Hereby, we present results of finite-difference time-domain simulations of technologically undemanding photonic structures offering a significant improvement in the spectrally broad extraction efficiency of emission from a quantum emitter at the third telecommunication window. The modelling is performed for cylindrical and cuboidal mesa structures containing an exciton confined in a single InAs/InP quantum dot. We investigate the emission pattern from such mesas made of InP (which can be exchanged with AlGaInAs lattice-matched to InP) for two cases: monolithic InP material or InP/AlGaInAs distributed Bragg reflector (DBR) underneath the mesa. The calculations are performed as a function of geometrical parameters, i.e. mesa shape and dimensions, and the emitter position. For the case with DBR, we obtain extraction efficiencies above 25% (for a numerical aperture of 0.4 of a common optical detection system), which also exhibits weak spectral dependence – values above 20% can be obtained in the range of 60 nm around 1550 nm. When the numerical aperture is increased to 0.9, extraction efficiencies about 45% are reachable within the proposed solution. The extraction efficiency is rather weakly sensitive to the in-plane dipole alignment (in the range of 100–200 nm), however, it is more susceptible to even slight changes in its vertical position or to mesa sizes. Eventually, we also comment on the Purcell effect in such weak photonic confinement structures, influence of which on the source brightness is not negligible in some cases.