Abstract

Spatially-variant photonic crystals (SVPCs), in which the orientation of the unit cell changes as a function of position, are shown to be capable of abruptly controlling light beams using just low index materials and can be made to have high polarization selectivity. Multi-photon direct laser writing in the photo-polymer SU-8 was used to fabricate three-dimensional SVPCs that direct the flow of light around a 90 degree bend. The lattice spacing and fill factor were maintained nearly constant throughout the structure. The SVPCs were characterized at a wavelength of 2.94 μm by scanning the faces with optical fibers and the results were compared to electromagnetic simulations. The lattices were shown to direct infrared light of one polarization through sharp bends while the other polarization propagated straight through the SVPC. This work introduces a new scheme for controlling light that should be useful for integrated photonics.

© 2014 Optical Society of America

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2014 (1)

O. Miţă, C.-G. Bostan, and P. Şchiopu, “Structureless interconnects for photonic integrated circuits,” U. Politeh. Buch. Ser. A 76(1), 205–214 (2014).

2013 (5)

W. Shin, W. S. Cai, P. B. Catrysse, G. Veronis, M. L. Brongersma, and S. H. Fan, “Broadband sharp 90-degree bends and T-splitters in plasmonic coaxial waveguides,” Nano Lett. 13(10), 4753–4758 (2013).
[Crossref] [PubMed]

R. C. Rumpf, J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, “3D printed lattices with spatially variant self-collimation,” Prog. Electromagnetics Res. 139, 1–14 (2013).
[Crossref]

R. Wollhofen, J. Katzmann, C. Hrelescu, J. Jacak, and T. A. Klar, “120 nm resolution and 55 nm structure size in STED-lithography,” Opt. Express 21(9), 10831–10840 (2013).
[Crossref] [PubMed]

B. B. Oner, M. Turduev, and H. Kurt, “High-efficiency beam bending using graded photonic crystals,” Opt. Lett. 38(10), 1688–1690 (2013).
[Crossref] [PubMed]

R. C. Rumpf and J. J. Pazos, “Optimization of planar self-collimating photonic crystals,” J. Opt. Soc. Am. A 30(7), 1297–1304 (2013).
[Crossref] [PubMed]

2012 (10)

K. V. Do, X. Le Roux, D. Marris-Morini, L. Vivien, and E. Cassan, “Experimental demonstration of light bending at optical frequencies using a non-homogenizable graded photonic crystal,” Opt. Express 20(4), 4776–4783 (2012).
[Crossref] [PubMed]

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

H. E. Williams, Z. Luo, and S. M. Kuebler, “Effect of refractive index mismatch on multi-photon direct laser writing,” Opt. Express 20(22), 25030–25040 (2012).
[Crossref] [PubMed]

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat Commun 3, 1217 (2012).
[Crossref] [PubMed]

R. C. Rumpf, “Simple implementation of arbitrarily shaped total-field/scattered-field regions in finite-difference frequency-domain,” Prog. Electromagnetics Res. 36, 221–248 (2012).
[Crossref]

Y. Liu and X. Zhang, “Recent advances in transformation optics,” Nanoscale 4(17), 5277–5292 (2012).
[Crossref] [PubMed]

S. Hayashi and T. Okamoto, “Plasmonics: visit the past to know the future,” J. Phys. D Appl. Phys. 45(43), 433001 (2012).
[Crossref]

K. L. Tsakmakidis and O. Hess, “Extreme control of light in metamaterials: Complete and loss-free stopping of light,” Physica B 407(20), 4066–4069 (2012).
[Crossref]

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (6)

D. H. Spadoti, L. H. Gabrielli, C. B. Poitras, and M. Lipson, “Focusing light in a curved-space,” Opt. Express 18(3), 3181–3186 (2010).
[Crossref] [PubMed]

D. J. Dikken, M. Spasenović, E. Verhagen, D. van Oosten, and L. K. Kuipers, “Characterization of bending losses for curved plasmonic nanowire waveguides,” Opt. Express 18(15), 16112–16119 (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]

