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Caustics in a field negatively refracted at a plane interface
Author(s) -
SHENDELEVA M. L.
Publication year - 2008
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.2008.01927.x
Subject(s) - caustic (mathematics) , refractive index , optics , physics , plane (geometry) , geometrical optics , field (mathematics) , refraction , plane wave , snell's law , point source , point (geometry) , cusp (singularity) , geometry , mathematics , pure mathematics , mathematical physics
Summary An electromagnetic field radiated by a line source situated near a plane interface between a medium with positive refractive index and a medium with negative refractive index is considered by using the geometrical optics approach. Rays and wave fronts of the refracted field are constructed using Fermat's principle. It is shown that the negatively refracted rays intersecting in pairs create 2‐fold caustics that meet at a cusp point. The cusp of the caustic is directed towards the interface for | n | > 1 and away from the interface for | n | < 1, where n is the relative refractive index. It is also shown that wave fronts of the refracted field propagate towards the interface, in the direction from negative to positive optical path lengths.