A double-layer broadband achromatic metalens based on meta-atoms and its preparation method

Abstract

The present invention discloses a double-layer broadband achromatic metalens based on meta-atoms and a method for preparing the same. The double-layer broadband achromatic metalens includes: a first layer of meta-atoms, a substrate, and a second layer of meta-atoms. The method includes: determining the phase resonance curve of the double-layer broadband achromatic metalens; determining the relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens based on the focal depth of the diffraction lens; determining the electric field intensity of the double-layer broadband achromatic metalens, and constructing the double-layer broadband achromatic metalens by combining the phase resonance curve of the double-layer broadband achromatic metalens and the relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens. By using the present invention, the design process of the double-layer broadband achromatic metalens can be simplified, and the discrete wavelength region design space can be fully utilized to achieve achromatism. As a double-layer broadband achromatic metalens based on meta-atoms and a method for preparing the same, the present invention can be widely used in the field of integrated device technology.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated devices, and in particular to a double-layer broadband achromatic metalens based on meta-atoms and a preparation method thereof. Background Art

[0002] An achromatic metalens, or a metalens, possesses the same focal point at different operating wavelengths. According to the design methods of geometric optics achromatic lenses, the greater the number of operating wavelengths, the greater the complexity of the optical system. Thanks to the ultra-high degrees of freedom of meta-atoms, a single metalens can achieve achromatic performance over a wide operating wavelength range. Currently, various achromatic metalens design schemes have been developed, which can be categorized into three main types based on their implementation: broadband achromatic metalens based on group delay or phase compensation; discrete wavelength achromatic metalens based on region-based achromatic systems; and achromatic metalens based on intelligent algorithms. Existing quasi-achromatic metalens have numerically simulated a 2 mm aperture quasi-achromatic metalens by extending the group delay, addressing to some extent the inability of meta-atoms to generate large group delays. However, this method is essentially discrete wavelength achromatic, which differs from the strict broadband achromatic system used in dispersion engineering. Extending the group delay can transform the overall chromatic aberration curve from an inversely proportional function to a sawtooth shape, resulting in lower overall chromatic aberration. However, due to the low space utilization of discrete wavelength region-based designs, true achromatic aberration cannot be achieved. Summary of the Invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide a double-layer broadband achromatic metalens based on meta-atoms and a preparation method thereof, which can simplify the design process of the double-layer broadband achromatic metalens and make full use of the discrete wavelength region design space to achieve achromatism.

[0004] The first technical solution adopted by the present invention is: a double-layer broadband achromatic metalens based on meta-atoms, comprising a first layer of meta-atoms, a substrate and a second layer of meta-atoms, wherein the substrate is located between the first layer of meta-atoms and the second layer of meta-atoms, and the wavelength of the incident polarized light controlled by the first layer of meta-atoms is , the wavelength of the output polarized light controlled by the second layer of meta-atoms is ,in:

[0005] The first layer of meta-atoms is used to generate The polarized light can be controlled;

[0006] The substrate is used to support the first layer of metaatoms and the second layer of metaatoms;

[0007] The second layer of meta-atoms is used to generate The polarization of light can be controlled.

[0008] The second technical solution adopted by the present invention is: a method for preparing a double-layer broadband achromatic metalens based on meta-atoms, comprising the following steps:

[0009] Obtaining a relationship between polarized light input and output of a double-layer broadband achromatic metalens, determining a phase resonance curve of the double-layer broadband achromatic metalens, a transmission matrix of a first layer of metaatoms, and a transmission matrix of a second layer of metaatoms, wherein the double-layer broadband achromatic metalens is composed of a first layer of metaatoms and a second layer of metaatoms;

[0010] The relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens is determined based on the focal depth of the diffraction lens;

[0011] The electric field intensity of the double-layer broadband achromatic metalens was determined. Combining the phase resonance curve of the double-layer broadband achromatic metalens with the relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens, a double-layer broadband achromatic metalens was constructed by photolithography using the laser direct writing method.