W. S. Cai, W. Shin, S. H. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater. 22(45), 5120–5124 (2010).
[Crossref] [PubMed]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

D.-H. Kwon and D. H. Werner, “Transformation Electromagnetics: an overview of the theory and applications,” IEEE Trans. Antenn. Propag. 52(1), 24–46 (2010).
[Crossref]

2009 (1)

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324(5929), 910–913 (2009).
[Crossref] [PubMed]

2008 (5)

D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

S. Keller, G. Blagoi, M. Lillemose, D. Haefliger, and A. Boisen, “Processing of thin SU-8 films,” J. Micromech. Microeng. 18(12), 125020 (2008).
[Crossref]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[Crossref]

Y. Y. Li, M. Y. Li, P. F. Gu, Z. R. Zheng, and X. Liu, “Graded wavelike two-dimensional photonic crystal made of thin films,” Appl. Opt. 47(13), C70–C74 (2008).
[Crossref] [PubMed]

D. Gao, Z. Zhou, and D. S. Citrin, “Self-collimated waveguide bends and partial bandgap reflection of photonic crystals with parallelogram lattice,” J. Opt. Soc. Am. A 25(3), 791–795 (2008).
[Crossref] [PubMed]

2007 (2)

Q. Wang, G. Farrell, P. F. Wang, G. Rajan, and T. Freir, “Design of integrated wavelength monitor based on a Y-branch with an S-bend waveguide,” Sens. Actuator A-Phys. 134(2), 405–409 (2007).
[Crossref]

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

2005 (3)

2002 (1)

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quant. 8(6), 1246–1257 (2002).
[Crossref]

1969 (1)

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48(7), 2103–2132 (1969).
[Crossref]

Akmansoy, E.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[Crossref]

Blagoi, G.

S. Keller, G. Blagoi, M. Lillemose, D. Haefliger, and A. Boisen, “Processing of thin SU-8 films,” J. Micromech. Microeng. 18(12), 125020 (2008).
[Crossref]

Boisen, A.

S. Keller, G. Blagoi, M. Lillemose, D. Haefliger, and A. Boisen, “Processing of thin SU-8 films,” J. Micromech. Microeng. 18(12), 125020 (2008).
[Crossref]

Bostan, C.-G.

O. Miţă, C.-G. Bostan, and P. Şchiopu, “Structureless interconnects for photonic integrated circuits,” U. Politeh. Buch. Ser. A 76(1), 205–214 (2014).

Brongersma, M. L.

W. Shin, W. S. Cai, P. B. Catrysse, G. Veronis, M. L. Brongersma, and S. H. Fan, “Broadband sharp 90-degree bends and T-splitters in plasmonic coaxial waveguides,” Nano Lett. 13(10), 4753–4758 (2013).
[Crossref] [PubMed]

W. S. Cai, W. Shin, S. H. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater. 22(45), 5120–5124 (2010).
[Crossref] [PubMed]

Bückmann, T.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Caer, C.

Cai, W. S.

W. Shin, W. S. Cai, P. B. Catrysse, G. Veronis, M. L. Brongersma, and S. H. Fan, “Broadband sharp 90-degree bends and T-splitters in plasmonic coaxial waveguides,” Nano Lett. 13(10), 4753–4758 (2013).
[Crossref] [PubMed]

W. S. Cai, W. Shin, S. H. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater. 22(45), 5120–5124 (2010).
[Crossref] [PubMed]

Cassagne, D.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[Crossref]

E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. 30(17), 2278–2280 (2005).
[Crossref] [PubMed]

Cassan, E.

Catrysse, P. B.

W. Shin, W. S. Cai, P. B. Catrysse, G. Veronis, M. L. Brongersma, and S. H. Fan, “Broadband sharp 90-degree bends and T-splitters in plasmonic coaxial waveguides,” Nano Lett. 13(10), 4753–4758 (2013).
[Crossref] [PubMed]

Centeno, E.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[Crossref]

E. Centeno and D. Cassagne, “Graded photonic crystals,” Opt. Lett. 30(17), 2278–2280 (2005).
[Crossref] [PubMed]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Chen, C. H.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Chen, H.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Citrin, D. S.

