Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Microscale Architected Materials for Elastic Waveguiding: Fabrication and Dynamic Characterization across Length and Time Scales

Vignesh Kannan*,§

Charles Dorn†,§

Ute Drechsler

Dennis M. Kochmann‡

  • Mechanics & Materials Laboratory, ETH Zurich, Zurich, 8092, Switzerland

  • *Contact author: vignesh.kannan@polytechnique.edu
  • †Contact author: cdorn@uw.edu
  • ‡Contact author: dmk@ethz.ch
  • §Also at Mechanics & Materials Laboratory, ETH Zurich, Zurich, 8092, Switzerland.

Phys. Rev. X 16, 011047 – Published 5 March, 2026

DOI: https://doi.org/10.1103/21w4-zn1s

Abstract

We present an experimental protocol for the fabrication and characterization of scalable microarchitected elastic waveguides. Using silicon microfabrication techniques, we develop free-standing 2D truss-based architected waveguides with a maximum diameter of 80 mm, unit cells size of 100  μm, and minimum beam width of 5  μm, thus achieving scale separation. To characterize elastic wave propagation, we introduce a custom-built scanning optical pump-probe experiment that enables contactless excitation of elastic wave modes and full spatiotemporal reconstruction of wave propagation across hundreds of unit cells with subunit cell resolution. Results on periodic architectures show excellent agreement with finite element simulations and equivalent experimental data at larger length scales. Motivated by scalable computational inverse design, we fabricate a specific example of a spatially graded waveguide and demonstrate its ability to guide elastic waves along an arbitrary predesigned path.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Article Text

References (75)

