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Nano Lett
Nano Lett
nl
nalefd
Nano Letters
1530-6984
1530-6992
American Chemical Society

39192436
10.1021/acs.nanolett.4c02995
Letter
Multiwavelength Achromatic Deflector in the Visible Using a Single-Layer Freeform Metasurface
Choi Taewon †
Choi Chulsoo †‡
Bang Junseo †
Kim Youngjin †
Son Hyunwoo †
Kim Changhyun †
Jang Junhyeok †
https://orcid.org/0000-0001-9554-4438
Jeong Yoonchan *†
https://orcid.org/0000-0002-0477-9539
Lee Byoungho †
† Inter-University Semiconductor Research Center, School of Electrical and Computer Engineering, Seoul National University, 1 Gwanakro, Gwanak-Gu, Seoul 08826, Republic of Korea
‡ System LSI Division, Samsung Electronics Co., Ltd, Samsung-ro 1, Giheung-gu, Yongin-si, Gyeonggi-do 17113, Republic of Korea
* Email: yoonchan@snu.ac.kr.
27 08 2024
04 09 2024
24 35 1098010986
25 06 2024
20 08 2024
19 08 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

Deflectors are essential for modulating beam direction in optical systems but often face form factor issues or chromatic aberration with conventional optical elements, such as prisms, mirrors, and diffractive/holographic optical elements. Despite recent efforts to address such issues using metasurfaces, their practicality remains limited due to operation wavelengths in the near-infrared or the fabrication difficulties inherent in the multilayer scheme. Here, we propose a novel single-layer metasurface achieving multiwavelength chromatic aberration-free deflection across the visible spectrum by employing the robust freeform design strategy to simplify the fabrication process. By properly selecting diffraction orders for red, green, and blue wavelengths to achieve identical wavelength-diffraction-order products, the metasurface deflects light at a consistent angle of 41.3° with a high efficiency. The coupled Bloch mode analysis explains the physical properties, and experimental fabrication and characterization confirm its effectiveness. This approach holds potential for various applications such as AR/VR, digital cameras, and high-quality optical systems.

dielectric metasurface
multifunctional metasurface
freeform metasurface
achromatic devices
beam steering
topology optimization
Institute for Information and Communications Technology Promotion 10.13039/501100010418 2017-0-00787 Institute for Information and Communications Technology Promotion 10.13039/501100010418 2021-0-00091 document-id-old-9nl4c02995
document-id-new-14nl4c02995
ccc-price
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pmcDeflectors, which are designed to modulate the direction of beams, enabling precise control over their propagation paths, play a crucial role in a wide range of optical systems including imaging, communication, laser processing, and spectroscopy.1−6 Especially, these optical components that steer at identical angles across multiple wavelengths of visible light are often required for practical applications. However, conventional refractive optics consists of quite bulky systems, such as mirrors and prisms. Furthermore, conventional diffractive optics, such as diffractive/holographic optical elements, suffer from chromatic aberration, resulting in a deterioration of image or light quality and causing significant performance degradation in various devices such as augmented/virtual reality devices, displays, and digital cameras that operate at multiple wavelengths in visible region.7−10 Naturally, multilayer diffractive optics are considered to address these defects, but complex fabrication issues cannot be avoided.11−15 To overcome these challenges, among various types of deflectors, metasurface-based devices have garnered considerable attention due to their ability to manipulate light at the subwavelength scale.

