In photonics, resonators are versatile elements designed with the aim of guiding light. They encompass various orders of magnitude for their sizes and the power of their laser sources. Accordingly some effects can be considered as negligible, leading to simplified mathematical models. We will focus on two such models: one related to Whispering Gallery Mode resonators and the other to ring/Fabry-Perot resonators. In the first case the retained model leads to a two-dimensional linear Helmholtz equation in the whole space with material laws having a jump along a bounded interface. The set of complex resonances is analyzed close to the real axis, corresponding to modes concentrated close to the interface. In the second case a one-dimensional model with cubic nonlinearity based on the LugiatoLefever equation is considered. Branches of stationary solutions issued from flat solutions are highlighted, providing frequency comb solutions.