Properties of interface between PML and vacuum?

Excuse me, it is known that the properties of PML is defined well by polynomial approximation in the FDTD bible by Allen Taflove.
however, is there any difference just at the interface between the vacuum region and PML domain.
Sigma=(x(n)/lambda).^m
at this point, at the interface, x should be equal to zero. is that means the Sigma at the interface should be the same as the vacuum.
or there is another way (or equations,formula) to define it?

I would appreciate your great help.