Dikken, D. J.

Do, K. V.

Eberl, C.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Etrich, C.

Fan, S. H.

W. Shin, W. S. Cai, P. B. Catrysse, G. Veronis, M. L. Brongersma, and S. H. Fan, “Broadband sharp 90-degree bends and T-splitters in plasmonic coaxial waveguides,” Nano Lett. 13(10), 4753–4758 (2013).
[Crossref] [PubMed]

W. S. Cai, W. Shin, S. H. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater. 22(45), 5120–5124 (2010).
[Crossref] [PubMed]

Farrell, G.

Q. Wang, G. Farrell, P. F. Wang, G. Rajan, and T. Freir, “Design of integrated wavelength monitor based on a Y-branch with an S-bend waveguide,” Sens. Actuator A-Phys. 134(2), 405–409 (2007).
[Crossref]

Fourkas, J. T.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324(5929), 910–913 (2009).
[Crossref] [PubMed]

Freir, T.

Q. Wang, G. Farrell, P. F. Wang, G. Rajan, and T. Freir, “Design of integrated wavelength monitor based on a Y-branch with an S-bend waveguide,” Sens. Actuator A-Phys. 134(2), 405–409 (2007).
[Crossref]

Frölich, A.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Gabrielli, L. H.

Gajic, R.

Gao, D.

Garcia, C. R.

R. C. Rumpf, J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, “3D printed lattices with spatially variant self-collimation,” Prog. Electromagnetics Res. 139, 1–14 (2013).
[Crossref]

Gattass, R. R.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324(5929), 910–913 (2009).
[Crossref] [PubMed]

Gershgoren, E.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324(5929), 910–913 (2009).
[Crossref] [PubMed]

Gramotnev, D. K.

Gu, P. F.

Haefliger, D.

S. Keller, G. Blagoi, M. Lillemose, D. Haefliger, and A. Boisen, “Processing of thin SU-8 films,” J. Micromech. Microeng. 18(12), 125020 (2008).
[Crossref]

Hamm, J. M.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Hayashi, S.

S. Hayashi and T. Okamoto, “Plasmonics: visit the past to know the future,” J. Phys. D Appl. Phys. 45(43), 433001 (2012).
[Crossref]

Hess, O.

K. L. Tsakmakidis and O. Hess, “Extreme control of light in metamaterials: Complete and loss-free stopping of light,” Physica B 407(20), 4066–4069 (2012).
[Crossref]

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Hingerl, K.

Hrelescu, C.

Hwang, H.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324(5929), 910–913 (2009).
[Crossref] [PubMed]

Iliew, R.

Isic, G.

Jacak, J.

Johnson, S. G.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat Commun 3, 1217 (2012).
[Crossref] [PubMed]

Kadic, M.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Kaschke, J.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Katzmann, J.

Keller, S.

S. Keller, G. Blagoi, M. Lillemose, D. Haefliger, and A. Boisen, “Processing of thin SU-8 films,” J. Micromech. Microeng. 18(12), 125020 (2008).
[Crossref]

Kennerknecht, T.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Klar, T. A.

Kuebler, S. M.

Kuipers, L. K.

Kurt, H.

Kwon, D.-H.

D.-H. Kwon and D. H. Werner, “Transformation Electromagnetics: an overview of the theory and applications,” IEEE Trans. Antenn. Propag. 52(1), 24–46 (2010).
[Crossref]

D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

Le Roux, X.

Lederer, F.

Li, L. J.

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324(5929), 910–913 (2009).
[Crossref] [PubMed]

Li, M. Y.

Li, Y. Y.

Lillemose, M.

S. Keller, G. Blagoi, M. Lillemose, D. Haefliger, and A. Boisen, “Processing of thin SU-8 films,” J. Micromech. Microeng. 18(12), 125020 (2008).
[Crossref]

Lipson, M.

Liu, D.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat Commun 3, 1217 (2012).
[Crossref] [PubMed]

Liu, X.

Liu, Y.

