In this example we present a series of subwavelength filter designs and their operational principle in producing structural colors. The design configurations include a Fabry-Perot multilayer thin film, a guided mode resonance grating (GMR), and a plasmonic metasurface nanostructure. We investigate their color output capability and efficiency under various design parameters such as thickness, period, material, polarization, and incident angle. Altering these parameters allows us to control their color output in the visible optical spectrum.
Overview
Understand the simulation workflow and key results
For the example of a thin film application, the reflection and transmission of a plane wave travelling through a multilayer stack was analytically calculated using the STACK solver as shown below .
Grating mode resonance (GMR) and metasurface color filters are based on manipulating and enhancing the electromagnetic fields [2]. Following the plasmonics simulation methodology these nano-arrayed periodic structures can be modeled in Lumerical using the FDTD solver .
The designs are parameterized, and scripts are provided to automate the design and visualization. We used the colormatch script command to calculate the XYZ tristimulus coordinates (CIE 1931) based on the transmission or reflection spectrum. An online color match converter was used to visualize the output color [3].
Run and Results
Instructions for running the model and discussion of key results
Thin Film planar stack
- Open the simulation file “Thin_film_planar_stack.fsp”
- Run the script file “Thin_film_planar_stack.lsf”
In this example, a Fabry-Perot (FP) cavity color filter is used. The design consists of a TiO2 /Ag/TiO2 /Ag structure. The thickness for both Ag layers (mirrors) is set at 23 nm, while for the top coating TiO2 , is at 60 nm. The middle layer (cavity) thickness is a variable parameter, and is made of a high refractive index material, titanium dioxide (TiO2 ). TiO2 is also used to enhance angular sensitivity and suppress back reflections from the incident light.
The transmission spectra for cavity thicknesses of 50 nm, 75 nm, and 100 nm show a red shift with thicker cavity., resulting in three distinct spectra corresponding to blue, green and red with similar peak transmission. The corresponding XYZ tristimulus coordinates and their colors show a good match with the reference [1].
The transmission map in terms of wavelength and incident angle is shown below for a cavity thickness of 75 nm. The transmission spectra remain stable with a negligible redshift at longer wavelengths.
Tristimulus XYZ coordinates can be calculated from the transmission spectra and converted into RGB color values. A 10x10 color map in terms of the cavity thickness and the incident angle is shown below. A strong correlation between the color and the cavity thickness can be seen, while the color changes are minimal with respect to the incident angle. Due to the limited degree of design freedom, it is challenging to obtain structural colors with both high brightness and high purity using a single FP cavity. However, it is possible to use multiple cavities and an absorbing layer to further improve the color performance.
1D Grating – Guided mode resonance (GMR)
- Open the simulation file “1D_grating_GMR.fsp”
- Run script “1D_grating_GMR.lsf”.
Guided mode resonator (GMR)s leverages the evanescent coupling of the waveguide mode with the diffracted light from the grating. When diffracted light is phase matched with the waveguide’s leaky mode, a sharp resonance can occur in the transmission and reflection.
The device comprises titanium oxide (TiO2) gratings and waveguides on a silica substrate, leveraging the high refractive index of the TiO2 for high diffraction efficiency.
The reflection spectra, XYZ tristimulus values and corresponding colors for the grating periods of 260 nm, 340 nm and 400 nm are shown below. The resonant peaks peaks show redshift with larger grating periods.
The device is sensitive to the incident angle of the light. For a grating with a period of 400 nm, the reflection spectrum shifts to longer wavelengths as the incident angle increases from 0° to 50°, with minor changes to its peak intensity and linewidth.
As is typical of 1D grating, the device is also sensitive to the polarization of the incident light. For the TE-polarization, where the electric field is parallel to the line grating, the reflected light appears violet while the TM-polarization, where the E-field is normal to the grating, results in a grayish turquoise color.
A 10x10 color map with regards to angle of incidence and grating period for TE-polarization is shown below. It is noticeable that color changes with an incidence angle, from blue to red, while the changes are relatively small with changes in grating period.
