Reflection and diffraction at the end of a cylindrical dielectric nanowire: Exact analytical solution

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 8, 2008, Pages

  Bordo, V G ^a  

^a PROKHOROV GENERAL PHYSICS INSTITUTE   (Russian Federation)

Author keywords

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Indexed keywords

EID: 50449085559     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.085318     Document Type: Article

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39. One can show that the Fourier-transformed amplitudes given by Eq. 28 tend to zero when |β| →∞. Then, according to the Jordan's lemma, the integral about the semicircle is equal to zero if z<0.
40. The quantity qj2 = kj2 - β2 changes its sign twice when one moves from one edge of the cut to another around the branch point. This means that its argument acquires a shift of 2π. Correspondingly, the quantity qj acquires a factor exp (iπ) =-1.
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