  We report a high-statistics measurement of the differential cross section of
the process gamma gamma --> K^0_S K^0_S in the range 1.05 GeV <= W <= 4.00 GeV,
where W is the center-of-mass energy of the colliding photons, using 972
fb^{-1} of data collected with the Belle detector at the KEKB asymmetric-energy
e^+ e^- collider operated at and near the Upsilon-resonance region. The
differential cross section is fitted by parameterized S-, D_0-, D_2-, G_0- and
G_2-wave amplitudes. In the D_2 wave, the f_2(1270), a_2(1320) and f_2'(1525)
are dominant and a resonance, the f_2(2200), is also present. The f_0(1710) and
possibly the f_0(2500) are seen in the S wave. The mass, total width and
product of the two-photon partial decay width and decay branching fraction to
the K bar{K} state Gamma_{gamma gamma}B(K bar{K}) are extracted for the
f_2'(1525), f_0(1710), f_2(2200) and f_0(2500). The destructive interference
between the f_2(1270) and a_2(1320) is confirmed by measuring their relative
phase. The parameters of the charmonium states chi_{c0} and chi_{c2} are
updated. Possible contributions from the chi_{c0}(2P) and chi_{c2}(2P) states
are discussed. A new upper limit for the branching fraction of the P- and
CP-violating decay channel eta_c --> K^0_S K^0_S is reported. The detailed
behavior of the cross section is updated and compared with QCD-based
calculations.
