Designing a metacomponent for compact wide-field imaging using a single metalens and aperture.
Introduction
A Metalens can be used to build very small imaging systems, but conventional designs usually use a Hyperbolic phase profile, which focuses light well only when the light arrives straight onto the lens. When light comes from an angle, the focus becomes distorted, causing aberrations and reducing image quality across the field of view.
A landscape metalens improves wide-angle imaging by placing an aperture infront of the metasurface and using a parabolic phase profile. This design keeps the focal spot shape almost unchanged when the incident angle changes, so the focus mainly shifts sideways instead of becoming distorted.
Goal
To create a compact wide-field imaging system using a single metasurface lens and aperture, based on a parabolic phase profile designed for angle invariant focusing at 940 nm.
Outline
Design parameters
As a reference case we choose the following parameters:
Parameter
Wavelength
Focal length
Image size
Aperture size
Value
940 nm
2 mm
1.8 mm
0.5 mm
Where it is shown that for a parabolic profile with a set focal length f. The phase profile and thus focal spot is identical except when changing angle except for a shift in position of
.
Combining this consideration with our set image size and focal length, our landscape lens should have a field of view of
. Finally this allows us to back calculate the position of the aperture. Taking into account the propagation through an SiO2 substrate the aperture should be position at 2.861mm in front of the metalens.
| Derived quantity | Value |
|---|---|
| Aperture position | 2.861 mm |
| Opening angle | 54 degrees |
| Clear Aperture (component diameter) | 2300 µm |
Design
Metacell design
The metasurface design process begins by generating a library of meta-atoms using the MetaCell module in PlanOpSim, as shown in Figure 2. In this example, silicon cylindrical pillars are defined on an SiO₂ substrate with a unit-cell period of 500 nm and a design wavelength of 940 nm. PlanOpSim allows the user to parameterize the geometry of the meta-atom, such as the pillar radius and height, and automatically simulate the optical response of each structure.
Each meta-atom behaves as a subwavelength optical element that locally controls the phase and amplitude of the transmitted light. By sweeping the pillar dimensions, different transmission responses are obtained and stored in the meta-atom library. The library response shown in Figure X presents the transmission amplitude as a function of the transmitted phase for the generated structures.
For efficient metasurface operation, the library should provide a phase coverage close to 2π while maintaining high transmission efficiency. This enables accurate wavefront shaping by assigning the appropriate meta-atom to each position across the metasurface according to the required phase profile. Once generated, the optimized structures are automatically organized in the PlanOpSim library and can later be used for metasurface layout generation and device optimization.
You can download the simulation file from here:
Creating metacomponents
In this step, a new meta-component is created using the selected MetaCell group.
The component represents the full optical aperture of the lens, while each meta-cell defines the local unit-cell response used to build the final metasurface.
For this design, the metacomponent size is set to 2300 µm × 2300 µm, with a meta-cell size of 0.5 µm × 0.5 µm.
The target phase profile is then defined as a parabolic lens phase profile with a focal length of 2000 µm at a wavelength of 940 nm.
The focal length and wavelength can be parametrized easily with the script interface using the following snippet. Where wavelength and f are set as parameters.
# 1. Calculate the phase profile for a parabolic lens
phase = (np.pi / wavelength / f) * (x**2 + y**2)
# 2. Wrap the phase into the standard [0, 2*pi] range
phase = np.mod(phase, 2 * np.pi)
# 3. Define the amplitude of the wavefront
amplitude = np.sqrt(n) * np.ones_like(x)
By default the incident light of the target is set to the wavelength and angles used in the MetaCell calculation. These can be adjusted per target under ‘Incident Light’. You Generate the target by clicking ‘Generate’. Then navigate to MetaComponent>Design and run the design via ‘(re)start design’. After the design is completed the design file can be downloaded.
The parabolic phase profile assigns a spatially varying phase delay across the aperture so that
light from different positions on the metasurface interferes constructively at the focal plane.
The centre of the lens has a different phase delay compared with the outer regions, creating the
required focusing behaviour.
This file contains the landscape.data.zip and can be directly uploaded in the MetaComponent project tree
Analysis
Now that our metalens have been populated with meta-atoms, we can analyse it’s behaviour in the analysis tab.
To simulate the effect of the aperture, the incident light setting should be set to a Gaussian beam of the same width. The figure below shows the settings used for this analysis. The beam divergence angle is set so that its width corresponds to the aperture radius of 0.25mm.
Near field analysis
With these settings we can inspect the incident beam pattern on the metalens. By choosing the ‘Near Field’ analysis type.
The simulation shows the amplitude and phase of the beam exiting the metalens. The plots below respectively show an incident angle of 0° and 10°. As expected, the amplitude patterns shift laterally with an increasing angle. Variations in the meta-surface transmission create an perturbation on the smooth Gaussian beam. The phase plots show that the a concentric (lens) phase profile occurs for both angles with its center at the respective peak of the Gaussian beam.
Far field analysis
To visualize the focal spots, we perform a far field analysis at the z=f (2000 µm). The plots below show the spot profile for an angler of incidence of 0 and 10°. Both spots are near identical with their positions at respectively 0 and 510 µm.
Finally we can run the MTF analysis on these spots. To run MTF analysis enable the ‘Run MTF analysis’ checkbox in ‘Far-field Wavefront Parameters’. When the analysis is complete, choose the MTF analysis tab.
The generate plot looks like the figure below. As we intended this design has an MTF that is nearly not changing versus angle of incidence.
Remarks
- The wavefront used here was derived to be invariant under different angles of incidence. The parabolic wavefront causes spherical aberrations. These can be further addressed by refining the wavefront or introducing additional elements.
- Note that in order to design the full area, plane wave incidence is used in the design step. In the analysis step a Gaussian beam with finite width is used to replicate the effect of the aperture.
Applications
This design form is relevant for these applications (among others):
- Miniaturised imaging systems
References
[1] Shalaginov, M. Y., An, S., Yang, F., Su, P., Lyzwa, D., Agarwal, A. M., Zhang, H., Hu, J., & Gu, T. (2020). Single-Element Diffraction-Limited Fisheye Metalens. Nano Letters, 20(10), 7429–7437. https://doi.org/10.1021/acs.nanolett.0c02783
[2] Luo, X. (2019). Engineering Optics 2.0. In Engineering Optics 2.0. https://doi.org/10.1007/978-981-13-5755-8
