Abstract

Radio waves carrying orbital angular momentum (OAM) may potentially increase spectrum efficiency and channel capacity based on their extra rotational degree of freedom. However, due to their divergence characteristics, vortex waves are not suitable to transmit over a long distance in the radio frequency (RF) and microwave domains. In this paper, a transformation optics (TO) based all-dielectric converging lens is proposed. The beam divergence angle of the vortex wave passing through the lens can be decreased from 25° to 9°. The transformed material parameters of the converging lens are determined by solving Laplace’s equation subject to specific boundary conditions. Far-field antenna radiation patterns as well as near-field helical phase and electric field amplitude distributions obtained from numerical simulations are reported, demonstrating the broadband characteristics of the proposed microwave lens. Moreover, the all-dielectric compact lens design comprised by a graded permittivity profile can be fabricated by additive manufacturing technology, which greatly facilitates the potential development and application of vortex wave based wireless communications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (2)

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).

M. Ebrahimpouri and O. Quevedo-Teruel, “Bespoke lenses based on quasi-conformal transformation optics technique,” IEEE Trans. Antennas Prop. 65, 2256–2264 (2017).

2016 (1)

J. Yi, S. N. Burokur, G. P. Piau, and A. De Lustrac, “3d printed broadband transformation optics based all-dielectric microwave lenses,” J. Opt. 18, 044010 (2016).

2015 (5)

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (oam) mode antennas,” Sci. Rep. 5, 10148 (2015).

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9, 822 (2015).

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107, 024101 (2015).

J. Yi, P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117, 084903 (2015).

2014 (1)

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Spiral-like multi-beam emission via transformation electromagnetics,” J. Appl. Phys. 115, 024901 (2014).

2013 (2)

P. H. Tichit, S. N. Burokur, C. W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven lc resonator metamaterials,” Phys. Rev. Lett. 111, 133901 (2013).

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).

2012 (2)

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antennas Prop. 60, 5063–5074 (2012).

O. Edfors and A. J. Johansson, “Is orbital angular momentum (oam) based radio communication an unexploited area?” IEEE Trans. Antennas Propag. 60, 1126–1131 (2012).

2011 (7)

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: First experimental test,” New J. Phys. 14, 811–815 (2011).

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Science 331, 290–291 (2011).

P. H. Tichit, S. N. Burokur, D. Germain, and A. De Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83, 155108 (2011).

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84, 165111 (2011).

I. B. Djordjevic, “Deep-space and near-earth optical communications by coded orbital angular momentum (oam) modulation,” Opt. Express 19, 14277–14289 (2011).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19, 20551–20556 (2011).

2010 (4)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18, 767–772 (2010).

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

2009 (3)

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 (2009).

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).

2008 (4)

D. Roberts, M. Rahm, J. Pendry, and D. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93, 251111 (2008).

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).

2007 (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

2006 (2)

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).

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

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic microstructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).

1909 (1)

J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. Lond. A 82, 560–567 (1909).

Atwater, H. A.

A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Science 331, 290–291 (2011).

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Bergman, J. E. S.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

Bianchini, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: First experimental test,” New J. Phys. 14, 811–815 (2011).

Boltasseva, A.

A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Science 331, 290–291 (2011).

Burokur, S. N.

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt. Express 26, 11708–11717 (2018).

J. Yi, S. N. Burokur, G. P. Piau, and A. De Lustrac, “3d printed broadband transformation optics based all-dielectric microwave lenses,” J. Opt. 18, 044010 (2016).

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107, 024101 (2015).

J. Yi, P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117, 084903 (2015).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Spiral-like multi-beam emission via transformation electromagnetics,” J. Appl. Phys. 115, 024901 (2014).

P. H. Tichit, S. N. Burokur, C. W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven lc resonator metamaterials,” Phys. Rev. Lett. 111, 133901 (2013).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19, 20551–20556 (2011).

P. H. Tichit, S. N. Burokur, D. Germain, and A. De Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83, 155108 (2011).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18, 767–772 (2010).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 (2009).

Carozzi, T. D.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

Chan, C. T.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).

Chen, H.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).

Chen, Y.

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (oam) mode antennas,” Sci. Rep. 5, 10148 (2015).

Cheng, Q.

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).

Chi, H.

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (oam) mode antennas,” Sci. Rep. 5, 10148 (2015).

Coassini, P.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

Cui, T. J.

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).

Daldorff, L. K. S.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

De Lustrac, A.

J. Yi, S. N. Burokur, G. P. Piau, and A. De Lustrac, “3d printed broadband transformation optics based all-dielectric microwave lenses,” J. Opt. 18, 044010 (2016).

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107, 024101 (2015).

J. Yi, P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117, 084903 (2015).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Spiral-like multi-beam emission via transformation electromagnetics,” J. Appl. Phys. 115, 024901 (2014).

P. H. Tichit, S. N. Burokur, C. W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven lc resonator metamaterials,” Phys. Rev. Lett. 111, 133901 (2013).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19, 20551–20556 (2011).

P. H. Tichit, S. N. Burokur, D. Germain, and A. De Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83, 155108 (2011).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18, 767–772 (2010).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 (2009).