Metasurfaces are optical devices that provide outstanding optical performance by manipulating the amplitude, phase, or polarization of incident light on an ultrathin platform consisting of the subwavelength-scale nanostructures.16−24 To date, research on metasurfaces spans a wide range of applications, including imaging systems, holography, deflectors, sensors, and communication technologies.21,25−43 So far, multiwavelength achromatic approaches based on metasurfaces have involved compensating for wavelength-dependent phase retardation or correcting chromatic aberration using multilayer design.11−15,40,44−48 Yet, previous studies still suffer from a number of challenges. The inappropriate operating region of near-infrared (NIR) precludes its application in AR/VR devices or displays.11,40,44−46 Additionally, multilayered structures have strict requirements for precise alignment, making them exceedingly difficult to fabricate.11−15,46 Therefore, in order to reduce the complexity of the system while setting the target wavelength to visible light, there is a need to propose multiwavelength achromatic devices that exhibit high efficiency at multiple wavelengths of visible light with a single-layer structure. Unfortunately, the conventional design method of finding a preshaped structure, such as a circle or square with the desired phase profile, and arranging it as needed without considering near-field interference may simply achieve a device with adequate performance, but it does not guarantee a multifunctional and highly efficient device.49 In other words, the restricted degree of freedom that comes with fixed structures has led us to explore methods for designing structures with more complex shapes. Consequently, efficient design optimization strategies have accordingly evolved with the development of freeform metasurfaces, as the demand for nanophotonic devices that offer multiple functionalities and high performance has grown.50−55 Such freeform metasurfaces overcome the limitations of conventional optical devices and enable more precise and efficient manipulation of light for advanced optical functions.49,56−62

In this paper, we propose a novel achromatic deflector at multiple wavelengths within a single-layer structure using freeform metasurfaces and experimentally demonstrate its multiwavelength achromatic performance. In detail, we focus on the nanostructure design without chromatic aberration behavior using different diffraction orders for three wavelength conditions: red (660 nm), green (550 nm), and blue (470 nm) through the optimization of the freeform nanostructure and the experimental measurement of the optical response. In particular, the target diffraction orders are chosen to satisfy the least common multiple of the products of each wavelength and the target diffraction order. To do this, we conduct advanced optical simulation for topology optimization and employ nanofabrication techniques to manufacture freeform metasurface as multiwavelength achromatic deflectors that provide consistent steering angle at different wavelengths. Additionally, we discuss the operation principle using the coupled Bloch mode analysis,49,61−63 demonstrating that the freeform structure must be required in these systems. This work presents a new paradigm for the design of multiwavelength achromatic metasurface deflectors and provides an important foundation for enhancing their optical performance, exploring their potential applications, and further developing high-quality optical systems in miniaturized form factor. Our findings are anticipated to offer innovative solutions in various optical applications demanding consideration of chromatic aberration issues, such as waveguide-type AR/VR devices, digital cameras, and displays.

A metasurface deflector, designed as a periodic phase gradient metasurface governed by a generalized Snell’s law,23 is often utilized for beam steering with normally incident light. This results in varying diffraction angles depending on the diffraction order, as described by the equation below:1

where nt and ni are the refractive indices of the transmitted and incident mediums, θt and θi are the angles of light traveling in the transmitted and incident mediums, and the diffraction order is m, the operating wavelength is λ, and the period of the structure is Λ. According to eq 1, for a given diffraction order, the deflection angle θt depends on the wavelength, generally resulting in chromatic aberration.

As a proof of concept, we select three representative wavelengths in the visible spectrum: red (660 nm), green (550 nm), and blue (470 nm), designing a multiwavelength achromatic deflector to demonstrate its achromatic behavior. By setting the diffraction order for each wavelength such that it equals the product of the diffraction order and the wavelength (mλ = 7 × 470 nm = 6 × 550 nm = 5 × 660 nm), the identical beam steering angle is induced as prescribed by the above eq 1. In short, it is considered that the fifth order of red, the sixth order of green, and the seventh order of blue are adopted for obtaining identical deflection angle. When designing such a metasurface beam deflector, it is quite challenging to simultaneously maximize the efficiency of different diffraction orders for multiple wavelengths using traditional unit-cell library-based design methods. As an alternative, topology optimization methods can be applied to the deflector, overcoming this limitation.12,13,64

