Rights statement: This is the author’s version of a work that was accepted for publication in Wave Motion. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Wave Motion, 77, 2017 DOI: 10.1016/j.wavemoti.2017.11.002
Accepted author manuscript, 1.32 MB, PDF document
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Generalized transformation design
T2 - Metrics, speeds, and diffusion
AU - Kinsler, Paul
AU - McCall, Martin W.
N1 - This is the author’s version of a work that was accepted for publication in Wave Motion. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Wave Motion, 77, 2017 DOI: 10.1016/j.wavemoti.2017.11.002
PY - 2018/3
Y1 - 2018/3
N2 - We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary to specify the physical process for which a specific transformation design is to be implemented. The principal approximation is the neglect of wave impedance, an attribute that plays no role in ray propagation, and is therefore irrelevant for pure ray devices; another constraint is that for waves the spatial variation in material parameters needs to be sufficiently small compared with the wavelength. The key link between our general formulation and a specific implementation is how the spatial metric relates to the speed of disturbance in a given medium, whether it is electromagnetic, acoustic, or diffusive. Notably, we show that our generalised ray theory, in allowing for anisotropic indexes (speeds), generates the same predictions as does a wave theory, and the results are closely related to those for diffusion processes.
AB - We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary to specify the physical process for which a specific transformation design is to be implemented. The principal approximation is the neglect of wave impedance, an attribute that plays no role in ray propagation, and is therefore irrelevant for pure ray devices; another constraint is that for waves the spatial variation in material parameters needs to be sufficiently small compared with the wavelength. The key link between our general formulation and a specific implementation is how the spatial metric relates to the speed of disturbance in a given medium, whether it is electromagnetic, acoustic, or diffusive. Notably, we show that our generalised ray theory, in allowing for anisotropic indexes (speeds), generates the same predictions as does a wave theory, and the results are closely related to those for diffusion processes.
KW - Propagation
KW - Transformation
KW - Metric
KW - Speed
KW - Diffusion
KW - Ray
U2 - 10.1016/j.wavemoti.2017.11.002
DO - 10.1016/j.wavemoti.2017.11.002
M3 - Journal article
VL - 77
SP - 91
EP - 106
JO - Wave Motion
JF - Wave Motion
SN - 0165-2125
ER -