Dehdashti, S.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).

Deng, Y.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).

Djordjevic, I. B.

Dyke, A.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).

Dyke, H.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).

Ebrahimpouri, M.

M. Ebrahimpouri and O. Quevedo-Teruel, “Bespoke lenses based on quasi-conformal transformation optics technique,” IEEE Trans. Antennas Prop. 65, 2256–2264 (2017).

Edfors, O.

O. Edfors and A. J. Johansson, “Is orbital angular momentum (oam) based radio communication an unexploited area?” IEEE Trans. Antennas Propag. 60, 1126–1131 (2012).

Feng, R.

Forozesh, K.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Germain, D.

P. H. Tichit, S. N. Burokur, D. Germain, and A. De Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83, 155108 (2011).

Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Gregory, M. D.

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antennas Prop. 60, 5063–5074 (2012).

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84, 165111 (2011).

Han, D.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).

Hao, Y.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Haq, S.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic microstructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).

Horng, J.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Hu, Y.

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (oam) mode antennas,” Sci. Rep. 5, 10148 (2015).

Huangfu, J.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).

Hui, X.

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (oam) mode antennas,” Sci. Rep. 5, 10148 (2015).

Isham, B.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

Jiang, W. X.

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).

Jiang, Y.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).

Jiang, Z. H.

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antennas Prop. 60, 5063–5074 (2012).

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84, 165111 (2011).

Jin, X.

X. Hui, S. Zheng, Y. Chen, Y. Hu, X. Jin, H. Chi, and X. Zhang, “Multiplexed millimeter wave communication with dual orbital angular momentum (oam) mode antennas,” Sci. Rep. 5, 10148 (2015).

Johansson, A. J.

O. Edfors and A. J. Johansson, “Is orbital angular momentum (oam) based radio communication an unexploited area?” IEEE Trans. Antennas Propag. 60, 1126–1131 (2012).

Ju, L.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Kahn, J. M.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9, 822 (2015).

Kang, L.

Karlsson, R. L.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

Lai, Y.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).

Li, G.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9, 822 (2015).

Li, R.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).

Li, X.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication,” Nat. Photonics 9, 822 (2015).

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Luo, Y.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).

Ma, H. F.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).

W. X. Jiang, H. F. Ma, Q. Cheng, and T. J. Cui, “Illusion media: Generating virtual objects using realizable metamaterials,” Appl. Phys. Lett. 96, 121910 (2010).

Mari, E.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: First experimental test,” New J. Phys. 14, 811–815 (2011).

Martin, M.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Mitchell-Thomas, R. C.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).

Mohammadi, S. M.

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

Ng, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).

Oldoni, M.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

Parisi, G.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

Pendry, J.

D. Roberts, M. Rahm, J. Pendry, and D. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93, 251111 (2008).

Pendry, J. B.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).

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

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic microstructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).

Piau, G. P.

J. Yi, S. N. Burokur, G. P. Piau, and A. De Lustrac, “3d printed broadband transformation optics based all-dielectric microwave lenses,” J. Opt. 18, 044010 (2016).

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107, 024101 (2015).

Poynting, J. H.

J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. Lond. A 82, 560–567 (1909).

Qiu, C. W.

P. H. Tichit, S. N. Burokur, C. W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven lc resonator metamaterials,” Phys. Rev. Lett. 111, 133901 (2013).

Quevedo-Teruel, O.

M. Ebrahimpouri and O. Quevedo-Teruel, “Bespoke lenses based on quasi-conformal transformation optics technique,” IEEE Trans. Antennas Prop. 65, 2256–2264 (2017).

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).

D. Roberts, M. Rahm, J. Pendry, and D. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93, 251111 (2008).

Ran, L.

Y. Luo, J. Zhang, H. Chen, J. Huangfu, and L. Ran, “High-directivity antenna with small antenna aperture,” Appl. Phys. Lett. 95, 193506 (2009).

Ravanelli, R. A.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).

Roberts, D.

D. Roberts, M. Rahm, J. Pendry, and D. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93, 251111 (2008).

Roberts, D. A.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).

Romanato, F.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: First experimental test,” New J. Phys. 14, 811–815 (2011).

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).

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

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41–48 (2007).

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).

Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Smith, D.

D. Roberts, M. Rahm, J. Pendry, and D. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93, 251111 (2008).

Smith, D. R.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16, 11555–11567 (2008).

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100, 063903 (2008).

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6, 87–95 (2008).

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

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).

Someda, C. G.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

Spinello, F.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

Sponselli, A.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: First experimental test,” New J. Phys. 14, 811–815 (2011).

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic microstructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).

Tamburini, F.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: First experimental test,” New J. Phys. 14, 811–815 (2011).

Tang, W.

O. Quevedo-Teruel, W. Tang, R. C. Mitchell-Thomas, A. Dyke, H. Dyke, L. Zhang, S. Haq, and Y. Hao, “Transformation optics for antennas: why limit the bandwidth with metamaterials?” Sci. Rep. 3, 1903 (2013).

