The directional behavior of dominant components of algebraically special
spin-s fields near a spacelike, timelike or null conformal infinity is studied.
By extending our previous general investigations we concentrate on fields which
admit a pair of equivalent algebraically special null directions, such as the
Petrov type D gravitational fields or algebraically general electromagnetic
fields. We introduce and discuss a canonical choice of the reference tetrad
near infinity in all possible situations, and we present the corresponding
asymptotic directional structures using the most natural parametrizations.Comment: 20 pages, 6 figure