Diffractive optics in advanced optic design

One of the challenges in the design of hybrid diffractive/refractive optical systems is their effective simulation. The mixture of large area and micro- to nanoscaled structures makes modelling of diffractive structures difficult, especially when realistic diffracting structures need to be taken into account. Here, the distribution of unwanted stray light varies with the local periodicity of the diffractive optical element (DOE) and the illumination wavelength. We have developed a model based local grating approximation approach that can be implemented into commercial ray tracing software[1].

The basic idea is to extend the standard local grating approximation (LGA) approach with a simulation based on a diffraction model that takes into account fabrication limitations and other above-mentioned dependencies. This can be an analytical model, a numerical model or even a model fed from experimental data. The model returns the probability to scatter light into the different diffraction orders, depending from the incoming ray data (angle, wavelength) and the local grating parameters (line density, orientation). This information is then used to decide into which diffraction order an incoming ray is directed. If the system contains several diffractive elements, this allows an automatic and efficient further splitting of the power.

Our implementation in ZEMAX uses the built-in scatter functionality with a self-programmed dynamic link library (DLL) to integrate the more realistic diffractive simulation. This implementation works in sequential mode, which allows us to use the numerous analysis and even some available functions for optimization. The first model we have integrated is simple scalar diffraction on rotational symmetric diffraction gratings with continuously changing periods that were fabricated by gray scale laser writing. Here, the diffraction limited writing spot limits the quality of the obtained structures. Other models might take into account the effects of alignment errors in multi-step mask processes. For calculation efficiency purposes the model is saved to the RAM as a look-up table that is linearly interpolated. This approach still permits quite efficient ray tracing with only about two times increased calculation time.

One of the most important benefits of the new simulation capability is that it can be used within an automated optimization process. This allows taking fabrication constraints quantitatively into account during the optimization. Fig. 1 shows a simple system for focussing light onto a  detector with finite size. The system consists of a plano-convex lens and a DOE. Free parameters are the radius of the refractive lens and the phase function of the DOE.

Fig. 1: Test configuration for automatic optimization taking fabrication effects of the DOE into account.

With the standard diffractive surface in ZEMAX, the optimizer puts a considerable amount of power into the DOE, reducing the formation of spherical aberration but leading to high line densities, since there is no penalty for the difficulties in fabricating those structures, see fig. 2.

Fig. 2: Optimizing results. Left: standard simulation that does not take into account fabrication dependent artefacts, right: fabrication artefacts are considered

The realistic DOE simulation leads to considerably reduced line densities, here the diffractive surface acts as a correction element for spherical aberration. We simulated the fabrication for both designs and calculated the amount of light that would reach the detector. We obtained 85% for the optimization with the realistic model vs. only 63% for a design with conventional optimization.

Supported by: BMBF (FKZ 13N9456), Project: “MIMODIA”