Thide, B.

M. Oldoni, F. Spinello, E. Mari, G. Parisi, C. G. Someda, F. Tamburini, F. Romanato, R. A. Ravanelli, P. Coassini, and B. Thide, “Space-division demultiplexing in orbital-angular-momentum-based mimo radio systems,” IEEE Trans. Antennas Prop. 63, 4582–4587 (2015).

S. M. Mohammadi, L. K. S. Daldorff, J. E. S. Bergman, R. L. Karlsson, B. Thide, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antennas Prop. 58, 565–572 (2010).

Thidé, B.

F. Tamburini, E. Mari, A. Sponselli, B. Thidé, A. Bianchini, and F. Romanato, “Encoding many channels on the same frequency through radio vorticity: First experimental test,” New J. Phys. 14, 811–815 (2011).

B. Thidé, Electromagnetic Field Theory (Upsilon Books, 2017).

Tichit, P. H.

J. Yi, P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117, 084903 (2015).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Spiral-like multi-beam emission via transformation electromagnetics,” J. Appl. Phys. 115, 024901 (2014).

P. H. Tichit, S. N. Burokur, C. W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven lc resonator metamaterials,” Phys. Rev. Lett. 111, 133901 (2013).

P. H. Tichit, S. N. Burokur, D. Germain, and A. De Lustrac, “Design and experimental demonstration of a high-directive emission with transformation optics,” Phys. Rev. B 83, 155108 (2011).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Transformation media producing quasi-perfect isotropic emission,” Opt. Express 19, 20551–20556 (2011).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18, 767–772 (2010).

P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105, 104912 (2009).

Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).

Wang, H.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).

Werner, D. H.

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt. Express 26, 11708–11717 (2018).

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Broadband high directivity multibeam emission through transformation optics-enabled metamaterial lenses,” IEEE Trans. Antennas Prop. 60, 5063–5074 (2012).

Z. H. Jiang, M. D. Gregory, and D. H. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Phys. Rev. B 84, 165111 (2011).

Xiao, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).

Xu, Z.

H. Wang, Y. Deng, B. Zheng, R. Li, Y. Jiang, S. Dehdashti, Z. Xu, and H. Chen, “Panoramic lens designed with transformation optics,” Sci. Rep. 7, 40083 (2017).

Yi, J.

R. Feng, J. Yi, S. N. Burokur, L. Kang, H. Zhang, and D. H. Werner, “Orbital angular momentum generation method based on transformation electromagnetics,” Opt. Express 26, 11708–11717 (2018).

J. Yi, S. N. Burokur, G. P. Piau, and A. De Lustrac, “3d printed broadband transformation optics based all-dielectric microwave lenses,” J. Opt. 18, 044010 (2016).

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107, 024101 (2015).

J. Yi, P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117, 084903 (2015).

Youngs, I.

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Figures (8)

Fig. 1
Fig. 1 Space transformation from the virtual space to the physical space for the design of the proposed converging lens. (a) Virtual space (vacuum). (b) Physical space composed of a gradient index medium.
Fig. 2
Fig. 2 The calculated permittivity (εzz) distribution varies from 1 to 2.8.
Fig. 3
Fig. 3 Schematic view of the 3D converging lens composed of 12 layers and a total of 216 circular rings. The lens is illuminated by a circular antenna array capable of generating vortex waves.
Fig. 4
Fig. 4 Amplitude distributions of EM field in the x-y plane 5.4 λ away from the feeding source for two configurations at different frequencies of the source only (without lens) case (a)–(e), and with the proposed microwave lens (k)–(o). Amplitude distributions of EM field in the x-z plane of the source only (without lens) configuration (f)–(j), and with the proposed microwave lens (p)–(t).
Fig. 5
Fig. 5 Phase distributions of the EM field component in the cross-section parallel to the x-y plane for two configurations at different frequencies where the upper panel corresponds to the no lens case and the lower panel corresponds to the proposed microwave lens. The cross-section is 2λ away from the lens plane and the phase changes from −π (blue) to π (red).
Fig. 6
Fig. 6 Simulated antenna radiation patterns of the source alone and of the source in the presence of the lens from 6 GHz to 14 GHz. (a), (d), (g), (j), and (m) correspond to the 3D far-field radiation patterns for the system without lens. (b), (e), (h), (k), and (n) correspond to the 3D far-field radiation patterns for the microwave lens system. (c), (f), (i), (l), and (o) are the 2D far-field radiation pattern cuts.
Fig. 7
Fig. 7 Numerical simulation results when a vortex beam having a topological charge of respectively +2 and +3 is used as an emitter at 10 GHz.
Fig. 8
Fig. 8 Simulated antenna radiation patterns of the source alone and of the source in presence of the lens at 10 GHz. The source used is a vortex beam carrying an OAM with a topological charge of +2 and +3.

Equations (3)

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{ x | A B , B C , C D = x n ^ x | A E , D E = 0
{ z | A B , B C , C D = z z | A E = tan θ ( W / 2 + x ) z | D E = tan θ ( W / 2 x )
ε = ε r d e t ( J 1 ) , μ = 1

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