Selective excitation of localized acoustic skyrmion modes based on directional sound sources

ZHANG Xiaoyue; XU Huafeng; CHEN Wanna; ZHOU Nong; WU Hongwei

doi:10.7498/aps.74.20241286

Abstract

Acoustic skyrmion modes are topological texture structures of velocity field vectors generated on the surface of acoustic structures. This protected vector distribution provides new opportunities for processing sound information, transmission, and data storage. In this study, a combined structure of waveguides and spiral structures is designed by using directional acoustic sources to excite waveguide mode transmission, thereby achieving selective excitation of localized acoustic skyrmion modes. Through theoretical analysis and numerical simulations, the pressure field distribution and velocity field distribution excited by spin acoustic sources, Huygens acoustic sources, and Janus acoustic sources in this structure are investigated, demonstrating the directional transmission properties of acoustic surface waves and the selectively excited acoustic skyrmion modes in the combined structure. Numerical calculations reveal that when the spin acoustic source excites acoustic surface waves propagating along the waveguide, the acoustic skyrmion modes in the helical structure in the direction corresponding to the propagation are selectively excited. When the Huygens source excites acoustic surface waves propagating along the waveguide, the acoustic skyrmion modes in the right or left direction are selectively excited. However, when the Janus source excites acoustic surface waves propagating along the waveguide, the acoustic skyrmion modes in the upward or downward direction are selectively excited. This selective excitation of acoustic skyrmion modes by a directional acoustic source provides a new way to design advanced acoustic information processing functional devices.

Keywords:

Authors and contacts

1.
School of Mechanics and Photoelectric Physics, Anhui University of Science and Technology, Huainan 232001, China
2.
Center for Fundamental Physics, Anhui University of Science and Technology, Huainan 232001, China

Corresponding author: XU Huafeng, xhfeng716@126.com ; WU Hongwei, hwwu@aust.edu.cn

Funds: Project supported by the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant Nos. 2023AH051206, 2022AH040114) and the University Synergy Innovation Program of Anhui Province, China (Grant No. GXXT-2022-015).

