A transmissive metasurface generates a predefined dot pattern by controlling the phase of transmitted light. The target output can be defined in different ways depending on the application.
Introduction
Metasurfaces enable precise control of optical wavefronts by tailoring the phase response of subwavelength structures. In dot pattern generation, the goal is to create a specific light distribution, such as lens arrays[BR1.1]. This target optical output can be defined in three ways: at a fixed distance from the metasurface, as an angular far-field spot distribution, or through a known near-field wavefront. In the first two cases, PlanOpSim calculates the required near-field phase profile from the desired output using inverse design methods such as IFTA or angular wavefront synthesis. In the third case, which is adopted in this work, the near-field wavefront is already known, such as for a lens array under plane wave illumination, and can be directly imported. The resulting phase profile is then implemented by selecting suitable meta-atoms to reproduce the target optical function.
Goal
To design a transmissive metasurface operating at 940 nm that generates a predefined lens array in the far field by optimizing the near-field phase distribution and implementing it using silicon square pillar meta-atoms.
Outline
Design parameters
Parameter
Operating Wavelength
Target function
Lens pattern distance
Lens array size
Meta-atom type
Number of selected atoms
Spot spacing
Value
940 nm
20×20 dot array
250 µm
1 mm x 1 mm
Silicon square pillars
8
50 µm
Steps taken
PlanOpSim allows the target dot pattern to be defined in three ways: at a fixed distance from the metasurface, in angular far-field space, or by directly importing a known near-field wavefront. In this work, the known near-field wavefront approach was used by defining the target optical function as a 20 × 20 lens array focused at 250 µm. A script was used to generate the required phase map at 940 nm from the lens geometry[BR4.1], and PlanOpSim then selected the silicon pillar meta-atoms whose phase responses best matched the target distribution to create the final metasurface layout.
- Create the metacell group; in this work, silicon square pillars were used, although any metacell group that provides the required phase coverage can be applied.
- Define the target optical function as a 20 × 20 lens array focused at 250 µm.
- Generate the required near-field wavefront or phase map at a wavelength of 940 nm using a script based on the lens geometry.
- Design the metasurface by assigning the selected meta-atoms across the surface to match the target phase distribution.
- Simulate the optical response to verify the focused dot array.
- Export the final metasurface layout for fabrication.
Design
Creating meta-atoms
The meta-atoms consist of silicon square pillars fabricated on a SiO₂ substrate. Individual pillar geometries were simulated to extract their transmission amplitude and phase response at a wavelength of 940 nm, forming a library of candidate structures. The meta-atom response was characterized by sweeping the pillar length (equal to the width for square pillars) while keeping the height fixed at 400 nm. The transmission amplitude remains relatively high (above ~0.55 and up to ~0.95) across the sweep, indicating low optical loss for all geometries. The phase response exhibits a continuous variation with pillar size, enabling the selection of eight discrete meta-atoms that provide approximately uniform phase steps across the available phase range.
The simulation file can be downloaded from here:
Dot_pattern_metaatoms.data.zip
Creating metacomponents
In this work, a 1 mm × 1 mm transmissive metasurface operating at 940 nm was designed using silicon square pillar meta-atoms. The target optical function was defined as a 20 × 20 array of spots at a propagation distance of 250 µm, implemented using a lens-array phase profile. The required near-field phase map was generated using the built-in microlens array functionality in PlanOpSim by specifying the relevant design parameters. This phase map represents the spatial phase delay needed to focus light into the desired dot array. PlanOpSim then assigned the selected silicon pillar meta-atoms across the metasurface by matching their phase responses to the target phase distribution, creating the final nanostructured layout. The optical response was subsequently simulated to verify the formation of the far-field spot array.
Simulation files can be found here:
dot_pattmetacomponent.data.zip
Analysis
After constructing the metasurface layout, the optical response was analysed in PlanOpSim using the local periodic approximation. A normally incident TE-polarized plane wave with an amplitude of 1 and a wavelength of 940 nm was used as the input source. The far-field response was evaluated over a 1000 µm × 1000 µm observation window with a spatial resolution of 2500 × 2500 points, corresponding to the full metasurface aperture. The focal plane was set at a propagation distance of 250 µm to match the designed lens-array focal length. A Fourier wavefront analysis with a 180° angular range in both x and y directions was also performed to examine the angular light distribution. The simulated near-field phase distribution closely matched the target lens-array phase map, confirming that the selected silicon pillar meta-atoms reproduced the required wavefront accurately. The far-field results showed a well-defined 20 × 20 focused dot patterns at the focal plane, while the calculated Farfield efficiency of 84.3% [BR8.1]i[BR9.1]ndicated effective transmission and focusing performance.
Applications
The application depends on where and how the dot pattern is designed to appear. If the pattern is defined at a fixed distance from the metasurface. Here, the metasurface acts as a flat lens array that focuses light into a regular grid of spots at a set focal distance. This is useful for:
- Compact imaging systems
- Optical alignment
- Calibration
- Beam splitting
and any application that needs a stable and repeatable array of focused light spots [1]
References
[1] Ozdemir, A., Yilmaz, N., Bagci, F. T., Takashima, Y., & Kurt, H. (2018). Broadband polarization-independent low-crosstalk metasurface lens array-based mid wave infrared focal plane arrays. arXiv preprint arXiv:1803.05637.
