakawa, Y.

Arigong, B.

Arrizón, V.

Biswas, R.

Blanco, A.

Boguslawski, M.

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20(24), 27331–27343 (2012).
[Crossref] [PubMed]

Busch, K.

Campbell, M.

Chaikin, P. M.

Chan, C. T.

Chan, T. Y. M.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046610 (2006).
[Crossref] [PubMed]

Chen, K. P.

K. P. Chen, P. R. Herman, and R. Tam, “Strong fiber Bragg grating fabrication by hybrid 157- and 248-nm laser exposure,” IEEE Photon. Technol. Lett. 14(2), 170–172 (2002).
[Crossref]

Chomski, E.

Chutinan, A.

Crespi, V. H.

Darmawikarta, K.

Dasgupta, R.

de-la-Llave, D. S.

Denning, R. G.

Denz, C.

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20(24), 27331–27343 (2012).
[Crossref] [PubMed]

Deubel, M.

Divliansky, I.

Garrett, D.

Geoffrey, A.

George, D.

Grabtchak, S.

Guimard, D.

Gupta, P. K.

Harb, A.

Harrison, M. T.

Herman, P. R.

K. P. Chen, P. R. Herman, and R. Tam, “Strong fiber Bragg grating fabrication by hybrid 157- and 248-nm laser exposure,” IEEE Photon. Technol. Lett. 14(2), 170–172 (2002).
[Crossref]

Ho, K. M.

Holliday, K. S.

Ibisate, M.

Imada, M.

Ishida, S.

Iwamoto, S.

John, S.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046610 (2006).
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

Joseph, J.

M. Kumar and J. Joseph, “Embedding a nondiffracting defect site in helical lattice wave-field by optical phase engineering,” Appl. Opt. 52(23), 5653–5658 (2013).
[Crossref] [PubMed]

J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36(3), 403–405 (2011).
[Crossref] [PubMed]

Kelberer, A.

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20(24), 27331–27343 (2012).
[Crossref] [PubMed]

Kim, H. S.

Kumar, M.

M. Kumar and J. Joseph, “Embedding a nondiffracting defect site in helical lattice wave-field by optical phase engineering,” Appl. Opt. 52(23), 5653–5658 (2013).
[Crossref] [PubMed]

Leonard, S. W.

Leonhardt, U.

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

Li, Z.-Y.

Lin, Y.

K. Ohlinger, J. Lutkenhaus, H. Zhang, and Y. Lin, “Spatially addressable design of Luneburg lens through spatial light modulator based holographic lithography,” J. Appl. Phys.submitted.

Liu, Y.

Lopez, C.

Lozano, K.

Lutkenhaus, J.

K. Ohlinger, J. Lutkenhaus, H. Zhang, and Y. Lin, “Spatially addressable design of Luneburg lens through spatial light modulator based holographic lithography,” J. Appl. Phys.submitted.

Mao, Q.-H.

Marino, A.

Mayer, T. S.

Megens, M.

Méndez, G.

Meng, Z.-M.

Meseguer, F.

Miguez, H.

Mochizuki, M.

Mondia, J. P.

Noda, S.

Nomura, M.

Ohlinger, K.

K. Ohlinger, J. Lutkenhaus, H. Zhang, and Y. Lin, “Spatially addressable design of Luneburg lens through spatial light modulator based holographic lithography,” J. Appl. Phys.submitted.

Ozin, G. A.

Pazos, J.

R. C. Rumpf and J. Pazos, “Synthesis of spatially variant lattices,” Opt. Express 20(14), 15263–15274 (2012).
[Crossref] [PubMed]

Pendry, J. B.

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

Pereira, S.

Piccirillo, B.

Qin, F.

Rodriguez, D.

Rose, P.

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20(24), 27331–27343 (2012).
[Crossref] [PubMed]

Ruiz, U.

Rumpf, R. C.

R. C. Rumpf and J. Pazos, “Synthesis of spatially variant lattices,” Opt. Express 20(14), 15263–15274 (2012).
[Crossref] [PubMed]

Russel, W. B.

Santamato, E.

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.

Sigalas, M.

Smith, D. R.