FullText HTML

References

[1]	Skyrme T H R 1962 Nucl. Phys. 31 556 Google Scholar
[2]	Adkins G S, Nappi C R, Witten E 1983 Nucl. Phys. 228 3
[3]	Khawaja U AI, Stoof H 2001 Nature 411 918 Google Scholar
[4]	Su S W, Liu I K, Tsai Y C, Liu W M, Gou S C 2012 Phys. Rev. A 86 023601 Google Scholar
[5]	Fukuda J I, Zumer S 2011 Nat. Commun 2 246 Google Scholar
[6]	Duzgun A, Selinger J, Saxena A 2018 Phys. Rev. E 97 062706 Google Scholar
[7]	Robler U K, Bogdanov A N, Pfleiderer C 2006 Nature 442 7104
[8]	Tokura Y, Kanazawa N 2021 Chem. Rev. 121 5
[9]	Muhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Boni P 2009 Science 323 5916
[10]	Yu X Z, Koshibae W, Tokunaga Y, Shibata K, Taguchi Y, Nagaosa N, Tokura Y 2018 Nature 564 95 Google Scholar
[11]	陈崇, 马铭远, 潘峰, 宋成 2024 物理学报 73 058502 Google Scholar Chen C, Ma M Y, Pan F, Song C 2024 Acta Phys. Sin. 73 058502 Google Scholar
[12]	Zhang X C, Xia J, Zhou Y, Wang D W, Liu X X, Zhao W S, Ezawa M 2016 Phys. Rev. B 94 094420 Google Scholar
[13]	Zhang S L, Kronast F, Van der Laan G, Hesjedal T 2018 Nano Lett. 18 2
[14]	Bhukta M M M, Mishra A, Pradhan G, Mallick S, Singh B B, Bedanta S 2018 arXiv: 1810: 08262
[15]	Kezsmarki I, Bordacs S, Milde P, et al. 2015 Nat. Mater. 14 1116 Google Scholar
[16]	Nayak A K, Kumar V, Ma T, Werner P, Pippel E, Sahoo R, Damay F, Robler U K, Felser C, Parkin S S P 2017 Nature 548 561 Google Scholar
[17]	Gilbert D A, Maranville B B, Balk A L, et al. 2015 Nat. Commun. 6 8462 Google Scholar
[18]	Xia J, Zhang X C, Ezawa M, Tretiakov O A, Hou Z P, Wang W H, Zhao G P, Liu X X, Diep H T, Zhou Y 2020 Appl. Phys. Lett. 117 012403 Google Scholar
[19]	Nagaosa N, Tokura Y 2013 Nat. Nanotechnol. 8 899 Google Scholar
[20]	Fert A, Reyren N, Cros V 2017 Nat. Rev. Mater. 2 17031 Google Scholar
[21]	Du L P, Yang A P, Zayats A V, Yuan X C 2019 Nat. Phys. 15 650 Google Scholar
[22]	Davis T J, Janoschka D, Dreher P, Frank B, Meyer zu Heringdorf F J, Giessen H 2020 Science 368 6489
[23]	Tsesses S, Ostrovsky E, Cohen K, Gjonaj B, Lindner N H, Bartal G 2018 Science 361 6406
[24]	Bai C Y, Chen J, Zhang Y X, Zhang D W 2020 Opt. Express 28 10320 Google Scholar
[25]	Bliokh K Y, Rodriguez-Fortuno F J, Nori F, Zayats A V 2015 Nat. Photonics 9 796 Google Scholar
[26]	Shi P, Du L P, Yuan X C 2020 Nanophotonics 9 4619 Google Scholar
[27]	Karnieli A, Tsesses S, Bartal G, Arie A 2021 Nat. Commun. 12 1092 Google Scholar
[28]	Deng Z L, Shi T, Krasnok A, Li X P, Alu A 2022 Nat. Commun. 13 1
[29]	Li X H, Liu L L, Zhou Z X, Shen J R, Zhang Y R, Han G D, Li Z 2022 Adv. Opt. Mater. 10 15
[30]	Shi C Z, Zhao R K, Long Y, Yang S, Wang Y, Chen H, Ren J, Zhang X 2019 Natl. Sci. Rev. 6 4
[31]	Burns L, Bliokh K Y, Nori F, Dressel J 2020 New. J. Phys. 22 053050 Google Scholar
[32]	Long Y, Zhang D M, Yang C W, Ge J M, Chen H, Ren J 2020 Nat. Commun. 11 4716 Google Scholar
[33]	Bliokh K Y, Nori F 2019 Phys. Rev. B 99 020301
[34]	Bliokh K Y, Nori F 2019 Phys. Rev. B 99 174310 Google Scholar
[35]	Weiner M, Ni X, Alu A, Khanikaev A B 2022 Nat. Commun. 13 6332 Google Scholar
[36]	Long Y, Ge H, Zhang D M, Xu X Y, Ren J, Lu M H, Bao M, Chen H, Chen Y F 2020 NSR 7 6
[37]	Sun Q L, Peng Y G, Gao F, Li B, Zhu X F 2023 Phys. Rev. Appl. 20 024025 Google Scholar
[38]	Ge H, Xu X Y, Liu L, Xu R, Lin Z K, Yu S Y, Bao M, Jiang J H, Lu M H, Chen Y F 2021 Phys. Rev. Lett. 127 144502 Google Scholar
[39]	Hu P, Wu H W, Sun W J, Zhou N, Chen X, Yang Y Q, Sheng Z Q 2023 Appl. Phys. Lett. 122 022201 Google Scholar
[40]	Cselyuszka N, Secujski M, Engheta N, Crnojevic-Bengin V 2016 New. J. Phys. 18 103006 Google Scholar
[41]	Zhu J, Chen Y Y, Zhu X F, Garcia-Vidal F J, Yin X B, Zhang W L, Zhang X 2013 Sci. Rep. 3 1728 Google Scholar
[42]	Jia H, Lu M H, Ni X, Bao M, Li X D 2014 J. Appl. Phys. 116 124504 Google Scholar
[43]	Ooi K, Okada T, Tanaka K 2011 Phys. Rev. B 84 115405 Google Scholar
[44]	Xie P X, Sheng Z Q, Huang Z X, Hu P, Wu H W 2023 Appl. Phys. Lett. 122 222202 Google Scholar
[45]	Morse P, Ingard K 1986 Theoretical Acoustics (Princeton: Princeton University Press
[46]	张孝悦, 徐华锋, 陈婉娜, 周农, 孙文军, 吴宏伟 2024 物理学报 73 144301 Google Scholar Zhang X Y, Xu H F, Chen W N, Zhou N, Sun W J, Wu H W 2024 Acta Phys. Sin. 73 144301 Google Scholar

Cited By

图 1 (a) 组合结构示意图; (b) 不同波导宽度$ {\mathrm{Q}}{\mathrm{U}}{\mathrm{O}}{\mathrm{T}}{\mathrm{E}}{\mathrm{W}}{\mathrm{W}} $的色散关系曲线; (c)螺旋结构示意图; (d) 声学skyrmion模式图

Figure 1. (a) Schematic diagram of combination structure; (b) dispersion relation curves for different waveguide widths $ W $; (c) schematic diagram of spiral structure; (d) acoustic skyrmion pattern diagram.

