本篇論文由設計超穎介面出發，並應用於開放性共振腔。首先針對波的傳遞性質進行簡述，並在廣義司乃耳定律的基礎上，藉由超穎表面的相位偏移，控制波傳。我們設計了聲學超穎介面與彈性超穎介面，藉由調整內部結構以改變相位偏移，控制折射波的角度，並使用有限元素軟體COMSOL Multiphysics進行模擬驗證，也在模擬過程中，探討高階繞射的現象。最後，我們將超穎介面的負折射現象應用於開放性共振腔，使波傳在開放空間中進行建設性干涉，匯集能量。不同於過往以在特定頻率下具有負折射率特性之超穎材料或光子晶體組成的開放性共振腔，超穎介面的組成增加了波傳可行的頻率範圍，在能量擷取領域具備應用潛力。

The article is about designing simple metasurfaces, and applies them to the open cavity. At first, we briefly introduce the properties of the wave propagation, according to the generalized Snell’s law, we try to manipulate the refraction wave with additional phase shifting. We design both acoustic and elastic metasurfaces to control the refraction angle by adjusting the interior structures and use the finite elements software, COMSOL Multiphysics, to verify the results. We also investigate the high order diffraction . This study shows that metasurfaces can exhibit wave trapping through the geometry design, which realizes the concept of the open cavity. Different from the past research on open cavity , using metasurfaces broadens the range of feasible frequency in open cavity, and further expands the potential applications of energy harvesting.

[1] V. G. Veselago, ” The electrodynamics of substances with simultaneously negative values of and μ,” Sov. Phys. Usp. 10(4): 509-514, 1968.

[2] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, ” Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25): 4773, 1996.

[3] J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, ” Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter. 10(22): 4785, 1998.

[4] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, ” Magnetism from conductors and enhanced nonlinear phenomena,” IEEE T Microw Theory. 47(11): 2075-2084, 1999.

[5] D. R. Smith, D. C. Vier, W. Padilla, S. C. Nemat-Nasser, and S. Schultz, ” Loop-wire medium for investigating plasmons at microwave frequencies,” Appl. Phys. Lett. 75(10): 1425-1427, 1999.

[6] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz,
” Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18): 4184, 2000.

[7] J. B. Pendry, ” Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18): 3966, 2000.

[8] Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng,
” Locally resonant sonic materials,” Science 289(5485): 1734-1736, 2000.

[9] J. Li and C. T. Chan, ” Double-negative acoustic metamaterial,” Phys. Rev. E. 70(5): 055602, 2004.

[10] S. Yao, X. Zhou, and G. Hu, ” Experimental study on negative effective mass in a 1D mass–spring system,” New. J. Phys. 10(4): 043020, 2008.

[11] H. H. Huang, C. T. Sun, and G. L. Huang, ” On the negative effective mass density in acoustic metamaterials,” Int. J. Eng. Sci. 47(4): 610-617, 2009.
[12] I. L. Chang, Z. X. Liang, H. W. Kao, S. H. Chang, and C. Y. Yang, ” The wave attenuation mechanism of the periodic local resonant metamaterial,” J. Sound. Vib. 412: 349-359, 2018.

[13] N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, ” Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054): 333-337, 2011.

[14] D. Lin, P. Fan, E. Hasman, and M. L. Brongersma1, ” Dielectric gradient metasurface optical elements,” Science 345(6194): 298-302, 2014.

[15] P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. V. Shkunov, F. Strohkendl, Y. A. Zakharenkov, R. K. Dodds, and R. Byren, ” All-dielectric subwavelength metasurface focusing lens,” Opt. Express. 22(21): 26212-26221, 2014.

[16] S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, C. H. Chu, J. W. Chen, S. H. Lu, J. Chen, B. Xu, C. H. Kuan, T. Li, S. Zhu, and D. P. Tsai, ” Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1): 1-9, 2017.

[17] M. R. Schroeder, ” Diffuse sound reflection by maximum−length sequences,” J Acoustic. Soc. Am. 57(1): 149-150, 1975.

