We propose an analytical model of the self-imaging of Gaussian beams and discuss the impact of the finite aperture and the beam truncation on the quality of the self-image reconstruction. Extension to polychromatic operation is then presented in the context of wavelength division multiplexing systems. From the first point we derive conditions for good self-imaging, compatible with the requirements of the telecommunication environment. A basic optical setup is then proposed to implement both wavelength demultiplexing and routing in a lensless configuration.