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

Soukoulis, C. M.

Tam, R.

K. P. Chen, P. R. Herman, and R. Tam, “Strong fiber Bragg grating fabrication by hybrid 157- and 248-nm laser exposure,” IEEE Photon. Technol. Lett. 14(2), 170–172 (2002).
[Crossref]

Tandaechanurat, A.

Tkachenko, V.

Toader, O.

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046610 (2006).
[Crossref] [PubMed]

Turberfield, A. J.

van Driel, H. M.

von Freymann, G.

Wegener, M.

Wiltzius, P.

Xavier, J.

J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36(3), 403–405 (2011).
[Crossref] [PubMed]

Xu, D.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]

Yang, S.

Yokoyama, M.

Zhang, H.

K. Ohlinger, J. Lutkenhaus, H. Zhang, and Y. Lin, “Spatially addressable design of Luneburg lens through spatial light modulator based holographic lithography,” J. Appl. Phys.submitted.

Zhou, F.

Zito, G.

Adv. Mater. (1)

Appl. Opt. (1)

M. Kumar and J. Joseph, “Embedding a nondiffracting defect site in helical lattice wave-field by optical phase engineering,” Appl. Opt. 52(23), 5653–5658 (2013).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

Chem. Mater. (1)

IEEE Photon. Technol. Lett. (1)

K. P. Chen, P. R. Herman, and R. Tam, “Strong fiber Bragg grating fabrication by hybrid 157- and 248-nm laser exposure,” IEEE Photon. Technol. Lett. 14(2), 170–172 (2002).
[Crossref]

J. Appl. Phys. (2)

K. Ohlinger, J. Lutkenhaus, H. Zhang, and Y. Lin, “Spatially addressable design of Luneburg lens through spatial light modulator based holographic lithography,” J. Appl. Phys.submitted.

Nat. Mater. (1)

Nat. Photonics (1)

Nature (2)

Opt. Express (5)

R. C. Rumpf and J. Pazos, “Synthesis of spatially variant lattices,” Opt. Express 20(14), 15263–15274 (2012).
[Crossref] [PubMed]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20(24), 27331–27343 (2012).
[Crossref] [PubMed]

Opt. Lett. (1)

J. Xavier and J. Joseph, “Tunable complex photonic chiral lattices by reconfigurable optical phase engineering,” Opt. Lett. 36(3), 403–405 (2011).
[Crossref] [PubMed]

Opt. Mater. Express (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

T. Y. M. Chan, O. Toader, and S. John, “Photonic band-gap formation by optical-phase-mask lithography,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 73(4), 046610 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[Crossref] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[Crossref] [PubMed]

Proc. SPIE (1)

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]

Solid State Commun. (1)

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Fig. 1 Scheme of experimental optics setup using the SLM for multi-beam interference lithography. Phase pattern was displayed on the SLM. Imaging lenses f₁ and f₂ were arranged in a 4f configuration.

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Fig. 2 (a) An enlarged view of designed pattern. The gray levels in six equilateral triangles inside a hexagon are assigned digitally. The diffractions are formed in directions having periodic patterns. The diffraction pattern is predicted following the diffraction direction. (b) Experimentally recorded diffraction pattern. (c) A scheme of an enlarged view of the pattern. The red hexagon indicates a unit cell of the pattern. The phases of the diffracted beams (1-6) are determined by the averaged gray levels of kite-type four-side polygons inside the red hexagon.

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Fig. 3 (a1, b1, c1) A scheme of an enlarged view of designed patterns with a gray level in a set of triangles changed from 153 to 102 and to 51. The hexagon indicates the unit cell of the designed pattern. (a2, b2, c2) CCD recorded images for four-beam interference pattern from beams 1, 3, 4 and 5 diffracted from phase patterns in (a1, b1, c1), respectively. (a3, b3, c3) Simulated four-beam interference pattern formed by beams 1, 3, 4 and 5 with phases assignments from the gray levels in (a1, b1, c1), respectively. Labels a and b in (a3) indicates the lattice constants and red arrows in (b3) indicate the pattern shifting directions. (a4, b4, c4) 3D view of simulated four-beam interference patterns given in (a3, b3, c3).