DownLoad: Full-Size Img PowerPoint

图 2 (a) 顺时针旋转的自旋声源激发声表面波沿波导定向传播示意图; (b) 声表面波沿上方波导向右传播的声压强度变化曲线图; (c) 声表面波沿波导前后向传输比随频率变化的曲线图; (d) 声表面波沿下方波导向左传播的声压强度变化曲线图

Figure 2. (a) Schematic diagram of the directional propagation of surface acoustic waves along a waveguide excited by a clockwise rotating spin acoustic source; (b) graph of the variation of sound pressure intensity of surface acoustic waves propagating to the right along the upper waveguide; (c) graph of the ratio of forward and backward transmission of surface acoustic waves along the waveguide as a function of frequency; (d) graph of the variation in sound pressure intensity of surface acoustic waves propagating to the left along the lower waveguide.

DownLoad: Full-Size Img PowerPoint

图 3 (a) 顺时针旋转的自旋声源激发的组合结构中压力场分布; (b) 顺时针旋转的自旋声源激发的组合结构中的声学skyrmion模式; (c) 逆时针旋转的自旋声源激发的组合结构中的压力场分布; (d) 逆时针旋转的自旋声源激发的组合结构中的声学skyrmion模式

Figure 3. (a) Pressure field distribution in a combined structure excited by a clockwise rotating spin source; (b) acoustic skyrmion modes in combinatorial structures excited by clockwise rotating spin sources; (c) pressure field distribution in a combined structure excited by a counterclockwise rotating spin source; (d) acoustic skyrmion modes in combinatorial structures excited by counterclockwise rotating spin sources.

DownLoad: Full-Size Img PowerPoint

图 4 (a) 声学表面波沿波导向1号方向传播的示意图; (b) 螺旋结构中的声学skyrmion模式; (c) 声学表面波沿波导向2号方向传播; (d) 螺旋结构中的声学skyrmion模式; (e) 声学表面波沿波导向3号方向传播; (f) 螺旋结构中的声学skyrmion模式; (g) 声学表面波沿波导向4号方向传播; (h) 螺旋结构中的声学skyrmion模式

Figure 4. (a) Schematic diagram of acoustic surface waves propagating along the waveguide in the direction of No.1; (b) acoustic skyrmion modes in helical structures; (c) schematic diagram of acoustic surface waves propagating along the waveguide in the direction of No.2; (d) acoustic skyrmion modes in helical structures; (e) schematic diagram of acoustic surface waves propagating along the waveguide in the direction of No.3; (f) acoustic skyrmion modes in helical structures; (g) schematic diagram of acoustic surface waves propagating along the waveguide in the direction of No.4; (h) acoustic skyrmion modes in helical structures.

DownLoad: Full-Size Img PowerPoint

图 5 (a) 前向的Huygens声源激发的组合结构中的压力场分布; (b) 前向的Huygens声源激发的组合结构中的声学skyrmion模式; (c) 后向的Huygens声源激发的组合结构中的压力场分布; (d) 后向的Huygens声源激发的组合结构中的声学skyrmion模式

Figure 5. (a) Pressure field distribution in the combined structure excited by a forward Huygens sound source; (b) acoustic skyrmion modes in the composite structure excited by forward Huygens sound sources; (c) pressure field distribution in the combined structure excited by a backward Huygens sound source; (d) acoustic skyrmion modes in composite structures excited by backward Huygens acoustic sources.

DownLoad: Full-Size Img PowerPoint

图 6 (a) 向上的Janus声源激发的组合结构中的压力场分布; (b) 向上的Janus声源激发的组合结构中的声学skyrmion模式; (c) 向下的Janus声源激发的组合结构中的压力场分布; (d) 向下的Janus声源激发的组合结构中的声学skyrmion模式

Figure 6. (a) Pressure field distribution in a combined structure excited by an upward Janus source; (b) acoustic skyrmion modes in combinatorial structures excited by upward Janus sources; (c) pressure field distribution in a combined structure excited by a downward Janus source; (d) acoustic skyrmion modes in combinatorial structures excited by downward Janus sources.

