Construction method of metasurface lens, metasurface lens

Abstract

A method for constructing a metasurface lens, the metasurface lens, the method for constructing a metasurface lens includes: establishing a structural unit library; determining the lowest-frequency phase and phase dispersion at any arbitrary spatial position on the surface of the metasurface lens operating in an ideal state at a target wavelength band and a target focal length according to the ideal distribution relationship between the spatial position on the surface of the metasurface lens and the spectral phase; simulating each structural unit in the structural unit library, and extracting the lowest-frequency phase and phase dispersion that each structural unit can provide; traversing each spatial position on the surface of the metasurface lens, and screening the structural units in the structural unit library according to the lowest-frequency phase and phase dispersion that each structural unit can provide to determine the target structural unit at the spatial position; placing all the target structural units at their corresponding spatial positions respectively to complete the construction of the metasurface lens, and the constructed metasurface lens achieves continuous achromatism at the target wavelength band.

Description

Technical Field

[0001] The present invention relates to the technical field of optical lenses, and particularly to a construction method of a metasurface lens and a metasurface lens. Background Art

[0002] Infrared rays have a very high transmittance in three band intervals in the atmosphere, which are called "atmospheric windows", namely: the 1-3μm band in the short-wave infrared region, the 3-5μm band in the mid-wave infrared region, and the 8-14μm band in the long-wave infrared region. Thermal imaging devices operating in the mid-wave infrared band and the long-wave infrared band play an important role in many fields such as industry, medical treatment, and scientific research. Therefore, the research and development of mid-wave infrared and long-wave infrared imaging systems have important practical value.

[0003] In an imaging system, due to the dispersion phenomenon, lights of different wavelengths cannot be focused on the imaging surface at the same time, resulting in blurred graphics and degraded imaging quality. This effect is called chromatic aberration, and chromatic aberration is an important factor affecting the imaging quality of lenses. Most focusing elements in an imaging system have a dispersion effect. Traditional refractive lenses have a positive dispersion (higher frequencies have smaller focal lengths) characteristic, while diffractive focusing elements (such as Fresnel zone plates) have a negative dispersion characteristic. Planar optical devices based on metasurfaces are similar to diffractive optical elements and have relatively obvious negative dispersion. Dispersion and the resulting chromatic aberration effect have become the key bottleneck restricting the further development of metasurface lens technology.

[0004] Traditional refractive lenses can eliminate dispersion by cascading two materials with opposite dispersion attributes. An achromatic lens realized by using multiple lenses is called a doublet or a triplet lens, which is large in volume and weight and is not conducive to integration. The chromatic aberration of diffractive devices cannot be eliminated by cascading different materials because the origin of the dispersion of diffractive devices is independent of material properties and is related to factors such as the dispersion generated by the periodic lattice and the light field confinement. It is relatively difficult to eliminate the chromatic aberration of diffractive devices with existing technologies.

[0005] Similar to diffractive devices, typical metasurface devices represented by metasurface lenses can also be regarded as a special type of diffractive device and have relatively obvious negative dispersion. For a metasurface lens without special design, due to the existence of the dispersion effect, its working bandwidth is generally relatively narrow, and incident lights of different wavelengths cannot be focused on the same focal point position, resulting in degraded imaging quality. Eliminating the chromatic aberration of metasurface lenses has great technical difficulties. In particular, in order to avoid the adverse factors such as the increase in thickness, volume, and weight caused by cascading multiple metasurface lenses, it is quite technically difficult to achieve broadband achromatic focusing only by the delicate design of a single-layer metasurface device.

[0006] In the prior art, one method is to stack multiple achromatic single-wavelength metasurfaces to construct a metasurface lens group operating at several discrete wavelengths, achieving a certain degree of achromatism at several discrete wavelengths. However, this method also relies on cascading, which will increase the thickness, volume, and weight of the system, is not conducive to integration, and has a narrow bandwidth and discontinuous achromatic bandwidth. Another technical solution is to use the method of bonding a refractive lens with positive dispersion and a metasurface lens with negative dispersion to achieve achromatism. This technical solution also requires cascading two optical elements and has the disadvantage of increased size and weight. At the same time, the alignment technology during the bonding of the two devices is difficult. Summary of the Invention

[0007] In view of the above problems, the present invention provides a construction method of a metasurface lens and a metasurface lens, in order to solve at least one of the above problems. The above method includes:

[0008] Establish a structural unit library, the structural unit library includes a variety of structural units, the structural unit includes a substrate and a columnar structure, the cross-sectional pattern of the columnar structure has 90° rotational symmetry, and the shapes and sizes of the cross-sections of any two structural units are different;

