Abstract

Orbital angular momentum (OAM) vortex waves generated by conventional spiral phase plates and metasurfaces have been widely discussed. In this work, we propose an innovative OAM generation method based on transformation optics (TO). By solving Laplace’s equation with specific boundary conditions, an oblate cylindrical shaped physical domain is designed to imitate a gradient shaped virtual domain which is able to generate a vortex beam upon reflection. As a proof-of-concept demonstration, a broadband all-dielectric microwave lens for vortex beam generation is presented with a topological charge of + 1. The corresponding far-field patterns as well as near-field helical phase and doughnut-shaped amplitude distributions of the lens, obtained from numerical simulations, are reported along with a wide operational bandwidth spanning from 8 to 16 GHz. As a transformation method, the proposed TO technique provides an effective way to realize a conversion from plane waves to vortex waves, which can greatly facilitate the potential implementation of OAM waves in microwave wireless communication systems.

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

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2018 (1)

2017 (5)

M. L. N. Chen, L. J. Jiang, and W. E. I. Sha, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave Frequencies,” IEEE Trans. Antenn. Propag. 65(1), 396–400 (2017).

M. Ebrahimpouri and O. Quevedo-Teruel, “Bespoke lenses based on quasi-conformal transformation optics technique,” IEEE Trans. Antenn. Propag. 65(5), 2256–2264 (2017).

T. Ding, J. Yi, H. Li, H. Zhang, and S. N. Burokur, “3D field-shaping lens using all-dielectric gradient refractive index materials,” Sci. Rep. 7(1), 782 (2017).

Q. L. Li, S. W. Cheung, D. Wu, and T. I. Yuk, “Microwave lens using periodic dielectric sheets for antenna-gain enhancement,” IEEE Trans. Antenn. Propag. 65(4), 2068–2073 (2017).

A. K. Azad, A. V. Efimov, S. Ghosh, J. Singleton, A. J. Taylor, and H. T. Chen, “Ultra-thin metasurface microwave flat lens for broadband applications,” Appl. Phys. Lett. 110(22), 224101 (2017).

2016 (4)

J. Yi, S. N. Burokur, G.-P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).

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(4), 044010 (2016).

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).

2015 (5)

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

W. Wei, K. Mahdjoubi, C. Brousseau, and O. Emile, “Generation of OAM waves with circular phase shifter and array of patch antennas,” Electron. Lett. 51(6), 442–443 (2015).

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).

P.-H. Tichit, S. N. Burokur, J. Yi, and A. de Lustrac, “Transformation electromagnetics for antennas with an illusion on the radiation pattern,” IEEE Antennas Wirel. Propag. Lett. 13, 1796–1799 (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(8), 084903 (2015).

2014 (4)

Q. Bai, A. Tennant, and B. Allen, “Experimental circular phased array for generating OAM radio beams,” Electron. Lett. 50(20), 1414–1415 (2014).

P. Schemmel, G. Pisano, B. Maffei, and B. Maffei, “Modular spiral phase plate design for orbital angular momentum generation at millimetre wavelengths,” Opt. Express 22(12), 14712–14726 (2014).

R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM flat-plate antenna in the millimeter frequency band,” IEEE Antennas Wirel. Propag. Lett. 13, 1011–1014 (2014).

L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814–4818 (2014).

2013 (3)

D. Zelenchuk and V. Fusco, “Split-ring FSS spiral phase plate,” IEEE Antennas Wirel. Propag. Lett. 12, 284–287 (2013).

H. Ma, B. Cai, T. Zhang, Y. Yang, W. Jiang, and T. J. Cui, “Three-dimensional gradient-index materials and their applications in microwave lens antennas,” IEEE Trans. Antenn. Propag. 61(5), 2561–2569 (2013).

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).

2012 (1)

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(3), 033001 (2012).

2011 (2)

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E 83(2), 026601 (2011).

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).

2010 (3)

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).

D.-H. Kwon and D. H. Werner, “Transformation electromagnetics: An overview of the theory and its application,” IEEE Antennas Propag. Mag. 52(1), 24–26 (2010).

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).

2009 (2)

J. Hu, X. Zhou, and G. Hu, “Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation,” Opt. Express 17(3), 1308–1320 (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(25), 253902 (2009).

2008 (6)

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

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 Nanost. Fundam. Appl. 6(1), 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(15), 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(6), 063903 (2008).

L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, “Design of electromagnetic refractor and phase transformer using coordinate transformation theory,” Opt. Express 16(10), 6815–6821 (2008).