DownLoad: Full-Size Img PowerPoint

图 7 (a) 向上的Janus声源激发的组合结构中的压力场分布; (b) 向上的Janus声源激发的组合结构中的声学skyrmion模式; (c) 向下的Janus声源激发的组合结构中的压力场分布; (d) 向下的Janus声源激发的组合结构中的声学skyrmion模式

Figure 7. (a) Pressure field distribution in a combined structure excited by an upward Janus source; (b) acoustic skyrmion modes in combinatorial structures excited by upward Janus sources; (c) pressure field distribution in a combined structure excited by a downward Janus source; (d) acoustic skyrmion modes in combinatorial structures excited by downward Janus sources.

DownLoad: Full-Size Img PowerPoint

[1]	Skyrme T H R 1962 Nucl. Phys. 31 556 Google Scholar
[2]	Adkins G S, Nappi C R, Witten E 1983 Nucl. Phys. 228 3
[3]	Khawaja U AI, Stoof H 2001 Nature 411 918 Google Scholar
[4]	Su S W, Liu I K, Tsai Y C, Liu W M, Gou S C 2012 Phys. Rev. A 86 023601 Google Scholar
[5]	Fukuda J I, Zumer S 2011 Nat. Commun 2 246 Google Scholar
[6]	Duzgun A, Selinger J, Saxena A 2018 Phys. Rev. E 97 062706 Google Scholar
[7]	Robler U K, Bogdanov A N, Pfleiderer C 2006 Nature 442 7104
[8]	Tokura Y, Kanazawa N 2021 Chem. Rev. 121 5
[9]	Muhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Boni P 2009 Science 323 5916
[10]	Yu X Z, Koshibae W, Tokunaga Y, Shibata K, Taguchi Y, Nagaosa N, Tokura Y 2018 Nature 564 95 Google Scholar
[11]	陈崇, 马铭远, 潘峰, 宋成 2024 物理学报 73 058502 Google Scholar Chen C, Ma M Y, Pan F, Song C 2024 Acta Phys. Sin. 73 058502 Google Scholar
[12]	Zhang X C, Xia J, Zhou Y, Wang D W, Liu X X, Zhao W S, Ezawa M 2016 Phys. Rev. B 94 094420 Google Scholar
[13]	Zhang S L, Kronast F, Van der Laan G, Hesjedal T 2018 Nano Lett. 18 2
[14]	Bhukta M M M, Mishra A, Pradhan G, Mallick S, Singh B B, Bedanta S 2018 arXiv: 1810: 08262
[15]	Kezsmarki I, Bordacs S, Milde P, et al. 2015 Nat. Mater. 14 1116 Google Scholar
[16]	Nayak A K, Kumar V, Ma T, Werner P, Pippel E, Sahoo R, Damay F, Robler U K, Felser C, Parkin S S P 2017 Nature 548 561 Google Scholar
[17]	Gilbert D A, Maranville B B, Balk A L, et al. 2015 Nat. Commun. 6 8462 Google Scholar
[18]	Xia J, Zhang X C, Ezawa M, Tretiakov O A, Hou Z P, Wang W H, Zhao G P, Liu X X, Diep H T, Zhou Y 2020 Appl. Phys. Lett. 117 012403 Google Scholar
[19]	Nagaosa N, Tokura Y 2013 Nat. Nanotechnol. 8 899 Google Scholar
[20]	Fert A, Reyren N, Cros V 2017 Nat. Rev. Mater. 2 17031 Google Scholar
[21]	Du L P, Yang A P, Zayats A V, Yuan X C 2019 Nat. Phys. 15 650 Google Scholar
