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1

Chen, Haibing, Qiang Cheng, Aihua Huang, Junyan Dai, Huiying Lu, Jie Zhao, Huifeng Ma, Weixiang Jiang, and Tiejun Cui. "Modified Luneburg Lens Based on Metamaterials." International Journal of Antennas and Propagation 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/902634.

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We present the design, fabrication, and experimental characterization of a modified two-dimensional Luneburg lens based on bulk metamaterials. The lens is composed by a number of concentric layers. By varying the geometric dimensions of unit cells in each layer, the gradient refractive index profile required for the modified Luneburg lens can be achieved. The cylindrical waves generated from a point source at the focus point of the lens could be transformed into plane waves as desired in the microwave frequency. The proposed modified Luneburg lens can realize wide-angle beam scanning when the source moves along the circumferential direction inside the lens. Numerical and experimental results validate the performance of the modified Luneberg lens.
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2

Mattheakis, M. M., G. P. Tsironis, and V. I. Kovanis. "Luneburg lens waveguide networks." Journal of Optics 14, no. 11 (July 27, 2012): 114006. http://dx.doi.org/10.1088/2040-8978/14/11/114006.

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3

Peng, Huiyan, Huashuo Han, Pinchao He, Keqin Xia, Jiaxiang Zhang, Xiaochao Li, Qiaoliang Bao, Ying Chen, and Huanyang Chen. "The Luneburg-Lissajous lens." EPL (Europhysics Letters) 129, no. 6 (April 11, 2020): 64001. http://dx.doi.org/10.1209/0295-5075/129/64001.

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4

Nikolic, Nasiha, and Andrew Hellicar. "Fractional Luneburg Lens Antenna." IEEE Antennas and Propagation Magazine 56, no. 5 (October 2014): 116–30. http://dx.doi.org/10.1109/map.2014.6971923.

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5

Garcia-Ortiz, C. E., R. Cortes, J. E. Gómez-Correa, E. Pisano, J. Fiutowski, D. A. Garcia-Ortiz, V. Ruiz-Cortes, H. G. Rubahn, and V. Coello. "Plasmonic metasurface Luneburg lens." Photonics Research 7, no. 10 (September 4, 2019): 1112. http://dx.doi.org/10.1364/prj.7.001112.

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6

Bykov, Konstantin A., Yuri G. Pasternak, Vladimir A. Pendyurin, and Fyodor S. Safonov. "Flat Luneberg lens based on a printed circuit with curved conductors." Physics of Wave Processes and Radio Systems 24, no. 1 (May 6, 2021): 48–57. http://dx.doi.org/10.18469/1810-3189.2021.24.1.48-57.

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The use of a printed Luneberg lens is promising for powering ultra-wideband phased array antennas with full-azimuth scanning. This article describes in detail the model for constructing a flat Luneberg lens based on a printed circuit with curved conductors. A certain pattern(pattern) with a relative permittivity er1 was etched on the copper-coated substrate. This was done in order to realize the value of the refractive index. By printing a grid of intersecting conducting lines, a refractive index of was achieved in the center of the lens. The diameter of the Luneburg lens antenna was chosen to be 28.6 cm, which corresponds to 12,4l0 (l0 is the wavelength of free space) to achieve a half-power beam width of 5 at an estimated frequency of up to 20 GHz. Since the design of the Luneberg lens is based on geometric optics, the lens diameter must be a multiple of the wavelength to limit diffraction effects. Operating frequencies up to 20 GHz were selected. The lens was sampled into single cells. If the unit cell size is small enough, the lens can be described as a medium with a certain effective refractive index. As a result, this propagation theory can be used for lens design. The substrate used for the lens was 1 mm thick, the material used was Rohacell 31HF, which has a permittivity of 1,046 and a loss tangent of tg(d) = 0,002.
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7

Yu, Run, Hanlu Wang, Weicen Chen, Chunling Zhu, and Dawei Wu. "Latticed underwater acoustic Luneburg lens." Applied Physics Express 13, no. 8 (July 28, 2020): 084003. http://dx.doi.org/10.35848/1882-0786/aba7a7.

