Abstract

It is well established that, under certain conditions, imaging systems with either isotropic negative index, or hyperbolic (indefinite) media can achieve super-resolution. However, achieving sub-diffraction limited imaging along with uniform aberration-free magnification can be challenging. In this article, we design, simulate, and evaluate the performance of planar 2D near-field magnifying lenses, based on the transformation-optic design principle. Specifically, we investigate a grid-relaxed transformation, that results in material properties that are more amenable to implementation. We discuss possible design choices in terms of: material properties, achievable resolution enhancement, adverse effect of loss tangent, magnification factor, and other design constraints affecting the imaging performance. We also present imaging performance results for a planar, near-field, 3× magnifier operating on a standard resolution target, based on a rigorous, 3D, electromagnetic simulation. This computational intensive result was achieved using cylindrical harmonic decomposition and the 2.5D electromagnetic simulation technique. Further, we investigate and propose a path to achieve higher magnification factors using cascaded elements.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]
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    [Crossref]

2018 (1)

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

2017 (3)

J. Li, C. Shen, A. Díaz-Rubio, S. Tretyakov, and S. Cummer, “Design and measurement of an acoustic bi-anisotropic metasurface for scattering-free manipulation of the refracted wavefront,” The J. Acoust. Soc. Am. 142, 2549 (2017).
[Crossref]

K. Agarwal, C. Liu, D. Joung, H.-R. Park, S.-H. Oh, and J.-H. Cho, “Three-dimensional anisotropic metamaterials as triaxial optical inclinometers,” Sci. Reports 7, 2680 (2017).
[Crossref]

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

2016 (2)

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

S. Venkatesh and D. Schurig, “Computationally fast EM field propagation through axi-symmetric media using cylindrical harmonic decomposition,” Opt. Express 24, 29246–29268 (2016).
[Crossref] [PubMed]

2014 (1)

J. Sun, N. M. Litchinitser, and J. Zhou, “Indefinite by nature: from ultraviolet to terahertz,” ACS Photonics 1, 293–303 (2014).
[Crossref]

2013 (3)

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. materials 12, 25 (2013).
[Crossref]

V. P. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic metamaterials: New physics behind a classical problem,” Opt. Express 21, 15048–15064 (2013).
[Crossref] [PubMed]

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

2012 (1)

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

2011 (1)

2009 (3)

N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17, 14872–14879 (2009).
[Crossref] [PubMed]

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94, 203108 (2009).
[Crossref]

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. materials 8, 931–934 (2009).
[Crossref] [PubMed]

2008 (5)

X. Ao and C. Chan, “Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials,” Phys. Rev. E 77, 025601 (2008).
[Crossref]

A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. letters 33, 43–45 (2008).
[Crossref]

W. Wang, H. Xing, L. Fang, Y. Liu, J. Ma, L. Lin, C. Wang, and X. Luo, “Far-field imaging device: Planar hyperlens with magnification using multi-layer metamaterial,” Opt. Express 16, 21142–21148 (2008).
[Crossref] [PubMed]

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: A transformation optics approach,” Nano Lett. 8, 4243–4247 (2008).
[Crossref]

D. Schurig, “An aberration-free lens with zero f-number,” New J. Phys. 10, 115034 (2008).
[Crossref]

2007 (3)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. letters 32, 3432–3434 (2007).
[Crossref]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref] [PubMed]

2006 (3)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref] [PubMed]

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

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

2005 (3)

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[Crossref]

V. A. Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Opt. letters 30, 75–77 (2005).
[Crossref]

D. Schurig and D. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys. 7, 162 (2005).
[Crossref]

2004 (2)

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

D. R. Smith, P. Kolinko, and D. Schurig, “Negative refraction in indefinite media,” J. Opt. Soc. Am. B 21, 1032–1043 (2004).
[Crossref]

2003 (2)

S. A. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).
[Crossref]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[Crossref]

2002 (1)

S. A. Ramakrishna, J. Pendry, D. Schurig, D. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[Crossref]

2000 (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Agarwal, K.