Y. Liu and X. Zhang, “Recent advances in transformation optics,” Nanoscale 4(17), 5277–5292 (2012).
[Crossref] [PubMed]

Loncar, M.

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quant. 8(6), 1246–1257 (2002).
[Crossref]

Lourtioz, J. M.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[Crossref]

Luo, Z.

Maier, S. A.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Marcatili, E. A. J.

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48(7), 2103–2132 (1969).
[Crossref]

Marris-Morini, D.

Martin, R.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Miao, B. L.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Mita, O.

O. Miţă, C.-G. Bostan, and P. Şchiopu, “Structureless interconnects for photonic integrated circuits,” U. Politeh. Buch. Ser. A 76(1), 205–214 (2014).

Murakowski, J.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Ochoa, L.

R. C. Rumpf, J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, “3D printed lattices with spatially variant self-collimation,” Prog. Electromagnetics Res. 139, 1–14 (2013).
[Crossref]

Okamoto, T.

S. Hayashi and T. Okamoto, “Plasmonics: visit the past to know the future,” J. Phys. D Appl. Phys. 45(43), 433001 (2012).
[Crossref]

Oner, B. B.

Oulton, R. F.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Pazos, J.

R. C. Rumpf, J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, “3D printed lattices with spatially variant self-collimation,” Prog. Electromagnetics Res. 139, 1–14 (2013).
[Crossref]

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

Pazos, J. J.

Pendry, J. B.

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Pile, D. F.

Poitras, C. B.

Prather, D. W.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Rajan, G.

Q. Wang, G. Farrell, P. F. Wang, G. Rajan, and T. Freir, “Design of integrated wavelength monitor based on a Y-branch with an S-bend waveguide,” Sens. Actuator A-Phys. 134(2), 405–409 (2007).
[Crossref]

Rumpf, R. C.

R. C. Rumpf, J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, “3D printed lattices with spatially variant self-collimation,” Prog. Electromagnetics Res. 139, 1–14 (2013).
[Crossref]

R. C. Rumpf and J. J. Pazos, “Optimization of planar self-collimating photonic crystals,” J. Opt. Soc. Am. A 30(7), 1297–1304 (2013).
[Crossref] [PubMed]

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

R. C. Rumpf, “Simple implementation of arbitrarily shaped total-field/scattered-field regions in finite-difference frequency-domain,” Prog. Electromagnetics Res. 36, 221–248 (2012).
[Crossref]

Scherer, A.

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quant. 8(6), 1246–1257 (2002).
[Crossref]

Schiopu, P.

O. Miţă, C.-G. Bostan, and P. Şchiopu, “Structureless interconnects for photonic integrated circuits,” U. Politeh. Buch. Ser. A 76(1), 205–214 (2014).

Schneider, G. J.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Sharkawy, A.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Sheng, P.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

Shi, S. Y.

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Shin, W.

W. Shin, W. S. Cai, P. B. Catrysse, G. Veronis, M. L. Brongersma, and S. H. Fan, “Broadband sharp 90-degree bends and T-splitters in plasmonic coaxial waveguides,” Nano Lett. 13(10), 4753–4758 (2013).
[Crossref] [PubMed]

W. S. Cai, W. Shin, S. H. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater. 22(45), 5120–5124 (2010).
[Crossref] [PubMed]

Shur, M.

M. Shur, “Terahertz technology: devices and applications,” Proceedings of the 35th European Solid-State Device Research Conference (Grenoble, France, 2005), pp. 13–25.

Spadoti, D. H.

Spasenovic, M.

Stenger, N.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Thiel, M.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Tsakmakidis, K. L.

K. L. Tsakmakidis and O. Hess, “Extreme control of light in metamaterials: Complete and loss-free stopping of light,” Physica B 407(20), 4066–4069 (2012).
[Crossref]

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

Turduev, M.

van Oosten, D.

Vasic, B.

Verhagen, E.

Veronis, G.

W. Shin, W. S. Cai, P. B. Catrysse, G. Veronis, M. L. Brongersma, and S. H. Fan, “Broadband sharp 90-degree bends and T-splitters in plasmonic coaxial waveguides,” Nano Lett. 13(10), 4753–4758 (2013).
[Crossref] [PubMed]

Vivien, L.

