Manipulating elastic waves via engineered spatial curvature profiles

Matteo Mazzotti, Mohit Gupta, Christian Santangelo, Massimo Ruzzene

Research output: Chapter in Book/Entry/PoemConference contribution

2 Scopus citations


We investigate curved surfaces operating as geodesic lenses for elastic waves. Consistently with findings in optics, we show that wave propagation occurs along rays that correspond to the geodesics of the curved surfaces, and we establish the geometric equivalence between Gaussian curvature and refractive index. This equivalence is formulated for flexural waves in curved shells by showing that, in the short wavelength limit, the ray equation corresponds to the classical equation of geodesics. We leverage this result to identify a non-Euclidean transformation that maps the geometric profile of a isotropic curved waveguide into a spatially varying refractive index distribution for a planar waveguide. These theoretical predictions are validated first through numerical simulations, and subsequently through experiments on 3D printed curved membranes with different curvature distributions. Numerical and experimental findings confirm that focal regions and caustic networks are correctly predicted based on geodesic evaluations. Our results form the basis for the design of curved profiles that correspond to spatial distributions of the refractive index and induce focal points by forcing waves to propagate along predefined trajectories. The findings of this study also suggest curvature as an attractive alternative to strategies based on the local tailoring of material properties and geometrical patterns that have gained in popularity for gradient-index lens design.

Original languageEnglish (US)
Title of host publicationHealth Monitoring of Structural and Biological Systems XVI
EditorsPaul Fromme, Zhongqing Su
ISBN (Electronic)9781510649712
StatePublished - 2022
EventHealth Monitoring of Structural and Biological Systems XVI 2022 - Virtual, Online
Duration: Apr 4 2022Apr 10 2022

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceHealth Monitoring of Structural and Biological Systems XVI 2022
CityVirtual, Online


  • 3D printing
  • Elastic waves
  • Gaussian curvature
  • curved waveguides
  • geodesics
  • non-Euclidean transformations
  • ray tracing
  • refractive index

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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