Construction of trapped modes for wave guides and diffraction gratings
Philip McIver
Christopher Linton
Maureen McIver
2134/11796
https://repository.lboro.ac.uk/articles/journal_contribution/Construction_of_trapped_modes_for_wave_guides_and_diffraction_gratings/9377456
This paper describes various methods for the construction of trapped-mode solutions
within wave guides and along diffraction gratings; in the latter case the solutions are
often called Rayleigh-Bloch waves. One of the main results is the explicit construction
of a number of new trapped-mode solutions within a wave guide that correspond
to eigenvalues that are embedded in the continuous spectrum of the relevant operators.
The method of construction is to take 'trial' solutions of the field equation
that satisfy the required conditions on the guide walls and have the correct decay
at large distances and then to identify lines that can be interpreted as the boundary
of a structure within the wave guide. The same idea is also investigated for
Rayleigh-Bloch waves within the context of diffraction gratings. Sensible choices of
trial function are made by reference to solutions for a grating of circular cylinders,
obtained by a multipole expansion method, and an approximate solution for more
general geometries.
2013-02-27 08:46:31
Eigenvalues
Unbounded domain
Gratings
Mathematical Sciences not elsewhere classified