Vynck, K.

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[Crossref]

Wang, P. F.

Q. Wang, G. Farrell, P. F. Wang, G. Rajan, and T. Freir, “Design of integrated wavelength monitor based on a Y-branch with an S-bend waveguide,” Sens. Actuator A-Phys. 134(2), 405–409 (2007).
[Crossref]

Wang, Q.

Q. Wang, G. Farrell, P. F. Wang, G. Rajan, and T. Freir, “Design of integrated wavelength monitor based on a Y-branch with an S-bend waveguide,” Sens. Actuator A-Phys. 134(2), 405–409 (2007).
[Crossref]

Wegener, M.

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Werner, D. H.

D.-H. Kwon and D. H. Werner, “Transformation Electromagnetics: an overview of the theory and applications,” IEEE Trans. Antenn. Propag. 52(1), 24–46 (2010).
[Crossref]

D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

Wicker, R.

R. C. Rumpf, J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, “3D printed lattices with spatially variant self-collimation,” Prog. Electromagnetics Res. 139, 1–14 (2013).
[Crossref]

Williams, H. E.

Witzens, J.

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quant. 8(6), 1246–1257 (2002).
[Crossref]

Wollhofen, R.

Zhang, X.

Y. Liu and X. Zhang, “Recent advances in transformation optics,” Nanoscale 4(17), 5277–5292 (2012).
[Crossref] [PubMed]

Zheng, Z. R.

Zhou, Z.

Adv. Mater. (2)

W. S. Cai, W. Shin, S. H. Fan, and M. L. Brongersma, “Elements for plasmonic nanocircuits with three-dimensional slot waveguides,” Adv. Mater. 22(45), 5120–5124 (2010).
[Crossref] [PubMed]

T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. 24(20), 2710–2714 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J. M. Lourtioz, “Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[Crossref]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, “Bends in optical dielectric guides,” Bell Syst. Tech. J. 48(7), 2103–2132 (1969).
[Crossref]

IEEE J. Sel. Top. Quant. (1)

J. Witzens, M. Lončar, and A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quant. 8(6), 1246–1257 (2002).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

D.-H. Kwon and D. H. Werner, “Transformation Electromagnetics: an overview of the theory and applications,” IEEE Trans. Antenn. Propag. 52(1), 24–46 (2010).
[Crossref]

J. Lightwave Technol. (1)

J. Micromech. Microeng. (1)

S. Keller, G. Blagoi, M. Lillemose, D. Haefliger, and A. Boisen, “Processing of thin SU-8 films,” J. Micromech. Microeng. 18(12), 125020 (2008).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Phys. D Appl. Phys. (2)

S. Hayashi and T. Okamoto, “Plasmonics: visit the past to know the future,” J. Phys. D Appl. Phys. 45(43), 433001 (2012).
[Crossref]

D. W. Prather, S. Y. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. H. Chen, B. L. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007).
[Crossref]

Nano Lett. (1)

W. Shin, W. S. Cai, P. B. Catrysse, G. Veronis, M. L. Brongersma, and S. H. Fan, “Broadband sharp 90-degree bends and T-splitters in plasmonic coaxial waveguides,” Nano Lett. 13(10), 4753–4758 (2013).
[Crossref] [PubMed]

Nanoscale (1)

Y. Liu and X. Zhang, “Recent advances in transformation optics,” Nanoscale 4(17), 5277–5292 (2012).
[Crossref] [PubMed]

Nat Commun (1)

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat Commun 3, 1217 (2012).
[Crossref] [PubMed]

Nat. Mater. (2)

O. Hess, J. B. Pendry, S. A. Maier, R. F. Oulton, J. M. Hamm, and K. L. Tsakmakidis, “Active nanoplasmonic metamaterials,” Nat. Mater. 11(7), 573–584 (2012).
[Crossref] [PubMed]

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9(5), 387–396 (2010).
[Crossref] [PubMed]

New J. Phys. (1)

D.-H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

Opt. Express (9)

