  A simple invisible structure made of two anisotropic homogeneous layers is
analyzed theoretically in temporal regime. The frequency dispersion is
introduced and analytic expression of the transient part of the field is
derived for large times when the structure is illuminated by a causal
excitation. This expression shows that the limiting amplitude principle applies
with transient fields decaying as the power -3/4 of the time. The quality of
the cloak is then reduced at short times and remains preserved at large times.
The one-dimensional theoretical analysis is supplemented with full-wave
numerical simulations in two-dimensional situations which confirm the effect of
dispersion.
