@article{Maling:2016:10.1098/rspa.2016.0103,
author = {Maling, B and Craster, RV},
doi = {10.1098/rspa.2016.0103},
journal = {Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences},
title = {Whispering Bloch modes},
url = {http://dx.doi.org/10.1098/rspa.2016.0103},
volume = {472},
year = {2016}
}

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TY  - JOUR
AB  - We investigate eigenvalue problems for the planar Helmholtz equation in open systems with a high order of rotational symmetry. The resulting solutions have similarities with the whispering gallery modes exploited in photonic micro-resonators and elsewhere, but unlike these do not necessarily require a surrounding material boundary, with confinement instead resulting from the geometry of a series of inclusions arranged in a ring. The corresponding fields exhibit angular quasi-periodicity reminiscent of Bloch waves, and hence we refer to them as whispering Bloch modes (WBMs). We show that if the geometry of the system is slightly perturbed such that the rotational symmetry is broken, modes with asymmetric field patterns can be observed, resulting in field enhancement and other potentially desirable effects. We investigate the WBMs of two specific geometries first using expansion methods and then by applying a two-scale asymptotic scheme.
AU  - Maling,B
AU  - Craster,RV
DO  - 10.1098/rspa.2016.0103
PY  - 2016///
SN  - 1364-5021
TI  - Whispering Bloch modes
T2  - Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2016.0103
UR  - http://hdl.handle.net/10044/1/38971
VL  - 472
ER  - 

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