Abstract

Cancellation of optical diffraction is an intriguing phenomenon enabling optical fields to preserve their transverse intensity profiles upon propagation. In this work, we introduce a metamaterial design that exhibits this phenomenon for three-dimensional optical beams. As an advantage over other diffraction-compensating materials, our metamaterial is impedance-matched to glass, which suppresses optical reflection at the glass-metamaterial interface. The material is designed for beams formed by TM-polarized plane-wave components. We show, however, that unpolarized optical images with arbitrary shapes can be transferred over remarkable distances in the material without distortion. We foresee multiple applications of our results in integrated optics and optical imaging.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (1)

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
[Crossref]

2015 (2)

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

V. Kivijärvi, M. Nyman, A. Karrila, P. Grahn, A. Shevchenko, and M. Kaivola, “Interaction of optical beams with metamaterials,” New J. Phys. 17(6), 063019 (2015).
[Crossref]

2014 (2)

A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophotonics 8(1), 083074 (2014).
[Crossref]

S. Karbasi, R. Frazier, K. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref] [PubMed]

2013 (3)

P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(6432), 113044 (2013).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471 (2013).
[Crossref] [PubMed]

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

2012 (2)

J. Arlandis, E. Centero, R. Polles, A. Moreau, and J. Campos, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

2011 (2)

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

Y. Chuang and T. Suleski, “Photonic crystals for broadband, omnidirectional self-collimation,” J. Opt. 13(3), 035103 (2011).
[Crossref]

2010 (5)

W. Park, “Controlling the flow of light with silicon nanostructures,” Laser Phys. Lett. 7(2), 93–103 (2010).

B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using three-dimensional metamaterials nanolens,” Appl. Phys. Lett. 96(2), 023114 (2010).
[Crossref]

Y. Chuang and T. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12(3), 035102 (2010).
[Crossref]

N. Yogesh and V. Subramanian, “Analysis of self-collimation based cavity resonator formed by photonic crystal,” Prog. Electromagn. Res. M 12, 115–130 (2010).
[Crossref]

T. Paul, C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced optical metamaterials,” Adv. Mater. 22(21), 2354–2357 (2010).
[Crossref] [PubMed]

2009 (1)

T. Paul, C. Rockstuhl, C. Menzel, and F. Lederer, “Anomalous refraction, diffraction, and imaging in metamaterials,” Phys. Rev. B 79(11), 115430 (2009).
[Crossref]

2008 (5)

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
[Crossref]

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystals,” J. Phys. D: Appl. Phys. 41(11), 115108 (2008).
[Crossref]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

K. Kempa, X. Wang, Z. Ren, and M. Naughton, “Discretely guided electromagnetic effective medium,” Appl. Phys. Lett. 92(4), 043114 (2008).
[Crossref]

2007 (3)

T. Muldoon, M. Pierce, D. Nida, M. Williams, A. Gillenwater, and R. Richards-Kortum, “Subcellular-resolution molecular imaging within living tissue by fiber microendoscopy,” Opt. Express 15(25), 16413 (2007).
[Crossref] [PubMed]

D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

A. Matthews, S. Morrison, and Y. Kivshar, “Self-collimation and beam splitting in low-index photonic crystals,” Opt. Commun. 279(2), 313–319 (2007).
[Crossref]

2006 (2)

Z. Lu, S. Shi, J. Murakowski, G. Schneider, C. Schuetz, and D. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96(17), 173902 (2006).
[Crossref] [PubMed]

B. Wood and J. Pendry, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

2005 (2)

2002 (1)

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

1999 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

1998 (1)

H. Ghaemi, Y. Tineke, and T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72(10), 1137–1139 (1998).
[Crossref]

1972 (1)

P. Johnson and R. Christy, “Optical constants of noble metals,” Phys. Rev. B. 6(12), 4370–4379 (1972).
[Crossref]

Arlandis, J.

J. Arlandis, E. Centero, R. Polles, A. Moreau, and J. Campos, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Ballato, J.

S. Karbasi, R. Frazier, K. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref] [PubMed]

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Belov, P.

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Campos, J.

J. Arlandis, E. Centero, R. Polles, A. Moreau, and J. Campos, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Casse, B.

B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using three-dimensional metamaterials nanolens,” Appl. Phys. Lett. 96(2), 023114 (2010).
[Crossref]

Centero, E.

J. Arlandis, E. Centero, R. Polles, A. Moreau, and J. Campos, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Chen, C.

D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

Christy, R.