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

2007 (1)

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

2006 (3)

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

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

1996 (1)

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4–6), 183–188 (1996).

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Allen, B.

Q. Bai, A. Tennant, and B. Allen, “Experimental circular phased array for generating OAM radio beams,” Electron. Lett. 50(20), 1414–1415 (2014).

Allen, L.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4–6), 183–188 (1996).

Azad, A. K.

A. K. Azad, A. V. Efimov, S. Ghosh, J. Singleton, A. J. Taylor, and H. T. Chen, “Ultra-thin metasurface microwave flat lens for broadband applications,” Appl. Phys. Lett. 110(22), 224101 (2017).

Bai, Q.

Q. Bai, A. Tennant, and B. Allen, “Experimental circular phased array for generating OAM radio beams,” Electron. Lett. 50(20), 1414–1415 (2014).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Bergman, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

Bergman, J. E.

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 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(3), 033001 (2012).

Brousseau, C.

W. Wei, K. Mahdjoubi, C. Brousseau, and O. Emile, “Generation of OAM waves with circular phase shifter and array of patch antennas,” Electron. Lett. 51(6), 442–443 (2015).

R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM flat-plate antenna in the millimeter frequency band,” IEEE Antennas Wirel. Propag. Lett. 13, 1011–1014 (2014).

Burokur, S. N.

K. Zhang, Y. Yuan, D. Zhang, X. Ding, B. Ratni, S. N. Burokur, M. Lu, K. Tang, and Q. Wu, “Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region,” Opt. Express 26(2), 1351–1360 (2018).

T. Ding, J. Yi, H. Li, H. Zhang, and S. N. Burokur, “3D field-shaping lens using all-dielectric gradient refractive index materials,” Sci. Rep. 7(1), 782 (2017).

J. Yi, S. N. Burokur, G.-P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).

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(4), 044010 (2016).

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).

P.-H. Tichit, S. N. Burokur, J. Yi, and A. de Lustrac, “Transformation electromagnetics for antennas with an illusion on the radiation pattern,” IEEE Antennas Wirel. Propag. Lett. 13, 1796–1799 (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(8), 084903 (2015).

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).

Cai, B.

H. Ma, B. Cai, T. Zhang, Y. Yang, W. Jiang, and T. J. Cui, “Three-dimensional gradient-index materials and their applications in microwave lens antennas,” IEEE Trans. Antenn. Propag. 61(5), 2561–2569 (2013).

Carozzi, T. D.

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

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(25), 253902 (2009).

Chen, H.

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(25), 253902 (2009).

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

Chen, H. T.

A. K. Azad, A. V. Efimov, S. Ghosh, J. Singleton, A. J. Taylor, and H. T. Chen, “Ultra-thin metasurface microwave flat lens for broadband applications,” Appl. Phys. Lett. 110(22), 224101 (2017).

Chen, M. L. N.

M. L. N. Chen, L. J. Jiang, and W. E. I. Sha, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave Frequencies,” IEEE Trans. Antenn. Propag. 65(1), 396–400 (2017).

Cheng, L.

L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814–4818 (2014).

Cheng, Q.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).

Cheung, S. W.

Q. L. Li, S. W. Cheung, D. Wu, and T. I. Yuk, “Microwave lens using periodic dielectric sheets for antenna-gain enhancement,” IEEE Trans. Antenn. Propag. 65(4), 2068–2073 (2017).

Chi, H.

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Cui, J.

Cui, T. J.

H. Ma, B. Cai, T. Zhang, Y. Yang, W. Jiang, and T. J. Cui, “Three-dimensional gradient-index materials and their applications in microwave lens antennas,” IEEE Trans. Antenn. Propag. 61(5), 2561–2569 (2013).

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E 83(2), 026601 (2011).

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).

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 Nanost. Fundam. Appl. 6(1), 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(6), 063903 (2008).

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

Daldorff, L. K.

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 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(4), 044010 (2016).

J. Yi, S. N. Burokur, G.-P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (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(8), 084903 (2015).

P.-H. Tichit, S. N. Burokur, J. Yi, and A. de Lustrac, “Transformation electromagnetics for antennas with an illusion on the radiation pattern,” IEEE Antennas Wirel. Propag. Lett. 13, 1796–1799 (2015).

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).

Ding, T.

T. Ding, J. Yi, H. Li, H. Zhang, and S. N. Burokur, “3D field-shaping lens using all-dielectric gradient refractive index materials,” Sci. Rep. 7(1), 782 (2017).