Plasmonic nano-squared metasurface
- Open the simulation file “2D_plasmonic_metasurface.fsp”.
- Run the script “2D_plasmonic_metasurface.lsf”.
In this example, we simulate a 2D aluminum (Al) square pillar array on a glass substrate. The operational principle is based on the electromagnetic oscillations at the metal/dielectric interface, called surface plasmon polaritons (SPPs) and localized surface plasmons (LSP). The color of reflected or transmitted light can be controlled by changing the shapes and periods of the device.
This device exhibits polarization insensitiveness, due to its two-dimensional symmetry [1]. The results can be obtained by running and visualizing the “polarization” parameter sweep in optimizations and sweeps tab. The transmission spectra for different polarization angles with a fixed period of 400 nm are shown below, confirming the device’s polarization insensitivity.
The transmission spectra and corresponding colors at normal incidence for grating periods of 260 nm, 330 nm and 400 nm are shown below. The increase of the period causes the resonant wavelength to shift to longer wavelengths (red shift).
Furthermore, the effect of incidence angle and period are considered to generate a more detailed 10x10 color map in terms of both parameters.
Again, a 10x10 color map with regards to incident angle and grating period is shown below. The colors change significantly as the period changes, allowing a wide range of colors. However, the device remains mostly insensitive to the incidence angle due to the strong localized resonances. The color becomes slightly darker at larger angles.
Important model settings
Description of important objects and settings used in model.
Model Setting
Material
The optical response of color filters can be significantly affected by the materials. When comparing the simulation results with measured results, using material models that best represent the actual material used in the experiment is essential.
The plots below show the reflection and transmission spectra of the planar stack and plasmonic metasurfaces examples, respectively. The former shows noticeable differences depending on the reference materials, resulting in slight changes in the brightness, hue, and saturation of the color, but the latter has negligible differences for “CRC” and “Palik” Al models.
Override mesh accuracy
Mesh size can impact the accuracy of the simulation output. It is recommended to use coarse meshes at the initial stage of the simulations, and then continue to smaller meshes for convergence tests as shown below for the plasmonic metasurface a period of 400 nm.
The above plots can be obtained by running the “convergence(mesh)” parameter sweep in optimizations and sweeps tab. The transmission result converges at the mesh size of 1 nm. The inset figure shows an enlarged view of the results around the minimum transmission region.
Taking the model further
Information and tips for users that want to further customize the model.
Color map
We used Python scripts to create the 10x10 color map for each device above. For the plasmonic metasurface device we used the following formulas to convert the XYZ coordinates to RGB values [3].
$$
R=255*((2.04137*\frac{X}{100}) - (0.56495*\frac{Y}{100}) - (0.34469*\frac{Z}{100}))^{\frac{1}{2.19921875}}
$$
$$
G=255*((-0.96927*\frac{X}{100}) + (1.87601*\frac{Y}{100}) + (0.04156*\frac{Z}{100}))^{\frac{1}{2.19921875}}
$$
$$
B=255*((0.01345*\frac{X}{100}) - (0.11839*\frac{Y}{100}) + (1.01541*\frac{Z}{100}))^{\frac{1}{2.19921875}}
$$
The generated “column_color_10x10.txt” file contains the RGB values for every pixel of the color map, following the format shown below.
The image below shows the screenshot of the Python script “color_map_10x10.py” and the color map generated with the script.
Additional resources
Additional documentation, examples, and training material
Related publications
- Danyan Wang, Zeyang Liu, Haozhu Wang, Moxin Li, L. Jay Guo, and Cheng Zhang. “Structural color generation: from layered thin films to optical metasurfaces”. https://doi.org/10.1515/nanoph-2022-0063.
- Rao Fu, Kuixian Chen, Zile Li, Shaohua Yu and Guoxing Zheng, “Metasurface-based nanoprinting: principle, design and advances.”, DOI: 10.29026/oes.2022.220011.
- https://www.easyrgb.com/en/match.php#inputFORM .