  1. L. Brillouin, Wave Propagation in Periodic Structures (McGraw-Hill, New York, 1946), p. 2.
  2. M. I. Hussein, M. J. Leamy, and M. Ruzzene, Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook, Appl. Mech. Rev. 66, 040802 (2014).
  3. A. S. Phani, J. Woodhouse, and N. Fleck, Wave propagation in two-dimensional periodic lattices, J. Acoust. Soc. Am. 119, 1995 (2006).
  4. B. R. Thompson, Elastic-wave propagation in random polycrystals: Fundamentals and application to nondestructive evaluation, in Imaging of Complex Media with Acoustic and Seismic Waves (Springer, Berlin Heidelberg, 2002), pp. 233–257.
  5. J. O. Vasseur, P. A. Deymier, G. Frantziskonis, G. Hong, B. Djafari-Rouhani, and L. Dobrzynski, Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media, J. Phys. Condens. Matter 10, 6051 (1998).
  6. O. Sigmund and J. Søndergaard Jensen, Systematic design of phononic band-gap materials and structures by topology optimization, Phil. Trans. R. Soc. A 361, 1001 (2003).
  7. G. Trainiti, J. J. Rimoli, and M. Ruzzene, Wave propagation in undulated structural lattices, Int. J. Solids Struct. 97–98, 431 (2016).
  8. A. J. Zelhofer and D. M. Kochmann, On acoustic wave beaming in two-dimensional structural lattices, Int. J. Solids Struct. 115–116, 248 (2017).
  9. O. R. Bilal and M. I. Hussein, Ultrawide phononic band gap for combined in-plane and out-of-plane waves, Phys. Rev. E 84, 065701(R) (2011).
  10. M. Schaeffer, G. Trainiti, and M. Ruzzene, Optical measurement of in-plane waves in mechanical metamaterials through digital image correlation, Sci. Rep. 7, 42437 (2017).
  11. M. Miniaci, R. K. Pal, B. Morvan, and M. Ruzzene, Experimental observation of topologically protected helical edge modes in patterned elastic plates, Phys. Rev. X 8, 031074 (2018).
  12. B. Telgen, V. Kannan, J.-C. Bail, C. Dorn, H. Niese, and D. M. Kochmann, Rainbow trapping of out-of-plane mechanical waves in spatially variant beam lattices, J. Mech. Phys. Solids 191, 105762 (2024).
  13. C. Dorn and D. M. Kochmann, Conformally graded metamaterials for elastic wave guidance, Extreme Mech. Lett. 65, 102091 (2023).
  14. M. Wormser, F. Wein, M. Stingl, and C. Körner, Design and additive manufacturing of 3D phononic band gap structures based on gradient based optimization, Materials 10, 1125 (2017).
  15. A. Kruisová, M. Ševčík, H. Seiner, P. Sedlák, B. Román-Manso, P. Miranzo, M. Belmonte, and M. Landa, Ultrasonic bandgaps in 3D-printed periodic ceramic microlattices, Ultrasonics 82, 91 (2018).
  16. H. Rice, J. Kennedy, P. Göransson, L. Dowling, and D. Trimble, Design of a kelvin cell acoustic metamaterial, J. Sound Vib. 472, 115167 (2020).
  17. Y. Xie, Y. Fu, Z. Jia, J. Li, C. Shen, Y. Xu, H. Chen, and S. A. Cummer, Acoustic imaging with metamaterial Luneburg lenses, Sci. Rep. 8, 16188 (2018).
  18. L. Zhao, E. Laredo, O. Ryan, A. Yazdkhasti, H.-T. Kim, R. Ganye, T. Horiuchi, and M. Yu, Ultrasound beam steering with flattened acoustic metamaterial Luneburg lens, Appl. Phys. Lett. 116, 071902 (2020).
  19. G. J. Chaplain, D. Pajer, J. M. De Ponti, and R. V. Craster, Delineating rainbow reflection and trapping with applications for energy harvesting, New J. Phys. 22, 063024 (2020).
  20. R. V. Craster, J. Kaplunov, and A. V. Pichugin, High-frequency homogenization for periodic media, Proc. R. Soc. A 466, 2341 (2010).
  21. O. Schnitzer, Waves in slowly varying band-gap media, SIAM J. Appl. Math. 77, 1516 (2017).
  22. C. Dorn and D. M. Kochmann, Ray theory for elastic wave propagation in graded metamaterials, J. Mech. Phys. Solids 168, 105049 (2022).
  23. C. Dorn and D. M. Kochmann, Inverse design of graded phononic materials via ray tracing, J. Appl. Phys. 134, 195103 (2023).
  24. C. Dorn, V. Kannan, U. Drechsler, and D. M. Kochmann, Graded phononic metamaterials: Scalable design meets scalable microfabrication, arXiv:2507.01874.
  25. L. R. Meza, G. P. Phlipot, C. M. Portela, A. Maggi, L. C. Montemayor, A. Comella, D. M. Kochmann, and J. R. Greer, Reexamining the mechanical property space of three-dimensional lattice architectures, Acta Mater. 140, 424 (2017).
  26. A. Vyatskikh, S. Delalande, A. Kudo, X. Zhang, C. M. Portela, and J. R. Greer, Additive manufacturing of 3D nano-architected metals, Nat. Commun. 9, 593 (2018).
