  Boundary modes localized on the boundaries of a finite-size lattice
experience a finite size effect (FSE) that could result in unwanted couplings,
crosstalks and formation of gaps even in topological boundary modes. It is
commonly believed that the FSE decays exponentially with the size of the system
and thus requires many lattices before eventually becoming negligibly small.
Here we identify a special type of FSE of some boundary modes that apparently
vanishes at some particular wave vectors along the boundary. Meanwhile, the
number of wave vectors where the FSE vanishes equals the number of lattices
across the strip. We analytically prove this type of FSE in a simple model and
prove this peculiar feature. We also provide a physical system consisting of a
plasmonic sphere array where this FSE is present. Our work points to the
possibility of almost arbitrarily tunning of the FSE, which facilitates
unprecedented manipulation of the coupling strength between modes or channels
such as the integration of multiple waveguides and photonic non-abelian
braiding.
