Multiple interfacing between classical ray-tracing and wave-optical simulation approaches: a study on applicability and accuracy

Abstract

In this study the applicability of an interface procedure for combined ray-tracing and finite difference time domain (FDTD) simulations of optical systems which contain two diffractive gratings is discussed. The simulation of suchlike systems requires multiple FDTD↔RT steps. In order to minimize the error due to the loss of the phase information in an FDTD→RT step, we derive an equation for a maximal coherence correlation function (MCCF) which describes the maximum degree of impact of phase effects between these two different diffraction gratings and which depends on: the spatial distance between the gratings, the degree of spatial coherence of the light source and the diffraction angle of the first grating for the wavelength of light used. This MCCF builds an envelope of the oscillations caused by the distance dependent coupling effects between the two diffractive optical elements. Furthermore, by comparing the far field projections of pure FDTD simulations with the results of an RT→FDTD→RT→FDTD→RT interface procedure simulation we show that this function strongly correlates with the error caused by the interface procedure.

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

“…Since the MCCF depends on the distance between the two diffraction gratings d BC , the divergence angle α of the incident light and the diffraction angle β of the first diffraction grating (see Eq. 1), one can explain this similarity with the results in [11] by the fact, that the shape of the diffraction grating structure does not have a strong impact on the overall behavior. This result motivates the usage of the MCCF according to Eq.…”

“…In the case of a diffraction grating the latter is the angle β between the zeroth and the 1 th order. In [11] we proved that assumption by comparing far-field intensity distributions as a function of the distance of a pure FDTD-simulation with RT→FDTD→RT→FDTD→RT interface simulations of a double grating structure with two identical gratings having rectangular shapes. As a result, the far-field calculated with the interface procedure converges to the far-field calculated by pure FDTD simulations as the distance between the two gratings increases.…”

“…In our recent publication [11] we investigated the influence of neglecting the phase information after a FDTD→RT step. In order to estimate the maximal impact of the phase effects on the simulation result, we derived a maximal coherence correlation function (MCCF) sin( ) ( , , ) , tan…”

“…4. In order to examine possible additional effects due to the asymmetry similar investigations according to [11] are made. Figure 4a illustrates the orientation of the FDTD simulation area of the two diffraction gratings separated by the spatial distance d BC .…”

“…For such simulation settings the coherence correlation between different DOEs gives reason for additional interference effects which, due to the loss of the phase relations of the different wave fronts upon switching from FDTD back to RT, cannot be considered. Therefore on the basis of an optical system with two identical diffraction gratings we derived a maximum coherence correlation function (MCCF) which describes the degree of the maximum impact of phase effects between two diffraction gratings [11]. The MCCF envelops the oscillations of the square of the time averaged Poynting vector |<S>|² caused by the distance dependent coupling effects between the two DOEs.…”