[22]	Davis T J, Janoschka D, Dreher P, Frank B, Meyer zu Heringdorf F J, Giessen H 2020 Science 368 6489
[23]	Tsesses S, Ostrovsky E, Cohen K, Gjonaj B, Lindner N H, Bartal G 2018 Science 361 6406
[24]	Bai C Y, Chen J, Zhang Y X, Zhang D W 2020 Opt. Express 28 10320 Google Scholar
[25]	Bliokh K Y, Rodriguez-Fortuno F J, Nori F, Zayats A V 2015 Nat. Photonics 9 796 Google Scholar
[26]	Shi P, Du L P, Yuan X C 2020 Nanophotonics 9 4619 Google Scholar
[27]	Karnieli A, Tsesses S, Bartal G, Arie A 2021 Nat. Commun. 12 1092 Google Scholar
[28]	Deng Z L, Shi T, Krasnok A, Li X P, Alu A 2022 Nat. Commun. 13 1
[29]	Li X H, Liu L L, Zhou Z X, Shen J R, Zhang Y R, Han G D, Li Z 2022 Adv. Opt. Mater. 10 15
[30]	Shi C Z, Zhao R K, Long Y, Yang S, Wang Y, Chen H, Ren J, Zhang X 2019 Natl. Sci. Rev. 6 4
[31]	Burns L, Bliokh K Y, Nori F, Dressel J 2020 New. J. Phys. 22 053050 Google Scholar
[32]	Long Y, Zhang D M, Yang C W, Ge J M, Chen H, Ren J 2020 Nat. Commun. 11 4716 Google Scholar
[33]	Bliokh K Y, Nori F 2019 Phys. Rev. B 99 020301
[34]	Bliokh K Y, Nori F 2019 Phys. Rev. B 99 174310 Google Scholar
[35]	Weiner M, Ni X, Alu A, Khanikaev A B 2022 Nat. Commun. 13 6332 Google Scholar
[36]	Long Y, Ge H, Zhang D M, Xu X Y, Ren J, Lu M H, Bao M, Chen H, Chen Y F 2020 NSR 7 6
[37]	Sun Q L, Peng Y G, Gao F, Li B, Zhu X F 2023 Phys. Rev. Appl. 20 024025 Google Scholar
[38]	Ge H, Xu X Y, Liu L, Xu R, Lin Z K, Yu S Y, Bao M, Jiang J H, Lu M H, Chen Y F 2021 Phys. Rev. Lett. 127 144502 Google Scholar
[39]	Hu P, Wu H W, Sun W J, Zhou N, Chen X, Yang Y Q, Sheng Z Q 2023 Appl. Phys. Lett. 122 022201 Google Scholar
[40]	Cselyuszka N, Secujski M, Engheta N, Crnojevic-Bengin V 2016 New. J. Phys. 18 103006 Google Scholar
[41]	Zhu J, Chen Y Y, Zhu X F, Garcia-Vidal F J, Yin X B, Zhang W L, Zhang X 2013 Sci. Rep. 3 1728 Google Scholar
[42]	Jia H, Lu M H, Ni X, Bao M, Li X D 2014 J. Appl. Phys. 116 124504 Google Scholar
[43]	Ooi K, Okada T, Tanaka K 2011 Phys. Rev. B 84 115405 Google Scholar
[44]	Xie P X, Sheng Z Q, Huang Z X, Hu P, Wu H W 2023 Appl. Phys. Lett. 122 222202 Google Scholar
[45]	Morse P, Ingard K 1986 Theoretical Acoustics (Princeton: Princeton University Press
[46]	张孝悦, 徐华锋, 陈婉娜, 周农, 孙文军, 吴宏伟 2024 物理学报 73 144301 Google Scholar Zhang X Y, Xu H F, Chen W N, Zhou N, Sun W J, Wu H W 2024 Acta Phys. Sin. 73 144301 Google Scholar

