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

1. Introduction

Vortex waves carrying orbital angular momentum (OAM) have attracted considerable attention in both the optical and radio frequency regimes, due to their unique properties that can significantly improve the channel capacity of a communication system [1–3]. In sharp contrast to common wireless communication systems that typically employ schemes based on the linear momentum of an electromagnetic (EM) field, vortex waves facilitate a new angular momentum based form of signal modulation. The signal space consisting of orthogonal OAM eigenstates provides wireless communication systems with a new dimension of physical characteristics by exploiting the rotational degree of freedom. An EM wave carrying OAM has a helical transverse phase structure quantified by exp (i), in which ϕ is the transverse azimuthal angle and l is an unbounded integer (the OAM state number). OAM beams with different l values are mutually orthogonal, allowing them to be multiplexed together along the same beam axis and de-multiplexed with low crosstalk. Such vortex waves offer a solution to the problem of radio-band congestion by allowing the development of new techniques for achieving high spectral density in wireless communications.

As a consequence, generation techniques for vortex waves carrying OAM have recently been explored in depth. Spiral phase plates (SPPs) [4–10] and helicoidal parabolic antennas [1], as conventional OAM generation methods, tailor the phase of the transmitting wave in proportion to the azimuthal angle φ around the center. Antenna array synthesis techniques [11-12] represent another effective way to generate OAM vortex beams. However, they generally require an intricate feeding system to achieve radiating beams with the desired helical phase fronts, which dramatically increases the complexity and cost of the corresponding systems. Recently, metasurfaces operating in reflection and transmission modes have been designed to generate vortex beams due to their considerable potential for manipulation of electromagnetic waves [13–16]. However, most of them suffer from narrow-band response and/or moderate efficiency. Nevertheless, OAM generation methods based on spatial transformations, which can modify the phase distribution by compressing the field, are rarely discussed.

Transformation optics has been demonstrated as a powerful design tool for the manipulation of EM fields in unprecedented ways through the use of judiciously engineered materials with parameters that vary spatially [17–19]. An equivalence has been proposed by Hu et al. [20] between coordinate transformation and spatial deformation by using Laplace’s equation to determine the deformation of coordinate grids during the transformation. The transformed material parameters were determined by the solution of Laplace’s equation under proper Dirichlet-Neumann boundary conditions. This concept has led to the widely publicized carpet cloak design [21], but also to the development of many other conceptual as well as functional devices such as novel waveguiding structures [22–27], microwave lens antennas [28–37], illusion devices [38–43] and so on.

In this work, we propose a spatial transformation optics based OAM generation method. An oblate cylindrical shaped physical domain is designed to mimic a gradient shaped virtual domain whose bottom surface acts as a helicoidal parabolic reflective surface. In order to establish the quasi-conformal mapping between the physical domain and the virtual domain, Neumann and Dirichlet sliding boundary conditions are set at the edges of the transformation zones. The Jacobian matrix of the coordinates in the physical and virtual domains is calculated by solving the Laplace’s equation under the specific boundary conditions. The transformed medium with quasi-isotropic material permittivity distribution is calculated from the Jacobian matrix and assigned to the physical domain to achieve the spiral phase creation. To further demonstrate the proposed TO based OAM generation method, an all-dielectric lens which can be easily illuminated by a standard feeding source and which can operate over a wide frequency band is designed. It is shown that the concentric circular phase distribution and Gaussian amplitude distribution on the cross-section of a plane wave is tailored into helical shaped and doughnut-shaped distributions respectively. Full wave finite element method (FEM) numerical simulations are performed to validate the broadband performances of the proposed device due to its non-resonant properties.

2. Theoretical design of the vortex beam generation

A helicoidal parabolic antenna, which is commonly fabricated by joining together several discrete surfaces, is used to generate a vortex wave with a feeding source located along the y-axis. The helicoidal parabolic system is composed of discrete parabolic surfaces and an associated feeding port, as illustrated in Fig. 1(a). The plane wave generated by the feeding source is transformed into a vortex wave through the reflection from the discrete parabolic surfaces. The parabolic antenna is composed of 8 discrete surfaces with an average gap of K/7 along the y-axis and has an overall diameter N. The vertices of the top surface are located in the xoz plane. The feeding source of the discrete parabolic antenna is positioned at a distance T from the origin. The general formula for each discrete parabolic surface in the x-y plane is given by

y=HW2x2(L+H)
where the focal distance of the parabola DC is W2/(4H), such that W and H are constants, and L is a variable.

 figure: 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.