P. Johnson and R. Christy, “Optical constants of noble metals,” Phys. Rev. B. 6(12), 4370–4379 (1972).
[Crossref]

Chuang, Y.

Y. Chuang and T. Suleski, “Photonic crystals for broadband, omnidirectional self-collimation,” J. Opt. 13(3), 035103 (2011).
[Crossref]

Y. Chuang and T. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12(3), 035102 (2010).
[Crossref]

Cizmar, T.

T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

Dholakia, K.

T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

Etrich, C.

Fan, S.

Frazier, R.

S. Karbasi, R. Frazier, K. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref] [PubMed]

Garcia, C.

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

Ghaemi, H.

H. Ghaemi, Y. Tineke, and T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72(10), 1137–1139 (1998).
[Crossref]

Gillenwater, A.

Gong, Q.

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystals,” J. Phys. D: Appl. Phys. 41(11), 115108 (2008).
[Crossref]

Grahn, P.

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

V. Kivijärvi, M. Nyman, A. Karrila, P. Grahn, A. Shevchenko, and M. Kaivola, “Interaction of optical beams with metamaterials,” New J. Phys. 17(6), 063019 (2015).
[Crossref]

A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophotonics 8(1), 083074 (2014).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(6432), 113044 (2013).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471 (2013).
[Crossref] [PubMed]

Gultepe, E.

B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using three-dimensional metamaterials nanolens,” Appl. Phys. Lett. 96(2), 023114 (2010).
[Crossref]

Hao, Y.

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Hawkins, T.

S. Karbasi, R. Frazier, K. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref] [PubMed]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
[Crossref]

Huang, Y.

B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using three-dimensional metamaterials nanolens,” Appl. Phys. Lett. 96(2), 023114 (2010).
[Crossref]

Ikonen, P.

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Iliew, R.

Jiang, X.

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystals,” J. Phys. D: Appl. Phys. 41(11), 115108 (2008).
[Crossref]

Johnson, P.

P. Johnson and R. Christy, “Optical constants of noble metals,” Phys. Rev. B. 6(12), 4370–4379 (1972).
[Crossref]

Kaivola, M.

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
[Crossref]

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

V. Kivijärvi, M. Nyman, A. Karrila, P. Grahn, A. Shevchenko, and M. Kaivola, “Interaction of optical beams with metamaterials,” New J. Phys. 17(6), 063019 (2015).
[Crossref]

A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophotonics 8(1), 083074 (2014).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(6432), 113044 (2013).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471 (2013).
[Crossref] [PubMed]

Karbasi, S.

S. Karbasi, R. Frazier, K. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref] [PubMed]

Karrila, A.

V. Kivijärvi, M. Nyman, A. Karrila, P. Grahn, A. Shevchenko, and M. Kaivola, “Interaction of optical beams with metamaterials,” New J. Phys. 17(6), 063019 (2015).
[Crossref]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

Kempa, K.

K. Kempa, X. Wang, Z. Ren, and M. Naughton, “Discretely guided electromagnetic effective medium,” Appl. Phys. Lett. 92(4), 043114 (2008).
[Crossref]

Kivijärvi, V.

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
[Crossref]

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

V. Kivijärvi, M. Nyman, A. Karrila, P. Grahn, A. Shevchenko, and M. Kaivola, “Interaction of optical beams with metamaterials,” New J. Phys. 17(6), 063019 (2015).
[Crossref]

Kivshar, Y.

A. Matthews, S. Morrison, and Y. Kivshar, “Self-collimation and beam splitting in low-index photonic crystals,” Opt. Commun. 279(2), 313–319 (2007).
[Crossref]

Koch, K.

S. Karbasi, R. Frazier, K. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref] [PubMed]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

Lalanne, P.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

Lederer, F.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

T. Paul, C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced optical metamaterials,” Adv. Mater. 22(21), 2354–2357 (2010).
[Crossref] [PubMed]

T. Paul, C. Rockstuhl, C. Menzel, and F. Lederer, “Anomalous refraction, diffraction, and imaging in metamaterials,” Phys. Rev. B 79(11), 115430 (2009).
[Crossref]

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
[Crossref]

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]

Lindfors, K.

