Abstract: The known term cutoff denoting an abrupt transition from the guided mode to the leaky one becomes undefined when absorption losses in fiber material are taken into consideration.In order to study continuous transformation of the HE$-1m$/ guided mode into the leaky one in the fiber taper with absorbing cladding we have analyzed behavior of eigenvalue equation solutions in the complex plane of transverse wavenumber of the mode in cladding. Radial profiles of cylindrical components of power flow density showing HE$-12$/ mode transformation in the fiber taper are plotted. Size of the region of cutoff is found depending on the losses in the fiber material. Caustical spatial structures are shown forming by the rays which has different directions in the radial points of transverse cross-sections of the fiber. Radial power flow is shown to form multiple cones of the power distribution in the plane parallel to the fiber axis, the number of the cones depending on the absorption losses. !7
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