Introduction
Conventional refractive lenses focus light by accumulating phase as light propagates through thick bulk materials, which makes optical systems bulky. Metasurfaces provide a much thinner alternative by controlling the wavefront at a flat interface using subwavelength structures called meta-atoms.
In geometric phase, also known as the Pancharatnam–Berry (PB) phase, the phase control is achieved by rotating anisotropic meta-atoms that behave like half-wave plates. When circularly polarized light passes through these structures, the handedness of the polarization is converted while an additional phase shift is introduced. By gradually changing the rotation angle of the meta-atoms across the surface, a spatial phase profile can be created to focus light, forming a compact and efficient meta-lens.
This example demonstrates how to simulate a PB meta-lens in the PlanOpSim Meta-cell and Meta-component modules.
Goal
To design a geometric phase metalens that converts incident circularly polarized light into the opposite handiness while focusing it at predefiend focal length of 725 um at a wavelength of 660 nm.
Outline
Design parameters
Parameter
Wavelength
Substrate
Structure
Unit Cell period
Structure Height
Incidence
Polarization
Value
660 nm
430 nm
600 nm
0ׄ°
LCP
Steps taken
Meta-atom library
- Structure library
- Select meta-atoms
Meta-lens design
- Target setting
- Meta-atom placement
- Validation
Performance analysis
- Target matching
- Mask generation
Design
Meta cells design
As a starting point, the meta-atom dimensions reported in [1] are used. The structure consists of a rectangular TiO2 nano-pillar on an SiO2 substrate with a unit-cell size of 430 × 430 nm, a width of 85 nm, a length of 410 nm, and a height of 600 nm. The design operates at a wavelength of 660 nm under left-handed circularly polarized (LCP) illumination.
To utilize the Pancharatnam–Berry (PB) phase, the meta-atom must behave as a birefringent half-wave retarder. In this case, the structure converts the incident LCP light into right-handed circularly polarized (RCP) light while introducing a phase shift controlled by the rotation angle of the meta-atom.
To verify this behaviour, the wavelength is swept from 400–700 nm in steps of 10 nm while monitoring the polarization conversion efficiency into the RCP state. Figure 2 shows high polarization conversion efficiency near 660 nm, confirming that the structure operates as a half-wave retarder at the design wavelength.
Next, the wavelength is fixed at 660 nm and the rotation angle is swept from 0° to 360° in steps of 10°. According to geometric phase theory, the phase of the converted light follows φ = 2α, where α is the rotation angle of the structure. Figure 2 shows that the transmitted phase changes continuously with rotation angle, providing nearly 360° phase coverage. Small deviations from perfect linearity occur because the rectangular nano-structure is not fully rotationally symmetric.
These results demonstrate that the phase can be controlled simply by rotating the TiO2 meta-atoms, enabling their use in PB metasurfaces and metalenses.
The simulation file for the metaatoms can be downloaded here:
Creating metacomponents
After creating the MetaCell group, the meta-lens can be designed in the Meta-component module by arranging the rotated meta-atoms according to the target phase profile. The metasurface is designed over an area of 2000 × 2000 µm2; with a focal length of 725 μm at a wavelength of 660 nm.
Because the PB phase converts circular polarization, the incident light is set to left-handed circularly polarized (LCP) light, while the output polarization is set to the orthogonal right-handed circularly polarized (RCP) state using the “cross” transmission setting. The target lens phase profile is defined by:
where λ is the operating wavelength and f is the focal length. This phase distribution determines the required rotation angle of each TiO2 metaatom across the metasurface.
The target response is then specified in the Metacomponent target settings using the generated meta-atom library from Step 1. With these settings, the full PB metalens design can be generated and exported as a GDS layout containing the spatial distribution of rotated rectangular nano-structures.
The simulation file for the metacomponents and the GDS mask can be downloaded here:
GDS_MaskAnalysis
The emitted wavefront is engineered to produce a tight focal spot at the designed focal plane. To further evaluate the metalens performance, a far-field analysis is performed by plotting the point-spread function (PSF). For this analysis, the output polarization is set to the “cross” state to visualize the converted polarization generated by the PB meta-lens. Figure 3 shows the emitted wavefront, the far-field intensity distribution at the focal plane, and the corresponding cross-sectional intensity profile.
The simulated PSF heatmap shows a well-confined focal spot at z = 725 μm, confirming correct focusing behaviour at the target focal length. Cross-sectional analysis along the x- and y-directions can also be used to evaluate the intensity distribution and focal spot width.
The far-field results indicate:
- Far-field point-spread function (PSF)
- Simulated FWHM: 0.44 μm
- Diffraction-limited FWHM: 0.41 μm
- Polarization conversion efficiency (PCE): 78.6%
- Focusing efficiency: 62.8%
Applications
- Compact imaging & Diffraction limited focusing [1]
Holographic display [2]
References
[1] Khorasaninejad, M., Chen, W. T., Devlin, R. C., Oh, J., Zhu, A. Y., & Capasso, F. (2016). Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging. Science, 352(6290), 1190-1194.
[2] Huang, L., Chen, X., Mühlenbernd, H., Zhang, H., Chen, S., Bai, B., … & Zhang, S. (2013). Three-dimensional optical holography using a plasmonic metasurface. Nature communications, 4(1), 2808.
PlanOpSim develops dedicated simulation software for the design of metasurfaces, metalenses, and other planar optical components. For more information, please contact us at: info@planopsim.com