K. Agarwal, C. Liu, D. Joung, H.-R. Park, S.-H. Oh, and J.-H. Cho, “Three-dimensional anisotropic metamaterials as triaxial optical inclinometers,” Sci. Reports 7, 2680 (2017).
[Crossref]

Alekseyev, L. V.

Ao, X.

X. Ao and C. Chan, “Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials,” Phys. Rev. E 77, 025601 (2008).
[Crossref]

Bartal, G.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. materials 8, 931–934 (2009).
[Crossref] [PubMed]

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: A transformation optics approach,” Nano Lett. 8, 4243–4247 (2008).
[Crossref]

Beechem, T. E.

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

Belov, P. A.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Byun, M.

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

Campione, S.

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

Chan, C.

X. Ao and C. Chan, “Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials,” Phys. Rev. E 77, 025601 (2008).
[Crossref]

Chang, Y. C.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

Cho, J.-H.

K. Agarwal, C. Liu, D. Joung, H.-R. Park, S.-H. Oh, and J.-H. Cho, “Three-dimensional anisotropic metamaterials as triaxial optical inclinometers,” Sci. Reports 7, 2680 (2017).
[Crossref]

Cummer, S.

J. Li, C. Shen, A. Díaz-Rubio, S. Tretyakov, and S. Cummer, “Design and measurement of an acoustic bi-anisotropic metasurface for scattering-free manipulation of the refracted wavefront,” The J. Acoust. Soc. Am. 142, 2549 (2017).
[Crossref]

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref] [PubMed]

Díaz-Rubio, A.

J. Li, C. Shen, A. Díaz-Rubio, S. Tretyakov, and S. Cummer, “Design and measurement of an acoustic bi-anisotropic metasurface for scattering-free manipulation of the refracted wavefront,” The J. Acoust. Soc. Am. 142, 2549 (2017).
[Crossref]

Drachev, V. P.

Fang, L.

Fedorov, S. V.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Fok, L.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. materials 8, 931–934 (2009).
[Crossref] [PubMed]

Genov, D.

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: A transformation optics approach,” Nano Lett. 8, 4243–4247 (2008).
[Crossref]

Hamm, J.

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

Han, S.

X. Ni, S. Ishii, M. D. Thoreson, V. M. Shalaev, S. Han, S. Lee, and A. V. Kildishev, “Loss-compensated and active hyperbolic metamaterials,” Opt. express 19, 25242–25254 (2011).
[Crossref]

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: A transformation optics approach,” Nano Lett. 8, 4243–4247 (2008).
[Crossref]

Hess, O.

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

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref] [PubMed]

Ishii, S.

Jacob, Z.

Joung, D.

K. Agarwal, C. Liu, D. Joung, H.-R. Park, S.-H. Oh, and J.-H. Cho, “Three-dimensional anisotropic metamaterials as triaxial optical inclinometers,” Sci. Reports 7, 2680 (2017).
[Crossref]

Kildishev, A. V.

Kim, K.

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

Kim, M.

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

Kim, Y.

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

Kivshar, Y. S.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Klem, J. F.

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

Kolinko, P.

Landy, N.

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. materials 12, 25 (2013).
[Crossref]

Landy, N. I.

Lee, D.

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

Lee, H.

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Lee, S.

Li, J.

J. Li, C. Shen, A. Díaz-Rubio, S. Tretyakov, and S. Cummer, “Design and measurement of an acoustic bi-anisotropic metasurface for scattering-free manipulation of the refracted wavefront,” The J. Acoust. Soc. Am. 142, 2549 (2017).
[Crossref]

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. materials 8, 931–934 (2009).
[Crossref] [PubMed]

Lin, L.

Litchinitser, N. M.

J. Sun, N. M. Litchinitser, and J. Zhou, “Indefinite by nature: from ultraviolet to terahertz,” ACS Photonics 1, 293–303 (2014).
[Crossref]

Liu, C.

K. Agarwal, C. Liu, D. Joung, H.-R. Park, S.-H. Oh, and J.-H. Cho, “Three-dimensional anisotropic metamaterials as triaxial optical inclinometers,” Sci. Reports 7, 2680 (2017).
[Crossref]

Liu, C. H.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

Liu, Y.

