Structural color metasurface high quality factor narrow band filter suitable for non-normal incidence angle

Abstract

The application discloses a structural color super surface high-quality factor narrow-band filter suitable for non-normal incidence angle, which comprises a substrate layer, an intermediate layer and a nanowire array which are stacked in sequence. The substrate layer is made of Al2O3 material, and the intermediate layer is made of Si3N4 material. The nanowire array comprises a plurality of elliptical cylindrical nanowires arranged in a matrix form on the surface of the intermediate layer, and the distance between the center points of two adjacent elliptical cylindrical nanowires is equal. The elliptical cylindrical nanowire is in a straight elliptical cylindrical shape, and a half-ellipsoidal groove is arranged on the top surface, and the opening profile of the groove is the same as the bottom surface profile of the elliptical cylindrical nanowire. By adjusting the size and distance of the elliptical cylindrical nanowire, the transmission light wave band can be tuned. The application can maintain a relatively narrow full width at half maximum while realizing high reflectivity and high quality factor, and the resonance peak position remains basically unchanged within the range of 0-60° incidence angle. The application is stable under non-normal incidence angle and is not easy to discolor.

Description

Technical Field

[0001] This invention belongs to the field of color filter design technology, and relates to the modeling and simulation of structured color metasurface narrowband filter devices. Specifically, it relates to a structured color metasurface high-quality factor narrowband filter suitable for non-positive incident angles. Background Technology

[0002] Color generation mechanisms are mainly divided into pigment-based coloring and structural coloring. Filters are commonly used optical devices, typically used to transmit or reflect light of specific wavelengths to display desired colors. They are widely used in displays, imaging sensors, anti-counterfeiting technology, color decoration, and color printing. Traditional pigment-based filters absorb specific wavelengths of light through surface dyes to achieve the desired color. These filters are not heat-resistant and cannot withstand prolonged ultraviolet radiation. They degrade under prolonged illumination, resulting in a significant decline in performance over time, and the degradation products are environmentally unfriendly. Structural colors are generated through the interaction of microstructures with natural light. These microstructures are small enough to interfere with visible light, typically occurring in optical phenomena such as interference, diffraction, and scattering. Compared to pigment-based coloring, structural coloring is more stable, less prone to fading, and more environmentally friendly, offering significant advantages in wide color gamut, high saturation, high brightness, and high resolution. Therefore, filters based on structural colors can overcome the shortcomings of traditional chemical dye filters.

[0003] Existing technologies utilize various physical phenomena to design and apply metal and dielectric nanostructures to structural color filters, such as guided-mode resonance, Fano resonance, surface plasmon resonance, Mie resonance or Fabry-Perot resonance, and Rayleigh-Wood diffraction anomalies. However, most existing structural color filters are quite sensitive to the incident angle, often exhibiting different colors under light sources with different incident angles, indicating instability and thus affecting their application scenarios. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a high-quality factor narrowband filter with a structured color metasurface suitable for non-normal incident angles. This filter exhibits high reflectivity, a small full width at half maximum (FWHM), and a high quality factor (P). λ is the target center wavelength. Furthermore, it maintains stable performance even at non-normal incident angles.

[0005] A high-quality factor narrowband filter with a structured color metasurface suitable for non-positive incident angles comprises a substrate layer, an intermediate layer, and a nanowire array stacked sequentially. The substrate layer is made of Al2O3. The intermediate layer is made of Si3N4.

[0006] The nanowire array comprises multiple elliptical cylindrical nanowires arranged in a matrix; the elliptical cylindrical nanowires are made of Si. Each elliptical cylindrical nanowire is a straight elliptical cylinder with a major axis radius *a* of 45 nm–150 nm, a minor axis radius *b* of 30 nm–150 nm, and a height of 100 nm. A semi-ellipsoidal groove with a depth *c* of 30 nm–70 nm is formed on the top surface, and the opening profile of the groove is the same as the bottom profile of the elliptical cylindrical nanowire. The center-to-center distance *p* between any two adjacent elliptical cylindrical nanowires is equal, ranging from 210 to 450 nm.