[0012] Furthermore, the step of obtaining the relationship between polarized light input and output of the double-layer broadband achromatic metalens specifically includes:

[0013] Using plane wave incidence, the complex amplitude distribution of the electromagnetic wave when passing through the meta-atom surface is:

[0014]

[0015] According to the complex amplitude distribution of electromagnetic waves when passing through the meta-atom surface, the relationship between the polarized light input and output of the double-layer broadband achromatic metalens is determined by the transmission matrix, and its expression is:

[0016]

[0017] In the above formula, represents the transmission matrix, represents the complex amplitude distribution, Indicates the A superatom, Indicates that there is A superatom, represents the complex amplitude distribution of the meta-atoms, represents the coordinates of the meta-atoms on the single-layer plane, represents the wavelength, Indicates the The phase of a metaatom, Indicates the The superatom has a wavelength of The coordinates are The complex amplitude distribution of Indicates the The superatom has a wavelength of The coordinates are The phase, 、 Indicates that after Left-handed circularly polarized light and right-handed circularly polarized light after the super lens, 、 Indicates that after Left-handed circularly polarized light and right-handed circularly polarized light after a superlens.

[0018] Furthermore, the expression of the transmission matrix is:

[0019]

[0020] In the above formula, represents the wavelength, Indicates the The wavelength of the metalens is The size of the PCR, Indicates that the wavelength is The next phase.

[0021] Furthermore, the expression of the phase resonance curve of the double-layer broadband achromatic metalens is:

[0022]

[0023]

[0024] In the above formula, represents the size of the lower superlens PCR, represents a step function, represents the size of the upper superlens PCR, Represents the designed phase interval Maximum value (max), represents the middle value of the designed phase interval, represents the minimum value of the designed phase interval, and Describes two superatoms in and The shape of the PCR curve in the two intervals.

[0025] Furthermore, the relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens is:

[0026]

[0027] In the above formula, represents the focal length, Indicates the diameter of the lens.

[0028] Furthermore, the electric field intensity of the double-layer broadband achromatic metalens is expressed as:

[0029]

[0030] In the above formula, represents the amplitude of the first layer of metalens, represents the amplitude of the second-layer metalens, represents the phase of the first layer of metalens, Represents the phase of the second-layer metalens.

[0031] The method and array of the present invention have the following beneficial effects: By proposing a method for dividing the operating wavelength range, the present invention designs two metalenses operating in different wavelength bands, cascades them together, and uses two types of metaatoms, avoiding the need to build a large database of metaatoms, accelerating the design process, and utilizing the metalens cascade system to achieve broadband achromatism. Thus, the proposed method of dividing the operating wavelength range into two parts achieves the reduction of metalens chromatic aberration. Finally, the overall achromatism is achieved by combining the focal depth of the metalens. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of the structure of a double-layer broadband achromatic metalens based on meta-atoms of the present invention;

[0033] Figure 2 1 is a schematic diagram of the steps of a method for preparing a double-layer broadband achromatic metalens based on meta-atoms of the present invention;

[0034] Figure 3 Schematic diagram of achieving achromatism with a double-layer broadband achromatic metalens provided by a specific embodiment of the present invention;

[0035] Figure 4 Schematic diagram of a double-layer superatom double-layer structure provided by a specific embodiment of the present invention;

[0036] Figure 5 Schematic diagram of phase control of a double-layer superatomic double-layer structure provided by a specific embodiment of the present invention;

[0037] Figure 6 Schematic diagram of the self-normalized electric field distribution of the chromatic and achromatic metalens in the XZ plane provided by a specific embodiment of the present invention;

[0038] Figure 7 1 is a schematic diagram of a curve showing how chromatic aberration and focal length of an achromatic lens vary with wavelength, provided by a specific embodiment of the present invention;

[0039] Figure 8 1 is a schematic diagram of a curve showing how chromatic aberration and achromatic focusing efficiency vary with wavelength, provided by a specific embodiment of the present invention;

[0040] Figure 9 Schematic diagram of the planar self-normalized electric field distribution of the chromatic / achromatic lens provided by a specific embodiment of the present invention;

[0041] Figure 10 Schematic diagram of a curve showing the change in focal length of a chromatic / achromatic lens with wavelength according to a specific embodiment of the present invention;

[0042] Figure 11 2 is a schematic diagram of a curve showing a change in focusing efficiency of an achromatic metalens as a function of wavelength provided by a specific embodiment of the present invention;

[0043] Figure 12 Schematic diagram of chromatic aberration and MTF curves in sagittal and tangential directions of an achromatic lens at different wavelengths provided by a specific embodiment of the present invention. DETAILED DESCRIPTION

[0044] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are provided for ease of description only and do not limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted based on the understanding of those skilled in the art.