By using topology optimization to increase the efficiency of the diffraction order corresponding to each wavelength, the multiwavelength achromatic metasurfaces can achieve previously unattainable high performance (Figure 1a). First, we define the single-layer space for optimization to have periods of 5000 and 800 nm in the x and y directions, respectively. Then, the steering angle for the calculated target diffraction order is set to 41.3° under normal incidence condition. Due to its single-layer structure, this structure enables easy fabrication that cannot be achievable by conventional achromatic metasurface deflectors designed using multilayer grating. The process of topology optimization involves three steps to update the index distribution at each iteration. First, a random continuous distribution with values between the refractive indices of air and a-Si is established as the initial index input, and iterative optimization is performed to improve the objective function, i.e., Figure of Merit (FoM), which represents transmittance characteristics of the device for target operating wavelengths (Figure 1b). Second, electromagnetic (EM) simulation is conducted using rigorous coupled-wave analysis (RCWA) to calculate the gradient of the FoM on each grid. Subsequently, an adaptive moment estimation (ADAM) optimization algorithm is utilized to update the index distribution, considering the calculated gradient for each grid.65 For the consideration of fabrication constraints, we also additionally simulated the eroded and dilated versions of the updated structure during the optimization process to obtain the average value of the gradient and used Gaussian blurring to remove features smaller than the minimum feature size (approximately 40 nm) for lithography.54,66 This process is repeated until the final index distribution converges to the refractive index of air or a-Si for metasurface structure design, as illustrated in Figure 1.

Figure 1 Overview of freeform metasurface for multiwavelength achromatic deflector and its optimization flow. (a) Freeform metasurface with a periodic array deflects normally incident light at the red, green, and blue to the target diffraction order with identical diffraction angle, respectively. (b) Schematic of the optimization flow for freeform structure. The flow of topology optimization includes various pattern deviations with eroded, normal, and dilated version to incorporate robustness.

We design a multiwavelength achromatic deflector using the freeform metasurface design method as proposed above. To improve the performance of the device, FoM is defined by the following equation.2

The simulation results are presented in Figure 2, where the optimization is conducted to increase the FoM defined above (Figure 2a), and the discretization of the index is carried out to converge toward a structure that is easy to fabricate as shown in Figure 2b. The performance of the final freeform structure is depicted in Figure 2c, demonstrating a high efficiency under transverse magnetically (TM) polarized light illumination for the designed wavelengths at the target diffraction order. Notably, the fifth order of red (660 nm) has an efficiency of 26.2%, the sixth order of green (550 nm) has an efficiency of 21.2%, and the seventh order of blue (470 nm) has an efficiency of 10.7%. Although there is no constraints over the nontarget diffraction order except for the target diffraction order for each wavelength, these problems can be addressed by modifying the FoM in a different way and increasing the degree of freedom of the design structure. In addition, using other materials with lower absorption coefficients, the relatively low average efficiency of the blue wavelengths can be improved.

Figure 2 Optimization results of multiwavelength achromatic deflector. (a) Plot of the combination of target diffraction efficiency at each wavelength, including red, green, and blue as figure of merit (FoM). (b) Unit cell structure of the freeform metasurface at initial, middle, and final iterations of the optimization process. (c) Distribution of theoretical diffraction efficiencies of the transmitted light for the multiwavelength achromatic deflector at red (660 nm), green (550 nm), blue (470 nm) wavelengths. A dashed black box indicates the target diffraction order at each wavelength.

To investigate the physical properties of the freeform metasurface device designed above, we describe it based on the interactions between the different modes operating within the metasurface through the coupled Bloch mode analysis using the open-source (RETICOLO V8) of MATLAB library.67 The coupled Bloch mode analysis is a method used to analyze light propagation, in which the propagation and scattering of light induced by a periodic optical structure are decomposed based on multiple Bloch modes.49,61−63 This analysis allows for the inspection of the interaction between modes and the quantitative calculation of their impact on optical performance and diffraction efficiency. The numerous Bloch modes defined at the interface of the metasurface abutting the substrate and air layers consist of propagation Bloch modes and evanescent Bloch modes. Among these, the evanescent Bloch modes attenuate very quickly through a sufficiently thick metasurface in the vertical direction and are not coupled to any diffractive efficiency, making it possible to ignore them when analyzing optical performance. Using the formula shown in Supporting Information Figure S1 (see Supporting Information for more details), we conduct the coupled Bloch mode analysis of our proposed metasurface for more rigorous interpretation. Specifically, by dividing the hundreds of Bloch modes into propagation and evanescent Bloch modes according to the effective refractive index of the dielectric constant between air and a-Si, and selecting the dominant Bloch modes among the propagation Bloch modes according to their contribution, a few propagation Bloch modes can be observed for each wavelength (See Figure S1 in the Supporting Information for more details). A number of propagation Bloch modes for each wavelength combine with each other to ultimately affect diffraction efficiency, and intricate field profiles can be explored by selecting the most dominant modes, as presented in Figure S2. Metasurfaces with these many modes offer more design degree of freedom, giving them the potential to be fitted to have higher properties (see Figure S2 in the Supporting Information for more details). In other words, this analysis demonstrates that freeform metasurfaces are importantly required for designing metasurfaces with complex multifunctionality.