  27. J. Bauer, L. R. Meza, T. A. Schaedler, R. Schwaiger, X. Zheng, and L. Valdevit, Nanolattices: An emerging class of mechanical metamaterials, Adv. Mater. 29, 1701850 (2017).
  28. A. Shaikeea, H. Cui, M. O’Masta, X. R. Zheng, and V. S. Deshpande, The toughness of mechanical metamaterials, Nat. Mater. 21, 297 (2022).
  29. S. Krödel and C. Daraio, Microlattice metamaterials for tailoring ultrasonic transmission with elastoacoustic hybridization, Phys. Rev. Appl. 6, 064005 (2016).
  30. P. Kiefer, V. Hahn, S. Kalt, Q. Sun, Y. M. Eggeler, and M. Wegener, A multi-photon (7×7)-focus 3D laser printer based on a 3D-printed diffractive optical element and a 3D-printed multi-lens array, Light Sci. Appl. 4, 28 (2024).
  31. V. Harinarayana and Y. Shin, Two-photon lithography for three-dimensional fabrication in micro/nanoscale regime: A comprehensive review, Opt. Laser Technol. 142, 107180 (2021).
  32. M. A. Saccone, R. A. Gallivan, K. Narita, D. W. Yee, and J. R. Greer, Additive manufacturing of micro-architected metals via hydrogel infusion, Nature (London) 612, 685 (2022).
  33. H. Espinosa, B. Prorok, and M. Fischer, A methodology for determining mechanical properties of freestanding thin films and MEMS materials, J. Mech. Phys. Solids 51, 47 (2003).
  34. M. D. Uchic, D. M. Dimiduk, J. N. Florando, and W. D. Nix, Sample dimensions influence strength and crystal plasticity, Science 305, 986 (2004).
  35. Y. Zhu, C. Ke, and H. D. Espinosa, Experimental techniques for the mechanical characterization of one-dimensional nanostructures, Exp. Mech. 47, 7 (2007).
  36. S. Naceri, M. Rusinowicz, M. Coulombier, and T. Pardoen, Cracking resistance of nanostructured freestanding tungsten films, J. Mech. Phys. Solids 200, 106143 (2025).
  37. O. Loh, A. Vaziri, and H. D. Espinosa, The potential of MEMS for advancing experiments and modeling in cell mechanics, Exp. Mech. 49, 105 (2007).
  38. S. Hosmane, A. Fournier, R. Wright, L. Rajbhandari, R. Siddique, I. H. Yang, K. T. Ramesh, A. Venkatesan, and N. Thakor, Valve-based microfluidic compression platform: Single axon injury and regrowth, Lab Chip 11, 3888 (2011).
  39. B. L. Boyce, A sequential tensile method for rapid characterization of extreme-value behavior in microfabricated materials, Exp. Mech. 50, 993 (2009).
  40. Y. Kai, S. Dhulipala, R. Sun, J. Lem, W. DeLima, T. Pezeril, and C. M. Portela, Dynamic diagnosis of metamaterials through laser-induced vibrational signatures, Nature (London) 623, 514 (2023).
  41. I. Chasiotis, Experimental mechanics of MEMS and thin films, in Micromechanics and Nanoscale Effects (Springer, Netherlands, 2004), pp. 3–37.
  42. W. N. Sharpe, J. Pulskamp, D. S. Gianola, C. Eberl, R. G. Polcawich, and R. J. Thompson, Strain measurements of silicon dioxide microspecimens by digital imaging processing, Exp. Mech. 47, 649 (2007).
  43. F. Kotz, A. S. Quick, P. Risch, T. Martin, T. Hoose, M. Thiel, D. Helmer, and B. E. Rapp, Two-photon polymerization of nanocomposites for the fabrication of transparent fused silica glass microstructures, Adv. Mater. 33, 2006341 (2021).
  44. L. Jonušauskas, D. Gailevičius, S. Rekštytė, T. Baldacchini, S. Juodkazis, and M. Malinauskas, Mesoscale laser 3D printing, Opt. Express 27, 15205 (2019).
  45. E. Skliutas, G. Merkininkaitė, S. Maruo, W. Zhang, W. Chen, W. Deng, J. Greer, G. v. Freymann, and M. Malinauskas, Multiphoton 3D lithography, Nat. Rev. Methods Primers 5, 15 (2025).
  46. J. Cha and C. Daraio, Electrical tuning of elastic wave propagation in nanomechanical lattices at MHz frequencies, Nat. Nanotechnol. 13, 1016 (2018).
  47. J. Cha, K. W. Kim, and C. Daraio, Experimental realization of on-chip topological nanoelectromechanical metamaterials, Nature (London) 564, 229 (2018).
  48. M. Thelen, N. Bochud, M. Brinker, C. Prada, and P. Huber, Laser-excited elastic guided waves reveal the complex mechanics of nanoporous silicon, Nat. Commun. 12, 3597 (2021).
  49. R. H. Olsson III, I. F. El-Kady, M. F. Su, M. R. Tuck, and J. G. Fleming, Microfabricated VHF acoustic crystals and waveguides, Sens. Actuators A 145–146, 87 (2008).
  50. R. H. Olsson and I. El-Kady, Microfabricated phononic crystal devices and applications, Meas. Sci. Technol. 20, 012002 (2008).
  51. F. Maspero, J. M. De Ponti, L. Iorio, A. Esposito, R. Bertacco, A. di Matteo, A. Corigliano, and R. Ardito, Phononic graded meta-MEMS for elastic wave amplification and filtering, J. Microelectromech. Syst. 32, 522 (2023).