[0009] According to the ideal distribution relationship between the spatial position and spectral phase of the surface of the metasurface lens, determine the lowest-frequency phase and phase dispersion at any spatial position on the surface of the metasurface lens operating in the target band and target focal length in the ideal state. Among them, the incident light in the target band is focused at the target focal length, and the surface of the metasurface lens is a two-dimensional plane;

[0010] Simulate each structural unit in the structural unit library, and extract the lowest-frequency phase and phase dispersion that each structural unit can provide;

[0011] Traverse each spatial position on the surface of the metasurface lens, and screen the structural units in the structural unit library according to the lowest-frequency phase and phase dispersion that each structural unit can provide to determine the target structural unit at the spatial position. The lowest-frequency phase and phase dispersion of the target structural unit have the smallest error relative to the lowest-frequency phase and phase dispersion at the spatial position in the ideal state;

[0012] Place all the target structural units at their corresponding spatial positions respectively to complete the construction of the metasurface lens. The constructed metasurface lens achieves continuous achromatism in the target band.

[0013] According to an embodiment of the present invention, the target band is the mid-wave infrared band of 3-5 μm, the columnar structure includes: a square column, a rectangular frame column, a concentric rectangular column, a cross column, and a cross column with a rectangular frame. The constructed metasurface lens achieves broadband continuous achromatism within a bandwidth of 2 μm; or

[0014] The target band is the long-wave infrared band of 8 - 14 μm. The columnar structures include square columns, rectangular frame columns, concentric rectangular columns, cross-shaped columns, cross-shaped columns with rectangular frames, cylindrical columns, circular ring columns, and concentric cylindrical columns. The constructed metasurface lens achieves broadband continuous achromatism within a bandwidth of 6 μm.

[0015] According to an embodiment of the present invention, the material of the substrate is one of silicon, germanium, CaF2, and MgF2, and the material of the columnar structure is silicon or germanium.

[0016] According to an embodiment of the present invention, determining the lowest-frequency phase and phase dispersion at any arbitrary spatial position on the surface of the metasurface lens that operates in the target band and at the target focal length in the ideal state based on the ideal distribution relationship between the spatial position and spectral phase of the metasurface lens includes:

[0017] According to the ideal distribution relationship, using different sampling wavelengths within the target band to determine the optimal structural units at different spatial positions on the surface of the metasurface lens corresponding to multiple sets of phase compensation parameters;

[0018] Determining the figure of merit corresponding to each set of phase compensation parameters based on the optimal structural units at different spatial positions corresponding to each set of phase compensation parameters;

[0019] Determining the optimal parameters among multiple sets of phase compensation parameters according to the figure of merit corresponding to each set of phase compensation parameters, where the optimal parameters are used to determine the lowest-frequency phase and phase dispersion at any arbitrary spatial position on the surface of the metasurface lens that operates in the target band and at the target focal length in the ideal state.

[0020] According to an embodiment of the present invention, the method further includes: simulating the metasurface lens to obtain the near-field light field distribution and far-field light field distribution of the metasurface lens.

[0021] According to an embodiment of the present invention, the lowest-frequency phase is the phase of the lowest-frequency incident light at each spatial position on the surface of the metasurface lens or at each structural unit within the target band; the phase dispersion is the difference between the phase of the highest-frequency incident light and the phase of the lowest-frequency incident light at each spatial position on the surface of the metasurface lens or at each structural unit within the target band.

[0022] According to an embodiment of the present invention, simulating each structural unit in the structural unit library includes: using optical simulation software to simulate each structural unit to obtain the transmittance and phase information of each structural unit within the target band, and extracting the lowest-frequency phase and phase dispersion of each structural unit.

[0023] According to an embodiment of the present invention, the ideal distribution relationship between the spatial position and spectral phase of the metasurface lens in the ideal state is expressed as follows:

[0024]

[0025] Wherein, r is the distance between the spatial position and the lens center, f is the target focal length, c is the speed of light, ω is the angular frequency of the incident light, and r0 and C0 are parameters.

[0026] As the second aspect of the present invention, a metasurface lens fabricated by a method is also provided.

[0027] According to an embodiment of the present invention, the substrates of the structural units of the metasurface lens are connected and arranged periodically; when the target wavelength band is the mid-wave infrared band of 3 - 5 μm, the numerical aperture of the structural unit is 0.20 - 0.32, the height of the structural unit is 2.5 - 3.4 μm, and the deviation of the average focal length at each wavelength within the target wavelength band from the target focal length is 2.67 - 4.67%; or

[0028] when the target wavelength band is the long-wave infrared band of 8 - 14 μm, the numerical aperture of the structural unit is 0.32 - 0.71, the height of the structural unit is 7 - 16.5 μm, and the maximum deviation of the focal length at each wavelength within the target wavelength band from the average focal length is 2.48% - 5.02%.