[0045] First, it should be noted that in practical optical imaging systems, achromatic aberration at two wavelengths is often insufficient. For example, in common visible light imaging, a lens assembly must be achromatically achromatic for at least three wavelengths. The more wavelengths achromatized, the better the image quality. Therefore, building on dual-wavelength achromatism, we propose a dual-layer broadband achromatic metalens design. We select two meta-atoms with unique polarization conversion curves and use them to design metalenses operating in different wavelength ranges. These two metalenses are then spatially cascaded to create the entire operating wavelength range. Since the lens operating range is part of the design operating range, the chromatic aberration of each lens is also reduced. Choosing the appropriate design wavelength ensures that the maximum chromatic aberration of the cascaded lens is equal to the maximum chromatic aberration of the two lenses. Combined with the inherent focal depth of the lens, the broadband achromatic metalens design is realized. Finally, we simulate the broadband achromatic metalens using FDTD and compare it with a chromatic lens. The performance of the achromatic metalens is evaluated using MTF curves.

[0046] Based on this, in order to address the problem of space utilization in the discrete wavelength region design method, we proposed a design method for dual-wavelength phase-independently controlled meta-atoms. Each meta-atom simultaneously bears the phase information of two wavelengths, thereby achieving efficient manipulation of the wavelength. Since the phase of the two wavelengths can be arbitrarily controlled, efficient achromatism can also be achieved when the size or NA of the metalens is large. To address the problem of broadband achromatism, we proposed a method to divide the working wavelength range. By designing two metalenses working in different bands and cascading them together, the maximum chromatic aberration of the lens is reduced by more than 50%. This design only uses two types of meta-atoms, avoiding the establishment of a large database of meta-atoms and speeding up the design process.

[0047] The working band is 10-14 , numerical aperture is 0.45, focal length is 200 Design of broadband achromatic meta-lens. First, we analyzed the use of a cascaded metalens system to achieve broadband achromatism, and then proposed a method to reduce the chromatic aberration of the metalens by dividing the working wavelength range into two parts. Finally, the focal depth of the metalens was combined to achieve overall achromatism. We used a double-layer meta-atoms to implement a band-splitting design and optimized the meta-atoms. Finally, we constructed achromatic metalens with large numerical aperture (0.71) and small numerical aperture (0.45). The large numerical aperture achromatic metalens reduces the chromatic aberration by 59% compared to traditional lenses. The small numerical aperture achromatic metalens achieves broadband achromatism on the basis of halving the chromatic aberration and combining the metalens' own focal depth with the overall focusing efficiency of more than 35%. Our design only uses two types of meta-atoms, which is simpler, and the two-layer lens does not require point-to-point alignment between structures, which has practical application value.

[0048] Reference Figure 1 The present invention provides a double-layer broadband achromatic metalens based on meta-atoms, comprising a first layer of meta-atoms, a substrate and a second layer of meta-atoms, wherein the substrate is located between the first layer of meta-atoms and the second layer of meta-atoms, and the wavelength of the incident polarized light controlled by the first layer of meta-atoms is , the wavelength of the output polarized light controlled by the second layer of meta-atoms is ,in:

[0049] The first layer of meta-atoms is used to generate The polarized light can be controlled;

[0050] The substrate is used to support the first layer of metaatoms and the second layer of metaatoms;

[0051] The second layer of meta-atoms is used to generate The polarization of light can be controlled.

[0052] Reference Figure 2 A method for preparing a double-layer broadband achromatic metalens based on meta-atoms comprises the following steps:

[0053] S100, obtaining a relationship between polarized light input and output of a double-layer broadband achromatic metalens, determining a phase resonance curve of the double-layer broadband achromatic metalens, a transmission matrix of a first layer of metaatoms, and a transmission matrix of a second layer of metaatoms, wherein the double-layer broadband achromatic metalens is composed of a first layer of metaatoms and a second layer of metaatoms;

[0054] Specifically, using plane wave incidence, the complex amplitude distribution of the electromagnetic wave when passing through the surface of the last metalens is:

[0055]

[0056] Further, The complex amplitude distribution of the metastructure atoms on the metalens is used express, is the radial position of the lens.

[0057] No. The complex amplitude distribution of the input and output light of a metalens can be expressed using a transmission matrix The recursive formula is used to describe the The expression of the complex amplitude distribution of the input and output light of a metalens is:

[0058]

[0059] And then through Indicates the size of PCR at each point on the metalens at different wavelengths

[0060] Transmission Matrix The expression is:

[0061]

[0062] The relationship between the input and output light of the entire cascade lens can be described as:

[0063]

[0064] In the above formula, and Indicates that after Complex amplitude distribution of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light after a superlens.