Liu, Z.

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94, 203108 (2009).
[Crossref]

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: A transformation optics approach,” Nano Lett. 8, 4243–4247 (2008).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Luk, T. S.

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

Luo, X.

Ma, J.

Maier, S. A.

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

Marder, S. R.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

Mock, J.

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[Crossref]

Montaño, I.

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

Narimanov, E.

Narimanov, E. E.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. letters 32, 3432–3434 (2007).
[Crossref]

V. A. Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Opt. letters 30, 75–77 (2005).
[Crossref]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Ni, X.

Norris, T. B.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

Oh, S.-H.

K. Agarwal, C. Liu, D. Joung, H.-R. Park, S.-H. Oh, and J.-H. Cho, “Three-dimensional anisotropic metamaterials as triaxial optical inclinometers,” Sci. Reports 7, 2680 (2017).
[Crossref]

Ok, J. G.

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

Oulton, R. F.

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

Padilla, W. J.

N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express 17, 14872–14879 (2009).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Park, H.-R.

K. Agarwal, C. Liu, D. Joung, H.-R. Park, S.-H. Oh, and J.-H. Cho, “Three-dimensional anisotropic metamaterials as triaxial optical inclinometers,” Sci. Reports 7, 2680 (2017).
[Crossref]

Pendry, J.

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

S. A. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).
[Crossref]

S. A. Ramakrishna, J. Pendry, D. Schurig, D. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[Crossref]

Pendry, J. B.

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

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

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[Crossref]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

Podolskiy, V. A.

Ramakrishna, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[Crossref]

S. A. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).
[Crossref]

S. A. Ramakrishna, J. Pendry, D. Schurig, D. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[Crossref]

Rho, J.

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

Rosanov, N. N.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[Crossref]

Savelev, R. S.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[Crossref]

S. A. Ramakrishna, J. Pendry, D. Schurig, D. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[Crossref]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Schurig, D.

S. Venkatesh and D. Schurig, “Computationally fast EM field propagation through axi-symmetric media using cylindrical harmonic decomposition,” Opt. Express 24, 29246–29268 (2016).
[Crossref] [PubMed]

D. Schurig, “An aberration-free lens with zero f-number,” New J. Phys. 10, 115034 (2008).
[Crossref]

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

D. Schurig and D. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys. 7, 162 (2005).
[Crossref]

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[Crossref]

D. R. Smith, P. Kolinko, and D. Schurig, “Negative refraction in indefinite media,” J. Opt. Soc. Am. B 21, 1032–1043 (2004).
[Crossref]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[Crossref]

S. A. Ramakrishna, J. Pendry, D. Schurig, D. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[Crossref]

Shadrivov, I. V.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Shalaev, V. M.

Shen, C.

J. Li, C. Shen, A. Díaz-Rubio, S. Tretyakov, and S. Cummer, “Design and measurement of an acoustic bi-anisotropic metasurface for scattering-free manipulation of the refracted wavefront,” The J. Acoust. Soc. Am. 142, 2549 (2017).
[Crossref]

Sinclair, M. B.

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

Smith, D.

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[Crossref]

D. Schurig and D. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys. 7, 162 (2005).
[Crossref]

S. A. Ramakrishna, J. Pendry, D. Schurig, D. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[Crossref]

Smith, D. R.

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. materials 12, 25 (2013).
[Crossref]

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

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

D. R. Smith, P. Kolinko, and D. Schurig, “Negative refraction in indefinite media,” J. Opt. Soc. Am. B 21, 1032–1043 (2004).
[Crossref]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[Crossref]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref] [PubMed]

Soni, B. K.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC press, 1998).

Starr, A.

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[Crossref]

Stewart, W.

S. A. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).
[Crossref]

Sukhorukov, A. A.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Sun, J.

J. Sun, N. M. Litchinitser, and J. Zhou, “Indefinite by nature: from ultraviolet to terahertz,” ACS Photonics 1, 293–303 (2014).
[Crossref]

Thompson, J. F.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC press, 1998).