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8

Di Falco, Andrea, Susanne C. Kehr, and Ulf Leonhardt. "Luneburg lens in silicon photonics." Optics Express 19, no. 6 (March 3, 2011): 5156. http://dx.doi.org/10.1364/oe.19.005156.

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9

Xue, L., and V. F. Fusco. "Printed holey plate Luneburg lens." Microwave and Optical Technology Letters 50, no. 2 (February 2008): 378–80. http://dx.doi.org/10.1002/mop.23087.

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10

Rondineau, S., M. Himdi, and J. Sorieux. "A sliced spherical Luneburg lens." IEEE Antennas and Wireless Propagation Letters 2 (2003): 163–66. http://dx.doi.org/10.1109/lawp.2003.819045.

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11

Kim, Sang Hoon. "Acoustic Luneburg Lens as a New Sonar System." Applied Mechanics and Materials 763 (May 2015): 101–4. http://dx.doi.org/10.4028/www.scientific.net/amm.763.101.

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Luneburg lens is a gradient index lens that focuses the incoming wave to the opposite side of the lens without aberration. We developed a two-dimensional acoustic Luneburg lens by variable density method of space inside the lens. The lens is composed of hundreds of aluminum columns with various radii of less than 1cm. We tested the ability as sonar in the air. It focuses the incoming acoustic wave on the edge of the opposite side of the lens as well in the frequency range of 1,000Hz ~ 3,000Hz. It showed a dynamic response depending on the motion of the acoustic source. It could be a strong candidate of a next generation of sonar.
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12

Zhang, Lei, Lin Wang, Yanqing Wu, and Renzhong Tai. "Plasmonic Luneburg lens and plasmonic nano-coupler." Chinese Optics Letters 18, no. 9 (2020): 092401. http://dx.doi.org/10.3788/col202018.092401.

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13

Bor, Jonathan, Benjamin Fuchs, Olivier Lafond, and Mohamed Himdi. "Design and characterization of a foam-based Mikaelian lens antennas in millimeter waves." International Journal of Microwave and Wireless Technologies 7, no. 6 (July 30, 2014): 769–73. http://dx.doi.org/10.1017/s1759078714001019.

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The design principles and radiation performances of Mikaelian lens antennas are presented. The ways to manufacture gradient index lenses are briefly reviewed. An innovative technique based on the variation of the foam density is described and applied to the Mikaelian lenses. This yields low cost and lightweight gradient index lenses. The focusing properties of Mikaelian lenses are compared numerically to Luneburg lenses. A foam-based planar Mikaelian lens antenna is manufactured and its radiation performances are characterized at 60 GHz. With its flat shape in contact to the primary source, the cylindrical Mikaelian lens turns out to be, for focusing purposes, an interesting alternative to the well-known Luneburg lens.
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14

Demetriadou, Angela, and Yang Hao. "Slim Luneburg lens for antenna applications." Optics Express 19, no. 21 (September 27, 2011): 19925. http://dx.doi.org/10.1364/oe.19.019925.

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15

Whitehead, N. J., S. A. R. Horsley, T. G. Philbin, and V. V. Kruglyak. "A Luneburg lens for spin waves." Applied Physics Letters 113, no. 21 (November 19, 2018): 212404. http://dx.doi.org/10.1063/1.5049470.

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16

Gladyshev, V. O., and A. A. Tereshin. "A Luneburg lens in moving coordinates." Optics and Spectroscopy 120, no. 5 (May 2016): 773–80. http://dx.doi.org/10.1134/s0030400x16030097.

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17

Xue, L., and V. F. Fusco. "Patch fed 2D planar Luneburg lens." Microwave and Optical Technology Letters 49, no. 12 (2007): 2922–24. http://dx.doi.org/10.1002/mop.22942.

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18

Gaufillet, F., and E. Akmansoy. "Graded Photonic Crystals for Luneburg Lens." IEEE Photonics Journal 8, no. 1 (February 2016): 1–11. http://dx.doi.org/10.1109/jphot.2016.2521261.

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19

Pfeiffer, Carl, and Anthony Grbic. "A Printed, Broadband Luneburg Lens Antenna." IEEE Transactions on Antennas and Propagation 58, no. 9 (September 2010): 3055–59. http://dx.doi.org/10.1109/tap.2010.2052582.