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Liu, Z.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

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

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B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using three-dimensional metamaterials nanolens,” Appl. Phys. Lett. 96(2), 023114 (2010).
[Crossref]

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Z. Lu, S. Shi, J. Murakowski, G. Schneider, C. Schuetz, and D. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96(17), 173902 (2006).
[Crossref] [PubMed]

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S. Karbasi, R. Frazier, K. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref] [PubMed]

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D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

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A. Matthews, S. Morrison, and Y. Kivshar, “Self-collimation and beam splitting in low-index photonic crystals,” Opt. Commun. 279(2), 313–319 (2007).
[Crossref]

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B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using three-dimensional metamaterials nanolens,” Appl. Phys. Lett. 96(2), 023114 (2010).
[Crossref]

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T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

T. Paul, C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced optical metamaterials,” Adv. Mater. 22(21), 2354–2357 (2010).
[Crossref] [PubMed]

T. Paul, C. Rockstuhl, C. Menzel, and F. Lederer, “Anomalous refraction, diffraction, and imaging in metamaterials,” Phys. Rev. B 79(11), 115430 (2009).
[Crossref]

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
[Crossref]

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D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

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J. Arlandis, E. Centero, R. Polles, A. Moreau, and J. Campos, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

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A. Matthews, S. Morrison, and Y. Kivshar, “Self-collimation and beam splitting in low-index photonic crystals,” Opt. Commun. 279(2), 313–319 (2007).
[Crossref]

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Murakowski, J.

D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

Z. Lu, S. Shi, J. Murakowski, G. Schneider, C. Schuetz, and D. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96(17), 173902 (2006).
[Crossref] [PubMed]

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K. Kempa, X. Wang, Z. Ren, and M. Naughton, “Discretely guided electromagnetic effective medium,” Appl. Phys. Lett. 92(4), 043114 (2008).
[Crossref]

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Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
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[Crossref]

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V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
[Crossref]

V. Kivijärvi, M. Nyman, A. Karrila, P. Grahn, A. Shevchenko, and M. Kaivola, “Interaction of optical beams with metamaterials,” New J. Phys. 17(6), 063019 (2015).
[Crossref]

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

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P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Park, W.

W. Park, “Controlling the flow of light with silicon nanostructures,” Laser Phys. Lett. 7(2), 93–103 (2010).

Paul, T.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

T. Paul, C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced optical metamaterials,” Adv. Mater. 22(21), 2354–2357 (2010).
[Crossref] [PubMed]

T. Paul, C. Rockstuhl, C. Menzel, and F. Lederer, “Anomalous refraction, diffraction, and imaging in metamaterials,” Phys. Rev. B 79(11), 115430 (2009).
[Crossref]

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
[Crossref]

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

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B. Wood and J. Pendry, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

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Polles, R.

J. Arlandis, E. Centero, R. Polles, A. Moreau, and J. Campos, “Mesoscopic self-collimation and slow light in all-positive index layered photonic crystals,” Phys. Rev. Lett. 108(3), 037401 (2012).
[Crossref] [PubMed]

Prather, D.

D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

Z. Lu, S. Shi, J. Murakowski, G. Schneider, C. Schuetz, and D. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96(17), 173902 (2006).
[Crossref] [PubMed]

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K. Kempa, X. Wang, Z. Ren, and M. Naughton, “Discretely guided electromagnetic effective medium,” Appl. Phys. Lett. 92(4), 043114 (2008).
[Crossref]

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Rockstuhl, C.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

T. Paul, C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced optical metamaterials,” Adv. Mater. 22(21), 2354–2357 (2010).
[Crossref] [PubMed]

T. Paul, C. Rockstuhl, C. Menzel, and F. Lederer, “Anomalous refraction, diffraction, and imaging in metamaterials,” Phys. Rev. B 79(11), 115430 (2009).
[Crossref]

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
[Crossref]

Rumpf, R.

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

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

Scherer, A.

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

Schneider, G.

D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

Z. Lu, S. Shi, J. Murakowski, G. Schneider, C. Schuetz, and D. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96(17), 173902 (2006).
[Crossref] [PubMed]

Schuetz, C.

Z. Lu, S. Shi, J. Murakowski, G. Schneider, C. Schuetz, and D. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96(17), 173902 (2006).
[Crossref] [PubMed]

Shao, Y.

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Sharkawy, A.

D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

Shevchenko, A.

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
[Crossref]

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

V. Kivijärvi, M. Nyman, A. Karrila, P. Grahn, A. Shevchenko, and M. Kaivola, “Interaction of optical beams with metamaterials,” New J. Phys. 17(6), 063019 (2015).
[Crossref]

A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophotonics 8(1), 083074 (2014).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(6432), 113044 (2013).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Theoretical description of bifacial optical nanomaterials,” Opt. Express 21(20), 23471 (2013).
[Crossref] [PubMed]

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D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

Z. Lu, S. Shi, J. Murakowski, G. Schneider, C. Schuetz, and D. Prather, “Experimental demonstration of self-collimation inside a three-dimensional photonic crystal,” Phys. Rev. Lett. 96(17), 173902 (2006).
[Crossref] [PubMed]

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Silveirinha, M.