Thoreson, M. D.

Tretyakov, S.

J. Li, C. Shen, A. Díaz-Rubio, S. Tretyakov, and S. Cummer, “Design and measurement of an acoustic bi-anisotropic metasurface for scattering-free manipulation of the refracted wavefront,” The J. Acoust. Soc. Am. 142, 2549 (2017).
[Crossref]

Tsai, D.

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

Tsakmakidis, K.

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

Venkatesh, S.

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Wang, C.

Wang, W.

Weatherill, N. P.

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC press, 1998).

Wiltshire, M.

S. A. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).
[Crossref]

Wiltshire, M. C.

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

Wolf, O.

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

Wood, B.

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

Xing, H.

Xiong, Y.

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94, 203108 (2009).
[Crossref]

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: A transformation optics approach,” Nano Lett. 8, 4243–4247 (2008).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Yin, X.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. materials 8, 931–934 (2009).
[Crossref] [PubMed]

Zhang, S.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

Zhang, X.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. materials 8, 931–934 (2009).
[Crossref] [PubMed]

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94, 203108 (2009).
[Crossref]

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: A transformation optics approach,” Nano Lett. 8, 4243–4247 (2008).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

Zhong, Z.

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

Zhou, J.

J. Sun, N. M. Litchinitser, and J. Zhou, “Indefinite by nature: from ultraviolet to terahertz,” ACS Photonics 1, 293–303 (2014).
[Crossref]

ACS Photonics (1)

J. Sun, N. M. Litchinitser, and J. Zhou, “Indefinite by nature: from ultraviolet to terahertz,” ACS Photonics 1, 293–303 (2014).
[Crossref]

Appl. Phys. Lett. (2)

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94, 203108 (2009).
[Crossref]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[Crossref]

J. Mod. Opt. (2)

S. A. Ramakrishna, J. Pendry, D. Schurig, D. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[Crossref]

S. A. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430 (2003).
[Crossref]

J. Opt. Soc. Am. B (1)

Nano Lett. (1)

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: A transformation optics approach,” Nano Lett. 8, 4243–4247 (2008).
[Crossref]

Nat. Commun. (1)

Y. C. Chang, C. H. Liu, C. H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref] [PubMed]

Nat. Mater. (1)

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

Nat. materials (2)

N. Landy and D. R. Smith, “A full-parameter unidirectional metamaterial cloak for microwaves,” Nat. materials 12, 25 (2013).
[Crossref]

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. materials 8, 931–934 (2009).
[Crossref] [PubMed]

New J. Phys. (2)

D. Schurig and D. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys. 7, 162 (2005).
[Crossref]

D. Schurig, “An aberration-free lens with zero f-number,” New J. Phys. 10, 115034 (2008).
[Crossref]

Opt. Express (5)

Opt. letters (3)

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. letters 32, 3432–3434 (2007).
[Crossref]

V. A. Podolskiy and E. E. Narimanov, “Near-sighted superlens,” Opt. letters 30, 75–77 (2005).
[Crossref]

A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. letters 33, 43–45 (2008).
[Crossref]

Phys. Rev. B (2)

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

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Phys. Rev. E (2)

D. Smith, J. Mock, A. Starr, and D. Schurig, “Gradient index metamaterials,” Phys. Rev. E 71, 036609 (2005).
[Crossref]

X. Ao and C. Chan, “Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials,” Phys. Rev. E 77, 025601 (2008).
[Crossref]

Phys. Rev. Lett. (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Sci. Reports (2)

M. Byun, D. Lee, M. Kim, Y. Kim, K. Kim, J. G. Ok, J. Rho, and H. Lee, “Demonstration of nanoimprinted hyperlens array for high-throughput sub-diffraction imaging,” Sci. Reports 7, 46314 (2017).
[Crossref]

I. Montaño, S. Campione, J. F. Klem, T. E. Beechem, O. Wolf, M. B. Sinclair, and T. S. Luk, “Semiconductor hyperbolic metamaterials at the quantum limit,” Sci. reports 8, 16694 (2018).
[Crossref]