[0065] in , It's about A function of .

[0066] Therefore, the PCR curves corresponding to the meta-atoms of the two-layer metalens are:

[0067]

[0068]

[0069] in and Describes two superatoms in and The shape of the PCR curve in the two intervals, is a step function. The upper metalens is represented by S1 (corresponding to ), the lower metalens is represented by S2 (corresponding to ), their transmission matrices are and .

[0070] S200, determining a relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens according to the focal depth of the diffraction lens;

[0071] Specifically, for a reference wavelength of , design focal length Diffraction lens. Its wavelength and focal length satisfy:

[0072]

[0073] We make Minimize and obtain the best The value is expressed as:

[0074]

[0075] From the basic inequality conclusion, we can know that when hour Reached minimum value.

[0076] At this point, we can get:

[0077]

[0078] The depth of focus of a diffractive lens can be expressed using the formula:

[0079]

[0080] Depend on The expression of and the focal depth expression of the diffraction lens can be used to deduce the relationship between the focal length and the lens aperture that needs to be satisfied in broadband achromatism:

[0081]

[0082] S300. Determine the electric field intensity of the double-layer broadband achromatic metalens. Combine the phase resonance curve of the double-layer broadband achromatic metalens with the relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens. Perform photolithography by laser direct writing to construct the double-layer broadband achromatic metalens.

[0083] Specifically, when the amplitudes are and , the phases are and When two beams of light interfere with each other, their total electric field can be expressed as:

[0084]

[0085] in , When the amplitudes of the two polarized beams are the same, the total electric field strength can be expressed as:

[0086]

[0087] It is easy to derive from the total electric field intensity expression that the phase and amplitude of the output light can be modulated by controlling the phase and amplitude of the two beams. By using a composite lattice and using two meta-atoms to control the phase of the output light for interference, the phase and amplitude of the output light can be independently controlled. When , the amplitude of the output light is expressed as:

[0088]

[0089] In summary, the embodiment of the present invention first uses the PCR curve described by the PCR curve expression corresponding to the meta-atoms of the two-layer metalens to screen the meta-atomic structure corresponding to the phase in each wavelength interval. Then, based on the principle of interference, the interference model and the total electric field expression, the total electric field intensity expression, and the output light amplitude expression are used to modulate the phase and amplitude of the output light by controlling the phase and amplitude of the two beams of light. This is used to screen the corresponding phase-matched meta-atom parameters. Finally, laser direct writing technology is used to write the lens array pattern onto a germanium (Ge) film deposited on a barium fluoride (BaF2) substrate, and the lens array is obtained by photolithography.

[0090] Further, the design of the super-atom is explained:

[0091] In order to realize the cascade metalens, it is necessary to design metaatoms to satisfy the (phase resonance) PCR curve described by the PCR curve expression corresponding to the metaatoms of the two-layer metalens. The phase response of each wavelength range is controlled by a metaatom through the PB phase. To achieve this special spectral response, the metaatoms need to be screened to a certain extent. Based on the interference principle, the amplitude and phase of circularly polarized light can be independently controlled. Through the interference model, we further analyze the design of the double-layer metalens. When the amplitudes are and , the phases are and When two beams of light interfere with each other, their total electric field can be expressed as:

[0092]

[0093] It is easy to derive from the expression of the total electric field that the phase and amplitude of the output light can be modulated by controlling the phase and amplitude of the two beams. By using a composite lattice and using two meta-atoms to control the phase of the output light for interference, the phase and amplitude of the output light can be independently controlled. When , the amplitude of the output light is expressed as:

[0094]

[0095] Considering the response of the meta-atom in the entire working wavelength range, the amplitude of the emitted light is a function of wavelength. The wavelength range 1 and wavelength range 2 are controlled by two structures T1 and T2 respectively. The amplitudes of the opposite rotation transmitted light of the two meta-atoms are expressed as 、 , then these two metaatoms can be used to control two wavelength ranges respectively. T1 can control the phase in the wavelength range of [10 μm, 11 μm], and T2 can control the phase in the wavelength range of [11 μm, 14 μm].

[0096] There are two schemes to achieve phase control in sub-wavelength intervals by interference. One is to use a double layer of meta-atoms, and the other design is based on a shared aperture scheme, that is, different meta-atoms are alternately arranged on a plane, such as Figure 4 and Figure 5 In the double-layer scheme, both supertransparent atoms can control the phase of the outgoing light through left-handed circularly polarized light.

