Eigenmode and frequency domain analysis of the third-order microring filters

In this paper we compare results of the eigenmode analysis of the third-order add/drop filter with the transfer functions (S-parameters) calculated in wide spectral range covering telecommunication C band. Both type of calculations are performed using 2D finite elements (FEM) method. The computational domain is closed using standard perfectly matched layer method. Also, the model of add/drop microring filter based on the temporal coupled mode is presented, since such models are usually used as a starting point in filter design procedure. The obtained results show excellent agreement between the two approaches. It is well known that when single microring is coupled to access waveguides or another rings, the resonance frequency will deviate from its original isolated resonator value. This effect, known as coupling-induced resonance frequency shift, causes resonance frequency mismatches between individual resonators and thus significantly impacts eigen spectra, as well as transfer characteristics, of the coupled-resonator systems. FEM calculations show that this effect has no significant importance when coupling between the access waveguide and the microring is strong enough, i.e. when the conditions for flat filter response are satisfied.