Shaping an incident beam to a focused line using a single flat metalens.
Introduction
Wavefront shaping using metasurfaces has emerged as powerful alternative to conventional refractive optics through spatially varying phase shifts at planar interface.
This example shows the design of cylindrical metalens which creates a focused at the focal plane. To do so a hyperbolic phase profile is used. This profile compensates for the differences in optical path length across the meta-surface.
Goal
To design a transmissive cylindrical metasurface lens operating at 1550 nm that focuses normally incident light into a line focus at a focal distance of 250 um using an analytically defined phase profile.
Outline
Design parameters
Parameter
Wavelength
Focal length
Image size
Height
Unit cell period
Material
Value
1550 nm
250 um
1-D (line focus)
850 nm
1000 nm
Silicon nano-pillars on Silicon oxide substrate
Steps taken
- Define target phase
- Generate phase map
- Designing meta-atoms
- Build metasurface
- Simulate and verify
Design
Creating meta-atoms
The metaatom consists of a cylindrical silicon nanopillar on a SiO2 substrate within a 1000 nm x 1000 nm unit cell, with a height of 850 nm. The pillar radius is varied to extract the phase and transmission response.
Simulation file “Si_pillars_1550.data.zip”
Creating metacomponents
The metacomponent is constructed by arranging 8 selected silicon meta-atoms, each providing an approximately 45° phase increment to discretely sample the required focusing phase. The focusing principle is illustrated in Figure 2, where normally incident light is redirected by the metasurface so that the transmitted rays interfere constructively at the focal line. The target wavefront is calculated using the cylindrical hyperbolic phase profile:
Here, λ is the operating wavelength and f is the focal length. This phase profile compensates for the optical path difference across the metasurface so that the transmitted light interferes constructively at the focal plane. As shown in Figure 3, the narrow vertical line in the target wavefront map represents the designed one-dimensional line focus produced by the cylindrical metalens.
Figure 2. Schematic illustration of the cylindrical metalens focusing principle. Normally incident light is redirected by the metasurface so that the transmitted rays interfere constructively at the focal line, producing one-dimensional line focusing.
Figure 3. Metacomponent configuration showing the selected silicon meta-atoms and the target wavefront in PlanOpSim.
Simulation file
Analysis
Far-Field Analysis
The far-field analysis of the cylindrical metalens is performed in PlanOpSim using the Angular Spectrum Method (ASM). A sweep variable is defined along the propagation direction (z) so that the transmitted field can be calculated at multiple z positions. This enables PlanOpSim to reconstruct the field evolution through the propagation axis and generate the xz-plane intensity distribution shown in Figure 4, confirming the formation of the designed one-dimensional line focus at the focal distance of 250 µm. Figure 4 shows the simulated far-field intensity distribution and the corresponding xz-plane cross section of the transmitted field. The results confirm constructive interference at the designed focal distance of 250 µm, producing a confined one-dimensional line focus along the x-direction.
- Operating wavelength: 1550 nm
- Focal distance: 250 µm
- One-dimensional line focusing response
- Far-field propagation calculated using analytical phase distribution
Figure 4. Simulated far-field intensity distribution and xz-plane cross section showing line focusing at the designed focal distance of 250 µm.
Applications
- Line focusing [1]
- High resolution Raman spectroscopy
- Focusing solar collectors
- Detection chips [2]
References
[1] Ha, J., Ndao, A., Hsu, L., Park, J. H., & Kante, B. (2018). All-dielectric metasurface cylindrical lens. arXiv preprint arXiv:1804.02356.
[2] Zhao, H., Liu, S., Chen, Z., Sang, Y., Han, X., Xue, L., … & Han, C. (2024). Cylindrical metalens for multidimensional control of terahertz waves. Infrared Physics & Technology, 138, 105272.
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.
