Weyl expansion
In
spherical wave as a linear combination of plane waves. In a Cartesian coordinate system, it can be denoted as[1][2]
- ,
where , and are the wavenumbers in their respective coordinate axes:
- .
The expansion is named after
evanescent wave components. It is often preferred to the Sommerfeld identity when the field representation is needed to be in Cartesian coordinates.[1]
The resulting Weyl integral is commonly encountered in
dipolar emissions near surfaces in nanophotonics,[6][7][8] holographic inverse scattering problems,[9] Green's functions in quantum electrodynamics[10] and acoustic or seismic waves.[11]
See also
- Angular spectrum method
- Fourier optics
- Green's function
- Plane wave expansion
- Sommerfeld identity
References
- ^ a b Chew 1990, p. 65-75.
- ^ Kinayman & Aksun 2005, p. 243-244.
- .
- doi:10.1109/8.9724.
- ^ Kinayman & Aksun 2005, p. 268.
- ^ Novotny & Hecht 2012, p. 335-338.
- hdl:2027.42/24649.
- S2CID 18698507.
- .
- .
- ^ Aki & Richards 2002, p. 189-192.
Sources
- ISBN 9781891389634.
- ISBN 9780780347496.
- Kinayman, Noyan; ISBN 9781844073832.
- Novotny, Lukas; Hecht, Bert (2012). Principles of Nano-Optics. Norwood: ISBN 9780511794193.
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