We numerically calculate and analyse the electromagnetic fields,optical intensity distributions,polarization states and orbital angular momentum of some elliptic hollow modes in an elliptic dielectric hollow fiber(EDHF) by using Mathieu functions,and also calculate the optical potential of the blue-detuned _eHE_(11) mode evanescent-light wave for ~85Rb atoms,including the position-dependent van der Waals potential,and discuss briefly some potential applications of our EDHF in atom and molecule optics,etc.Our study shows that the vector electric field distributions of the odd modes in the cross section of the EDHF are the same as that of the even modes and with different boundary ellipses by rotating an angle ofπ/2,and the orbital angular momentum(OAM) of single HE(EH) mode is exactly equal to zero, while that of dual-mode in the EDHF is fractional in h,and has a sinusoidal oscillation as z varies.The EDHF can be used to produce various elliptic hollow beams,even to generate and study various atomic vortices with a fractional charge and its fractional quantum Hall effect in atomic Bose-Einstein condensate,and so on.
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