Double-layer broadband achromatic super-lens based on super-structure atoms and preparation method of double-layer broadband achromatic super-lens

Abstract

The invention discloses a double-layer broadband achromatic super lens based on super-structure atoms and a preparation method thereof. The double-layer broadband achromatic super lens comprises a first layer of super-structure atoms, a substrate and a second layer of super-structure atoms. The method comprises the following steps: determining a phase resonance curve of the double-layer broadband achromatic superlens; determining a relational expression between the focal length of the double-layer broadband achromatic super lens and the lens aperture according to the focal depth of the diffraction lens; and determining the electric field intensity of the double-layer broadband achromatic super lens, and constructing the double-layer broadband achromatic super lens by combining the phase resonance curve of the double-layer broadband achromatic super lens and the relational expression between the focal length of the double-layer broadband achromatic super lens and the lens aperture. According to the invention, the design process of the double-layer broadband achromatic superlens can be simplified, the discrete wavelength is fully utilized to design the space in a regional manner, and then achromatism is realized. The double-layer broadband achromatic super-lens based on the super-structure atoms and the preparation method thereof can be widely applied to the technical field of integrated devices.

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] Achromatic superlens, that is, superlens has the same focus at different working wavelengths. According to the design method of geometric optics achromatic lens, the more working wavelengths there are, the higher the complexity of the optical system. Thanks to the ultra-high degree of freedom of meta-atoms, only a single super-lens is needed to achieve achromatic function in a wider working wavelength range. At present, a variety of achromatic superlens design schemes have been developed, which can be mainly divided into three types according to the implementation method. The first is a broadband achromatic superlens based on group delay or phase compensation; the second is a discrete wavelength achromatic superlens based on sub-regions; the third is an achromatic superlens based on intelligent algorithms. The existing quasi-achromatic superlens, by extending the group delay method, numerically simulates a quasi-achromatic superlens with an aperture of 2mm, which solves the problem that meta-atoms cannot produce large group delays to a certain extent, but this method is essentially a discrete wavelength achromatic and is different from the strict broadband achromatic in dispersion engineering. The method of extending the group delay can change the overall chromatic aberration curve from the inverse proportional function curve shape to a sawtooth shape, and the overall chromatic aberration is lower, but it cannot achieve true achromaticity due to the low space utilization of the discrete wavelength sub-region design. 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 regional 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, the wavelength phase of the incident polarized light controlled by the first layer of meta-atoms is [10μm, 11μm], and the wavelength phase of the output polarized light controlled by the second layer of meta-atoms is [11μm, 14μm], wherein:

[0005] The first layer of meta-atoms is used to control polarized light with a wavelength phase of [10 μm, 11 μm];

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

[0007] The second layer of metaatoms is used to control polarized light with a wavelength phase of [11μm, 14μm].

[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 the polarization input and output relationship of the double-layer broadband achromatic metalens, determining the phase resonance curve of the double-layer broadband achromatic metalens, the transmission matrix of the first layer of meta-atoms, and the transmission matrix of the second layer of meta-atoms, wherein the double-layer broadband achromatic metalens is composed of the first layer of meta-atoms and the second layer of meta-atoms;

[0010] Determine the relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens according to the focal depth of the diffraction lens;

[0011] The electric field intensity of the double-layer broadband achromatic superlens is determined, and the double-layer broadband achromatic superlens is constructed by lithography through laser direct writing method, combining the phase resonance curve of the double-layer broadband achromatic superlens with the relationship between the focal length and lens aperture of the double-layer broadband achromatic superlens.

[0012] Further, 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 passing through the surface of meta-atoms, 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, K i represents the transmission matrix, E represents the complex amplitude distribution, i represents the i-th superatom, n represents the number of n superatoms, A i represents the complex amplitude distribution of the meta-atom, x, y represent the coordinates of the meta-atom on the single-layer plane, λ represents the wavelength, represents the phase of the u-th superatom, A i (x,y,λ) represents the complex amplitude distribution of the ith superatom at wavelength λ and coordinate (x,y), represents the phase of the ith superatom at wavelength λ and coordinate (x, y), represents the left-handed circularly polarized light and the right-handed circularly polarized light after passing through the i-th superlens, Represents the left-handed circularly polarized light and the right-handed circularly polarized light after passing through the i-1th superlens.

