Diffractive Optical Elements (DOEs) and Metasurfaces / Metalenses are gaining increasing popularity in optical system design, for applications ranging from cell phone lenses to AR/VR headsets, from 3D sensing to illumination. But simulating and designing for systems that include DOEs or metalenses are always tricky. There is no generalized method to handle all situations. Designers need to decide the strategy for their systems case by case. Many design processes require two different optical theory/algorithms to separately handle the beam propagation in free space and in microstructure, while others use only pure raytracing to achieve the goal.

Since the simulation technology develops fast, it is possible this article does not cover all the methods available. If users provide new information or have any requests, please feel free to reach out to us and we can update this article accordingly.

In this blog post we start with a brief introduction of some possible design routes, with the full Knowledge Base Article provides details on the concept of phase profile and propagation methods in free space and DOE/metalens along with some useful DLLs customized for special phase profile design are introduced.

The main goal is to provide designers, new to this topic, a starting point to see what methods are available in OpticStudio.

Design process

1.1 Phase profile -> microstructure -> experimental verification

In this process, users first design the required phase profile for DOE/metalens with ray-tracing method. Then the microstructure is designed based on the given phase profile. Figure 1 shows a flow chart for the process. This chart does not cover the details of the design, for example, the microstructure can be traditional blaze grating or modern metalens. The required design and fabrication methods can be very different depending on the types of microstructures.

Reference [5] shows an example of generating blaze grating from given phase profile. It also discusses the fabrication with single-point diamond turning machine. The macro to generate the blaze grating can be found in our Knowledgebase article How to calculate the sag of a diffractive optical element with a macro. Alternatively, reference [3] shows how to design metalens for a given phase profile using Lumerical FDTD software.

The disadvantage of this method is that designers may not be able to check the performance of the whole system. For example, there is no way to check the real point spread function (PSF) considering all diffraction orders. Similarly, although rays from “non-working” order can be traced, there is no diffraction efficiency computed, therefore no way to know the power ratio in stray light paths.

Figure 1 A possible workflow to design DOE/metalens in OpticStudio.

1.2 Phase profile -> microstructure -> verify with POP+FDTD

To address the disadvantage of the previous process, where the system performance cannot be simulated before fabrication, Physical Optics Propagation (POP) together with FDTD can be used to accurately calculate the PSF. This method is mainly used by flat metalens designer. Zemax OpticStudio does not include FDTD engine, however, reference [3] shows an example of integrating Lumerical FDTD and Zemax OpticStudio for this process. Figure 2 highlights the concept of this process.

When the system only contains a single metalens, designers can directly start with a plane wavefront incident on the metalens in Lumerical FDTD. The electric field output after the metalens is exported as a ZBF file, which is further imported in OpticStudio POP for evaluating final PSF.

When the metalens, however, is placed in between lenses and the incident beam is not a plane wavefront, designers could start the simulation with a plane wave in POP. The beam is propagated in POP to the front of the metalens and exported as ZBF file. Then the ZBF is imported into FDTD as a source and being propagated through the metalens. The rest of the process remains the same as previously discussed.
One disadvantage of this process is that the FDTD engine cannot handle lenses of large dimensions, due to the need of intensive computation resources. Also, this method can only simulate PSFs at each individual field. Analyses like Image Simulation or Relative Illumination are not possible.

Figure 2 An enhanced version of the workflow shown in Figure 1. Before fabrication, designers could use POP and FDTD to check the final PSF.

 1.3 Parameterize DOE’s sag -> raytracing with FFT/Huygens PSF

Instead of using phase profile to represent DOE, it is also possible to directly model the detailed blazed sag in Sequential mode and design the DOE with traditional ray-tracing engine and analyses like FFT and Huygens PSF. This method only works when the DOE’s feature size is not too close to the wavelength scale, where vector diffraction effect is strong. For this reason, this method is not suitable for metalens. A good example is discussed in reference [4], where the DOE sag is described by an equation that generates blazed structure like a Fresnel lens.

In addition to the limitation of feature size, another disadvantage of this method is that designers may still need to customize some tools to enhance the functionalities provided by OpticStudio. For example, currently there is no native sequential surface supporting the blazed sag as described in reference [4]. Users need to create their own sequential surface DLL to model the unique surface sag. Also, currently OpticStudio does not support showing cross section PSF on, for example, Y-Z plane. A macro is required to scan PSF at different Z locations and create the plots as described in reference [4].

1.4 Parameterize DOE’s sag -> POP

Like the method described above, it is possible to simulate a Fresnel zone plate by modeling the binary-like sag in OpticStudio. However, for this type of DOE, ray-tracing engine will not work well. Rays perpendicularly incident on the DOE will not change its direction since there is no slope on the surface. However, the perpendicularly incident beam can be focused with adequately designed Fresnel zone plate. This effect should be handled by POP in OpticStudio.

As shown in Figure 3, in this system a collimated beam is incident on a glass plate. At the back side of the glass plate, a concentric binary structure has been created using Fresnel Zone Plate surface type. In the Layout window, you can see rays do not change their propagation directions and the beam remains collimated propagating from Object to Image surface.

Note, with this kind of structure, the maximum allowed diameter of the lens may strictly depend on the degree of coherence of the incident beam and the lens focal length. Principles of designing zone plate lenses will not be discussed in this article.

Figure 3 Layout of a system with Fresnel Zone Plate.

However, if the same situation is now modelled using POP analysis, one will observe that the beam comes to focus on the image surface, as shown in Figure 4. Here, we start with a Gaussian beam of waist size 2.6 mm and focus the beam down into a spot of a waist size about 0.4 mm. This example shows that this type of structure can only be simulated using POP.

Figure 4 POP result on image plane for Fresnel Zone Plate.

Note that POP is based on scalar diffraction theory, so it is not suitable for metalens where the feature size is typically sub-wavelength.

Interested in trying to design a DOE or metalens in OpticStudio? Check out the OpticStudio product page to learn more and access a free trial.

References:

[1] Chen, W.T., Zhu, A.Y. & Capasso, F. Flat optics with dispersion-engineered metasurfaces. Nat Rev Mater 5, 604–620 (2020). https://doi.org/10.1038/s41578-020-0203-3
[2] Faraji-Dana, M., Arbabi, E., Arbabi, A. et al. Compact folded metasurface spectrometer. Nat Commun 9, 4196 (2018). https://doi.org/10.1038/s41467-018-06495-5
[3] https://support.lumerical.com/hc/en-us/articles/360042097313-Metalens-Zemax-Interoperability
[4] Anna Nemes-Czopf, Dániel Bercsényi, and Gábor Erdei, "Simulation of relief-type diffractive lenses in ZEMAX using parametric modelling and scalar diffraction," Appl. Opt. 58, 8931-8942 (2019)
[5] RIEDL, Max J., “Diamond-turned diffractive optical elements for the infrared: suggestions for specification standardization and manufacturing remarks”, SPIE Vol 2540 / 257