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Simovski, C.

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Smigaj, W.

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

Sridhar, S.

B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using three-dimensional metamaterials nanolens,” Appl. Phys. Lett. 96(2), 023114 (2010).
[Crossref]

Stacy, A.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

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J. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

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N. Yogesh and V. Subramanian, “Analysis of self-collimation based cavity resonator formed by photonic crystal,” Prog. Electromagn. Res. M 12, 115–130 (2010).
[Crossref]

Suleski, T.

Y. Chuang and T. Suleski, “Photonic crystals for broadband, omnidirectional self-collimation,” J. Opt. 13(3), 035103 (2011).
[Crossref]

Y. Chuang and T. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12(3), 035102 (2010).
[Crossref]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

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H. Ghaemi, Y. Tineke, and T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72(10), 1137–1139 (1998).
[Crossref]

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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

Tretyakov, S.

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

Tse, S.

P. Belov, Y. Shao, S. Tse, P. Ikonen, M. Silveirinha, C. Simovski, S. Tretyakov, Y. Hao, and C. Parini, “Transmission of images with subwavelength resolution to distances of several wavelengths in the microwave range,” Phys. Rev. B 77(19), 193108 (2008).
[Crossref]

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H. Ghaemi, Y. Tineke, and T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72(10), 1137–1139 (1998).
[Crossref]

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K. Kempa, X. Wang, Z. Ren, and M. Naughton, “Discretely guided electromagnetic effective medium,” Appl. Phys. Lett. 92(4), 043114 (2008).
[Crossref]

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J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Wicker, R.

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

Williams, M.

Witzens, J.

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

Wood, B.

B. Wood and J. Pendry, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Yogesh, N.

N. Yogesh and V. Subramanian, “Analysis of self-collimation based cavity resonator formed by photonic crystal,” Prog. Electromagn. Res. M 12, 115–130 (2010).
[Crossref]

Zhang, X.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

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D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystals,” J. Phys. D: Appl. Phys. 41(11), 115108 (2008).
[Crossref]

Zhou, C.

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystals,” J. Phys. D: Appl. Phys. 41(11), 115108 (2008).
[Crossref]

Adv. Mater. (1)

T. Paul, C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced optical metamaterials,” Adv. Mater. 22(21), 2354–2357 (2010).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

B. Casse, W. Lu, Y. Huang, E. Gultepe, L. Menon, and S. Sridhar, “Super-resolution imaging using three-dimensional metamaterials nanolens,” Appl. Phys. Lett. 96(2), 023114 (2010).
[Crossref]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999).
[Crossref]

K. Kempa, X. Wang, Z. Ren, and M. Naughton, “Discretely guided electromagnetic effective medium,” Appl. Phys. Lett. 92(4), 043114 (2008).
[Crossref]

H. Ghaemi, Y. Tineke, and T. Wang, “Fiber image guide with subwavelength resolution,” Appl. Phys. Lett. 72(10), 1137–1139 (1998).
[Crossref]

IEEE J. Sel. Topics Quantum Electron. (1)

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

J. Nanophotonics (1)

A. Shevchenko, P. Grahn, and M. Kaivola, “Internally twisted spatially dispersive optical metamaterials,” J. Nanophotonics 8(1), 083074 (2014).
[Crossref]

J. Opt. (3)

Y. Chuang and T. Suleski, “Photonic crystals for broadband, omnidirectional self-collimation,” J. Opt. 13(3), 035103 (2011).
[Crossref]

V. Kivijärvi, M. Nyman, A. Shevchenko, and M. Kaivola, “An optical metamaterial with simultaneously suppressed optical diffraction and surface reflection,” J. Opt. 18(3), 035103 (2016).
[Crossref]

Y. Chuang and T. Suleski, “Complex rhombus lattice photonic crystals for broadband all-angle self-collimation,” J. Opt. 12(3), 035102 (2010).
[Crossref]

J. Phys. D. Appl. Phys. (1)

D. Prather, S. Shi, J. Murakowski, G. Schneider, A. Sharkawy, C. Chen, B. 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]

J. Phys. D: Appl. Phys. (1)

D. Zhao, C. Zhou, Q. Gong, and X. Jiang, “Lasing cavities and ultra-fast switch based on self-collimation of photonic crystals,” J. Phys. D: Appl. Phys. 41(11), 115108 (2008).
[Crossref]

Laser Phys. Lett. (1)

