A combined simulation approach using ray-tracing and finite-difference time-domain for optical systems containing refractive and diffractive optical elements

Optical and photonic devices often comprise optical elements which interact with light on different geometric length scales, ranging from (sub-) wavelength to several millimetres. Well-established physical models exist to describe coherent or incoherent effects, like refraction or diffraction including polarization effects, which form the basis for several simulation approaches. While at dimensions much larger than the light wavelength the incoherent ray-tracing (RT) techniques are commonly used, at dimensions in the (sub)-wavelength regime simulation tools like the Finite-Difference Time-Domain (FDTD) method are indispensable, as they allow for the simulation of coherence effects where phase relations play a crucial role. The two approaches are structurally entirely different, so that a proper description for the macroscopic and the (sub-) wavelength scale at once would only work by connecting the two approaches together, exploiting the best of both in a step-by-step simulation. In this contribution, the applicability of an interface procedure for combined ray-tracing and FDTD simulations of optical systems which contain two diffractive gratings is discussed. Suchlike systems require multiple FDTD <-> RT steps for a complete simulation. For minimizing the error due to the loss of the phase information in an FDTD -> RT step, we use a recently derived equation for calculating the maximal coherence correlation function (MCCF) to estimate the minimum distance between the different grating structures. In addition a waveguide system comprising two coupling grating structures is investigated with the MCCF and simulated using the simulation approach. As a consequence of the waveguide setup multiple FDTD <-> RT steps in an iterative manner are necessary; the corresponding results are discussed.