To experimentally demonstrate the multiwavelength achromatic performance, a freeform metasurface, as shown in Figure 3a, is fabricated using electron-beam (E-beam) lithography (see the Methods section for more details). The sample used in the experiment is fabricated by thin film deposition of hydrogenated amorphous silicon (a-Si:H) on SiO2 substrate (see Figure S3 in Supporting Information for more details), with a sample size of 400 × 400 μm2. The fabrication of the sample is confirmed by scanning electron microscopy (SEM), as presented in Figure 3b. To verify the operational performance, an experimental setup is set as shown in Figure S4 for measuring the distribution of all diffraction orders when three wavelengths of red, green, and blue are incident (see the Methods section for more details).30,31

Figure 3 Fabrication and measurement of the optimized structure with freeform metasurface. (a) A description of freeform metasurface with side view. (b) Scanning electron microscopy image of multiwavelength achromatic deflector with a scale bar of 1 μm. The blue-filled structure represents the proposed unit cell. (c) The experimental results of the far-field profiles of the transmitted light intensity captured by a CCD camera. The cropped images indicate the target deflection position with an intensity line graph of the desired diffraction order (white box). (d) Distribution of experimental diffraction efficiencies of the transmitted light for the multiwavelength achromatic deflector at red (660 nm), green (550 nm), blue (470 nm) wavelengths. A dashed black box indicates the target diffraction order at each wavelength.

As depicted in Figure 3c, when the red, green, and blue light are incident, respectively, it is demonstrated that the fifth order of red, the sixth order of green, and the seventh order of blue exhibit the highest efficiencies with an equal deflection angle, corresponding to the target diffraction order. In addition, when these three wavelengths are incident simultaneously, the three wavelengths of light are matched at the identical position, similar to the simulation result. Moreover, their experimental target deflection efficiencies (Figure S4 in Supporting Information for more details) are measured, with values of 22.7% for the fifth order of red, 14.3% for the sixth order of green, and 7.1% for the seventh order of blue as shown in Figure 3d. This discrepancy between simulation and experiment is due to the use of a blue wavelength laser operating at 473 nm, which is different from the designed wavelength 470 nm, slight misalignments in the experimental setup, and the imperfection of the sample fabrication (see Figure S5 in the Supporting Information for more details).

Furthermore, such an achromatic characteristic offers a distinct advantage for AR/VR devices and digital cameras that require devices capable of delivering multiple wavelengths of light to a specific location without chromatic aberration. To demonstrate the feasibility, we conducted additional imaging experiments to verify the stability of the target deflected light at an identical angle. An experimental setup is designed to demonstrate, as shown in Figure 4a. When a specific object image is incident, it passes through the device and delivers an identical image at the goal position. The United States Air Force (USAF) 1951 resolution test chart image is used as the input image at each wavelength. According to the results, it is demonstrated that when the three wavelengths for red, green, and blue are incident simultaneously, a nearly identical image is aligned at the identical location. Specifically, the imaging results are shown in Figure 4b and it can be seen that clear images of the USAF 1951 resolution test chart image are captured by the CCD when a combination of wavelengths of the red, green, and blue is incident. Under all conditions, the position of the USAF image remains nearly unchanged. Consequently, it has potential to be useful in various fields where the image information must be transmitted without distortion, taking into account this characteristic of not changing the position at multiple wavelengths (see Figure S6 in Supporting Information for more details).

Figure 4 Experimental characterization of the proposed freeform metasurface sample. (a) The schematic of imaging measurement setup. (b) The captured images of a USAF 1951 resolution test chart delivered by the multiwavelength achromatic deflector using a CCD camera (BFS- U3-120S4C-CS, FLIR). The combination of incident light is indicated above each image. The line width of the element 2 in group 4 of the resolution chart is 27.84 μm. Scale bars: 100 μm.

