Multiple Reflections Modeling for Multi-Layered Optical Structures

Fresnel equations and transfer matrix approach are usually employed to solve for exact solution to Maxwell’s equations for multi-layered optical structures. In this paper, we demonstrate that the Fresnel equations and transfer matrix approach can be expanded using Geometric series. This geometric series give an insight to how the light is trapped and behaves in multi-layered optical structures. It also allows us to calculate multiple reflections and count the number of round-trip inside the structure. One main issue in optical calculation is that layers are usually treated as an infinitely large layer. This is, of course, not practical in term of device fabrication. We also demonstrate how this simple geometric calculation will enable us to calculate a smallest practical size that can accommodate a required optical resonant effect.