[0007] Preferably, the target visible light wavelength of the filter is adjusted by changing the center distance p between two adjacent elliptical cylindrical nanowires. When the distance between two adjacent elliptical cylindrical nanowires decreases, the target visible light wavelength decreases; when the distance between two adjacent elliptical cylindrical nanowires increases, the target visible light wavelength increases.

[0008] Preferably, the target visible light wavelength of the filter is adjusted by the size of the major axis radius 'a' and the minor axis radius 'b' of the elliptical cylindrical nanowire. When the major axis radius 'a' and the minor axis radius 'b' of the elliptical cylindrical nanowire decrease, the target visible light wavelength decreases; when the major axis radius 'a' and the minor axis radius 'b' of the elliptical cylindrical nanowire increase, the target visible light wavelength increases.

[0009] Preferably, when the target wavelength is 399–418 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is 45 nm, the minor axis radius b is 30 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is 215–230 nm.

[0010] When the target wavelength is 418–438 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 52.5 nm, the minor axis radius 'b' is 35 nm, and the center-to-center distance 'p' between two adjacent elliptical cylindrical nanowires is 225–240 nm.

[0011] When the target wavelength is 435–500 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 60 nm, the minor axis radius 'b' is 40 nm, and the center distance 'p' between two adjacent elliptical cylindrical nanowires is 230–280 nm.

[0012] When the target wavelength is 496–568 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 75 nm, the minor axis radius 'b' is 50 nm, and the center distance 'p' between two adjacent elliptical cylindrical nanowires is 270–320 nm.

[0013] When the target wavelength is 559–637 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 90 nm, the minor axis radius 'b' is 60 nm, and the center distance 'p' between two adjacent elliptical cylindrical nanowires is 310–360 nm.

[0014] When the target wavelength is 625–689 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 105 nm, the minor axis radius 'b' is 70 nm, and the center distance 'p' between two adjacent elliptical cylindrical nanowires is 350–390 nm.

[0015] When the target wavelength is 677–741 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 120 nm, the minor axis radius 'b' is 80 nm, and the center distance 'p' between two adjacent elliptical cylindrical nanowires is 380–420 nm.

[0016] When the target wavelength is 728–780 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 135 nm, the minor axis radius 'b' is 90 nm, and the center distance 'p' between two adjacent elliptical cylindrical nanowires is 410–440 nm.

[0017] Preferably, the grooved surface of the top surface of the elliptical cylindrical nanowire is an ellipsoid; with the center of the top contour of the elliptical cylindrical nanowire as the origin, the expression for the grooved surface is:

[0018] Preferably, the thickness of the intermediate layer is 70 nm.

[0019] Preferably, the depth c of the groove formed on the top surface of the elliptical cylindrical nanowire is 40 nm.

[0020] Preferably, the substrate layer is made of Al2O3 with a thickness greater than or equal to 200 μm.

[0021] Preferably, the thickness of the intermediate layer is 40nm to 100nm.

[0022] The present invention has the following beneficial effects:

[0023] 1. The present invention sets up a nanowire array and forms a semi-ellipsoidal groove on the top surface of the nanowire, so that the entire structure has the characteristics of an optical micro-nano cavity. It has a strong energy confinement effect on the incident light in most wavelength bands, thereby obtaining a narrower full width at half maximum (FWHM), higher reflectivity, purer color, and higher quality factor.

[0024] 2. The semi-ellipsoidal groove at the tip of the nanowire in this invention can concentrate energy, making the filter provided by this invention insensitive to changes in the angle of incident light, and able to work stably even at non-normal incident angles to obtain the desired color. Furthermore, by adjusting the size of the elliptical cylindrical nanowires on the surface of the intermediate layer and the distance between adjacent elliptical cylindrical nanowires, the wavelength of the target visible light can be adjusted, achieving tuning of different color spectra. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the structure of the present invention.

[0026] Figure 2 This is a comparison of the reflectance spectra of filters with different sizes of nanowire arrays in this invention.

[0027] Figure 3 This is the reflection spectrum of the filter with the near-infrared band as the target band in this invention.

[0028] Figure 4 This is a comparison diagram of the reflection spectrum of the same filter under different incident angles in this invention.

[0029] Figure 5a This is a magnetic field energy distribution diagram of the elliptical cylindrical nanowire in this invention under 0° incident light.