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The TO based generation method is designed to transform a certain zone of virtual space above the helicoidal parabolic antenna into an oblate cylindrical physical space, as presented in Fig. 1(b). By transmitting through the calculated physical space, a plane wave emitted from the feed is transformed into a vortex beam after its reflection from the grounded planar surface rather than from a set of discrete helicoidal parabolic surfaces.

To determine the transformation from the helicoidal paraboloid to the planar surface, we propose a design based on the concept of spatial transformations, as illustrated by the schematics shown in Figs. 2(a) and 2(b). The physical and virtual space coordinates are respectively denoted by (x, y) and (x’, y’). The physical space is placed over a ground plane (metallic surface) and is illuminated by a plane wave generated by a feeding source as represented in Fig. 2. The distance between the wave port and the origin is identical in both the virtual and physical spaces and is set to a value of T = 90 mm, found after a parametric study is performed to evaluate the optimal distance T. As illustrated in Fig. 2(a), the orange colored arc CD represents the side view of one section of the discrete helicoidal parabolic surface. Both the arc CD and the straight line segment C’D’ represent perfect electric conductor (PEC) surfaces. Due to the transformation from arc CD to the straight line segment C’D’, the OAM beam can be tailored by a planar surface rather than a curved one. To obtain the desired mapping between the virtual space, which is free space, and the physical space, which is the transformed medium, the commercial partial differential equation (PDE) solver Comsol Multiphysics [44] is employed to evaluate Laplace’s equation subject to predefined boundary conditions. The virtual space represented in yellow and the physical space represented by a gradient color scheme are presented in Figs. 2(a) and 2(b), respectively.

 figure: 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.

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The coordinates A and A’ as well as B and B’ share the same locations such that the segments AB and A’B’ are equal to W. The length of the segment BC is taken to be a variable L, while the segment DE is assumed to be H, where CE is perpendicular to DA. The segment DA is transformed to segment D’A’ whose length is M, while the segment BC is transformed to segment B’C’. Similarly, the arc CD is transformed to the horizontal line segment C’D’. Therefore, the rectangle defined as A’B’C’D’ is mapped from the quadrilateral ABCD.

The designed model is based on a spatial transformation and achieved by solving Laplace’s equation. In order to establish an equivalence in the fields at the outer boundaries with the virtual space, Neumann and Dirichlet sliding boundary conditions are set at the edges of the microwave lens. These boundary conditions are:

{x|A'B',B'C',D'A'=x'n^x|C'D'=0,{y|A'B'=0y|C'D'=HW2(x')2(L+H)n^z|B'C',D'A'=0
where n^ is the normal vector to the boundaries of the surface. Considering the polarization of the excitation, the properties of the intermediate medium can be further simplified as:
ε=εrdet(J1),μ=1
where J=xixi'.

3. Demonstrated microwave lens model

In order to demonstrate the generation method introduced in the previous section, a lens assigned by the inhomogeneous medium calculated from the space transformation is built and analyzed at microwave frequencies. Continuous permittivity distributions for the different sectors are calculated by employing the PDE solver according to the corresponding values of surfaces m. Next, each of the sectors is discretized into 147 values of permittivity. The calculated permittivity distributions corresponding to the 8 discrete surfaces are shown in Fig. 3, which share similar parameter variations but have different ranges (minimum and maximum values).

 figure: 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.

