A graphical method in quantum optics

In this paperwe describe in detail a graphicalmethod allowing the computation offield operator transformations in quantumoptics (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). Itsmain advantage compared to the traditional computation step-by-stepmethod is its visual and intuitive approach, somehow similar to Feynman’s diagrammatic approach inQuantumField Theory. It also seems adapted to computerbased implementations since calculationsmainly consist on complex additions andmultiplications, notmatrix operations.