  We analytically investigate the plasmons propagating in a homogeneous
two-dimensional (2D) electron system, along the metal grating in the form of a
periodic array of strip-shaped electrodes (gates) in the vicinity of the 2D
system. We show that in the case of semi-infinite grating, the Tamm plasmon
modes localized near and propagating along the grating edge can exist in the
gaps of the plasmonic band structure provided that the last gate differs in
width from the other gates. When the last gate is wider, the spectrum of the
fundamental Tamm plasmon mode lies in the lowest frequency gap, below the first
plasmonic band. Importantly, we find the mode to exist in this case only for
finite values of the wave vector along the grating. Otherwise, if the width of
the last gate is smaller, the Tamm plasmon modes occupy higher frequency gaps,
and delocalized plasmons from the first frequency band become the lowest
frequency excitations.
