负质量密度声学超材料的反常多普勒效应
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摘要
能够按照人们的意愿控制声波的传播一直是研究者们想要解决的问题.一类由人工微结构组成的声学超材料吸引了研究者的注意,因为它具有许多天然材料所不能实现的奇特性质,例如负折射、平板聚焦和反常多普勒等.本文中,我们制备了一种二维的负质量密度声学超材料,在频率1560—5580 Hz范围内质量密度为负值,折射率在1500—5480 Hz范围内为负值,设计了一种测量多普勒效应的测试装置,测试了其在1200—6500 Hz内的多普勒效应.实验结果表明:在所制备的声学超材料负折射区域内,以声源的频率为2000 Hz为例,当声源靠近探测器时,探测器探测到的频率为1999.27 Hz,与声源相比有0.73 Hz的减小;而当声源远离探测器时,探测器探测到的频率为2000.68 Hz,与声源相比有0.68 Hz的增大,即在频率点为2000 Hz时,有明显的反常多普勒现象.对整个负区域内进行选点测量,发现在整个负区域内有宽频带的反常多普勒效应现象.
It is always an issue for researchers to control the propagation of sound wave at will. A kind of acoustic metamaterial built with artificial microunits attracts the attention of researchers, because it possesses many unique properties that cannot be realized by natural materials, such as negative refractive index, slab focusing, and cloak. The Doppler effect leads to the frequency change of a wave because of the relative motion between the observer and the source. In 1968,Veselago [Veselago V G 1968 Soviet Physics Uspekhi 10 509] theoretically proposed that a metamaterial with a negative refraction can result in an inverse Doppler effect. The investigation of inverse Doppler effect has been developed with the improvement of metamaterials. However, the design methods of these metamaterials generally need ideal material parameters, which are difficult to obtain experimentally. Besides, although the inverse Doppler effects are realized by some electromagnetic metamaterials in optical and microwave frequencies, the relevant researches in acoustic metamaterials make slow progress. In this work, a 2D acoustic metamaterial with negative mass density is fabricated. Our previous work has demonstrated that the air in the internal cavity of the unit cell will vibrate back and forth to generate the vibration velocity when the air is driven by a sound source. As the source frequency reaches the resonant frequency,large amounts of energy will be stored in the internal cavity. This accumulation of energy will cause the acceleration of the air in opposite direction to the sound pressure, thus this metamaterial will exhibit negative mass density. In this case, the direction of the phase velocity is exactly opposite to that of the group velocity of the sound wave. Therefore,the inverse Doppler effect of sound wave can be realized by this metamaterial. Since the unit cells with different lengths have different resonant frequencies and there is only weak interaction among the adjacent unit cells, the frequency band of the metamaterial with negative mass density can be broaden by combining several different unit cells. Our previous experiments have demonstrated that the mass density and refractive index of this metamaterial are negative over a broad frequency range from 1560 Hz to 5580 Hz and 1500 Hz to 5480 Hz, respectively. A testing equipment is constructed to measure the Doppler effect of this metamaterial from 1200 Hz to 6500 Hz. The experimental results show that when the sound source witha frequency of 2000 Hz approaches to the detector, the detected frequency is 1999.27 Hz, which is0.73 Hz smaller than the source frequency; when the sound source recedes from the detector, the detected frequency is2000.68 Hz, which is 0.68 Hz larger than the source frequency. Therefore, the inverse Doppler effect appears at 2000 Hz.The experimental results within the whole frequency range of negative refractive index show broadband inverse Doppler phenomena.