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

[0019]

[0020] In the above formula, λ represents the wavelength, R i (λ) represents the size of PCR on the i-th superlens at wavelength λ, represents the phase at wavelength λ.

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

[0022] R1=P1(λ)[u(λ-λ mid )-u(λ-λ min )]

[0023] R2=P2(λ)[u(λ-λmid max []]

[0024] In the above formula, R1 represents the size of the lower super lens PCR, u(·) represents the step function, R2 represents the size of the upper super lens PCR, and λmid max represents the maximum value (max) of the designed phase interval, λ mid represents the middle value of the designed phase interval, λ min represents the minimum value of the designed phase interval, P1(λ) and P2(λ) describe the two superatoms in (λ min ,λ mid ) and (λ mid ,λ max )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, f represents the focal length and D represents the aperture of the lens.

[0028] Further, the expression of the electric field intensity of the double-layer broadband achromatic metalens is:

[0029]

[0030] In the above formula, A1 represents the amplitude of the first layer of metalens, A2 represents the amplitude of the second layer of metalens, represents the phase of the first layer of metalens, Represents the phase of the first layer of metalens.

[0031] The beneficial effects of the method and array of the present invention are as follows: the present invention proposes a method for dividing the working wavelength range, designs two metalenses working in different wavelength bands, cascades them together, uses two types of meta-atoms, avoids the establishment of a large number of meta-atoms databases, speeds up the design process, and uses the metalens cascade system to achieve broadband achromatism, thereby proposing a method of dividing the working wavelength range into two parts to reduce the chromatic aberration of the metalens. Finally, the overall achromatism is achieved in combination with the focal depth of the metalens. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic structural diagram of a double-layer broadband achromatic metalens based on meta-atoms of the present invention;

[0033] Figure 2 It 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 This is a schematic diagram of achieving achromatism with a double-layer broadband achromatic metalens provided by a specific embodiment of the present invention;

[0035] Figure 4 is a schematic diagram of a double-layer super-structure atomic double-layer structure provided by a specific embodiment of the present invention;

[0036] Figure 5 It is a schematic diagram of phase control of a double-layer super-structure atomic 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 aberration and achromatic superlens in the XZ plane provided by a specific embodiment of the present invention;

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

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

[0040] Fig. 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] Fig.10 is a schematic diagram of a curve showing a change in focal length of a chromatic / achromatic lens with respect to wavelength provided by a specific embodiment of the present invention;

[0042] Fig.11 1 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] Fig.12 It is a schematic diagram of chromatic aberration at different wavelengths and MTF curves of the achromatic lens in the sagittal and tangential directions provided by a specific embodiment of the present invention. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only provided for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0045] First of all, it should be noted that in actual optical imaging systems, two wavelengths of achromatism are often not enough. For example, in common visible light imaging, the lens group needs to be achromatized for at least three wavelengths. The more achromatic wavelengths, the better the imaging quality. Therefore, based on dual-wavelength achromatism, we propose a design scheme for a double-layer broadband achromatic superlens. Two meta-atoms with special polarization conversion rate curve shapes are selected, and these two structures are used to design superlenses working in different wavelength ranges, and then these two superlenses are spatially cascaded to piece together the entire working wavelength range. Since the lens working range is part of the design working range, the chromatic aberration of each lens will also be reduced. Selecting a suitable design wavelength can make the maximum chromatic aberration of the cascade lens the maximum value of the chromatic aberration of the two lenses, and then combine the focal depth of the lens to realize the design of a broadband achromatic superlens. Finally, we use FDTD to simulate the broadband achromatic superlens and compare it with the chromatic aberration lens, and use the MTF curve to evaluate the performance of the achromatic superlens.

[0046] Based on this, in order to solve the problem of space utilization of the discrete wavelength region design method, we proposed a design method for dual-wavelength phase-independently controlled meta-atoms. Each meta-atom bears the phase information of two wavelengths at the same time, thereby realizing efficient manipulation of the wavelength. Since the phases of the two wavelengths can be controlled arbitrarily, efficient achromatism can also be achieved when the size or NA of the metalens is large. In order to solve 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, avoids the establishment of a large database of meta-atoms, and speeds up the design process.