K. Agarwal, C. Liu, D. Joung, H.-R. Park, S.-H. Oh, and J.-H. Cho, “Three-dimensional anisotropic metamaterials as triaxial optical inclinometers,” Sci. Reports 7, 2680 (2017).
[Crossref]

Science (4)

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

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref] [PubMed]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699–1701 (2007).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[Crossref] [PubMed]

The J. Acoust. Soc. Am. (1)

J. Li, C. Shen, A. Díaz-Rubio, S. Tretyakov, and S. Cummer, “Design and measurement of an acoustic bi-anisotropic metasurface for scattering-free manipulation of the refracted wavefront,” The J. Acoust. Soc. Am. 142, 2549 (2017).
[Crossref]

Other (2)

J. F. Thompson, B. K. Soni, and N. P. Weatherill, Handbook of Grid Generation (CRC press, 1998).

COMSOL Multiphysics, RF Module User’s Guide (COMSOL, 2012).

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Figures (13)

Fig. 1
Fig. 1 Shows the hyperbolic dispersion of anisotropic hyperbolic media. Two possible kz components are shown for the same kx component. The z components of k and vg can be of the same or opposite sign.
Fig. 2
Fig. 2 Shows the electric field norm for different configurations. (a & a1). Shows the case of an isotropic free space compensated bilayer. (b & b1; c & c1). Shows the case of isotropic free space compensated multilayer (4 and 8 respectively). The transmission magnitude increases with multi-layering. (d & d1). Shows the case of an anisotropic bilayer configuration and its equivalent limiting case of a multilayer configuration is shown in (e1). All these cases are simulated with two point sources separated by λ/4, with a loss tangent of δ = 0.001 and an overall thickness d = 2λ.
Fig. 3
Fig. 3 (a). Shows the transmission magnitude |τ| as a function of transverse vector kx for different cases along with varying loss tangent. All the cases have an overall thickness of d = 2λ. (b). Resolution enhancement limit calculated at |τ| = 0.1 = −20 dB as a function of loss tangent for different material property and configurations (overall thickness d = 2λ).
Fig. 4
Fig. 4 Harmonic grid relaxation technique for NFM. (a) Shows the 2D cylindrical coordinate transformation (ρ, ϕ, z) ⇒ (ρ′, ϕ, z′) of an anisotropic bilayer to a magnifier with a magnification factor of M = 3. The red line demarcates between the two layers which have different material property tensor. The brown curve in the transformed space is the Neumann-Dirichlet boundary (slipping boundary). Blue and green lines indicate the Dirichlet boundaries. (b) Shows a highlighted cell along with a central grid point and its nearest neighbors which are used in grid relaxation approach. An example grid cell is shown in orange box. (c) & (d) Show the aspect ratio distributions of cells before and after grid relaxation of the transformed space. (e) Shows the absolute principle components of the material property tensors represented in three color channels, namely: red, green and blue. The absolute principle values lie between 0.33 to 1.4 in the transformed-grid-relaxed domain. Different levels of gray indicate that the three absolute principle values are equal to one another and deviation from gray scale indicates that the green component has deviated from red and blue components. The principle directions are overlaid in the same figure. The green channel direction is out of plane and represents the ϕ-component which is untransformed.