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A 3D discrete lens model is designed for further realistic full-wave numerical simulations, as shown in Fig. 4. The microwave lens is comprised of 8 sectors (the cross section of sector 1 is shown illustrated in different colors), which correspond to the original 8 discrete helicoidal parabolic surfaces. The variable L is equal to md, where m is a serial number ranging from 1 to 8. Different values of m correspond to different surfaces, with the top surface indicated by m = 1. The gap between any two neighboring elements is d = K/7. The physical space presented in Fig. 2(b) represents the side view of one of the sectors. We further discretize each sector into 7 layers along the y-axis, where each layer consists of 21 unit cells. We assume that each unit cell has dimensions 5mm × 5mm × 5mm, small enough with regard to the operating wavelength of 3 cm (frequency of 10 GHz) so that an effective medium can be considered. As a result, the entire lens is composed of 1176 different circular rings containing a total of 9352 cubical unit cells. The proposed discrete lens model has an oblate cylindrical shape with a height of 3.5 cm and a bottom radius of 10.5 cm.

 figure: Fig. 4

Fig. 4 Design of the 3D discrete flat lens composed of 8 sectors and a total of 9352 cubic unit cells.

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According to existing theory, radio waves that carry OAM possess the particularity of having spiral shaped spatial phase fronts of the EM wave component along the propagation direction. The order of the OAM mode is determined by the eigenmode number l representing the topological charge, such that the helical phase distribution can be observed in a cross-section perpendicular to the beam axis.

In order to validate the proposed all-dielectric lens, full-wave simulations have been performed by employing the finite element method based HFSS software from ANSYS [45]. The simulated phase and amplitude profiles in the lateral xoz plane perpendicular to the beam axis for three different configurations are presented in Fig. 5. A regular wave port placed in the center of the top boundary of the cylindrically-shaped simulation domain is utilized as the feeding source. As a basis for comparison, a planar reflective surface and a helicoidal parabolic reflective surface are simulated and presented in Figs. 5(a)–5(d). A small circular region is omitted from the phase distribution cartography due to the presence of the feed structure. However, the major features of the spatial phase distribution of a beam carrying an OAM mode can be clearly observed from the proposed transformed lens (Fig. 5(e)), which is in good agreement with that of the helicoidal parabolic reflector shown in Fig. 5(c). The phase distributions shown in Figs. 5(c) and 5(e) present only one twist, corresponding to a topological charge of 1.

 figure: 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.

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The generation methods for OAM-carrying radio waves are derived from the study of OAM light beams, mainly those based on Laguerre-Gaussian (LG) beams. The EM field expression formula indicates that the intensity distribution in the cross-section of the LG light beam has a doughnut shape. In Fig. 5, we present the simulated EM field intensity distribution in the cross-section parallel to xoz plane for the three different configurations. Based on further comparisons between the amplitude distributions of the three different configurations, it is found that the simulated OAM spatial field distribution and the theoretical predictions are in very good agreement. It should be noted that a stronger radiation intensity suggests that better reception of the radio beams can be achieved at a fixed distance away from the transmitter. The EM field amplitude distribution of the transformed lens shows a doughnut shaped pattern as for the helicoidal parabolic reflector.

The 3D far-field radiation patterns for the three different configurations at 12 GHz are presented in Fig. 6. So as to highlight the influence of the lens, the radiation pattern obtained for the planar reflector is shown in Fig. 6(a), where a broad main beam can be observed. The radiation along y-axis is significantly reduced by the lens which produces a hollow-shaped main lobe. Although the lens imparts a slight dispersive effect on the two main lobes compared to the pattern of the helicoidal parabolic reflector, it can be clearly observed that OAM vortex waves can indeed be generated by the proposed all-dielectric lens. It should be noted that when solving the Laplace’s equation with both Dirichlet and Neumann boundaries, a material parameter distribution with non-diagonal terms is obtained, thus leading to challenges for a physical realization of the device. Therefore the anisotropy is ignored for a quasi-isotropic material implementation of the lens model. However, such approximation causes some degradation in the functionality of the lens [32-33], leading to slightly different radiation patterns of the proposed lens compared to those of the parabolic reflector.

 figure: 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.

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The all-dielectric lens operates over a wide frequency band ranging from 8 GHz to 16 GHz. Numerical simulation results for different operating frequencies are depicted in Fig. 7. The characteristics of the far-field patterns obtained from the lens are further compared in Fig. 7 at 8 GHz, 10 GHz, 14 GHz, and 16 GHz, which demonstrates a null in the amplitude at the center of each beam. Theoretically, the achieved bandwidth can be very broad since all-dielectric non-resonant materials are employed in the design.

 figure: 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.