[0029] According to an embodiment of the present invention, because the target structural units are respectively placed at corresponding spatial positions, and the surface of the formed metasurface lens is a two-dimensional plane, therefore, the metasurface lens of the present application is a single-layer metasurface lens, that is, the present application realizes the construction of a metasurface lens with continuous broadband achromatism within the target wavelength band by using a single metasurface, overcoming the disadvantages that the design of traditional achromatic lenses mostly relies on traditional lens cascades, with large volume, being relatively heavy and not easy to integrate. The embodiment of the present invention is based on a single metasurface, and realizes achromatism by ingeniously designing the micro-nano structural units of the metasurface, making the achromatic lens system thinner, lighter and more conducive to integration.

[0030] According to an embodiment of the present invention, because a variety of structural units with 90° rotational symmetry are adopted, the fabricated metasurface lens is insensitive to the polarization state of the incident light, applicable to various polarization states, and easy to process and manufacture. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Shows a method for fabricating a metasurface lens provided by an embodiment of the present invention;

[0032] Figure 2 Shows a schematic diagram of the converging optical path of incident polychromatic light through a metasurface lens provided by an embodiment of the present invention;

[0033] Figure 3 Shows a schematic diagram of a structural unit when the target wavelength band is the mid-wave infrared band of 3 - 5 μm provided by an embodiment of the present invention;

[0034] Figure 4 Shows a schematic diagram of a structural unit when the target band is the long-wave infrared band of 8-14 μm according to an embodiment of the present invention;

[0035] Figure 5 Shows the layout layout of a constructed metalens according to an embodiment of the present invention;

[0036] Figure 6 Shows the focal spot light field distribution diagram of the far-field x-z plane of incident light with different wavelengths after passing through the metasurface lens according to an embodiment of the present invention;

[0037] Figure 7 Shows the light field distribution of the focal plane of incident light with different wavelengths after passing through the meta-surface lens and the corresponding electric field distribution diagrams in the x and y directions according to an embodiment of the present invention;

[0038] Figure 8 Shows a schematic diagram of the normalized electric field distribution of incident light with different wavelengths on the z-axis according to an embodiment of the present invention;

[0039] Figure 9 Shows a schematic diagram of the variation of the focal length of a metasurface lens with different numerical apertures with the wavelength of incident light according to an embodiment of the present invention;

[0040] Figure 10 Shows the change in the focal length of a metasurface lens with a numerical aperture of 0.24 and a target focal length of 200 μm when the incident light is x-polarized and y-polarized according to an embodiment of the present invention;

[0041] Figure 11 Shows the focal spot light field distribution diagram of the far-field x-z plane of incident light with different wavelengths after passing through the metasurface lens according to another embodiment of the present invention;

[0042] Figure 12 Shows the light field distribution of the focal plane of incident light with different wavelengths after passing through the meta-surface lens and the corresponding electric field distribution diagrams in the x and y directions according to another embodiment of the present invention;

[0043] Figure 13 Shows a schematic diagram of the normalized electric field distribution of incident light with different wavelengths on the z-axis according to another embodiment of the present invention;

[0044] Figure 14 Shows a schematic diagram of the variation of the focal length of a metasurface lens with different numerical apertures with the wavelength of incident light according to another embodiment of the present invention;

[0045] Figure 15The figure shows the focal length variation of a metasurface lens with a numerical aperture of 0.32 and a target focal length of 300 μm provided according to another embodiment of the present invention when the incident light is x-polarized and y-polarized. DETAILED DESCRIPTION

[0046] In the process of realizing the present invention, it is found that the traditional optical imaging system is mainly assembled by various types of lenses, which has the limitations of being bulky, heavy, difficult to integrate and expensive. As modern optical systems develop towards miniaturization and integration, metasurface lenses (metalens) are expected to bring new technical approaches to the miniaturization and integration of optical imaging systems due to their advantages of thin thickness, small size, easy integration, and powerful light field multi-degree-of-freedom control capabilities.

[0047] Metasurface devices based on micro-nanostructure arrays use local phase discontinuity to control the wavefront of light, which can achieve abnormal reflection and refraction of light waves, and even arbitrary control of the light field. They are considered to be the third generation of new optical devices after the first generation of refractive optical elements and the second generation of diffractive elements.

[0048] The metasurface that realizes phase control through the optical path difference generated by the electromagnetic wave during transmission is called a transmission phase metasurface. It mainly obtains the sudden phase by changing the geometric shape and size of the nanostructure unit, thereby controlling the wavefront. Therefore, based on the transmission phase metasurface, a structural unit with 90° rotational symmetry (C4 symmetry) can be designed, which can easily achieve beneficial characteristics such as insensitivity to the polarization characteristics of the incident light.