[1]	Zhang Xiao-Yue, Xu Hua-Feng, Chen Wan-Na, Zhou Nong, Sun Wen-Jun, Wu Hong-Wei. Manipulation of directional acoustic spin angular momentum density based on gradient-structured waveguides. Acta Physica Sinica, 2024, 73(14): 144301. doi: 10.7498/aps.73.20240484
[2]	Liu Yi, Qian Zheng-Hong, Zhu Jian-Guo. Research progress of room temperature magnetic skyrmion and its application. Acta Physica Sinica, 2020, 69(23): 231201. doi: 10.7498/aps.69.20200984
[3]	Shen Hui-Jie, Yu Dian-Long, Tang Zhi-Yin, Su Yong-Sheng, Li Yan-Fei, Liu Jiang-Wei. Characteristics of low-frequency noise elimination in a fluid-filled pipe of dark acoustic metamaterial type. Acta Physica Sinica, 2019, 68(14): 144301. doi: 10.7498/aps.68.20190311
[4]	He Zi-Hou, Zhao Jing-Bo, Yao Hong, Jiang Juan-Na, Chen Xin. Sound insulation performance of thin-film acoustic metamaterials based on piezoelectric materials. Acta Physica Sinica, 2019, 68(13): 134302. doi: 10.7498/aps.68.20190245
[5]	Zhai Shi-Long, Wang Yuan-Bo, Zhao Xiao-Peng. A kind of tunable acoustic metamaterial for low frequency absorption. Acta Physica Sinica, 2019, 68(3): 034301. doi: 10.7498/aps.68.20181908
[6]	He Zi-Hou, Zhao Jing-Bo, Yao Hong, Chen Xin. Sound insulation performance of Helmholtz cavity with thin film bottom. Acta Physica Sinica, 2019, 68(21): 214302. doi: 10.7498/aps.68.20191131
[7]	Liu Shao-Gang, Zhao Yue-Chao, Zhao Dan. Bandgap and transmission spectrum characteristics of multilayered acoustic metamaterials with magnetorheological elastomer. Acta Physica Sinica, 2019, 68(23): 234301. doi: 10.7498/aps.68.20191334
[8]	Tian Yuan, Ge Hao, Lu Ming-Hui, Chen Yan-Feng. Research advances in acoustic metamaterials. Acta Physica Sinica, 2019, 68(19): 194301. doi: 10.7498/aps.68.20190850
[9]	Hu Yang-Fan, Wan Xue-Jin, Wang Biao. Magnetoelastic phenomena and mechanisms of magnetic skyrmion crystal. Acta Physica Sinica, 2018, 67(13): 136201. doi: 10.7498/aps.67.20180251
[10]	Liu Yi-Zhou, Zang Jiadong. Overview and outlook of magnetic skyrmions. Acta Physica Sinica, 2018, 67(13): 131201. doi: 10.7498/aps.67.20180619
[11]	Zhang Feng-Hui, Tang Yu-Fan, Xin Feng-Xian, Lu Tian-Jian. Micro-perforated acoustic metamaterial with honeycomb-corrugation hybrid core for broadband low frequency sound absorption. Acta Physica Sinica, 2018, 67(23): 234302. doi: 10.7498/aps.67.20181368
[12]	Liang Xue, Zhao Li, Qiu Lei, Li Shuang, Ding Li-Hong, Feng You-Hua, Zhang Xi-Chao, Zhou Yan, Zhao Guo-Ping. Skyrmions-based magnetic racetrack memory. Acta Physica Sinica, 2018, 67(13): 137510. doi: 10.7498/aps.67.20180764
[13]	Ding Chang-Lin, Dong Yi-Bao, Zhao Xiao-Peng. Research advances in acoustic metamaterials and metasurface. Acta Physica Sinica, 2018, 67(19): 194301. doi: 10.7498/aps.67.20180963
[14]	Hou Zhi-Peng, Ding Bei, Li Hang, Xu Gui-Zhou, Wang Wen-Hong, Wu Guang-Heng. Observation of new-type magnetic skymrions with extremerely high temperature stability and fabrication of skyrmion-based race-track memory device. Acta Physica Sinica, 2018, 67(13): 137509. doi: 10.7498/aps.67.20180419
[15]	Zheng Sheng-Jie, Xia Bai-Zhan, Liu Ting-Ting, Yu De-Jie. Subwavelength topological valley-spin states in the space-coiling acoustic metamaterials. Acta Physica Sinica, 2017, 66(22): 228101. doi: 10.7498/aps.66.228101
[16]	Liu Song, Luo Chun-Rong, Zhai Shi-Long, Chen Huai-Jun, Zhao Xiao-Peng. Inverse Doppler effect of acoustic metamaterial with negative mass density. Acta Physica Sinica, 2017, 66(2): 024301. doi: 10.7498/aps.66.024301
[17]	Liu Jiao, Hou Zhi-Lin, Fu Xiu-Jun. Mechanism for local resonant acoustic metamaterial. Acta Physica Sinica, 2015, 64(15): 154302. doi: 10.7498/aps.64.154302
[18]	Shen Hui-Jie, Wen Ji-Hong, Yu Dian-Long, Cai Li, Wen Xi-Sen. Research on a cylindrical cloak with active acoustic metamaterial layers. Acta Physica Sinica, 2012, 61(13): 134303. doi: 10.7498/aps.61.134303
[19]	Ding Chang-Lin, Zhao Xiao-Peng, Hao Li-Mei, Zhu Wei-Ren. Acoustic metamaterial with split hollow spheres. Acta Physica Sinica, 2011, 60(4): 044301. doi: 10.7498/aps.60.044301
[20]	Ding Chang-Lin, Zhao Xiao-Peng. Audible sound metamaterial. Acta Physica Sinica, 2009, 58(9): 6351-6355. doi: 10.7498/aps.58.6351

Catalog

Vol. 74, Issue 5 - 2025-03-05

Metrics

Abstract views: 913
PDF Downloads: 26
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板