D2.1 Theoretical formalism

This report describes a theoretical framework for simulating the propagation of specially structured laser beams, known as beams carrying orbital angular momentum, through biological tissues and other turbid, scattering media. These beams possess twisted, corkscrew-like wavefronts that give rise to characteristic ring-shaped intensity profiles and generate distinct speckle patterns upon scattering. By simulating light propagation at the level of individual photon packets while tracking both intensity and phase, the framework enables systematic investigation of how each scattering event, boundary interaction, and material property influences the final detected signal. The model also accounts for optically birefringent structures, such as collagen and elastin, which affect the polarization state of light. Overall, this theoretical and computational formalism provides a consistent tool for the design of structured-light imaging systems, the validation of experimental observations, and improved interpretation of measurements in biomedical optics and optical sensing applications.