A graphical method in quantum optics

In this paper we describe in detail a graphical method allowing the computation of field operator transformations in quantum optics (QO). Its applications include beam splitters (BS), Mach-Zehnder interferometers (MZI), optical resonators (Fabry-Perot etc) as well as non-linear crystals featuring the process of spontaneous parametric down-conversion (SPDC). Its main advantage compared to the traditional computation step-by-step method is its visual and intuitive approach, somehow similar to Feynman's diagrammatic approach in Quantum Field Theory. It also seems adapted to computer-based implementations since calculations mainly consist on complex additions and multiplications, not matrix operations.