  Spin fluctuations are considered to be one of the candidates that drive a
sign-reversed s^{\pm} superconducting state in the iron pnictides. In the
magnetic scenario, whether the spin fluctuation spectrum exhibits certain
unique fine structures is an interesting aspect for theoretical study in order
to understand experimental observations. We investigate the detailed momentum
dependence of the short-range spin fluctuations using a 2-orbital model in the
self-consistent fluctuation exchange approximation and find that a common
feature of those fluctuations that are capable of inducing a fully gapped
s^{\pm} state is the momentum anisotropy with lengthened span along the
direction transverse to the antiferromagnetic momentum transfer. Performing a
qualitative analysis based on the orbital character and the deviation from
perfect nesting of the electronic structure for the 2-orbital and a more
complete 5-orbital model, we gain the insight that this type of anisotropic
spin fluctuations favor superconductivity due to their enhancement of
intra-orbital, but inter-band, pair scattering processes. The momentum
anisotropy leads to elliptically shaped magnetic responses which have been
observed in inelastic neutron scattering measurements. Meanwhile, our detailed
study on the magnetic and the electronic spectrum shows that the dispersion of
the magnetic resonance mode in the nearly isotropic s^{\pm} superconducting
state exhibits anisotropic propagating behavior in an upward pattern and the
coupling of the resonance mode to fermions leads to a dip feature in the
spectral function.
