This paper proposes to use an Aperiodic Fourier Modal Method (A-FMM) to model an outgoing photonic jet from a dielectric loaded waveguide ended by a tip with a specific shape. The proposed method has several advantages. First of all, the method is fast, which allows to manage optimization investigations. Secondly, the study of excitation (and more particularly the impact of plane wave excitation) can be examined precisely. Using our modelling technique, we show, in comparison with an actual optimized elliptical tip, that an optimized rectangular tip improves energy concentration by 8% and reduces the calculation time by a factor of 10. Furthermore, A-FMM allows to show that plane wave excitation modifies the spatial distribution of the jet, especially in the case of T E polarization. This can explain the differences observed, in previous works, where only fundamental mode excitation was used in the modelling. To validate these general results, prototypes have been realized, and measurements in the microwave regime have been compared favorably with simulation results.