We show the results of simulation and experimental study of a 4-telescope zig-zag discrete beam combiner (DBC) for long-baseline stellar interferometry working at the astronomical L band (3 − 4 µm) under the influence of a narrow bandwidth light source. Following Saviauk et al. (2013), we used a quasi-monochromatic visibility-to-pixel matrix (V2PM) for retrieving the complex coherence functions from simulated and experimentally measured power at the output of the device. Simulation and coefficient of determination (R2) measurements show that we are able to retrieve the visibility amplitudes with >95 % accuracy of our chromatic model source up to a bandwidth of 100 nm centred at 3.5 µm. We characterized a DBC manufactured by 3D ultra-fast laser inscription (ULI) written on gallium lanthanum sulphate (GLS). Experimental results showed retrieval of visibility amplitude with an accuracy of 80-90 % at 69 nm bandwidth, validating our simulation. The standard deviation of experimental phase residuals are between 0.1-0.4 rad, which shows that the retrieval procedure is sufficient to get good quality images, where phase perturbations of less than 1 rad are expected under good seeing conditions for astronomical applications.