[0097] Therefore, if Figure 3As shown, the first layer, T1, controls the phase within the wavelength range of [10μm, 11μm], while the second layer, T2, controls the phase within the wavelength range of [11μm, 14μm]. The rotation of the two layers independently controls the phase within their respective wavelength ranges. The blue center portion is the substrate, with a thickness of 7μm. By cascading these two layers of metaatoms, broadband achromatism can be achieved.

[0098] Finally, it should be noted that in order to achieve the achromatic design, the reference wavelength of the two working wavelength ranges is set according to the actual selected meta-atom. Set to 12 respectively and 14 The meta-atoms are arranged according to the PB phase according to the phase profile determined by the expression of the PCR curve corresponding to the meta-atoms of the two-layer metalens. The focal coordinates is (0 , 0 , 200 ). We simulate a caliber of 300 , focal length is 150 The super lens (NA=0.71) contains and A total of 4674. The maximum chromatic aberration of this metalens in the two sub-operating wavelength ranges is 30 and 25 , so theoretically the maximum chromatic aberration of the entire lens is the maximum value of the two 30 For a chromatic aberration lens, according to the relationship between the wavelength and focal length of the diffraction lens, its maximum chromatic aberration is 60 We simulated the chromatic aberration lens of the same size, and the simulation results are as shown in the present invention. Figure 6 The simulation results show that compared with the chromatic aberration lens, the chromatic aberration of our specially designed super lens is significantly reduced. It can be clearly seen that the chromatic aberration is reduced by almost half compared to the chromatic aberration lens. and 12.5 It can be clearly seen that the focus is elongated. The reason for the elongated focus is consistent with the reason why the dual-focus metal lens has two focal points at these two wavelengths. Figure 7 The curve showing the change of focal length with wavelength can be presented in segmented form, which is consistent with the theoretical best The expression trend of the value is consistent. The maximum focal length change within the wavelength range is 33.8 , at 12-14 The maximum focus shift within the wavelength range is 25.6 , compared with the simulation results of chromatic aberration lens 83.4 The maximum chromatic aberration is reduced by 59.5%, which is not much different from the theoretical calculated value. The trend of the focus efficiency of the lens is consistent with the present invention. Figure 8 The wavelength variation of the metaatom's polarization conversion efficiency. Near the ends of the operating wavelength range, the metaatom's polarization conversion efficiency is higher, corresponding to higher focusing efficiency. In the middle of the operating wavelength range, the polarization conversion efficiency is lower, corresponding to lower focusing efficiency.

[0099] Now we also consider the effect of focal depth, so that the focal length and aperture of the metalens meet the relationship between focal length and lens aperture required for broadband achromatism. We set the lens focal length to 200 μm, the metalens aperture to 209 μm (NA=0.46), and the metalens contains and A total of 2234. Compared with the large NA (0.71) super lens, the small NA (0.46) super lens has a longer depth of focus. We observed the electric field distribution in the preset focal plane as shown in the present invention 9. The focus of the chromatic lens is already in a defocused state at short wavelengths, and the light spot is divergent and large in size. The focal length change of the super lens designed with sub-bands is significantly smoother. At z=200 μm, it is almost within the focal depth range of each wavelength. Compared with the chromatic lens, the spot size of the achromatic lens is much smaller. The focal length offset of the lens is reduced by 54% compared with the chromatic lens, among which, Figure 9 (a) and Figure 9 (b) shows the self-normalized electric field distribution of the chromatic / achromatic lens in the XZ plane. Figure 9 (c) and Figure 9 (d) Shows the self-normalized electric field distribution of the chromatic / achromatic lens in the XY plane at z = 200 μm.

[0100] Observe the curve of focal length changing with wavelength as shown in the present invention Figure 10 As shown in the figure, we can find that the slope of the focal length versus wavelength curve of the small NA metalens and the large NA metalens has a significant difference. The focal length of the former changes more slowly and is close to a continuous change process, while the focal length of the latter shows a clear segmented change when the focal depth is small; the reason for this change in focal length is attributed to the deviation of the meta-atom from the desired target phase. Figure 11 As shown, the overall focusing efficiency of the metalens is greater than 35%. When the NA is small, the focal spot size becomes larger. According to the method for calculating the focusing efficiency of the metalens in Chapter 2, three times the half-width will occupy a larger area of ​​the focal plane, and the calculated focusing efficiency is closer to the diffraction efficiency. Therefore, the focusing efficiency is generally higher than that of a large NA (D=300 μm, f=150 μm).