Ding, X.

Du, C.

Ebrahimpouri, M.

M. Ebrahimpouri and O. Quevedo-Teruel, “Bespoke lenses based on quasi-conformal transformation optics technique,” IEEE Trans. Antenn. Propag. 65(5), 2256–2264 (2017).

Efimov, A. V.

A. K. Azad, A. V. Efimov, S. Ghosh, J. Singleton, A. J. Taylor, and H. T. Chen, “Ultra-thin metasurface microwave flat lens for broadband applications,” Appl. Phys. Lett. 110(22), 224101 (2017).

Emile, O.

W. Wei, K. Mahdjoubi, C. Brousseau, and O. Emile, “Generation of OAM waves with circular phase shifter and array of patch antennas,” Electron. Lett. 51(6), 442–443 (2015).

R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM flat-plate antenna in the millimeter frequency band,” IEEE Antennas Wirel. Propag. Lett. 13, 1011–1014 (2014).

Forozesh, K.

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).

Fusco, V.

D. Zelenchuk and V. Fusco, “Split-ring FSS spiral phase plate,” IEEE Antennas Wirel. Propag. Lett. 12, 284–287 (2013).

Ghosh, S.

A. K. Azad, A. V. Efimov, S. Ghosh, J. Singleton, A. J. Taylor, and H. T. Chen, “Ultra-thin metasurface microwave flat lens for broadband applications,” Appl. Phys. Lett. 110(22), 224101 (2017).

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(25), 253902 (2009).

Han, T.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).

Hao, Z. C.

L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814–4818 (2014).

Hong, W.

L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814–4818 (2014).

Hu, G.

Hu, J.

Hu, Y.

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

Huangfu, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

Hui, X.

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

Ibragimov, N. H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

Isham, B.

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).

Istomin, Y. N.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

Jiang, L. J.

M. L. N. Chen, L. J. Jiang, and W. E. I. Sha, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave Frequencies,” IEEE Trans. Antenn. Propag. 65(1), 396–400 (2017).

Jiang, W.

H. Ma, B. Cai, T. Zhang, Y. Yang, W. Jiang, and T. J. Cui, “Three-dimensional gradient-index materials and their applications in microwave lens antennas,” IEEE Trans. Antenn. Propag. 61(5), 2561–2569 (2013).

Jiang, W. X.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E 83(2), 026601 (2011).

Jin, X.

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

Karlsson, R. L.

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).

Khamitova, R.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

Kong, F.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

Kong, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Kwon, D.-H.

D.-H. Kwon and D. H. Werner, “Transformation electromagnetics: An overview of the theory and its application,” IEEE Antennas Propag. Mag. 52(1), 24–26 (2010).

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

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(25), 253902 (2009).

Leonhardt, U.

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

Li, H.

T. Ding, J. Yi, H. Li, H. Zhang, and S. N. Burokur, “3D field-shaping lens using all-dielectric gradient refractive index materials,” Sci. Rep. 7(1), 782 (2017).

Li, L.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).

Li, Q. L.

Q. L. Li, S. W. Cheung, D. Wu, and T. I. Yuk, “Microwave lens using periodic dielectric sheets for antenna-gain enhancement,” IEEE Trans. Antenn. Propag. 65(4), 2068–2073 (2017).

Lin, L.

Lu, M.

Luo, X.

Ma, H.

H. Ma, B. Cai, T. Zhang, Y. Yang, W. Jiang, and T. J. Cui, “Three-dimensional gradient-index materials and their applications in microwave lens antennas,” IEEE Trans. Antenn. Propag. 61(5), 2561–2569 (2013).

Ma, H. F.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).

Maffei, B.

Mahdjoubi, K.

W. Wei, K. Mahdjoubi, C. Brousseau, and O. Emile, “Generation of OAM waves with circular phase shifter and array of patch antennas,” Electron. Lett. 51(6), 442–443 (2015).

R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM flat-plate antenna in the millimeter frequency band,” IEEE Antennas Wirel. Propag. Lett. 13, 1011–1014 (2014).

Mari, E.

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(3), 033001 (2012).

Ménard, A.

R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM flat-plate antenna in the millimeter frequency band,” IEEE Antennas Wirel. Propag. Lett. 13, 1011–1014 (2014).

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

Mohammadi, S. M.

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 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(25), 253902 (2009).

Niemiec, R.

R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM flat-plate antenna in the millimeter frequency band,” IEEE Antennas Wirel. Propag. Lett. 13, 1011–1014 (2014).