W. Park, “Controlling the flow of light with silicon nanostructures,” Laser Phys. Lett. 7(2), 93–103 (2010).

Nat. Commun. (2)

T. Cizmar and K. Dholakia, “Exploiting multimode waveguides for pure fibre-based imaging,” Nat. Commun. 3, 1027 (2012).
[Crossref] [PubMed]

S. Karbasi, R. Frazier, K. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 3362 (2014).
[Crossref] [PubMed]

New J. Phys. (2)

V. Kivijärvi, M. Nyman, A. Karrila, P. Grahn, A. Shevchenko, and M. Kaivola, “Interaction of optical beams with metamaterials,” New J. Phys. 17(6), 063019 (2015).
[Crossref]

P. Grahn, A. Shevchenko, and M. Kaivola, “Interferometric description of optical metamaterials,” New J. Phys. 15(6432), 113044 (2013).
[Crossref]

Opt. Commun. (1)

A. Matthews, S. Morrison, and Y. Kivshar, “Self-collimation and beam splitting in low-index photonic crystals,” Opt. Commun. 279(2), 313–319 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Appl. (1)

A. Shevchenko, V. Kivijärvi, P. Grahn, M. Kaivola, and K. Lindfors, “Bifacial metasurface with quadrupole optical response,” Phys. Rev. Appl. 4(2), 024019 (2015).
[Crossref]

Phys. Rev. B (5)

C. Menzel, C. Rockstuhl, T. Paul, and F. Lederer, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008).
[Crossref]

T. Paul, C. Menzel, W. Smigaj, C. Rockstuhl, P. Lalanne, and F. Lederer, “Reflection and transmission of light at periodic layered metamaterial films,” Phys. Rev. B 84(11), 115142 (2011).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Diffraction-compensating silver-nanobar metamaterial. The nanobars are 30 nm thick in the x- and y-directions and 130 nm long. They form a tetragonal lattice in glass and suppress optical diffraction for light propagating along the Poynting vector S. The unit-cell dimensions are Λx = Λy = 120 nm and Λz = 200 nm.

Fig. 2
Fig. 2

Refractive index n and normalized impedance Z/Z0, where Z0 is the impedance of glass, plotted in polar coordinates as functions of the plane-wave propagation angle θ for three different metamaterials. The black solid and red dashed curves represent the real and imaginary parts of the quantities, respectively. The imaginary parts are multiplied by factors of 100, ±10 and −1 as shown for each plot separately. The negative factors are chosen, if the quantity in question is negative. The angles unavailable for waves incident from glass are marked by the gray sectors. The parameter values by which the materials in (a), (b) and (c) differ from each other are as follows: (a) Lx = Ly = 30 nm, Λz = 200 nm and λvac = 913 nm, (b) Lx = Ly = 30 nm, Λz = 220 nm and λvac = 883 nm, and (c) Lx = Ly = 40 nm, Λz = 200 nm and λvac = 793 nm.

Fig. 3
Fig. 3

The longitudinal (a) and transverse (b) intensity profiles of a radially polarized hollow optical beam at λvac = 913 nm focused onto the surface of a diffraction-compensating metamaterial (white line). The cross sections in (b) correspond to the coordinates z of 0, 100 μm, 200 μm and 300 μm. The intensity is normalized to its maximum value at z = 0.

Fig. 4
Fig. 4

Propagation of an optical image of letter M in three different diffraction-compensating metamaterials. The z-coordinates of the presented intensity profiles are shown above each profile. The intensity is normalized to its maximum value at z = 0. In (a) and (b), the material corresponds to that in Fig. 2(a) and the image is originally formed by (a) unpolarized and (b) left-handed circularly polarized light. In (c), the material corresponds to that in Fig. 2(b) and the image is originally unpolarized. In (d), the material is as in Fig. 2(c) and the image is unpolarized. The two last pictures of case (d) show the total intensity (It) and the intensity of the y-polarized part of the image (Iy) at the same coordinate z = 50 μm.

Equations (5)

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k z = i Λ z log [ α 2 β ± ( α 2 4 β 2 1 β ) 1 / 2 ] + 2 π m Λ z ,
α = f 2 + f 1 1 ( 1 g 1 g 2 ) ,
β = f 2 / f 1 .
k vac 2 n 2 = k 0 x 2 + k 0 y 2 + k z 2 ,
Z = Z 0 ( k 0 k z k 0 z k ) σ g 2 + [ 1 f 1 exp ( i k z Λ z ) ] g 2 [ 1 f 1 exp ( i k z Λ z ) ] ,

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