[18] K. Fujiwara and T. Miyajima, ” Absorption characteristics of a practically constructed Shroeder diffuser of quadratic-residue type,” Appl. Acoust. 35(2): 149-152, 1992.

[19] T. J. Cox and Y. W. Lam, ” Prediction and evaluation of the scattering from quadratic residue diffusers,” J. Acoustic. Soc. Am. 95(1): 297-305, 1994.

[20] Y. Li, B. Liang, Z. M. Gu, X. Y. Zou, and J. C. Cheng, ” Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces,” Sci. Rep. 3(1): 1-6, 2013.

[21] J. Mei and Y. Wu, ” Controllable transmission and total reflection through an impedance-matched acoustic metasurface,” New. J. Phys. 16(12): 123007, 2014.

[22] Y. Li, X. Jiang, R. Q. Li, B. Liang, X. Y. Zou, L. L. Yin, and J. C. Cheng,
” Experimental realization of full control of reflected waves with subwavelength acoustic metasurfaces,” Phys. Rev. Applied 2(6): 064002, 2014.

[23] Y. Li, X. Jiang, B. Liang, J. C. Cheng, and L. Zhang, ” Metascreen-based acoustic passive phased array,” Phys. Rev. Applied 4(2): 024003, 2015.

[24] G. Ma, M. Yang, S. Xiao, Z. Yang, and P. Sheng, ” Acoustic metasurface with hybrid resonances,” Nat. Mater. 13(9): 873–878, 2014.

[25] Y. Xie, W. Wang, H. Chen, A. Konneker, B. I. Popa, and S. A. Cummer,
” Wavefront modulation and subwavelength diffractive acoustics with an acoustic metasurface,” Nat. Commin. 5(1): 1-5, 2014.

[26] Y. Xie, A. Konneker, B. I. Popa, and S. A. Cummer, ” Tapered labyrinthine acoustic metamaterials for broadband impedance matching,” Appl. Phys. Lett. 103(20): 201906, 2013.

[27] H. Lee, J. K. Lee, H. M. Seung, and Y. Y. Kim, ” Mass-stiffness substructuring of an elastic metasurface for full transmission beam steering,” J. Mech. Phys. Solids 112: 577-593, 2018.

[28] X. Shen, C. T. Sun, M. V. Barnhart, and G. Huang, ” Elastic wave manipulation by using a phasecontrolling meta-layer,” J. Appl. Phys. 123(9): 091708, 2018.

[29] X. Su, Z. Lu, and A. N. Norris, ” Elastic metasurfaces for splitting SV- and P waves in elastic solids,” J. Appl. Phys. 123(9): 091701, 2018.

[30] M. Notomi, ” Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16): 10696, 2000.

[31] S. He, Y. Jin, Z. Ruan, and J. Kuang, ” On subwavelength and open resonators involving metamaterials of negative refraction index,” New J. Phys. 7(1): 210, 2005.

[32] Z. Ruan and S. He, ” Open cavity formed by a photonic crystal with negative effective index of refraction,” Optics Letters 30(17): 2308-2310, 2005.

[33] Z. Yang, J. Mei, M. Yang, N. H. Chan, and P. Sheng, ” Membrane-type acoustic metamaterial with negative dynamic mass,” Phys. Rev. Lett. 101(20): 204301, 2008.

[34] N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang,
” Ultrasonic metamaterials with negative modulus,” Nat. Mater. 5(6): 452–456, 2006.

[35] S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, and C. K. Kim, ” Acoustic metamaterial with negative modulus,” J. Phys.: Condens. Matter 21(17): 175704, 2009.

[36] H. H. Huang and C. T. Sun, ” Theoretical investigation of the behavior of an acoustic metamaterial with extreme Young's modulus,” J. Mech. Phys. Solids 59(10): 2070-2081, 2011.

[37] L. Cao, Z. Yang, and Y. Xu, ” Steering elastic SH waves in an anomalous way by metasurface,” J. Sound. Vib. 418: 1-14, 2018.