Padgett, M. J.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4–6), 183–188 (1996).

Palmer, K.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

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(15), 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(6), 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 Nanost. Fundam. Appl. 6(1), 87–95 (2008).

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

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(4), 044010 (2016).

J. Yi, S. N. Burokur, G.-P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).

Pisano, G.

Qiu, C. W.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).

Quevedo-Teruel, O.

M. Ebrahimpouri and O. Quevedo-Teruel, “Bespoke lenses based on quasi-conformal transformation optics technique,” IEEE Trans. Antenn. Propag. 65(5), 2256–2264 (2017).

Rahm, M.

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 Nanost. Fundam. Appl. 6(1), 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(6), 063903 (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(15), 11555–11567 (2008).

Ran, L.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

Ratni, B.

Roberts, D. 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 Nanost. Fundam. Appl. 6(1), 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(15), 11555–11567 (2008).

Robertson, D. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4–6), 183–188 (1996).

Romanato, F.

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(3), 033001 (2012).

Schemmel, P.

Schurig, D.

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(6), 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 Nanost. Fundam. Appl. 6(1), 87–95 (2008).

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

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

Sha, W. E. I.

M. L. N. Chen, L. J. Jiang, and W. E. I. Sha, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave Frequencies,” IEEE Trans. Antenn. Propag. 65(1), 396–400 (2017).

Shi, G.

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).

Shi, Y.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).

Singleton, J.

A. K. Azad, A. V. Efimov, S. Ghosh, J. Singleton, A. J. Taylor, and H. T. Chen, “Ultra-thin metasurface microwave flat lens for broadband applications,” Appl. Phys. Lett. 110(22), 224101 (2017).

Sjöholm, J.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

Smith, D. R.

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 Nanost. Fundam. Appl. 6(1), 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(6), 063903 (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(15), 11555–11567 (2008).

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

Smith, G. M.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4–6), 183–188 (1996).

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(3), 033001 (2012).

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

Tamburini, F.

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(3), 033001 (2012).

Tang, K.

Taylor, A. J.

A. K. Azad, A. V. Efimov, S. Ghosh, J. Singleton, A. J. Taylor, and H. T. Chen, “Ultra-thin metasurface microwave flat lens for broadband applications,” Appl. Phys. Lett. 110(22), 224101 (2017).

Tennant, A.

Q. Bai, A. Tennant, and B. Allen, “Experimental circular phased array for generating OAM radio beams,” Electron. Lett. 50(20), 1414–1415 (2014).

Then, H.

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

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(3), 033001 (2012).

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

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(8), 084903 (2015).

P.-H. Tichit, S. N. Burokur, J. Yi, and A. de Lustrac, “Transformation electromagnetics for antennas with an illusion on the radiation pattern,” IEEE Antennas Wirel. Propag. Lett. 13, 1796–1799 (2015).

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).

Turnbull, G. A.

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4–6), 183–188 (1996).

Wang, D.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

Wang, W.

Wei, W.

W. Wei, K. Mahdjoubi, C. Brousseau, and O. Emile, “Generation of OAM waves with circular phase shifter and array of patch antennas,” Electron. Lett. 51(6), 442–443 (2015).

Werner, D. H.

D.-H. Kwon and D. H. Werner, “Transformation electromagnetics: An overview of the theory and its application,” IEEE Antennas Propag. Mag. 52(1), 24–26 (2010).

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

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

Wu, B.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

Wu, D.

Q. L. Li, S. W. Cheung, D. Wu, and T. I. Yuk, “Microwave lens using periodic dielectric sheets for antenna-gain enhancement,” IEEE Trans. Antenn. Propag. 65(4), 2068–2073 (2017).

Wu, Q.

Xi, S.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

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(25), 253902 (2009).

Xu, C.

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

Yang, X. M.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).

Yang, Y.

H. Ma, B. Cai, T. Zhang, Y. Yang, W. Jiang, and T. J. Cui, “Three-dimensional gradient-index materials and their applications in microwave lens antennas,” IEEE Trans. Antenn. Propag. 61(5), 2561–2569 (2013).

Yi, J.

T. Ding, J. Yi, H. Li, H. Zhang, and S. N. Burokur, “3D field-shaping lens using all-dielectric gradient refractive index materials,” Sci. Rep. 7(1), 782 (2017).

J. Yi, S. N. Burokur, G.-P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).

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(4), 044010 (2016).

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (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(8), 084903 (2015).

