A cascaded metalens for large field-of-view imaging in mid-infrared and its design method

Abstract

This invention discloses a cascaded metalens for achieving large field-of-view imaging in the mid-infrared range. It comprises a first metalens, a substrate, and a second metalens arranged sequentially from left to right. The first metalens acts as a correction lens, primarily correcting spherical aberration, while the second metalens acts as a focusing lens, focusing light from different incident angles onto different points on the image plane. Off-axis aberrations can be eliminated by controlling the distance between the first and second metalenses, i.e., the thickness of the substrate. This invention, a cascaded metalens for achieving large field-of-view imaging in the mid-infrared range and its design method, utilizes planar optical elements to achieve mid-infrared large field-of-view imaging. It can replace traditional stacked, bulky, and expensive large field-of-view imaging systems, reducing fabrication difficulty and system complexity, and features low cost, lightweight design, and integration.

Description

Technical Field

[0001] This invention relates to a cascaded metalens for achieving large field-of-view imaging in mid-wave infrared and its design method, belonging to the field of large field-of-view imaging technology. Background Technology

[0002] To achieve clear imaging, large field-of-view imaging systems typically require the elimination of certain off-axis monochromatic aberrations, including coma, astigmatism, and field curvature, caused by oblique angles of incidence. This means the system must produce near-diffraction-limited focusing within a certain angular range of incident angles. Traditional mid-wave infrared large field-of-view imaging systems generally consist of multiple layers of lenses of different sizes and functions, inevitably resulting in large size and weight, complex design, and difficulty in integration. In contrast, mid-wave infrared large field-of-view imaging systems based on metalenses offer advantages such as thinness and ease of integration, aligning with the current trend towards miniaturization and integration of optical systems. They can be widely applied in infrared alarm detection, VR / AR, remote sensing, and other fields. Currently, large field-of-view imaging designs based on metalenses mainly fall into two categories: combinations of aperture stops and metalenses, and cascaded metalenses. While combinations of aperture stops and metalenses effectively eliminate off-axis monochromatic aberrations, they cannot eliminate spherical aberration. Cascaded metalens designs can address this requirement. Most studies based on cascaded metalenses are conducted in the visible and near-infrared bands, and most operate at a single wavelength, which makes it difficult to meet the requirements of wide-band imaging. At the same time, there is an urgent need for a simple, easy-to-implement, and highly accurate design method. Summary of the Invention

[0003] This invention provides a cascaded metalens for achieving large field-of-view imaging in mid-wave infrared and its design method.

[0004] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0005] A cascaded metalens for achieving large field-of-view imaging in mid-wave infrared includes a first metalens, a substrate, and a second metalens arranged sequentially from left to right. The first metalens acts as a correction lens to primarily correct spherical aberration, while the second metalens acts as a focusing lens to focus light at different incident angles onto different points on the image plane. Off-axis aberrations can be eliminated by controlling the distance between the first and second metalenses, i.e., the thickness of the substrate.

[0006] Preferably, the substrate material is Si, BaF2, Ge, CaF2, MgF2, LiF, GaSb, or PbTe.

[0007] A design method for a cascaded metalens for large field-of-view imaging in mid-infrared wavelengths, the design method comprising the following steps:

[0008] S1. Determine the entrance pupil diameter, F-number, and the materials for the substrate and nanostructure;

[0009] S2. Using ZEMAX, the phase distribution profiles of the first and second metasurfaces are obtained, and the radius of the second metasurface is determined. At the same time, preliminary aggregation performance verification is performed.

[0010] S3. Calculate the phase shift generation phase database for nanostructures with different radii using FDTD;

[0011] S4 uses MATLAB and a database to match the phase required at each coordinate position of the metasurface to find the nanostructure with the closest phase.

[0012] S5. Verify the focusing performance of the double-layer metalens using FDTD.