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Fig. 4 (a1,a2,a3) CCD images of interference patterns recorded at different locations longitudinally translated along z-direction by 0, 127, and 254 microns. (b) SEM image of fabricated holographic structures in DPHPA. (c) An enlarged view of the SEM in (b). (d) Atomic force microscope image of the fabricated holographic structures in DPHPA. (e) A surface profile measured along the line in the AFM image in (d).

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Fig. 5 (a) A scheme of an enlarged view of a designed pattern with different gray levels in triangles from a to f. The gray levels are labeled in the right side of the pattern. The hexagon indicates the unit cell of the designed pattern. (b) Simulated four-beam interference pattern using the phase information in (a). Inset is a 3D view. (c) CCD recorded images for four-beam interference pattern from beams diffracted from phase patterns in (a). (d) SEM image of fabricated holographic structures in DPHPA. (e, f, g) Simulated four-beam interference patterns formed by beams 1, 3, 4 and 5 with phases assignments from the gray levels shown in Fig. 3(a1, b1, c1), respectively. The patterns were obtained by setting the iso-intensity surface to be a half of maximum intensity.

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Equations (5)

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\frac{1}{3} l i g h t g r a y + \frac{8}{18} b l a c k + \frac{1}{18} b l a c k + \frac{1}{6} b l a c k,

\frac{1}{3} d a r k g r e y + \frac{8}{18} b l a c k + \frac{1}{18} b l a c k + \frac{1}{6} b l a c k,

I (r) = I_{0} + Δ I (r) =< \sum_{i = 1}^{4} E_{i}^{2} (r, t) >+ \sum_{i < j}^{4} E_{i} E_{j} e_{i} \cdot e_{j} \cos [(k_{j} - k_{i}) \cdot r + (δ_{j} - δ_{i})],

\begin{array}{l} Δ I (r) = E_{1} E_{3} e_{1} \cdot e_{3} \cos [2 π ((3 / a) i - (1 / b) j) (x + y) + (δ_{3} - δ_{1})] \\ + E_{1} E_{5} e_{1} \cdot e_{5} \cos [2 π ((3 / a) i + (1 / b) j) (x + y) + (δ_{5} - δ_{1})] \\ + E_{1} E_{4} e_{1} \cdot e_{4} \cos [2 π ((4 / a) i + 0 j) (x + y) + (δ_{4} - δ_{1})] \\ + E_{3} E_{5} e_{3} \cdot e_{5} \cos [2 π ((0 i + (2 / b) j) (x + y) + (δ_{5} - δ_{3})] \\ + E_{3} E_{4} e_{3} \cdot e_{4} \cos [2 π ((1 / a) i + (1 / b) j) (x + y) + (δ_{4} - δ_{3})] \\ + E_{5} E_{4} e_{5} \cdot e_{4} \cos [2 π ((1 / a) i - (1 / b) j) (x + y) + (δ_{4} - δ_{5})], \end{array}

\begin{array}{l} Δ I (r e l a t e d t o b e a m 4) = E_{1} E_{4} e_{1} \cdot e_{4} \cos [2 π ((4 / a) i + 0 j) (x + y) - m π] \\ + E_{3} E_{4} e_{3} \cdot e_{4} \cos [2 π ((1 / a) i + (1 / b) j) (x + y) - m π] \\ + E_{5} E_{4} e_{5} \cdot e_{4} \cos [2 π ((1 / a) i - (1 / b) j) (x + y) - m π] \\ = E_{1} E_{4} e_{1} \cdot e_{4} \cos [2 π ((4 / a) i + 0 j) (x + y + m (- \frac{1}{8} a \pm \frac{3}{8} b))] \\ + E_{3} E_{4} e_{3} \cdot e_{4} \cos [2 π ((1 / a) i + (1 / b) j) (x + y + m (- \frac{1}{8} a - \frac{3}{8} b))] \\ + E_{5} E_{4} e_{5} \cdot e_{4} \cos [2 π ((1 / a) i - (1 / b) j) (x + y + m (- \frac{1}{8} a + \frac{3}{8} b))], \end{array}