P.-H. Tichit, S. N. Burokur, J. Yi, and A. de Lustrac, “Transformation electromagnetics for antennas with an illusion on the radiation pattern,” IEEE Antennas Wirel. Propag. Lett. 13, 1796–1799 (2015).

Yu, S.

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).

Yuan, Y.

Yuk, T. I.

Q. L. Li, S. W. Cheung, D. Wu, and T. I. Yuk, “Microwave lens using periodic dielectric sheets for antenna-gain enhancement,” IEEE Trans. Antenn. Propag. 65(4), 2068–2073 (2017).

Zelenchuk, D.

D. Zelenchuk and V. Fusco, “Split-ring FSS spiral phase plate,” IEEE Antennas Wirel. Propag. Lett. 12, 284–287 (2013).

Zhang, D.

Zhang, H.

T. Ding, J. Yi, H. Li, H. Zhang, and S. N. Burokur, “3D field-shaping lens using all-dielectric gradient refractive index materials,” Sci. Rep. 7(1), 782 (2017).

Zhang, J.

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

Zhang, K.

Zhang, S.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).

Zhang, T.

H. Ma, B. Cai, T. Zhang, Y. Yang, W. Jiang, and T. J. Cui, “Three-dimensional gradient-index materials and their applications in microwave lens antennas,” IEEE Trans. Antenn. Propag. 61(5), 2561–2569 (2013).

Zhang, X.

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

Zhang, Z. Q.

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(25), 253902 (2009).

Zheng, S.

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

Zhou, X.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).

J. Hu, X. Zhou, and G. Hu, “Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation,” Opt. Express 17(3), 1308–1320 (2009).

Zhu, C.

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).

Adv. Funct. Mater. (1)

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).

Appl. Phys. Lett. (5)

A. K. Azad, A. V. Efimov, S. Ghosh, J. Singleton, A. J. Taylor, and H. T. Chen, “Ultra-thin metasurface microwave flat lens for broadband applications,” Appl. Phys. Lett. 110(22), 224101 (2017).

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).

S. Yu, L. Li, G. Shi, C. Zhu, X. Zhou, and Y. Shi, “Design, fabrication, and measurement of reflective metasurface for orbital angular momentum vortex wave in radio frequency domain,” Appl. Phys. Lett. 108(12), 121903 (2016).

S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016).

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).

Electron. Lett. (2)

Q. Bai, A. Tennant, and B. Allen, “Experimental circular phased array for generating OAM radio beams,” Electron. Lett. 50(20), 1414–1415 (2014).

W. Wei, K. Mahdjoubi, C. Brousseau, and O. Emile, “Generation of OAM waves with circular phase shifter and array of patch antennas,” Electron. Lett. 51(6), 442–443 (2015).

IEEE Antennas Propag. Mag. (1)

D.-H. Kwon and D. H. Werner, “Transformation electromagnetics: An overview of the theory and its application,” IEEE Antennas Propag. Mag. 52(1), 24–26 (2010).

IEEE Antennas Wirel. Propag. Lett. (4)

X. Hui, S. Zheng, Y. Hu, C. Xu, X. Jin, H. Chi, and X. Zhang, “Ultralow reflectivity spiral phase plate for generation of millimeter-wave OAM beam,” IEEE Antennas Wirel. Propag. Lett. 14, 966–969 (2015).

P.-H. Tichit, S. N. Burokur, J. Yi, and A. de Lustrac, “Transformation electromagnetics for antennas with an illusion on the radiation pattern,” IEEE Antennas Wirel. Propag. Lett. 13, 1796–1799 (2015).

R. Niemiec, C. Brousseau, K. Mahdjoubi, O. Emile, and A. Ménard, “Characterization of an OAM flat-plate antenna in the millimeter frequency band,” IEEE Antennas Wirel. Propag. Lett. 13, 1011–1014 (2014).

D. Zelenchuk and V. Fusco, “Split-ring FSS spiral phase plate,” IEEE Antennas Wirel. Propag. Lett. 12, 284–287 (2013).

IEEE Trans. Antenn. Propag. (5)

S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio-a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010).

M. L. N. Chen, L. J. Jiang, and W. E. I. Sha, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave Frequencies,” IEEE Trans. Antenn. Propag. 65(1), 396–400 (2017).

Q. L. Li, S. W. Cheung, D. Wu, and T. I. Yuk, “Microwave lens using periodic dielectric sheets for antenna-gain enhancement,” IEEE Trans. Antenn. Propag. 65(4), 2068–2073 (2017).