In summary, we have proposed a multiwavelength achromatic deflector that steers red, green, and blue light at the identical angle. By comprehensively setting an objective function of optimization with numerous degrees of freedom, the proposed freeform metasurface design could readily be fabricated on a single layer configuration. Additionally, the underlying principle for its achromatic behavior was theoretically investigated by coupled Bloch mode analysis. Through experimental demonstration, the proposed device achieved high deflection efficiencies of 22.7%, 14.3%, and 7.1% for red, green, and blue light, respectively, at an identical diffraction angle of 41.3°. Furthermore, an additional imaging experiment was conducted to demonstrate that the proposed device is robustly capable of delivering an image to the same location, indicating its potential for practical applications. Thanks to the ability to adjust the incident beam to the desired angle by engineering chromatic aberration in multiwavelength operation of the visible regime, these devices are expected to be utilized in various optical applications including digital cameras, image combiners of AR/VR equipment, and holographic displays.

Methods

In this experimental setup, a commercial supercontinuum laser source with a tunable filter (Super K Extreme White Light Laser, NKT Photonics) for red and green wavelengths and a 473 nm single laser (04–01 Series Blue, Cobolt) for the blue wavelength are used. Additionally, a linear polarizer (LPVISE050-A, Thorlabs) is utilized for obtaining TM polarized light illumination. A tube lens is used to focus the spot size of the beam smaller than the sample, and a 40× objective lens (NA = 0.95) captivates all light after passing through the sample. Finally, a CCD camera (BFS-U3-120S4C-Cs, FLIR) is employed to capture images of the far-field profile (see Figure S5 in Supporting Information for more details).

The metasurface samples used in the experiment were fabricated by using the standard electron beam(E-beam) lithography patterning process. At first, the amorphous silicon of 200 nm was deposited on the glass using PECVD (Applied Materials P500, OEM Group) based on SiH4 and helium. Then, the negative type E-beam resist of Hydrogen silsesquioxane (HSQ A2, Microchem), was spin-coated on the samples at the rotation speed of 3000 rpm for 45 s, with postbaking for 4 min at the temperature of 80 C. The E-spacer (ESpacer 300Z, Showa Denko) was additionally coated on the resist already coated sample for preventing the negative charge accumulation on the substrate, causing beam distortion. Second, the commercial electron beam lithography system (JBX6300FS, JEOL) was utilized for nanopatterning at 100 kV condition. After patterning, the sample was developed using a developer solution TMAH (TMAH 25, Microchem) for 30 s and rinsed in flowing water for 30 s. Finally, the processed sample was etched by using ICP-RIE (Multiplex ICP, STS)

Numerical simulations of electromagnetic field analysis were implemented with the Python open-source code (Torcwa), which is based on the rigorous coupled-wave analysis (RCWA).65 The diffraction efficiency and the electric field on the dielectric pattern were calculated through RCWA simulations, and the calculated gradient value was updated based on the hyper parameters of adaptive moment estimation (ADAM) optimizer.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.4c02995.Description of the coupled Bloch mode analysis method and Bloch mode plot at each wavelength; The selected dominant Bloch mode field at each wavelength and constructed phase modulation profile; Comparison with simulated and experimental diffraction efficiencies; Experimental system of far-field profiles measurement setup (PDF)

Supplementary Material

nl4c02995_si_001.pdf

The authors declare no competing financial interest.

Acknowledgments

This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korean government(MSIT) (No. 2021-0-00091, Development of real-time high-speed renderer technology for ultrarealistic hologram generation), (No. 2017-0-00787, Development of vision assistant HMD and contents for legally blind and low visions). We would like to acknowledge the invaluable contributions of the late Professor Byoungho Lee, who unfortunately passed away during the course of this research. Professor Lee was a dedicated mentor who made significant contributions to the fields of 3D displays, metasurfaces, and nanophotonics. He will be greatly missed, and his impact in these areas will always be remembered and deeply appreciated.
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