The imaging system formed by an annular left-handed material (LHM) lens as well as the evanescent waves in the lens are simulated numerically with a finite-difference time-domain (FDTD) method. For b-a>\lambda (a and b are respectively the inner and outer radii of the annular lens, and \lambda is the wavelength), when a point source is placed at an internal grid point, we demonstrate that the evanescent waves are produced around the internal interface, and cannot propagate outwards. As for b-a<\lambda, the evanescent waves appear around both the internal and the external interfaces, which remarkably implies the coupling between the two interfaces. Hence it can be inferred that the evanescent waves around the external interface participating in the super-resolution imaging result from the coupling of the evanescent waves around the interface. Moreover, the partly uncomprehended properties of the evanescent waves in the LHM slab are also disclosed. It is conducive to understanding the evanescent waves in the LHMs further.