  In this article, we review our recent studies of microwave penetration depth,
lower critical fields, and quasiparticle conductivity in the superconducting
state of Fe-arsenide superconductors. High-sensitivity microwave surface
impedance measurements of the in-plane penetration depth in single crystals of
electron-doped PrFeAsO1-y (y~0.1) and hole-doped Ba1-xKxFe2As2 (x~0.55) are
presented. In clean crystals of Ba1-xKxFe2As2, as well as in PrFeAsO1-y
crystals, the penetration depth shows flat temperature dependence at low
temperatures, indicating that the superconducting gap opens all over the Fermi
surface. The temperature dependence of superfluid density in both systems is
most consistent with the existence of two different gaps. In Ba1-xKxFe2As2, we
find that the superfluid density is sensitive to degrees of disorder inherent
in the crystals, implying unconventional impurity effect. We also determine the
lower critical field $H_{c1}$ in PrFeAsO1-y by using an array of micro-Hall
probes. The temperature dependence of $H_{c1}$ saturates at low temperatures,
fully consistent with the superfluid density determined by microwave
measurements. The anisotropy of $H_{c1}$ has a weak temperature dependence with
smaller values than the anisotropy of upper critical fields at low
temperatures, which further supports the multi-gap superconductivity in
Fe-arsenide systems. The quasiparticle conductivity shows an enhancement in the
superconducting state, which suggests the reduction of quasiparticle scattering
rate due to the gap formation below $T_c$. From these results, we discuss the
structure of the superconducting gap in these Fe-arsenides, in comparison with
the high-$T_c$ cuprate superconductors.
