A model for confined Tamm plasmon devices

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.