  52. J. M. De Ponti, X. Zhao, L. Iorio, T. Maggioli, M. Colangelo, B. Davaji, R. Ardito, R. V. Craster, and C. Cassella, Localized topological states beyond fano resonances via counter-propagating wave mode conversion in piezoelectric microelectromechanical devices, Nat. Commun. 15, 9617 (2024).
  53. R. M. White and F. W. Voltmer, Direct piezoelectric coupling to surface elastic waves, Appl. Phys. Lett. 7, 314 (1965).
  54. S. J. Davies, C. Edwards, G. S. Taylor, and S. B. Palmer, Laser-generated ultrasound: Its properties, mechanisms and multifarious applications, J. Phys. D 26, 329 (1993).
  55. S. Krishnaswamy, Photoacoustic characterization of materials, in Springer Handbook of Experimental Solid Mechanics (Springer, US, 2008), pp. 769–800.
  56. K. A. Nelson, R. D. Miller, D. R. Lutz, and M. D. Fayer, Picosecond transient grating generation of tunable ultrasonic waves, in Picosecond Lasers and Applications, edited by L. S. Goldberg (SPIE, Los Angeles, 1982), Vol. 0322, pp. 68–74.
  57. J. A. Rogers, A. A. Maznev, M. J. Banet, and K. A. Nelson, Optical generation and characterization of acoustic waves in thin films: Fundamentals and applications, Annu. Rev. Mater. Sci. 30, 117 (2000).
  58. P. Stoklasová, T. Grabec, K. Zoubková, P. Sedlák, S. Krátký, and H. Seiner, Laser-ultrasonic characterization of strongly anisotropic materials by transient grating spectroscopy, Exp. Mech. 61, 663 (2021).
  59. S. Rezazadeh-Kalehbasti, L. W. Liu, H. J. Maris, and P. R. Guduru, In situ measurement of phase boundary kinetics during initial lithiation of crystalline silicon through picosecond ultrasonics, Exp. Mech. 59, 681 (2019).
  60. A. Khanolkar, S. Wallen, M. Abi Ghanem, J. Jenks, N. Vogel, and N. Boechler, A self-assembled metamaterial for lamb waves, Appl. Phys. Lett. 107, 071903 (2015).
  61. M. Hiraiwa, M. Abi Ghanem, S. P. Wallen, A. Khanolkar, A. A. Maznev, and N. Boechler, Complex contact-based dynamics of microsphere monolayers revealed by resonant attenuation of surface acoustic waves, Phys. Rev. Lett. 116, 198001 (2016).
  62. R. J. Dewhurst and Q. Shan, Optical remote measurement of ultrasound, Meas. Sci. Technol. 10, R139 (1999).
  63. N. R. Sottos, W. R. Scott, and R. L. McCullough, Micro-interferometry for measurement of thermal displacements at fiber/matrix interfaces, Exp. Mech. 31, 98 (1991).
  64. P. H. Otsuka, S. Mezil, O. Matsuda, M. Tomoda, A. A. Maznev, T. Gan, N. Fang, N. Boechler, V. E. Gusev, and O. B. Wright, Time-domain imaging of gigahertz surface waves on an acoustic metamaterial, New J. Phys. 20, 013026 (2018).
  65. KLayout Layout Viewer And Editor—klayout.de, https://www.klayout.de/doc.html, (Accessed 22-05-2025).
  66. A. Vega-Flick, J. K. Eliason, A. A. Maznev, A. Khanolkar, M. Abi Ghanem, N. Boechler, J. J. Alvarado-Gil, and K. A. Nelson, Laser-induced transient grating setup with continuously tunable period, Rev. Sci. Instrum. 86, 123101 (2015).
  67. I. Arias and J. D. Achenbach, Thermoelastic generation of ultrasound by line-focused laser irradiation, Int. J. Solids Struct. 40, 6917 (2003).
  68. R. Ganesh and S. Gonella, Experimental evidence of directivity-enhancing mechanisms in nonlinear lattices, Appl. Phys. Lett. 110, 084101 (2017).
  69. P. Celli, B. Yousefzadeh, C. Daraio, and S. Gonella, Bandgap widening by disorder in rainbow metamaterials, Appl. Phys. Lett. 114, 091903 (2019).
  70. R. Lakes, Viscoelastic properties of materials, in Viscoelastic Materials (Cambridge University Press, Cambridge, England, 2009), pp. 207–270.
  71. B. Telgen, V. Kannan, J.-C. Bail, C. Dorn, H. Niese, and D. M. Kochmann, Rainbow trapping of out-of-plane mechanical waves in spatially variant beam lattices, J. Mech. Phys. Solids 191, 105762 (2024).
  72. M. A. Hopcroft, W. D. Nix, and T. W. Kenny, What is the Young’s modulus of silicon?, J. Microelectromech. Syst. 19, 229 (2010).
  73. D. M. Kochmann, V. Kannan, and C. Dorn, Datasets and codes, 10.3929/ethz-b-000743304 (2026).
  74. tukey 2014; scipy v1.16.2 Manual—docs.scipy.org, https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.windows.tukey.html (Accessed 05-01-2026).
  75. Mechanics and Materials Lab, ae108 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation