Abstract
A method is presented for the calculation of vector near fields of a
tapered fiber probe in presence of a rotationally asymmetric sample by
numerically solving boundary integral equations of two scalar Borgnis
potentials. For the convenience of the description of all the boundaries,
cylindrical coordinates and Cartesian coordinates are, respectively, used in
the domains, where the rotationally symmetric tapered fiber probe and the
rotationally asymmetric sample are located. The Borgnis potentials on the
surface of the fiber probe are harmonically expanded in the azimuthal
direction of the cylindrical coordinates so that the fiber probe can be
treated as a 2-D structure. Only the Borgnis potentials on the surface of
the sample, rather than those on all surfaces, are first calculated. The
Borgnis potentials on other surfaces could be finally calculated by their
relationship with the solved Borgnis potentials on the surface of the
sample. With this method, the memory requirement can be considerably reduced
in calculation and the method can easily extend to the solution of
electromagnetic fields in structures much more complex.
© 2010 IEEE
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