  We present an approach to study the interaction between matter and evanescent
fields. The approach is based on the decomposition of evanescent plane waves
into multipoles of well-defined angular momentum transverse to both decay and
propagation directions. We use the approach to identify the origin of the
recently observed directional coupling of emitters into guided modes, and of
the opposite Zeeman state excitation of atoms near a fiber. We explain how to
rigorously quantify both effects, and show that the directionality and the
difference in excitation rates grow exponentially with the multipolar order of
the light-matter interaction. We also use the approach to study and maximize
the transverse torque exerted by an evanescent plane wave onto a given
spherical absorbing particle. The maximum occurs at the quadrupolar order of
the particle, and for a particular polarization of the plane wave. All the
obtained physical insights can be traced back to the two main features of the
decomposition of evanescent plane waves into transverse multipolar modes: A
polarization independent exponential dominance of modes with large transverse
angular momentum, and a polarization controlled parity selection rule.