[0047] The design of a broadband achromatic meta-lens with a working band of 10-14μm, a numerical aperture of 0.45, and a focal length of 200μm is realized. First, we analyzed the use of a cascade system of super-lenses to achieve broadband achromatism, and proposed a design that divides the working wavelength range into two parts to reduce the chromatic aberration of the super-lens. Finally, the overall achromatism is achieved by combining the focal depth of the super-lens. We used a double-layer meta-atom to realize the sub-band design and optimized the meta-atom. Finally, we constructed achromatic super-lenses with large numerical aperture (0.71) and small numerical aperture (0.45). The large numerical aperture achromatic super-lens reduces the chromatic aberration by 59% compared with the traditional lens. The small numerical aperture achromatic super-lens achieves broadband achromatism on the basis of reducing the chromatic aberration by half and combining the focal depth of the super-lens itself, and the overall focusing efficiency is higher than 35%. Our design uses only two types of meta-atoms, which is simpler, and the two-layer lens does not require point-to-point alignment between the 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, the wavelength phase of the incident polarized light controlled by the first layer of meta-atoms is [10μm, 11μm], and the wavelength phase of the output polarized light controlled by the second layer of meta-atoms is [11μm, 14μm], wherein:

[0049] The first layer of meta-atoms is used to control polarized light with a wavelength phase of [10 μm, 11 μm];

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

[0051] The second layer of metaatoms is used to control polarized light with a wavelength phase of [11μm, 14μm].

[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 the polarization input and output relationship of the double-layer broadband achromatic metalens, determining the phase resonance curve of the double-layer broadband achromatic metalens, the transmission matrix of the first layer of meta-atoms and the transmission matrix of the second layer of meta-atoms, wherein the double-layer broadband achromatic metalens is composed of the first layer of meta-atoms and the second layer of meta-atoms;

[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] Furthermore, the complex amplitude distribution of the metastructure atoms on the i-th superlens is expressed as Indicates that r is the radial position of the lens.

[0057] The complex amplitude distribution of the input and output light of the ith metalens can be expressed using a transmission matrix K i The recursive formula of is used to describe the complex amplitude distribution of the input and output light of the ith metalens:

[0058]

[0059] Then through R i (r,λ) represents the size of PCR at each point on the superlens at different wavelengths

[0060] Transmission matrix K i 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 Represents the complex amplitude distribution of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) after passing through the i-th superlens.

[0065] in T is a function of λ.

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

[0067] R1=P1(λ)[u(λ-λ mid )-u(λ-λ min )]

[0068] R2=P2(λ)[u(λ-λmid max []]

[0069] where P1(λ) and P2(λ) describe two superatoms in [λmid min []] and [λ mid ,λ max[]]The shape of the PCR curve in the two intervals, u(λ) is a step function. The upper superlens is represented by S1 (corresponding to R1), the lower superlens is represented by S2 (corresponding to R2), and their transfer matrices are K1 and K2 respectively.

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

[0071] Specifically, for a reference wavelength of λ0, a diffractive lens with a focal length of f0 is designed. Its wavelength and focal length satisfy:

[0072]

[0073] We obtain the optimal λ by minimizing Δf1+Δf2 mid The value is expressed as:

[0074]

[0075] From the basic inequality conclusion, we can know that When Δf1+Δf2 reaches its 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] From the expression of Δf1=Δf2 and the expression of focal depth of diffractive lens, it can be deduced that the expression of the relationship between focal length and lens aperture that needs to be satisfied in broadband achromatism is:

[0081]

[0082] S300, determining the electric field intensity of the double-layer broadband achromatic metalens, 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, performing photolithography by laser direct writing method, and constructing the double-layer broadband achromatic metalens.

[0083] Specifically, when the amplitudes are A1 and A2, 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 α=(A1-A2) / (A1+A2). When the amplitudes of the two polarized lights 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 of light. By using a composite lattice, 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 A1>>A2, the amplitude of the output light is expressed as:

[0088]

[0089] In summary, the embodiment of the present invention first describes the PCR curve according to the PCR curve expression corresponding to the meta-atoms of the two-layer metalens. The meta-atomic structure corresponding to the phase of each wavelength interval is screened, and then based on the interference principle, the interference model and the total electric field expression, the total electric field intensity expression and the expression of the amplitude of the output light are used: the phase and amplitude of the output light can be modulated by controlling the phase and amplitude of the two beams of light, and then the corresponding phase-matched meta-atomic parameters are screened out, and finally the laser direct writing technology is used to write the pattern of the lens array onto the germanium (Ge) film deposited on the substrate barium fluoride (BaF2), and the lens array is obtained by photolithography.

