A novel vectorial modal method is presented based on transverse magnetic (TM) and transverse electric (TE) mode expansion, which signicantly simplies the evaluation of the operator matrix.The method, which features a true open boundary condition, is introduced for an orthogonal curvilinear coordinate system with the specic examples of circular and elliptical geometries presented.We validate the method by considering challenging problems, such as the calculation of spontaneous emission rates, of modal reection coecients and of the eect of the emitter spatial misalignment on the spontaneous emission β factor. Results are compared with literature.