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The simulation results show that the proposed all-dielectric lens can be indeed used to generate vortex waves with orbital angular momentum in an effective manner over a wide frequency range. The vortex phase wavefronts can be generated with gradient distributed permittivity, due to the configuration of the sub-wavelength metamaterial elements. As a result, OAM vortex waves with different mode numbers can be feasibly realized. By utilizing the proposed configuration, it becomes much easier to produce vortex radio waves with different mode numbers over a broad operating bandwidth. Moreover, the proposed flat lens design provides a relatively simple way to generate OAM vortex waves for radio and microwave wireless communication applications.

4. Conclusion

In summary, a new generation method of vortex beam with orbital angular momentum has been proposed. Such a manipulation in phase variation was achieved by employing a spatial transformation optics concept by solving Laplace’s equation with specific boundary conditions. A flat surface below the oblate physical space, which is assigned by the designed inhomogeneous (i.e. gradient) permittivity profile, is able to transform a plane wave into a vortex wave. In order to further demonstrate the proposed design method, a microwave lens in the shape of the physical space was introduced as a vortex wave generator with a topological charge of + 1 for full-wave analysis. Analogous phase front and hollow wave front amplitude distributions represent the vortex wave generation functionality of the lens. Furthermore, far-field radiation patterns show good agreement with the performance of the conventional helicoidal parabolic reflector antenna counterpart. The lens has been numerically simulated and has shown to possess a wide operating frequency band extending from 8 GHz to 16 GHz due to the non-resonant material properties. Such transformation optics based design method, is not only an efficient way to realize the transformation between the plane wave and the vortex wave, but also can serve to significantly facilitate the potential implementation of OAM in microwave wireless communication systems by achieving the benefits of simple excitation, wide bandwidth, ease of fabrication and integration.

Funding

National Natural Science Foundation of China (NSFC) (No. 61601345); Fundamental Research Funds for the Central Universities (No. XJS16046, JB160109); Natural Science Foundation of Shaanxi Province of China (No. 2017JQ6025).

References and links

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4. 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).

5. 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).

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

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8. 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).

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References

  • View by:

  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).
  2. 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).
  3. 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).
  4. 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).
  5. 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).
  6. D. Zelenchuk and V. Fusco, “Split-ring FSS spiral phase plate,” IEEE Antennas Wirel. Propag. Lett. 12, 284–287 (2013).
  7. 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).
  8. 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).
  9. 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).
  10. 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).
  11. Q. Bai, A. Tennant, and B. Allen, “Experimental circular phased array for generating OAM radio beams,” Electron. Lett. 50(20), 1414–1415 (2014).
  12. 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).
  13. 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).
  14. 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).
  15. 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).
  16. 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).
  17. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
  18. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
  19. D. H. Werner and D.-H. Kwon, Transformation Electromagnetics and Metamaterials: Fundamental Principles and Applications (Springer, 2014).
  20. 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).
  21. 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).
  22. 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).
  23. 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).
  24. 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).
  25. 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).
  26. 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).
  27. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
  28. 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).
  29. 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).
  30. 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).
  31. 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).
  32. 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).
  33. 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).
  34. M. Ebrahimpouri and O. Quevedo-Teruel, “Bespoke lenses based on quasi-conformal transformation optics technique,” IEEE Trans. Antenn. Propag. 65(5), 2256–2264 (2017).
  35. 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).
  36. 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).
  37. 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).
  38. 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).
  39. W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E 83(2), 026601 (2011).
  40. 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).
  41. 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).
  42. 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).
  43. 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).
  44. Comsol MULTIPHYSICS Modeling, ( http://www.comsol.com ).
  45. ANSYS Electromagnetics Suite, release 18.2 (2017).

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).

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).

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, 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, 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).

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, 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).

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, 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, 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).

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. 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).

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).

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. 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, 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).

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, 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).

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).

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. 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, 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).

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

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).

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, “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).

Yu, S.

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).

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).

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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).

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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).

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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).

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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).

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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).

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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).

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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).

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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).

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).

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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).

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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).

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

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).

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).

IEEE Trans. Antenn. Propag. (5)

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).

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).

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. 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. 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. 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).

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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).

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

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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).

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).

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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).

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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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