Rigorous Derivation of Temporal Coupled Mode Theory Expressions for Travelling and Standing Wave Resonators Coupled to Optical Waveguides Topics: Optical Materials and Devices; Photonic and Optoelectronic Materials and Devices In Proceedings of the 7th International Conference on Photonics, Optics and Laser Technology PHOTOPTICS - Volume 1, 201-208, 2019 , Prague, Czech Republic