[0013] Compared with existing technologies, this invention presents a cascaded metalens for achieving large field-of-view imaging in the mid-infrared range, and its design method. This method utilizes planar optical elements to achieve large field-of-view imaging in the mid-infrared range, replacing traditional stacked, bulky, and expensive large field-of-view imaging systems. It reduces fabrication difficulty and system complexity, offering advantages such as low cost, lightweight design, and integration. The cascaded metalens designed based on this method can be used within a certain wavelength range. By selecting nanostructures of different shapes and sizes to construct different refractive indices and matching chromatic aberration with a database, it exhibits the advantage of broadband achromatic aberration. Utilizing the chromatic aberration characteristics of special nanostructures, large field-of-view imaging metalenses at arbitrary wavelengths can be designed, simultaneously achieving high NA and a large field of view. Combining the ZEMAX and FDTD optical design software allows for more efficient optimization design of the cascaded metalens. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the cascaded metalens for achieving large field-of-view imaging in the mid-wave infrared region according to the present invention.

[0015] Figure 2 This is a flowchart illustrating the design process of the cascaded metalens for achieving large field-of-view imaging in the mid-wave infrared region, as described in this invention.

[0016] Figure 3 This is the MTF curve of the cascaded metalens for achieving large field-of-view imaging in mid-wave infrared according to the present invention.

[0017] Figure 4 This is a geometric simulation image of the cascaded metalens used in the present invention to achieve large field-of-view imaging in the mid-wave infrared.

[0018] Figure 5 This is a phase curve diagram of the cascaded metalens used in the present invention to achieve large field-of-view imaging in the mid-wave infrared. Detailed Implementation

[0019] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0020] like Figures 1 to 5 As shown, a cascaded metalens for achieving large field-of-view imaging in mid-wave infrared includes a first metalens 1, a substrate 2, and a second metalens 3 arranged sequentially from left to right.

[0021] The basic configuration of the metalens consists of two different layers: a first metalens 1 and a second metalens 3, positioned on either side of a substrate 2. The first metalens 1 acts as a correction lens, primarily correcting spherical aberration, while the second metalens 3 acts as a focusing lens, focusing light at different incident angles onto different points on the image plane. Off-axis aberrations can be eliminated by controlling the distance between the first and second metalens 1, i.e., the thickness of the substrate 2. Materials suitable for the substrate 2 and the nanostructure, capable of achieving high efficiency in the mid-infrared band, are selected, along with the entrance pupil diameter and F-number. Ray tracing is performed using ZEMAX optical design software to determine the phase distribution of the first metalens 1, the substrate thickness, and the phase distribution and diameter of the second metalens 3, and preliminary verification of the focusing effect is conducted. The dimensional parameters of the nanounit structures are established. FDTD is used to calculate the phase corresponding to nanounit structures with different dimensional parameters, thus obtaining a phase database. MATLAB is used to match the required phase at each position of the metalens to find the nanostructure with the closest phase value. Focusing tests are conducted using FDTD simulation of the application environment. This design method is simple and easy to implement, and can be integrated with detectors to realize a lightweight infrared wide field-of-view detection system.

[0022] The phase distribution of the first layer of metalens 1 is determined by an even-degree polynomial of ρ:

[0023]

[0024] Where M is the diffraction order and the coefficient a n To optimize the parameters, n is the number of optimization coefficients. (x, y) represent the coordinates of each nanometer unit with the center of the metalens as the origin, ρ is the corresponding radial value, and R1 is the radius of the first metalens 1. The phase obtained according to this phase formula has a phase distribution similar to that of a Schmidt plate.

[0025] The phase distribution formula for the second layer of metalens 3 is obtained by adding an even-degree polynomial to the common hyperbolic profile phase:

[0026]

[0027] Where λ is the operating wavelength, f is the focal length, and b n To optimize the coefficients, R2 is the radius of the second metalens 3. When the working wavelength and focal length are constant, the above equation can be regarded as a function of ρ, that is, the entire equation can be replaced by a new even-degree polynomial of ρ:

[0028]

[0029] Among them, b′ n It is different from b n The new optimization coefficients are obtained. The cascaded metalens optimized according to the above formula can achieve near-diffraction-limited imaging over a continuously varying incident angle range.

