We investigate trapping geometries for cold, neutral atoms that can be created in the evanescent field of a tapered optical fibre by combining the fundamental mode with one of the next lowest possible modes, namely the HE21 mode. Counter propagating red-detuned HE21 modes are combined with a blue-detuned HE11 fundamental mode to form a potential in the shape of four intertwined spirals. By changing the polar- ization from circular to linear in each of the two counter-propagating HE21 modes simultaneously the 4-helix configuration can be transformed into a lattice configuration. The modification to the 4-helix configuration due to unwanted excitation of the the T E01 and T M01 modes is also discussed.
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