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

[0091] In order to realize a cascaded 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 a 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. 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 A1 and A2, 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 deduce 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 of light. By using a composite lattice, 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 A1>>A2, 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 A(λ). In wavelength range 1 and wavelength range 2, the two structures T1 and T2 respectively control the amplitude of the oppositely-rotated transmitted light of the two meta-atoms in these two ranges as A1(λ)>>A2(λ) and A1(λ)<<A2(λ), respectively. Then, the two wavelength ranges can be controlled by using these two meta-atoms. T1 can control the phase in the wavelength range [10μm, 11μm], and T2 controls the phase in the wavelength range [11μm, 14μm].

[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, to alternately arrange different meta-atoms on a plane, such as Figure 4 and Figure 5 In the double-layer scheme, two super-transparent atoms can control the phase of the outgoing light through left-handed circularly polarized light.

[0097] Therefore, if Figure 3 As shown, the first layer T1 can control the phase within the wavelength range of [10μm, 11μm], and the second layer T2 controls the phase within the wavelength range of [11μm, 14μm]. The rotation of the two layers does not affect the phase of their respective wavelength ranges. The blue part in the middle is the substrate with a thickness of 7μm. By cascading two layers of meta-atoms, broadband achromatic function can be achieved.

[0098] Finally, it should be noted that in order to achieve achromatic design, combined with the actual selected meta-atoms, the reference wavelength λ0 of the two working wavelength ranges is set to 12μm and 14μm respectively, and 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 layers of metalens, and the focal coordinates (x0, y0, f0) are (0μm, 0μm, 200μm). We simulated a metalens with an aperture of 300μm and a focal length of 150μm (NA=0.71). The metalens contains 4674 T2 and U3. The maximum chromatic aberration of this metalens in the two sub-working wavelength ranges is 30μm and 25μm respectively, so theoretically the maximum chromatic aberration of the entire lens is the maximum value of the two, 30μm. For a chromatic aberration lens, according to the relationship between the wavelength and focal length of the diffraction lens, its maximum chromatic aberration is 60μm. We simulated chromatic aberration lenses of the same size, and the simulation results are as shown in the present invention. Figure 6As shown. The simulation results show that compared with the chromatic aberration lens, the chromatic aberration of our specially designed super lens is significantly reduced. At a wavelength of 10μm, it can be clearly seen that the chromatic aberration is almost reduced by half compared with the chromatic aberration lens. At wavelengths of 12μm and 12.5μm, it can be clearly seen that the focus is elongated. The reason for the elongation of the focus is the same as the reason why the dual-focus super lens has two focal points at these two wavelengths. Figure 7 The curve showing focal length versus wavelength can be presented in segmented form, which is consistent with the theoretical optimal λ mid The expression trend of the value is consistent. The maximum focal length change in the 10-12μm wavelength range is 33.8μm, and the maximum focal length shift in the 12-14μm wavelength range is 25.6μm. Overall, the maximum chromatic aberration of 83.4μm compared to the simulation result of the chromatic aberration lens is reduced by 59.5%, which is not much different from the theoretical calculation value. The change trend of the focusing efficiency of the lens is consistent with the present invention. Figure 8 The change of polarization conversion efficiency of meta-atoms with wavelength. Near the two ends of the working wavelength range, the polarization conversion efficiency of meta-atoms is higher, and the corresponding focusing efficiency is higher; the polarization conversion efficiency in the middle part of the working band is lower, and the corresponding focusing efficiency is lower.