It is always an issue for researchers to control the propagation of sound wave at will. A kind of acoustic metamaterial built with artificial microunits attracts the attention of researchers, because it possesses many unique properties that cannot be realized by natural materials, such as negative refractive index, slab focusing, and cloak. The Doppler effect leads to the frequency change of a wave because of the relative motion between the observer and the source. In 1968,Veselago [Veselago V G 1968 Soviet Physics Uspekhi 10 509] theoretically proposed that a metamaterial with a negative refraction can result in an inverse Doppler effect. The investigation of inverse Doppler effect has been developed with the improvement of metamaterials. However, the design methods of these metamaterials generally need ideal material parameters, which are difficult to obtain experimentally. Besides, although the inverse Doppler effects are realized by some electromagnetic metamaterials in optical and microwave frequencies, the relevant researches in acoustic metamaterials make slow progress. In this work, a 2D acoustic metamaterial with negative mass density is fabricated. Our previous work has demonstrated that the air in the internal cavity of the unit cell will vibrate back and forth to generate the vibration velocity when the air is driven by a sound source. As the source frequency reaches the resonant frequency,large amounts of energy will be stored in the internal cavity. This accumulation of energy will cause the acceleration of the air in opposite direction to the sound pressure, thus this metamaterial will exhibit negative mass density. In this case, the direction of the phase velocity is exactly opposite to that of the group velocity of the sound wave. Therefore,the inverse Doppler effect of sound wave can be realized by this metamaterial. Since the unit cells with different lengths have different resonant frequencies and there is only weak interaction among the adjacent unit cells, the frequency band of the metamaterial with negative mass density can be broaden by combining several different unit cells. Our previous experiments have demonstrated that the mass density and refractive index of this metamaterial are negative over a broad frequency range from 1560 Hz to 5580 Hz and 1500 Hz to 5480 Hz, respectively. A testing equipment is constructed to measure the Doppler effect of this metamaterial from 1200 Hz to 6500 Hz. The experimental results show that when the sound source witha frequency of 2000 Hz approaches to the detector, the detected frequency is 1999.27 Hz, which is0.73 Hz smaller than the source frequency; when the sound source recedes from the detector, the detected frequency is2000.68 Hz, which is 0.68 Hz larger than the source frequency. Therefore, the inverse Doppler effect appears at 2000 Hz.The experimental results within the whole frequency range of negative refractive index show broadband inverse Doppler phenomena.
引文
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[2]Pendry J B,Holden A J,Robbins D J,Stewart W J1999 IEEE Trans.Microwave Theory Tech.47 10
[3]Shelby R A,Smith D R,Schultz S 2001 Science 292 77
[4]Smith D R,Pendry J B,Wiltshire M C K 2004 Science305 788
[5]Bongard F,Lissek H,Mosig J R 2010 Phys.Rev.B 82094306
[6]Zhang S,Park Y S,Li J S,Lu X C,Zhang W L,Zhang X 2009 Phys.Rev.Lett.102 023901
[7]Zhu W R,Zhao X P,Guo J Q 2008 Appl.Phys.Lett.92 3
[8]Valentine J,Zhang S,Zentgraf T,Ulin-Avila E,Genov D A,Bartal G,Zhang X 2008 Nature 455 376
[9]Zhang X,Liu Z W 2008 Nat.Mater.7 435
[10]Liu Z W,Lee H,Xiong Y 2007 Science 315 1686
[11]Chen H S,Chen M 2010 Mater.Today 14 34
[12]Chen H J,Zhai S L,Ding C L,Liu S,Luo C R,Zhao X P 2014 J.Appl.Phys.115 054905
[13]Zhai S L,Chen H J,Ding C L,Zhao X P 2013 J.Phys.D:Appl.Phys.46 475105
[14]Chen H J,Zeng H C,Ding C L,Luo C R,Zhao X P2013 J.Appl.Phys.113 104902
[15]Ding C L,Zhao X P,Hao L M,Zhu W R 2011 Acta Phys.Sin.60 044301(in Chinese)[丁昌林,赵晓鹏,郝丽梅,朱卫仁2011物理学报60 044301]
[16]Ding C L,Hao L M,Zhao X P 2010 J.Appl.Phys.108074911
[17]Zeng H C,Luo C R,Chen H J,Zhai S L,Ding C L,Zhao X P 2013 Solid State Commun.173 14
[18]Cheng Y,Zhou C,Yuan B G,Wu D J,Wei Q,Liu X J2015 Nat.Mater.14 1013
[19]Cheng Y,Xu J Y,Liu X J 2008 Phys.Rev.B 77 045134
[20]Pendry J B,Schurig D,Smith D R 2006 Science 3121780
[21]Zhu J,Christensen J,Jung J,Martin-Moreno L,Yin X,Fok L,Zhang X,Garcia-Vidal F J 2011 Nat.Phys.7 52
[22]Veselago V G 1968 Soviet Physics Uspekhi 10 509
[23]Chen J B,Wang Y,Jia B H 2011 Nat.Photonics 5 239
[24]Seddon N,Bearpark T 2003 Science 302 1537
[25]Zhai S L,Zhao X P,Liu S,Shen F L,Li L L,Luo C R2016 Sci.Rep.6 32388
[26]Lee S H,Park C M,Seo Y M,Kim C K 2010 Phys.Rev.B 81 241102