[0030] Figure 5b This is a magnetic field energy distribution diagram of the elliptical cylindrical nanowire in this invention under 20° incident light.

[0031] Figure 6 This is the reflection spectrum of the filter with the red band as the target band in this invention.

[0032] Figure 7 This is a schematic diagram of the full width at half maximum (FWHM) of the filter with a target wavelength of 559–637 nm in this invention.

[0033] Figure 8 This is a schematic diagram of the full width at half maximum (FWHM) of the filter with a target wavelength of 496–568 nm in this invention. Detailed Implementation

[0034] The present invention will be further explained and described below with reference to the accompanying drawings.

[0035] like Figure 1 As shown, a high-quality factor narrowband filter with structural color metasurface suitable for non-positive incident angles includes a substrate layer 1, an intermediate layer 2, and a nanowire array 3 stacked sequentially.

[0036] The base layer 1 is made of Al2O3 material, and its thickness should exceed the thickness of the intermediate layer 2 and the nanowire array 3. In this embodiment, the thickness of the base layer 1 is selected to be ≥200 μm. The intermediate layer 2 is made of Si3N4 material with a thickness of 70 nm. The nanowire array 3 includes multiple elliptical cylindrical nanowires arranged in a matrix, and the material is Si. The elliptical cylindrical nanowires are straight elliptical cylinders with a major axis radius a of 45–150 nm, a minor axis radius b of 30–150 nm, and a height of 100 nm. A semi-ellipsoidal groove 3-1 with a depth c of 40 nm is formed on the top surface. The surface of the groove 3-1 is an ellipsoidal surface. Taking the center position of the top surface contour of the elliptical cylindrical nanowire as the origin, the expression of the surface of the groove 3-1 is: At this point, the filter can maintain high reflectivity and narrow full width at half maximum (FWHM) under normal incidence. The elliptical cylindrical nanowires are arranged in an n×n matrix on the surface of intermediate layer 2, with the center-to-center distance p between any two adjacent elliptical cylindrical nanowires being equal, ranging from 210 to 450 nm.

[0037] By adjusting the center-to-center distance *p* between two adjacent elliptical cylindrical nanowires or the radius of the elliptical cylindrical nanowires, the target visible light wavelength of the filter, as well as the position and full width at half maximum (FWHM) of the resonance peak, can be changed, thereby achieving the filtering of light in different wavelength bands. The reflection spectrum of the filter was simulated using the finite-difference time-domain (FDTD) method when the major axis radius *a* of the elliptical cylindrical nanowires varied between 45 and 135 nm, the minor axis radius *b* varied between 30 and 90 nm, and the center-to-center distance *p* between two adjacent elliptical cylindrical nanowires varied between 220 and 440 nm. Figure 2 As shown, the spectrum gradually blue-shifts as the radius of the elliptical cylindrical nanowire decreases.

[0038] Therefore, when the target visible light center wavelength is between 399 and 418 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is set to 45 nm, the minor axis radius b is set to 30 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is set to 215 to 230 nm.

[0039] When the target visible light center wavelength is between 418 and 438 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is set to 52.5 nm, the minor axis radius b is set to 35 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is set to 225 to 240 nm.

[0040] When the target visible light center wavelength is between 435 and 500 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is set to 60 nm, the minor axis radius b is set to 40 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is set to 230 to 280 nm.

[0041] When the target visible light center wavelength is in the range of 496–568 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is set to 75 nm, the minor axis radius b is set to 50 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is set to 270–320 nm.

[0042] When the target visible light center wavelength is between 559 and 637 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is set to 90 nm, the minor axis radius b is set to 60 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is set to 310 to 360 nm.

[0043] When the target visible light center wavelength is between 625 and 689 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is set to 105 nm, the minor axis radius b is set to 70 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is set to 350 to 390 nm.

[0044] When the target visible light center wavelength is between 677 and 741 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is set to 120 nm, the minor axis radius b is set to 80 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is set to 380 to 420 nm.

[0045] When the target visible light center wavelength is between 728 and 780 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is set to 135 nm, the minor axis radius b is set to 90 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is set to 410 to 440 nm.