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20

Mirmozafari, M., M. Tursunniyaz, H. Luyen, J. H. Booske, and N. Behdad. "A Multibeam Tapered Cylindrical Luneburg Lens." IEEE Transactions on Antennas and Propagation 69, no. 8 (August 2021): 5060–65. http://dx.doi.org/10.1109/tap.2020.3048508.

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21

Ueng, Shyh Kuang, and Hsuan Muh. "Interactive Design and Simulation for Luneberg Lenses." Applied Mechanics and Materials 284-287 (January 2013): 2771–77. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.2771.

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In this paper, a CAD system is presented for the design, evaluation and simulation of Luneburg lenses. Since this system focuses on high-frequency spherical antenna design and simulation, electromagnetic waves are replaced by rays. A ray-tracing subroutine is employed to trace ray paths and compute phase variations along rays. In traditional CAD systems, the performance of a Luneburg lens is measured by using numerical algorithms, which are difficult to implement and require tremendous computational efforts. In the proposed system, the effectiveness of the target lens is evaluated solely by using the theory of Geometrical Optics (GO). Ray paths and wavefronts are rendered and displayed to show the directivity and focus characters of the lens. The ray phases along with ray paths are also illustrated in graphical media so that the gain and reflectivity of the lens can be predicted.
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22

Hunt, John, Talmage Tyler, Sulochana Dhar, Yu-Ju Tsai, Patrick Bowen, Stéphane Larouche, Nan M. Jokerst, and David R. Smith. "Planar, flattened Luneburg lens at infrared wavelengths." Optics Express 20, no. 2 (January 11, 2012): 1706. http://dx.doi.org/10.1364/oe.20.001706.

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23

Zhao, Liuxian, and Miao Yu. "Flattened structural Luneburg lens for broadband beamforming." Journal of the Acoustical Society of America 148, no. 1 (July 2020): EL82—EL87. http://dx.doi.org/10.1121/10.0001638.

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24

Cummer, Steven, Yangbo Xie, Yangyang Fu, Junfei Li, Zhetao Jia, Chen Shen, Yadong Xu, and Huanyang Chen. "Acoustic imaging with a metamaterial Luneburg lens." Journal of the Acoustical Society of America 144, no. 3 (September 2018): 1674. http://dx.doi.org/10.1121/1.5067454.

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25

Xue, L., and V. F. Fusco. "24 GHz automotive radar planar Luneburg lens." IET Microwaves, Antennas & Propagation 1, no. 3 (2007): 624. http://dx.doi.org/10.1049/iet-map:20050203.

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26

Badri, S. Hadi, and M. M. Gilarlue. "Ultrashort waveguide tapers based on Luneburg lens." Journal of Optics 21, no. 12 (November 6, 2019): 125802. http://dx.doi.org/10.1088/2040-8986/ab4fa3.

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27

Zhao, Yuan-Yuan, Yong-Liang Zhang, Mei-Ling Zheng, Xian-Zi Dong, Xuan-Ming Duan, and Zhen-Sheng Zhao. "Three-dimensional Luneburg lens at optical frequencies." Laser & Photonics Reviews 10, no. 4 (June 8, 2016): 665–72. http://dx.doi.org/10.1002/lpor.201600051.

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28

Bosiljevac, Marko, Massimiliano Casaletti, Francesco Caminita, Zvonimir Sipus, and Stefano Maci. "Non-Uniform Metasurface Luneburg Lens Antenna Design." IEEE Transactions on Antennas and Propagation 60, no. 9 (September 2012): 4065–73. http://dx.doi.org/10.1109/tap.2012.2207047.

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29

Quevedo-Teruel, Oscar, and Yang Hao. "Directive radiation from a diffuse Luneburg lens." Optics Letters 38, no. 4 (February 6, 2013): 392. http://dx.doi.org/10.1364/ol.38.000392.

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30

Amarasinghe, Yasith, Daniel M. Mittleman, and Rajind Mendis. "A Luneburg Lens for the Terahertz Region." Journal of Infrared, Millimeter, and Terahertz Waves 40, no. 11-12 (November 20, 2019): 1129–36. http://dx.doi.org/10.1007/s10762-019-00635-8.