H. Ma, B. Cai, T. Zhang, Y. Yang, W. Jiang, and T. J. Cui, “Three-dimensional gradient-index materials and their applications in microwave lens antennas,” IEEE Trans. Antenn. Propag. 61(5), 2561–2569 (2013).

M. Ebrahimpouri and O. Quevedo-Teruel, “Bespoke lenses based on quasi-conformal transformation optics technique,” IEEE Trans. Antenn. Propag. 65(5), 2256–2264 (2017).

J. Appl. Phys. (2)

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(8), 084903 (2015).

J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B. Wu, L. Ran, and J. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. 104(1), 014502 (2008).

J. Opt. (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(4), 044010 (2016).

New J. Phys. (2)

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

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(3), 033001 (2012).

Opt. Commun. (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5–6), 321–327 (1994).

G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, “The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate,” Opt. Commun. 127(4–6), 183–188 (1996).

Opt. Express (6)

Photonics Nanost. Fundam. Appl. (1)

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 Nanost. Fundam. Appl. 6(1), 87–95 (2008).

Phys. Rev. E (1)

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E 83(2), 026601 (2011).

Phys. Rev. Lett. (3)

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(6), 063903 (2008).

B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov, and R. Khamitova, “Utilization of photon orbital angular momentum in the low-frequency radio domain,” Phys. Rev. Lett. 99(8), 087701 (2007).

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(25), 253902 (2009).

Sci. Rep. (3)

T. Ding, J. Yi, H. Li, H. Zhang, and S. N. Burokur, “3D field-shaping lens using all-dielectric gradient refractive index materials,” Sci. Rep. 7(1), 782 (2017).

J. Yi, S. N. Burokur, G.-P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).

L. Cheng, W. Hong, and Z. C. Hao, “Generation of electromagnetic waves with arbitrary orbital angular momentum modes,” Sci. Rep. 4(1), 4814–4818 (2014).

Science (3)

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

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).

Other (3)

D. H. Werner and D.-H. Kwon, Transformation Electromagnetics and Metamaterials: Fundamental Principles and Applications (Springer, 2014).

Comsol MULTIPHYSICS Modeling, ( http://www.comsol.com ).

ANSYS Electromagnetics Suite, release 18.2 (2017).

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Figures (7)

Fig. 1
Fig. 1 (a) Configuration of the conventional discrete helicoidal parabolic reflector antenna. (b) Schematic view of the transformed lens over a planar grounded (metallic) reflector generating vortex beams.
Fig. 2
Fig. 2 Space transformation from the virtual space to the physical space for the design of the proposed microwave lens. (a) Virtual space (vacuum). (b) Physical space composed of a gradient index medium.
Fig. 3
Fig. 3 Calculated permittivity (εzz) values, which vary from 1.2 to 2.7. (a)-(h) Range of the permittivity variation in the eight different sectors.
Fig. 4
Fig. 4 Design of the 3D discrete flat lens composed of 8 sectors and a total of 9352 cubic unit cells.
Fig. 5
Fig. 5 Numerical simulation results for different configurations where the upper panel corresponds to a planar reflector (no lens) configuration, the middle panel corresponds to the classical discrete parabolic reflector, and the lower panel corresponds to the proposed microwave lens. (a), (c) and (e) Phase distributions of the EM field component in the cross-section parallel to xoz plane at a distance 2λ away from the feed plane. The phase changes from -π (blue) to π (red). (b), (d) and (f) Amplitude distributions of EM field in a cross-section parallel to xoz plane at a distance λ away from the feed plane. The intensity changes from minimum (blue) to maximum (red) to form a doughnut-shaped pattern.
Fig. 6
Fig. 6 3D and 2D simulated far-field radiation patterns of the considered different systems at 12 GHz. (a), (d) Planar reflector (no lens). (b), (e) Discrete parabolic reflector. (c), (f) Proposed flat microwave lens.
Fig. 7
Fig. 7 Simulation results of the proposed OAM generation lens at 8 GHz, 10 GHz, 14 GHz and 16 GHz. (a)-(d) 3D far-field radiation patterns. (e)-(h) 2D far-field radiation patterns.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

y = H W 2 x 2 ( L + H )
{ x | A ' B ' , B ' C ' , D ' A ' = x ' n ^ x | C ' D ' = 0 , { y | A ' B ' = 0 y | C ' D ' = H W 2 ( x ' ) 2 ( L + H ) n ^ z | B ' C ' , D ' A ' = 0
ε = ε r det ( J 1 ) , μ = 1

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