[0030] The cascaded metalens design method based on the above formula is mainly divided into two parts. The first part is to obtain a by optical tracing optimization based on ZEMAX. n With b n The second part of the two sets of optimization coefficient methods is a method for parametric scanning and simulated focusing imaging based on FDTD.

[0031] A design method for cascaded metalenses to achieve large field-of-view imaging in the mid-infrared range includes the following steps:

[0032] S1. Determine the entrance pupil diameter, F-number, and the materials for the substrate and nanostructure;

[0033] S2. Using ZEMAX, the phase distribution profiles of the first and second metasurfaces are obtained, and the radius of the second metasurface is determined. At the same time, preliminary aggregation performance verification is performed.

[0034] S3. Calculate the phase shift generation phase database for nanostructures with different radii using FDTD;

[0035] S4 uses MATLAB and a database to match the phase required at each coordinate position of the metasurface to find the nanostructure with the closest phase.

[0036] S5. Verify the focusing performance of the double-layer metalens using FDTD.

[0037] When conducting preliminary optical design based on ZEMAX, the entrance pupil diameter and F-number are first determined considering the simulation limits of FDTD and design requirements. Simultaneously, a substrate 2 with high transmittance in the mid-infrared band and capable of producing high refractive index contrast, and a nanostructure material are selected. Based on the established conditions, corresponding settings are made in ZEMAX. Due to the symmetry of the designed metalens, multiple fields of view with step sizes are only needed within half the field of view. Then, a total of six planes are set from left to right: the object plane, the entrance pupil plane (set as binary plane 2 (first layer metalens 1), the standard plane (substrate 2), binary plane 2 (second layer metalens 3), the standard plane, and the image plane. The thickness of the fifth plane is set as a fixed value, which is the focal length of the cascaded metalens, determined by the entrance pupil diameter and F-number. The thickness of substrate 2 and the radius of the second binary surface 2 are set as variables. The diffraction order of the two binary surfaces 2 is set to -1. The number of optimization coefficients is selected as 5, and these 5 optimization coefficients are set as variables. The Levenberg-Marquardt algorithm (also known as the damped least squares method) is used for optimization. The optimization objective is to obtain the smallest focal spot on the focal plane. Finally, the MTF curve and geometric image simulation are used as indicators to evaluate the imaging characteristics. After multiple optimizations, the optimization coefficient 'a' of the first metalens 1 is finally obtained. n The thickness of the substrate, and the b of the second metalens 3. n And the radius value, where the phase distribution of each layer of metalens can be obtained once the optimization coefficients are established.

[0038] The method for subsequent design using FDTD is as follows: First, based on the design requirement of polarization insensitivity, a rotationally symmetric nanostructure is selected. The size of the nanostructure unit, i.e., the unit period, is determined according to the Nyquist sampling theorem. Combining the fabrication limit and the unit period, the range of variation for the nanostructure unit size is determined. A phase database is generated by scanning various parameters. Using MATLAB, the required phase for each annulus of each layer of the metalens is matched from the phase database using structures with the closest phase values. In this design method, to reduce simulation time and improve simulation accuracy, the first layer metalens 1 and the second layer metalens 3 are simulated separately. The propagation between the two layers is calculated using far-field diffraction, and the propagation between the second layer metalens 3 and the image plane is also calculated using far-field diffraction. Preliminary settings are made for the simulation of the first layer metalens 1 in FDTD, such as... Figure 1As shown, a ring-shaped PEC material is placed on the left surface of substrate 2 to act as an aperture stop. The refractive index of the simulation environment is set to the refractive index of substrate 2. At the same time, a material with the refractive index of air is used to cover the area from the lower boundary of the simulation region to the left surface of substrate 2. A monitor is placed on the surface from which the light beam just exits the first layer of metalens 1. The electromagnetic field results obtained from the monitor are used for far-field diffraction to the front surface of the second layer of metalens 3. The result of the far-field diffraction is used as the incident light source of the second layer of metalens 3. Similarly, the monitor is placed on the surface from which the light beam just exits the second layer of metalens 3. Finally, far-field diffraction calculations are performed to obtain the intensity distribution map on the focal plane or along the focal length direction to check the focusing effect.