H. E. Williams, Z. Luo, and S. M. Kuebler, “Effect of refractive index mismatch on multi-photon direct laser writing,” Opt. Express 20(22), 25030–25040 (2012).
[Crossref] [PubMed]

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

D. J. Dikken, M. Spasenović, E. Verhagen, D. van Oosten, and L. K. Kuipers, “Characterization of bending losses for curved plasmonic nanowire waveguides,” Opt. Express 18(15), 16112–16119 (2010).
[Crossref] [PubMed]

R. Wollhofen, J. Katzmann, C. Hrelescu, J. Jacak, and T. A. Klar, “120 nm resolution and 55 nm structure size in STED-lithography,” Opt. Express 21(9), 10831–10840 (2013).
[Crossref] [PubMed]

L. H. Gabrielli and M. Lipson, “Integrated Luneburg lens via ultra-strong index gradient on silicon,” Opt. Express 19(21), 20122–20127 (2011).
[Crossref] [PubMed]

D. H. Spadoti, L. H. Gabrielli, C. B. Poitras, and M. Lipson, “Focusing light in a curved-space,” Opt. Express 18(3), 3181–3186 (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]

K. V. Do, X. Le Roux, D. Marris-Morini, L. Vivien, and E. Cassan, “Experimental demonstration of light bending at optical frequencies using a non-homogenizable graded photonic crystal,” Opt. Express 20(4), 4776–4783 (2012).
[Crossref] [PubMed]

R. Iliew, C. Etrich, and F. Lederer, “Self-collimation of light in three-dimensional photonic crystals,” Opt. Express 13(18), 7076–7085 (2005).
[Crossref] [PubMed]

Opt. Lett. (3)

Physica B (1)

K. L. Tsakmakidis and O. Hess, “Extreme control of light in metamaterials: Complete and loss-free stopping of light,” Physica B 407(20), 4066–4069 (2012).
[Crossref]

Prog. Electromagnetics Res. (2)

R. C. Rumpf, J. Pazos, C. R. Garcia, L. Ochoa, and R. Wicker, “3D printed lattices with spatially variant self-collimation,” Prog. Electromagnetics Res. 139, 1–14 (2013).
[Crossref]

R. C. Rumpf, “Simple implementation of arbitrarily shaped total-field/scattered-field regions in finite-difference frequency-domain,” Prog. Electromagnetics Res. 36, 221–248 (2012).
[Crossref]

Science (1)

L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324(5929), 910–913 (2009).
[Crossref] [PubMed]

Sens. Actuator A-Phys. (1)

Q. Wang, G. Farrell, P. F. Wang, G. Rajan, and T. Freir, “Design of integrated wavelength monitor based on a Y-branch with an S-bend waveguide,” Sens. Actuator A-Phys. 134(2), 405–409 (2007).
[Crossref]

U. Politeh. Buch. Ser. A (1)

O. Miţă, C.-G. Bostan, and P. Şchiopu, “Structureless interconnects for photonic integrated circuits,” U. Politeh. Buch. Ser. A 76(1), 205–214 (2014).

Other (4)

O. Vanbésien and E. Centeno, Dispersion Engineering for Integrated Nanophotonics (ISTE Ltd., 2014).

M. L. Brongersma and P. G. Kik, eds., Surface Plasmon Nanophotonics, Springer Series in Optical Sciences (Springer Verlag, 2007), Vol. 131.

S. M. Kuebler and M. Rumi, “Nonlinear optics–applications: three-dimensional microfabrication,” in Encyclopedia of Modern Optics, R. D. Guenther, D. G. Steel, and L. Bayvel, eds. (Elsevier, 2004), pp. 189–206.

M. Shur, “Terahertz technology: devices and applications,” Proceedings of the 35th European Solid-State Device Research Conference (Grenoble, France, 2005), pp. 13–25.

