Time evolution of photon-pulse propagation in scattering and absorbing media: The dynamic radiative transfer system. (March 2018) - Georgakopoulos, A.; Politopoulos, K.; Georgiou, E.
Highlights: The work addresses in its general form the solution of the time-dependent problem of photon propagation in absorbing and diffusive media, an important problem encountered in several diverse scientific and technological fields, as for example astrophysics, biophysics, medicine, imaging, optical diagnostics, etc. New general dynamic system "language" is introduced for the modeling description and solution of an important "old" physical problem. Solution will greatly improve the results in comparison with the previously established methodologies, especially in the time-domain. This work provides detailed solution in the space and time-domains, even for ultrafast (of femtosecond order), transient effects. This system provides potential for improved measurement concepts and research instrumentation design. Our method is expandable to include various physical effects, boundary conditions, sources, etc. to efficiently model and solve complicated realistic media and processes (e.g. laser-light propagation and detection in biological tissues). This system provides potential for improved measurement concepts and research instrumentation design. The mathematical system can be used as a basis for future works towards the solution of the inverse problem of propagation in scattering media. Futhermore it can also be generalized to provide solution for other important physical problems having similar mathematical model frameworks. Simulation results are presented for ultra-short light propagation in various absorbing and scattering media. Abstract: A new dynamic-system approach to the problem of radiative transfer inside scattering and absorbing media is presented, directly based on first-hand physical principles. This method, the Dynamic Radiative Transfer System (DRTS), employs a dynamical system formality using a global sparse matrix, which characterizes the physical, optical and geometrical properties of the material-volume of interest. The new system state is generated by the above time-independent matrix, using simple matrix-vector multiplication for each subsequent time step. DRTS is capable of calculating accurately the time evolution of photon propagation in media of complex structure and shape. The flexibility of DRTS allows the integration of time-dependent sources, boundary conditions, different media and several optical phenomena like reflection and refraction in a unified and consistent way. Various examples of DRTS simulation results are presented for ultra-fast light pulse 3-D propagation, demonstrating greatly reduced computational cost and resource requirements compared to other methods.