[0046] Further increasing the size of the elliptical cylindrical nanowires can make the target reflection band near the infrared band, and the reflection spectrum of the filter as shown in the figure. Figure 3 As shown, this demonstrates that the filter described in this application is not only applicable to visible light, but also has the potential for further expansion.

[0047] The major axis radius of the elliptical cylindrical nanowires in the filter was set to a = 210 nm, the minor axis radius to b = 140 nm, and the center distance between two adjacent elliptical cylindrical nanowires to p = 350 nm. Then, starting from a normal incident angle, the incident angle was gradually increased in 10° increments. The reflection spectrum of the filter at different incident angles was simulated using the finite-difference time-domain (FDTD) method, as shown below. Figure 4 As shown, it is evident that when the incident angle varies within the range of 0–50°, the reflected color remains stable, and the full width at half maximum (FWHM) is narrow, both less than 9 nm. Only when the incident angle reaches 60° does the reflectivity and FWHM significantly deteriorate. This demonstrates that the filter proposed in this application is insensitive to changes in incident light within a large angle range of 0–60°, making it suitable for scenarios with non-positive incident angles, and exhibiting greater stability and less susceptibility to color shifts.

[0048] In this embodiment, the magnetic field energy distribution diagrams of the elliptical cylindrical nanowires under incident light at 0° (i.e., normal light) and 20° are as follows: Figure 5a and 5b As shown; from Figure 5a and 5b As can be seen, as the angle of incident light changes, the energy is always concentrated in the groove 3-1.

[0049] This explains why the filter provided in this embodiment is insensitive to changes in the incident angle: the ellipsoidal groove 3-1 formed by etching the top surface of the elliptical cylindrical nanowire allows energy to be concentrated within the groove 3-1, effectively suppressing random energy scattering and leakage, improving energy convergence and energy coupling efficiency, and without disrupting the phase matching condition. Therefore, for incident light at different incident angles, the position of the center peak with higher reflectivity in the filter provided in this embodiment will not shift significantly, enabling the filter provided in this embodiment to adapt to specific wavelength bands of incident light.

[0050] While keeping the ratio of the major axis radius to the minor axis radius constant, appropriately increasing the ratio between the radius of the elliptical cylindrical nanowire and the center distance p (to ensure the target visible light wavelength, the radius of the elliptical cylindrical nanowire can be appropriately increased while p is appropriately decreased) can improve reflectivity at the appropriate sacrifice of full width at half maximum (FWHM). Conversely, appropriately decreasing the ratio between the radius of the elliptical cylindrical nanowire and the center distance p (to ensure the target visible light wavelength, the radius of the elliptical cylindrical nanowire can be appropriately decreased while p is appropriately increased) can improve the FWHM (narrowing) at the appropriate sacrifice of reflectivity.

[0051] If a higher reflectivity is required compared to full width at half maximum (FWHM), the ratio between the radius of the elliptical cylindrical nanowire and the center distance *p* can be appropriately increased to improve reflectivity. Taking a target visible light wavelength in the 625–780 nm band as an example, the major axis radius *a* of the elliptical cylindrical nanowire's base is set to 135 nm, the minor axis radius *b* to 90 nm, and the center distance *p* between two adjacent elliptical cylindrical nanowires to 410 nm. Figure 6 As shown, the reflectivity can reach up to 98%, and the center wavelength is located at 728nm.

[0052] If a higher requirement is placed on the full width at half maximum (FWHM) compared to reflectivity, the ratio between the radius of the elliptical cylindrical nanowire and the center distance *p* can be appropriately reduced to improve the FWHM. Taking a target visible light wavelength in the 559–637 nm band as an example, the major axis radius *a* of the elliptical cylindrical nanowire's base can be set to 90 nm, the minor axis radius *b* to 60 nm, and the center distance *p* between two adjacent elliptical cylindrical nanowires to 360 nm. Figure 7 As shown, the reflectivity is 83%, the center wavelength is 637 nm, the full width at half maximum (FWHM) is 3 nm, and the quality factor Q is 212.3. Taking a target visible light wavelength in the 496–568 nm band as another example, the major axis radius *a* of the elliptical cylindrical nanowire base is set to 75 nm, the minor axis radius *b* to 50 nm, and the center-to-center distance *p* between two adjacent elliptical cylindrical nanowires is 320 nm. Figure 8 As shown, the reflectivity is 92%, the center wavelength is 568nm, the full width at half maximum (FWHM) is 2nm, and the quality factor Q is 284.