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Figures (10)

Fig. 1
Fig. 1

False-color scanning electron microscopy (SEM) image of a spatially-variant photonic crystal (SVPC, depicted in yellow) having a fill factor of 53%, for which the orientation of adjacent unit cells is progressively rotated to direct the flow of light through a 90° turn (red). The SVPC is supported above the substrate by a pedestal (green). The blue ribbons are the experimentally measured relative intensity exiting each face of the SVPC when an optic fiber introduced light having λ0 = 2.94 μm onto the lattice. The data show that light was directed through a turn with radius Rbend = 6.4λ0. The SVPC was fabricated by multi-photon direct laser writing (DLW) in SU-8, a cross-linkable epoxide.

Fig. 2
Fig. 2

Plot of refractive index n and extinction coefficient κ obtained from ellipsometry measurements of a cross-linked 1.6 µm thick SU-8 film using VASE and IR-VASE instruments (J.A. Woollam). The values used to generate this plot are provided in Table 2.

Fig. 3
Fig. 3

Illustration of key steps in the process used to design the SVPC lattice. (a) Top- and (b) perspective-views and (c) isofrequency contours of the unit cell produced by modelling DLW exposure and acid diffusion. (d) Perspective view of the SVPC lattice. (e) Centroids of the lattice in one xy-plane and (f) the corresponding fabrication plan for DLW of the same.

Fig. 4
Fig. 4

Optical transmission microscopy images of SVPCs after fabrication by DLW. (a) An SVPC scaled to have a = 5.75 μm (base area of 125 μm × 125 μm) and fabricated without a pedestal. (b) An SVPC scaled for a = 2.0 μm (base area of 40 µm × 40 µm) and fabricated atop of 110 µm tall pedestal.

Fig. 5
Fig. 5

Apparatus used to characterize optical performance of the SVPCs. The objects are not depicted to scale; the SVPC and optical fibers in particular are drawn large for clarity. The “source fiber” introduces infrared light onto the SVPC. The remaining output fibers collect light emanating from the other SVPC faces and direct it to detectors for measurement. The “bent beam” face is that from which light emerges when directed through the 90° bend, whereas light collected at the “straight through” face is not self-collimated through the turn. The monitor shows a microscope image from an actual measurement.

Fig. 6
Fig. 6

2D model used for simulating the SVPCs that was generated from the 3D lattice using the effective index method.

Fig. 7
Fig. 7

False-color SEM images of an SVPC with a fill factor of 42%. The structure is viewed (a) from a perspective angle, (b & c) top-down, and (d & e) looking into the side face where the source beam enters during optical characterization.

Fig. 8
Fig. 8

(a - c) Top-view SEM images of SVPCs having the fill factors indicated and (d - f) simulations of the intensity of vertically-polarized light propagating within them. (g - i) Experimentally measured beam-bending efficiency of SVPCs versus fill factor. The bending efficiency is quantified as (g) the ratio of the peak-intensities for the bent- versus straight-through beams; (h) ratio of peak-intensities for the bent- versus source beams; and (i) the ratio of integrated power in the bent- and source beams.

Fig. 9
Fig. 9

Horizontal line-scans (blue traces) showing the relative intensity of light at λ0 = 2.94 μm at the input and output faces of an SVPC (top-view SEM image) with a fill factor of 44%. This SVPC bends light out of the straight-through path toward the bent-beam output face with a peak-to-peak ratio of 8.7.

Fig. 10
Fig. 10

Polarization dependence of beam bending for a 53% fill factor SVPCs. ( Left ) Experimental line-scans of the intensity for vertically or horizontally polarized light that is bent through the turn or passes straight through the SVPC. ( Right ) Simulations of beam bending in the same SVPC.

Tables (2)

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Table 2 Values of ordinary refractive index (n) and extinction coefficient (κ) versus vacuum wavelength (λ0) obtained from ellipsometry measurements of a cross-linked 1.6 µm thick SU-8 film using VASE and IR-VASE instruments (W. A. Woollam), as plotted in Fig. 2.

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Table 1 Comparison of approaches for bending a beam through a 90 degree turn or greater. Each entry includes the bend radius Rbend divided by the operating wavelength λ0 and the refractive index contrast Δn of the materials used to create the device. The performance metric (Rbend/λ0) × Δn is calculated to aid comparison between approaches.

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