G. J. Chaplain, S. C. Hawkins, M. A. Peter, L. G. Bennetts, T. A. Starkey
{"title":"声晶格共振和广义瑞利-布洛赫波","authors":"G. J. Chaplain, S. C. Hawkins, M. A. Peter, L. G. Bennetts, T. A. Starkey","doi":"arxiv-2409.10074","DOIUrl":null,"url":null,"abstract":"The intrigue of waves on periodic lattices and gratings has resonated with\nphysicists and mathematicians alike for decades. In-depth analysis has been\ndevoted to the seemingly simplest array system: a one-dimensionally periodic\nlattice of two-dimensional scatterers embedded in a dispersionless medium\ngoverned by the Helmholtz equation. We investigate such a system and\nexperimentally confirm the existence of a new class of generalised\nRayleigh--Bloch waves that have been recently theorised to exist in classical\nwave regimes, without the need for resonant scatterers. Airborne acoustics\nserves as such a regime and here we experimentally observe the first\ngeneralised Rayleigh--Bloch waves above the first cut-off, i.e., in the\nradiative regime. We consider radiative acoustic lattice resonances along a\ndiffraction grating and connect them to generalised Rayleigh--Bloch waves by\nconsidering both short and long arrays of non-resonant 2D cylindrical Neumann\nscatterers embedded in air. On short arrays, we observe finite lattice\nresonances under continuous wave excitation, and on long arrays, we observe\npropagating Rayleigh--Bloch waves under pulsed excitation. We interpret their\nexistence by considering multiple wave scattering theory and, in doing so,\nunify differing nomenclatures used to describe waves on infinite periodic and\nfinite arrays and the interpretation of their dispersive properties.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Acoustic Lattice Resonances and Generalised Rayleigh--Bloch Waves\",\"authors\":\"G. J. Chaplain, S. C. Hawkins, M. A. Peter, L. G. Bennetts, T. A. Starkey\",\"doi\":\"arxiv-2409.10074\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The intrigue of waves on periodic lattices and gratings has resonated with\\nphysicists and mathematicians alike for decades. In-depth analysis has been\\ndevoted to the seemingly simplest array system: a one-dimensionally periodic\\nlattice of two-dimensional scatterers embedded in a dispersionless medium\\ngoverned by the Helmholtz equation. We investigate such a system and\\nexperimentally confirm the existence of a new class of generalised\\nRayleigh--Bloch waves that have been recently theorised to exist in classical\\nwave regimes, without the need for resonant scatterers. Airborne acoustics\\nserves as such a regime and here we experimentally observe the first\\ngeneralised Rayleigh--Bloch waves above the first cut-off, i.e., in the\\nradiative regime. We consider radiative acoustic lattice resonances along a\\ndiffraction grating and connect them to generalised Rayleigh--Bloch waves by\\nconsidering both short and long arrays of non-resonant 2D cylindrical Neumann\\nscatterers embedded in air. On short arrays, we observe finite lattice\\nresonances under continuous wave excitation, and on long arrays, we observe\\npropagating Rayleigh--Bloch waves under pulsed excitation. We interpret their\\nexistence by considering multiple wave scattering theory and, in doing so,\\nunify differing nomenclatures used to describe waves on infinite periodic and\\nfinite arrays and the interpretation of their dispersive properties.\",\"PeriodicalId\":501312,\"journal\":{\"name\":\"arXiv - MATH - Mathematical Physics\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10074\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10074","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Acoustic Lattice Resonances and Generalised Rayleigh--Bloch Waves
The intrigue of waves on periodic lattices and gratings has resonated with
physicists and mathematicians alike for decades. In-depth analysis has been
devoted to the seemingly simplest array system: a one-dimensionally periodic
lattice of two-dimensional scatterers embedded in a dispersionless medium
governed by the Helmholtz equation. We investigate such a system and
experimentally confirm the existence of a new class of generalised
Rayleigh--Bloch waves that have been recently theorised to exist in classical
wave regimes, without the need for resonant scatterers. Airborne acoustics
serves as such a regime and here we experimentally observe the first
generalised Rayleigh--Bloch waves above the first cut-off, i.e., in the
radiative regime. We consider radiative acoustic lattice resonances along a
diffraction grating and connect them to generalised Rayleigh--Bloch waves by
considering both short and long arrays of non-resonant 2D cylindrical Neumann
scatterers embedded in air. On short arrays, we observe finite lattice
resonances under continuous wave excitation, and on long arrays, we observe
propagating Rayleigh--Bloch waves under pulsed excitation. We interpret their
existence by considering multiple wave scattering theory and, in doing so,
unify differing nomenclatures used to describe waves on infinite periodic and
finite arrays and the interpretation of their dispersive properties.