Fig. 5
Fig. 5 The anisotropy and orthogonality metric distribution (a & b respectively)in the transformed space before grid relaxation for a magnification factor of M = 3.
Fig. 6
Fig. 6 Shows the anisotropy and orthogonality metric distribution (a & b respectively)in the transformed space after grid relaxation for a magnification factor of M =3.
Fig. 7
Fig. 7 Shows the electric field norm distribution for the three simulated 2D NFM cases with a magnification factor M = 3. The three simulated cases are when the starting material property tensors in the undistorted space are: (a) Anisotropic Bilayer (b) Isotropic Bilayer (c) Isotropic Multilayer (∼200 layer stack of alternating positive and negative index). All of the above cases ((a), (b) & (c)), the object plane consists of two point sources separated by λ /4 and have a loss tangent factor δ = 0.01. (d) Shows the 1D plot of electric field norm at the magnified image plane of the NFM. (e) Shows the normalized far field norm when the image plane is far field propagated.
Fig. 8
Fig. 8 The effect of varying loss tangent factor δ on the image plane electric field norm. The effect of loss tangent is shown for the anisotropic bilayer NFM with M = 3. The point sources are separated by λ/10.
Fig. 9
Fig. 9 3D NFM simulation using the 2.5D technique. (a) Shows the perspective section view of a 3D NFM, which is the axial revolution of a 2D planar NFM in (ρ′, ϕ = 0, z′) plane. The axisymmetric axis is shown as a dotted red line. The material property tensors correspond to that of the anisotropic bilayer. (b) Shows the object plane transverse electric field norm and 3× magnified image plane transverse electric field norm. A 0.1 λ USAF resolution target was chosen for this demonstration.
Fig. 10
Fig. 10 (a) Shows the 0.1λ resolution target at the object plane. (b) Shows the 3× magnified resolution target at the image plane of the 3D NFM. (c) Shows the image plane far field propagated. (d) Shows the object plane far field propagated without NFM.
Fig. 11
Fig. 11 The electric field norm distribution for the simulated 2D NFM with different magnification factors. Namely, (a) M = 3 ×, (b) 5×, and (c) 9×. The two point sources in the object plane are separated by λ/10. All of the above three cases have a loss tangent factor δ = 0.01.
Fig. 12
Fig. 12 The effect of magnification on the anisotropy metric of the relaxed transformed grid.
Fig. 13
Fig. 13 Cascaded NFM strategy to achieve higher magnification factor is shown. (a) Shows the electric field norm distribution for a 2-stage cascaded NFM. Each stage provides a 3×magnification with an overall magnification of 9×. Stage 2 is a 3× scaled version of Stage 1 with exact material property spatial gradient(loss tangent factor for both stages is δ = 0.01). (b) Shows the electric field norm at different cut lines of cascaded Stage 1 image plane, cascaded Stage 2 image plane, and single stage M = 9 image plane.