Claims

1. A high-quality factor narrowband filter with structural color metasurface suitable for non-positive incident angles, comprising a substrate layer, an intermediate layer, and a nanowire array stacked sequentially; characterized in that: The base layer is made of Al2O3, and the intermediate layer is made of Si3N4. The nanowire array comprises multiple elliptical cylindrical nanowires arranged in a matrix. The elliptical cylindrical nanowires are made of Si. The elliptical cylindrical nanowires are straight elliptical cylinders with a major axis radius a of 45nm to 150nm, a minor axis radius b of 30nm to 150nm, and a height of 100nm. A semi-ellipsoidal groove with a depth c of 40nm is formed on the top surface, and the opening profile of the groove is the same as the bottom profile of the elliptical cylindrical nanowire. The center distance p between any two adjacent elliptical cylindrical nanowires is equal, ranging from 210 to 450nm. The grooved surface on the top surface of the elliptical cylindrical nanowire is an ellipsoid; with the center of the top contour of the elliptical cylindrical nanowire as the origin, the expression for the grooved surface is: , z≤0.

2. The structural color metasurface high-quality factor narrowband filter suitable for non-positive incident angles according to claim 1, characterized in that: The target visible light wavelength of the filter is adjusted by changing the center distance p between two adjacent elliptical cylindrical nanowires; when the distance between two adjacent elliptical cylindrical nanowires decreases, the target visible light wavelength decreases; when the distance between two adjacent elliptical cylindrical nanowires increases, the target visible light wavelength increases.

3. The structural color metasurface high-quality factor narrowband filter suitable for non-positive incident angles according to claim 1, characterized in that: The target visible light wavelength of the filter is adjusted by the size of the major axis radius 'a' and the minor axis radius 'b' of the elliptical cylindrical nanowire. When the major axis radius 'a' and the minor axis radius 'b' of the elliptical cylindrical nanowire decrease, the target visible light wavelength decreases; when the major axis radius 'a' and the minor axis radius 'b' of the elliptical cylindrical nanowire increase, the target visible light wavelength increases.

4. The structural color metasurface high-quality factor narrowband filter suitable for non-positive incident angles according to claim 1, characterized in that: When the target wavelength is 399–418 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is 45 nm, the minor axis radius b is 30 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is 215–230 nm. When the target wavelength is 418–438 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 52.5 nm, the minor axis radius 'b' is 35 nm, and the center-to-center distance 'p' between two adjacent elliptical cylindrical nanowires is 225–240 nm. When the target wavelength is 435–500 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is 60 nm, the minor axis radius b is 40 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is 230–280 nm. When the target wavelength is 496–568 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is 75 nm, the minor axis radius b is 50 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is 270–320 nm. When the target wavelength is 559–637 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is 90 nm, the minor axis radius b is 60 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is 310–360 nm. When the target wavelength is 625–689 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is 105 nm, the minor axis radius b is 70 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is 350–390 nm. When the target wavelength is 677–741 nm, the major axis radius a of the bottom surface of the elliptical cylindrical nanowire is 120 nm, the minor axis radius b is 80 nm, and the center distance p between two adjacent elliptical cylindrical nanowires is 380–420 nm. When the target wavelength is 728–780 nm, the major axis radius 'a' of the bottom surface of the elliptical cylindrical nanowire is 135 nm, the minor axis radius 'b' is 90 nm, and the center distance 'p' between two adjacent elliptical cylindrical nanowires is 410–440 nm.

5. The structural color metasurface high-quality factor narrowband filter suitable for non-positive incident angles according to claim 1, characterized in that: The thickness of the intermediate layer is 70 nm.

6. The structural color metasurface high-quality factor narrowband filter suitable for non-positive incident angles according to claim 1, characterized in that: The base layer is made of Al2O3 and has a thickness greater than or equal to 200 μm.

7. The structural color metasurface high-quality factor narrowband filter suitable for non-positive incident angles according to claim 1, characterized in that: The thickness of the intermediate layer is 40nm to 100nm.

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