[0039] The substrate 2 is made of Si, BaF2, Ge, CaF2, MgF2, LiF, GaSb and PbTe.

[0040] Nanostructures have rotationally symmetrical geometric shapes such as circles, squares, and crosses.

[0041] The period of the nanostructure unit should be selected based on the actual fabrication limits and should also satisfy the Nyquist sampling theorem.

[0042] To verify the feasibility and advantages of this design method, a cascaded metalens with an entrance pupil diameter of 150μm, an F-number of 0.5, and a field of view of ±20° at a single wavelength of 4.2μm is used as an example to further explain this design method in detail.

[0043] Based on the available nanostructure geometry, a circular structure is chosen here, with a square substrate selected for the unit cells. The substrate is BaF2, which has high transmittance in the mid-infrared range, and the nanostructure is Si, which also has high transmittance. The high refractive index contrast between the two materials results in better focusing. To ensure that the nanostructure unit cell period meets fabrication limits and the Nyquist sampling theorem, and guarantees the required phase for each layer of the metalens, the smallest possible nanostructure unit cell period size is chosen to achieve a more continuous phase distribution in the metalens.

[0044] The cascaded metalens design method for achieving large field-of-view imaging in the mid-infrared band proposed in this invention can achieve near-diffraction-limited focusing within a continuous incident angle range in the mid-infrared band, and this design method is simple, easy to implement, and time-saving.

[0045] This invention discloses a cascaded metalens for achieving large field-of-view imaging in the mid-infrared range and its design method. It utilizes planar optical elements to achieve large field-of-view imaging in the mid-infrared range, replacing traditional stacked, bulky, and expensive large field-of-view imaging systems. This reduces fabrication difficulty and system complexity, offering advantages such as low cost, lightweight design, and integration. The cascaded metalens designed based on this method can be used within a certain wavelength range. By selecting nanostructures of different shapes and sizes to construct different refractive indices and matching chromatic aberration with a database, it exhibits the advantage of broadband achromatic aberration. Utilizing the chromatic aberration characteristics of special nanostructures, large field-of-view imaging metalenses at arbitrary wavelengths can be designed, simultaneously achieving high NA and a large field of view. Combining the ZEMAX and FDTD optical design software allows for more efficient optimization design of the cascaded metalens.

[0046] Finally, it should be noted that the above embodiments are only illustrative of the technical solutions of the present invention, and not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for a cascaded metalens for large field-of-view imaging in mid-infrared wavelengths, characterized in that, The design method includes the following steps: S1. Determine the entrance pupil diameter, F-number, and the materials for the substrate and nanostructure; S2. Using ZEMAX, the phase distribution profiles of the first and second metasurfaces are obtained, and the radius of the second metasurface is determined. At the same time, preliminary aggregation performance verification is performed. S3. Calculate the phase shift generation phase database for nanostructures with different radii using FDTD; S4 uses MATLAB and a database to match the phase required at each coordinate position of the metasurface to find the nanostructure with the closest phase. S5. Verify the focusing performance of the double-layer metalens using FDTD; When conducting preliminary optical design based on ZEMAX, first consider the simulation limits of FDTD and design requirements to determine the entrance pupil diameter and F number, and select a substrate (2) and nanostructure material with high transmittance in the mid-infrared band and high refractive index contrast; Based on the established conditions, make the corresponding settings in ZEMAX. Due to the symmetry of the designed metalens, set multiple fields of view with step size in half field of view, and then set a total of 6 surfaces from left to right, namely: object surface, entrance pupil surface set as binary surface, i.e., the first layer metalens (1), standard surface, i.e., the substrate The substrate (2), the binary plane (2), the second layer of the superlens (3), the standard plane, and the image plane; the thickness of the fifth plane is set as a fixed value, which is the focal length of the cascaded superlens, determined by the entrance pupil diameter and the F number; the thickness of the substrate (2) and the radius of the second binary plane 2 are set as variables, the diffraction order of the two binary planes is set as -1, the number of optimization coefficients is selected as 5, and these 5 optimization coefficients are set as variables. The optimization method adopts the damped least squares method, and the optimization goal is to obtain the smallest focal spot on the focal plane. The MTF curve and the geometric image simulation diagram are used as indicators to evaluate the imaging characteristics. After multiple optimizations, the optimization coefficient a of the first layer of the superlens (1) is finally obtained. n The thickness of the substrate and the b of the second metalens (3) n And the radius value, where the phase distribution of each layer of metalens can be obtained after the optimization coefficients are established; the phase distribution of the first layer of metalens (1) is determined by an even-degree polynomial of ρ: ； Where M is the diffraction order and the coefficient a n To optimize the parameters, n is the number of optimization coefficients. (x, y) are the coordinate values ​​of each nanometer unit with the center of the metalens as the origin, ρ is the corresponding radial value, and R1 is the radius of the first layer of metalens 1; the phase obtained according to this phase formula has a phase distribution similar to that of a Schmidt plate. The phase distribution formula of the second-layer metalens (3) is obtained by adding an even-degree polynomial to the common hyperbolic contour phase: ； Where λ is the operating wavelength, f is the focal length, and b n To optimize the coefficients, R2 is the radius of the second meta-lens (3). When the working wavelength and focal length are constant, the above equation is considered as a function of ρ, that is, the polynomial is replaced by a new even-degree polynomial of ρ: ； in, It is different from b n The new optimization coefficients; the cascaded metalens obtained by optimization according to the above formula can achieve near-diffraction-limited imaging within a continuously varying incident angle range.