Equations (39)

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1 = μ 1 = [ + 0 0 0 + 0 0 0 ] , 2 = μ 2 = [ 0 0 0 0 0 0 + ]
E = y ^ e [ i ( k x x + k z z ω t ) ]
M = [ α β ζ + β ζ β ζ α + β ζ + ]
= [ x 0 0 0 y 0 0 0 z ] μ = [ μ x 0 0 0 μ y 0 0 0 μ z ] α = cos ( p z z 0 ) , β = i sin ( p z z 0 ) , ζ + = 1 2 ( p z μ x k z ± μ x k z p z )
k z = ± k 0 2 k x 2 , k 0 = ω / c = 2 π / λ
p z = ± y μ x k 0 2 = μ x μ z k x 2
τ = 1 M 11 and ρ = M 21 M 11 .
M = M 1 M 2 .
τ = 2 [ e i ( ϕ + ψ ) ( 1 Z 0 ) ( 1 + Z 1 ) ( 1 Z 2 ) + e i ( ϕ ψ ) ( 1 Z 0 ) ( 1 Z 1 ) ( 1 + Z 2 ) + e i ( ϕ ψ ) ( 1 + Z 0 ) ( 1 Z 1 ) ( 1 Z 2 ) + e i ( ϕ + ψ ) ( 1 + Z 0 ) ( 1 + Z 1 ) ( 1 + Z 2 ) ] 1
p z = ± i y μ 1 x k 0 2 μ 1 x μ 1 z k x 2 , q z = ± 2 y μ 2 x k 0 2 μ 2 x μ 2 z k x 2
Z 0 = p z μ 1 x k z , Z 1 = μ 1 x q z μ 2 x p z , Z 2 = μ 2 x k z q z
ϕ = p z d 1 , ψ = q 2 d 2
R = k max k 0 = λ λ min
M isotropic = M [ + + + ] [ ] = M [ + + + ] M [ ]
Z 0 1 i δ , Z 1 0 , Z 2 1 + i δ , p z = q z = k z i k x , | τ | | 2 cosh 2 ( k x λ ) + ( 1 + δ ) 2 sinh 2 ( k x λ ) |
R isotropic 1 2 π arcsinh ( 10 2 δ )
M anisotropic = M [ + + ] [ + ] = M [ + + ] M [ + ]
Z 0 i , Z 1 1 , Z 2 i , p z k x ( 1 + i δ ) , q z = k x ( 1 i δ ) , k z = i k x , | τ | sech ( 2 λ k x δ )
R anisotropic 3 4 π δ .
M multilayer = M 1 [ + + + ] [ ] M 2 [ + + + ] [ ] M i [ + + + ] [ ] M N [ + + + ] [ ] = i = 1 N M i [ + + + ] [ ] = [ M 1 [ + + + ] [ ] ] N
M multilayer = lim Δ 0 [ M 1 [ + + + ] [ ] ] d / 2 Δ = lim Δ 0 { P [ σ 1 0 0 σ 2 ] d / 2 Δ P 1 } M anisotropic
σ 1 e 2 λ k x δ , σ 2 e 2 λ k x δ P [ + i 1 i 1 ] then, | τ | sech ( 2 λ k x δ ) .
R multilayer R anisotropic
ρ ρ ρ z + z ρ z z = 0
ρ m max , n = 1 2 M [ M + 1 + ( M 1 ) cos ( π ( 1 τ m h 0 ) 3 / 2 ) ] z m max , n = τ m
ρ m , n = 1 4 ( ρ m + 1 , n + ρ m 1 , n + ρ m , n + 1 + ρ m , n 1 ) z m , n = 1 4 ( z m + 1 , n + z m 1 , n + z m , n + 1 + z m , n 1 )
κ [ α ] = max ( | ρ m , n [ α ] ρ m , n [ α 1 ] | , | z m , n [ α ] z m , n [ α 1 ] | )
p q = det ( Λ p p ) 1 Λ p p Λ q q p q
Λ p ^ p ^ = Λ p p ^ , Λ p p Λ p ^ p = [ 1 0 0 0 ρ 0 0 0 1 ] [ ρ ρ 0 ρ z 0 1 0 z ρ 0 z z ] [ 1 0 0 0 1 ρ 0 0 0 1 ]
AM = max [ | ξ 11 ξ 22 | , | ξ 11 ξ 33 | , | ξ 22 ξ 33 | ] mean ( ξ 11 , ξ 22 , ξ 33 )
OM = 2 | | n 0.5 | 2 / 3 Re [ ( w 12 w 21 ) Im [ w 12 w 21 ) + ( w 11 w 22 ) Im [ w 11 w 22 ] ] | Im [ w 11 w 22 ] Re [ w 12 w 21 ] + Im [ w 21 w 12 ] Re [ w 11 w 22 ] Γ | 2 / 3 |
h 0 1 M 2 n = 1 n k M 1 n + 0.5
M multilayer = lim Δ 0 [ M [ + + + ] [ ] ] d / 2 Δ
M [ + + + ] [ ] = [ 1 0 0 1 ] + [ P Q Q P ] Δ
P = k x 2 δ 3 2 k 0 2 ( δ + δ 3 ) ( 1 + δ 2 ) k 0 2 k x 2 , Q = k x 2 δ ( 2 + δ 2 ) ( 1 + δ 2 ) k 0 2 k x 2 , = λ P 2 Q 2 = 2 λ δ k 0 2 + k x 2 1 + δ 2 ,
M multilayer = lim Δ 0 [ 1 P Δ Q Δ Q Δ 1 + P Δ ] λ / Δ = [ cosh ( ) P sinh ( ) Q sinh ( ) Q sinh ( ) cosh ( ) + P sinh ( ) ] .
M anisotropic = lim Δ 0 [ M [ + + ] [ + ] d / 2 Δ
M [ + + ] [ + ] = [ 1 0 0 1 ] + [ P Q Q P ] Δ
M multilayer M anisotropioc .