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31

Mao, Xiurun, Yang Yang, Haitao Dai, Dan Luo, Baoli Yao, and Shaohui Yan. "Tunable photonic nanojet formed by generalized Luneburg lens." Optics Express 23, no. 20 (September 30, 2015): 26426. http://dx.doi.org/10.1364/oe.23.026426.

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32

Xue, L., and V. Fusco. "Patch-fed planar dielectric slab waveguide Luneburg lens." IET Microwaves, Antennas & Propagation 2, no. 2 (March 1, 2008): 109–14. http://dx.doi.org/10.1049/iet-map:20070146.

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33

Cheng, Qiang, Hui Feng Ma, and Tie Jun Cui. "Broadband planar Luneburg lens based on complementary metamaterials." Applied Physics Letters 95, no. 18 (November 2, 2009): 181901. http://dx.doi.org/10.1063/1.3257375.

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34

Bor, Jonathan, Olivier Lafond, Herve Merlet, Philippe Le Bars, and Mohamed Himdi. "FOAM BASED LUNEBURG LENS ANTENNA AT 60 GHZ." Progress In Electromagnetics Research Letters 44 (2014): 1–7. http://dx.doi.org/10.2528/pierl13092405.

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35

Viitanen, Ari J., Ismo V. Lindell, and An H. Sihvola. "Polarization correction of luneburg lens with chiral medium." Microwave and Optical Technology Letters 3, no. 2 (February 1990): 62–66. http://dx.doi.org/10.1002/mop.4650030207.

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36

Dhouibi, A., S. N. Burokur, A. de Lustrac, and A. Priou. "Compact Metamaterial-Based Substrate-Integrated Luneburg Lens Antenna." IEEE Antennas and Wireless Propagation Letters 11 (2012): 1504–7. http://dx.doi.org/10.1109/lawp.2012.2233191.

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37

Gómez-Correa, J. E., S. E. Balderas-Mata, B. K. Pierscionek, and S. Chávez-Cerda. "Composite modified Luneburg model of human eye lens." Optics Letters 40, no. 17 (August 20, 2015): 3990. http://dx.doi.org/10.1364/ol.40.003990.

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38

Doric, Sead. "Generalized nonfull-aperture Luneburg lens: a new solution." Optical Engineering 32, no. 9 (1993): 2118. http://dx.doi.org/10.1117/12.143948.

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39

Wang, Min, Cheng Huang, Ming-Bo Pu, Cheng-Gang Hu, Wen-Bo Pan, Ze-Yu Zhao, and Xian-Gang Luo. "Electric-controlled scanning Luneburg lens based on metamaterials." Applied Physics A 111, no. 2 (February 9, 2013): 445–50. http://dx.doi.org/10.1007/s00339-013-7603-9.

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40

Kim, Sang-Hoon, Jung-Woo Kim, and Gunn Hwang. "Design and Analysis of 2D Acoustic Luneburg Lens." Journal of Korean Institute of Communications and Information Sciences 43, no. 12 (December 31, 2018): 2168–74. http://dx.doi.org/10.7840/kics.2018.43.12.2168.

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41

Lazarev, Andrey V., Andrey Yu Kiselev, Anatoly M. Bobreshov, and Grigory K. Uskov. "Synthesis of a Luneburg lens with a flat surface using quasi-conformal transformation optics." Physics of Wave Processes and Radio Systems 23, no. 4 (February 11, 2021): 68–73. http://dx.doi.org/10.18469/1810-3189.2020.23.4.68-73.

