  It is shown that cavities formed between a multilayer quarter-wave Bragg
reflector and a metal mirror which support Tamm plasmons can be modelled by
using a hard-mirror approximation including appropriate penetration depths into
the mirrors. Results from this model are in excellent agreement with those
found by numerical methods. In addition Tamm modes that are laterally confined
by the presence of a metallic disc deposited on the Bragg reflector can be
described by the effective index model that is commonly used for
vertical-cavity surface-emitting lasers (VCSELs). This enables the lateral
modes confined by a circular disc to be found from conventional weakly-guiding
waveguide theory similar to that used for optical fibres. The resonant
wavelengths of these linearly-polarised (LP) guided modes are calculated as
functions of disc diameter and other parameters.