[0099] Now we also consider the influence of the depth of focus, so that the focal length and aperture of the metalens satisfy the relationship expression that the focal length and lens aperture need to satisfy when broadband achromatism is used. We set the focal length of the lens to 200μm, the aperture of the metalens to 209μm (NA=0.46), and the metalens contains 2234 T2 and U3 in total. Compared with the large NA (0.71) metalens, the small NA (0.46) metalens 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 aberration 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 metalens designed with sub-band design is obviously smoother. At z=200μm, it is almost within the focal depth range of each wavelength. Compared with the chromatic aberration 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 aberration lens, among which, Fig. 9 (a) and Fig. 9 (b) represents the self-normalized electric field distribution of the chromatic / achromatic lens in the XZ plane, Fig. 9 (c) and Fig. 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 Fig.10As shown in the figure, we can find that the slope of the focal length versus wavelength curve of the small NA superlens and the large NA superlens is significantly different. 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 an obvious 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. Fig.11 As shown in Figure 2, the overall focusing efficiency of the metalens is greater than 35%. When the NA is small, the focal size becomes larger. According to the method for calculating the focusing efficiency of the metalens in Chapter 2, the three-times half-height 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 = 300μm, f = 150μm).

[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 according to 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. Fig.12 As shown. In the wavelength range of 10-12μm, the MTF curve of the achromatic superlens we designed is higher than that of the traditional chromatic superlens, which shows that the achromatic superlens has a stronger ability to resolve details than the traditional lens. The MTF curves of the chromatic and achromatic superlenses in the meridian and sagittal directions are very close, which reflects the high degree of circular symmetry of the focus of the superlens. In the 12-14μm band, the MTF curves of the chromatic and achromatic superlenses almost overlap. This is due to the focal depth of the chromatic lens. The focus of the wavelength near the reference wavelength is within the focal depth range, which 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 may 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, the wavelength phase of the incident polarized light controlled by the first layer of meta-atoms is [10 μm, 11 μm], and the wavelength phase of the output polarized light controlled by the second layer of meta-atoms is [11 μm, 14 μm], wherein: The first layer of meta-atoms is used to control polarized light with a wavelength phase of [10 μm, 11 μm]; The substrate is used to support the first layer of meta-atoms and the second layer of meta-atoms; The second layer of metaatoms is used to control polarized light with a wavelength phase of [11μm, 14μm].

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

3. The method for preparing a double-layer broadband achromatic metalens based on meta-atoms according to claim 1, 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 passing through the surface of meta-atoms, 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, K i represents the transmission matrix, E represents the complex amplitude distribution, i represents the i-th superatom, n represents the number of n superatoms, A i represents the complex amplitude distribution of the meta-atom, x, y represent the coordinates of the meta-atom on the single-layer plane, λ represents the wavelength, represents the phase of the ith superatom, A i (x,y,λ) represents the complex amplitude distribution of the ith superatom at wavelength λ and coordinate (x,y), represents the phase of the ith superatom at wavelength λ and coordinate (x, y), represents the left-handed circularly polarized light and the right-handed circularly polarized light after passing through the i-th superlens, Represents the left-handed circularly polarized light and the right-handed circularly polarized light after passing through the i-1th superlens.

4. The method for preparing a double-layer broadband achromatic metalens based on meta-atoms according to claim 2, characterized in that: The expression of the transmission matrix is: In the above formula, λ represents the wavelength, R i (λ) represents the size of PCR on the i-th superlens at wavelength λ, represents the phase at wavelength λ.

5. 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 phase resonance curve of the double-layer broadband achromatic metalens is: R1=P1(λ)[u(λ-λ mid )-u(λ-λ min )] R2=P2(λ)[u(λ-λmid max []] In the above formula, R1 represents the size of the lower super lens PCR, u(·) represents the step function, R2 represents the size of the upper super lens PCR, and λmid max represents the maximum value (max) of the designed phase interval, λ mid represents the middle value of the designed phase interval, λ min represents the minimum value of the designed phase interval, P1(λ) and P2(λ) describe the two superatoms in (λ min ,λ mid ) and (λ mid ,λ max )The shape of the PCR curve in the two intervals.

6. The method for preparing a double-layer broadband achromatic metalens based on meta-atoms according to claim 4, characterized in that: The relationship between the focal length and lens aperture of the double-layer broadband achromatic metalens is: In the above formula, f represents the focal length and D represents the aperture of the lens.

7. The method for preparing a double-layer broadband achromatic metalens based on meta-atoms according to claim 5, characterized in that: The expression of the electric field intensity of the double-layer broadband achromatic metalens is: In the above formula, A1 represents the amplitude of the first layer of metalens, A2 represents the amplitude of the second layer of metalens, represents the phase of the first layer of metalens, Represents the phase of the first layer of metalens.

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