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Annotation In modern systems of radiolocation, navigation and communication, the requirements for antennas are becoming higher requirements every year, namely: operation in a wide frequency range, the ability to change of direction of the main lobe of the radiation pattern. Antenna systems with similar characteristics can be built using dielectric antenna beamforming structures. One of these structures is the Luneberg lens, the peculiarity of which is its spherical symmetry. However, the curved surface of this lens significantly complicates the placement of transmitting and receiving elements along it, which increases the complexity of constructing the entire antenna system. This paper proposes an algorithm for constructing a Luneberg lens with a flat surface. The lens was synthesized using the method of quasi-conformal optical transformations, the mathematical algorithm of which is also described in this work. The paper also presents the results of mathematical modeling of the antenna system using a Luneberg lens with a flat surface at different positions of the emitter relative to the center of the lens, as well as different cut angles. The simulation results show that the synthesized lens can be used to construct a multi-beam antenna system that allows the direction of the main lobe of the antenna radiation pattern to be rearranged over a wide range of angles. However, the scanning angles of this system are limited by the lens geometry, the larger the maximum scanning angle we choose, the more significant the influence of the side lobes on the radiation pattern becomes.
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42

Foster, Robert, Deepak Nagarkoti, Ju Gao, Benjamin Vial, Felix Nicholls, Chris Spooner, Sajad Haq, and Yang Hao. "Beam-Steering Performance of Flat Luneburg Lens at 60 GHz for Future Wireless Communications." International Journal of Antennas and Propagation 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/7932434.

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The beam-steering capabilities of a simplified flat Luneburg lens are reported at 60 GHz. The design of the lens is first described, using transformation electromagnetics, before discussion of the fabrication of the lens using casting of ceramic composites. The simulated beam-steering performance is shown, demonstrating that the lens, with only six layers and a highest permittivity of 12, achieves scan angles of ±30° with gains of at least 18 dBi over a bandwidth from 57 to 66 GHz. To verify the simulations and further demonstrate the broadband nature of the lens, raw high definition video was transmitted over a wireless link at scan angles up to 36°.
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43

Zhao, Liuxian, Changquan Lai, and Miao Yu. "Modified structural Luneburg lens for broadband focusing and collimation." Mechanical Systems and Signal Processing 144 (October 2020): 106868. http://dx.doi.org/10.1016/j.ymssp.2020.106868.

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44

Liu, Kunning, Shiwen Yang, Shi‐Wei Qu, Yikai Chen, and Jun Hu. "2D flat Luneburg lens antenna for multibeam scanning application." Electronics Letters 55, no. 25 (December 2019): 1317–18. http://dx.doi.org/10.1049/el.2019.2901.

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45

Liu, Wei, Xiaohong Sun, Minglei Gao, and Shuai Wang. "Luneburg and flat lens based on graded photonic crystal." Optics Communications 364 (April 2016): 225–32. http://dx.doi.org/10.1016/j.optcom.2015.11.058.

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46

Sun, Xiao-Hong, Yu-Long Wu, Wei Liu, Yu Hao, and Liu-Di Jiang. "Luneburg lens composed of sunflower-type graded photonic Crystals." Optics Communications 315 (March 2014): 367–73. http://dx.doi.org/10.1016/j.optcom.2013.11.022.

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47

Loo, Yoke Leng, Yarong Yang, Ning Wang, Yun Gui Ma, and Chong Kim Ong. "Broadband microwave Luneburg lens made of gradient index metamaterials." Journal of the Optical Society of America A 29, no. 4 (March 7, 2012): 426. http://dx.doi.org/10.1364/josaa.29.000426.

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48

de Pineda, Julia D., Rhiannon C. Mitchell-Thomas, Alastair P. Hibbins, and J. Roy Sambles. "A broadband metasurface Luneburg lens for microwave surface waves." Applied Physics Letters 111, no. 21 (November 20, 2017): 211603. http://dx.doi.org/10.1063/1.5003571.

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49

Flores, J. R., J. Sochacki, M. Sochacka, and R. Staroński. "Quasi-analytical ray tracing through the generalized Luneburg lens." Applied Optics 31, no. 25 (September 1, 1992): 5167. http://dx.doi.org/10.1364/ao.31.005167.

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50

Zhao, Liuxian, Eitan Laredo, Olivia Ryan, Amirhossein Yazdkhasti, Hyun-Tae Kim, Randy Ganye, Timothy Horiuchi, and Miao Yu. "Ultrasound beam steering with flattened acoustic metamaterial Luneburg lens." Applied Physics Letters 116, no. 7 (February 18, 2020): 071902. http://dx.doi.org/10.1063/1.5140467.

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