  Both explicit analysis and FEM numerical simulation are used to analyze the
field distribution of a line current in the so-called Maxwell's fish eye lens
[bounded with a perfectly electrical conductor (PEC) boundary]. We show that
such a 2D Maxwell's fish eye lens cannot give perfect imaging due to the fact
that high order modes of the object field can hardly reach the image point in
Maxwell's fish eye lens. If only zeroth order mode is excited, a subwavelength
image of a sharp object may be achieved in some cases, however, its spot-size
is larger than the spot size of the initial object field. The image resolution
is determined by the field spot size of the image corresponding to the zeroth
order component of the object field. Our explicit analysis consists very well
with the FEM results for a fish eye lens. Time-domain simulation is also given
to verify our conclusion. Multi-point imaging for a single object point is also
demonstrated.