[0101] The MTF curve reflects how much image detail information the lens can capture. The closer the MTF curve of the metalens is to the diffraction limit, the closer the metalens is to the ideal lens. The MTF curve of the metalens at the preset focal length f=200 μm is calculated based on the relationship expression that needs to be satisfied between the focal length and the lens aperture in broadband achromatism, as shown in the present invention. Figure 12 As shown. In the 10-12 μm wavelength range, the MTF curve of our designed achromatic metalens is higher than that of the traditional chromatic metalens, which shows that the achromatic metalens has a stronger ability to resolve details than the traditional lens. The MTF curves of the chromatic and achromatic metalens in the meridian and sagittal directions are very close, which reflects the high degree of circular symmetry of the focus of the metalens. In the 12-14 μm band, the MTF curves of the chromatic and achromatic metalens almost overlap. This is because the focal point of the chromatic lens near the reference wavelength is within the focal depth range and is not much different from the actual focal size.

[0102] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0103] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A double-layer broadband achromatic metalens based on meta-atoms, characterized in that: The invention comprises a first layer of meta-atoms, a substrate and a second layer of meta-atoms, wherein the substrate is located between the first layer of meta-atoms and the second layer of meta-atoms, wherein: The first layer of meta-atoms is used to generate The polarized light can be controlled; The substrate is used to support the first layer of metaatoms and the second layer of metaatoms; The second layer of meta-atoms is used to generate The polarized light can be controlled; The expression of the phase resonance curve PCR of the double-layer broadband achromatic metalens is: In the above formula, represents the size of the lower superlens PCR, represents a step function, represents the size of the upper superlens PCR, Represents the designed phase interval Maximum value (max), represents the middle value of the designed phase interval, represents the minimum value of the designed phase interval, and Describes two superatoms in and The shape of the PCR curve in the two intervals; The relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens is: In the above formula, represents the focal length, Indicates the aperture of the lens; The electric field intensity of the double-layer broadband achromatic metalens is expressed as: In the above formula, represents the amplitude of the first layer of metalens, represents the amplitude of the second-layer metalens, represents the phase of the first layer of metalens, Represents the phase of the second-layer metalens.

2. A method for preparing a double-layer broadband achromatic metalens based on meta-atoms according to claim 1, characterized in that: The following steps are involved: Obtaining a relationship between polarized light input and output of a double-layer broadband achromatic metalens, determining a phase resonance curve of the double-layer broadband achromatic metalens, a transmission matrix of a first layer of metaatoms, and a transmission matrix of a second layer of metaatoms, wherein the double-layer broadband achromatic metalens is composed of a first layer of metaatoms and a second layer of metaatoms; The relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens is determined based on the focal depth of the diffraction lens; The electric field intensity of the double-layer broadband achromatic metalens was determined. Combining the phase resonance curve of the double-layer broadband achromatic metalens with the relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens, a double-layer broadband achromatic metalens was constructed by photolithography using the laser direct writing method.

3. The method for preparing a double-layer broadband achromatic metalens based on meta-atoms according to claim 2, characterized in that: The step of obtaining the relationship between polarized light input and output of the double-layer broadband achromatic metalens specifically includes: Using plane wave incidence, the complex amplitude distribution of the electromagnetic wave when passing through the meta-atom surface is: According to the complex amplitude distribution of electromagnetic waves when passing through the meta-atom surface, the relationship between the polarized light input and output of the double-layer broadband achromatic metalens is determined by the transmission matrix, and its expression is: In the above formula, represents the transmission matrix, represents the complex amplitude distribution, Indicates the A superatom, Indicates that there is A superatom, represents the complex amplitude distribution of the meta-atoms, represents the coordinates of the meta-atoms on the single-layer plane, represents the wavelength, Indicates the The phase of a metaatom, Indicates the The superatom has a wavelength of The coordinates are The complex amplitude distribution of Indicates the The superatom has a wavelength of The coordinates are The phase, 、 Indicates that after Left-handed circularly polarized light and right-handed circularly polarized light after the super lens, 、 Indicates that after Left-handed circularly polarized light and right-handed circularly polarized light after a superlens.

4. The method for preparing a double-layer broadband achromatic metalens based on meta-atoms according to claim 3, characterized in that: The expression of the transmission matrix is: In the above formula, represents the wavelength, Indicates the The wavelength of the metalens is The size of the PCR, Indicates that the wavelength is The next phase.

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