2. The design method of a cascaded metalens for achieving large field-of-view imaging in mid-wave infrared according to claim 1, characterized in that, Using FDTD for subsequent design, firstly, a rotationally symmetric nanostructure is selected based on the polarization-insensitive design requirement. The size of the nanostructure unit, i.e., the unit period, is determined according to the Nyquist sampling theorem. The range of variation of the nanostructure unit size is determined by combining the processing limit and the unit period. The parameters are scanned to generate a phase database. Using MATLAB, the phase required for each annulus of each layer of the metalens is selected from the phase database to match the structure with the closest phase value. The first layer metalens (1) and the second layer metalens (3) are simulated separately. The propagation between the two layers of metalens is calculated by far-field diffraction. The propagation between the second layer metalens (3) and the image plane is calculated. The propagation is also calculated by far-field diffraction. The simulation of the first layer metalens (1) in FDTD is initially set up. A ring-shaped PEC material is set on the left surface of the substrate (2) to act as an aperture stop. The refractive index of the simulation environment is set to the refractive index of the substrate (2) material. At the same time, a material with the refractive index of air is used to cover the area from the lower boundary of the simulation area to the left surface of the substrate (2). The monitor is placed on the surface from which the beam just exits from the first layer metalens (1). The electromagnetic field result obtained by the monitor is used to perform far-field diffraction to the front surface of the second layer metalens (3). The result of far-field diffraction is used as the incident light source of the second layer metalens (3). Similarly, the monitor is placed on the surface from which the beam just exits from the second layer metalens (3). Finally, far-field diffraction calculation is performed to obtain the intensity distribution map on the focal plane or in the focal length direction to check the focusing effect.

3. The design method of a cascaded metalens for achieving large field-of-view imaging in mid-wave infrared according to claim 1, characterized in that, The cascaded meta-lens designed based on this design method includes a first meta-lens (1), a substrate (2), and a second meta-lens (3) arranged from left to right. The first meta-lens (1) serves as a correction lens to mainly correct spherical aberration, while the second meta-lens (3) serves as a focusing lens to focus light at different incident angles onto different points on the image plane. Off-axis aberrations are eliminated by controlling the distance between the first meta-lens (1) and the second meta-lens (3), i.e., the thickness of the substrate (2).

4. The design method of a cascaded metalens for achieving large field-of-view imaging in mid-wave infrared according to claim 1, characterized in that, The substrate (2) is made of Si, BaF2, Ge, CaF2, MgF2, LiF, GaSb and PbTe.

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