[0049] The present invention uses a single-layer metasurface structure, designs a variety of structural units with different cross-sectional shapes according to the transmission phase principle, and considers the phase and phase dispersion that each structural unit can provide, and proposes a method for constructing a broadband achromatic metasurface lens. In the present invention, by ingeniously designing artificial micro-nano structures, suitable phase and phase dispersion compensation are provided to achieve broadband achromatic focusing in the mid-wave infrared band and the long-wave infrared band. In order to improve the focusing efficiency, it is preferred to construct the all-medium superlens with a material having a high refractive index and low loss. In the present invention, the lens substrate is selected from silicon material, and the structural unit is selected from silicon material. Silicon absorbs less light in the long-wave infrared band (8-14μm) or the mid-wave infrared band (3-5μm). At the same time, since the shape and placement rules of the structural unit itself have C4 symmetry, it can overlap with itself after rotating 90°, so the superlens is insensitive to the polarization state of the incident light. The designed achromatic metasurface lens can achieve achromatic focusing covering the entire long-wave infrared band (8-14μm) or medium-wave infrared band (3-5μm), and the focal size is close to the diffraction limit.

[0050] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the following further elaborates on the present invention in detail with reference to specific embodiments and the accompanying drawings.

[0051] Figure 1 A method for constructing a metasurface lens according to an embodiment of the present invention is shown, including operations S1 - S5.

[0052] In operation S1, a structural unit library is established. The structural unit library includes various structural units (micro - nano structural units). The structural unit includes a substrate and a columnar structure. The cross - sectional pattern of the columnar structure has 90° rotational symmetry, and the shapes and sizes of the cross - sections of any two structural units are different.

[0053] In operation S2, according to the spatial position on the surface of the metasurface lens and the ideal distribution relationship between the spectral phase, the lowest - frequency phase and phase dispersion at any spatial position on the surface of the metasurface lens operating in the target band and at the target focal length in the ideal state are determined. Here, the incident light in the target band is focused at the target focal length, and the surface of the metasurface lens is a two - dimensional plane.

[0054] In operation S3, each structural unit in the structural unit library is simulated, and the lowest - frequency phase and phase dispersion that each structural unit can provide are extracted.

[0055] In operation S4, each spatial position on the surface of the metasurface lens is traversed. According to the lowest - frequency phase and phase dispersion that each structural unit can provide, the structural units in the structural unit library are screened to determine the target structural unit at the spatial position. The lowest - frequency phase and phase dispersion of the target structural unit have the minimum error relative to the lowest - frequency phase and phase dispersion at the spatial position in the ideal state.

[0056] In operation S5, all the target structural units are placed at their corresponding spatial positions respectively to complete the construction of the metasurface lens. The constructed metasurface lens achieves continuous achromatism in the target band.

[0057] According to the embodiments of the present invention, the design process of a metasurface lens capable of achieving achromatism includes determining parameter details such as the lens material system and the geometric shape of the structural unit, determining the required phase - phase dispersion distribution at each spatial position of the metasurface lens, determining the actual phase - phase dispersion characteristics that each structural unit can provide, and determining the structural units at each position of the metasurface. The key to the method for constructing a broadband achromatic metasurface lens lies in the design and selection of its structural units.

[0058] According to an embodiment of the present invention, the size and shape of the structural unit are designed, and a structural unit library is formed. The structural unit with high transmittance in the structural unit library is selected, and the phase-phase dispersion scatter diagram required at each position of the metasurface lens and the phase-phase dispersion scatter diagram that the structural unit can provide are drawn in the same figure with the phase as the horizontal coordinate and the phase dispersion as the vertical coordinate. The two are compared, and the structural unit closest to the phase-phase dispersion point required for the spatial position of the lens is selected, and then the structural unit is placed at the spatial position.

[0059] According to an embodiment of the present invention, after incident light of different frequencies is focused by a metasurface lens with negative dispersion, the focal positions are arranged on the optical axis in order of frequency, and the focal length increases as the frequency of the incident light increases. This is the case where dispersion exists. After eliminating chromatic aberration, the focal points of incident light of different frequencies are located at almost the same position on the optical axis. Figure 2 As shown, the present invention utilizes the spatial position-phase-phase dispersion distribution relationship of the metasurface lens and designs structural unit columns of different shapes and sizes to obtain phase mutation and phase dispersion. Incident light of different wavelengths (i.e., incident complex light) converges on the same focal plane after passing through the constructed metasurface lens, thereby achieving the purpose of regulating the light field distribution and realizing achromatic focusing.

[0060] According to the embodiment of the present invention, since the target structural units are placed at corresponding spatial positions, and the surface of the formed metasurface lens is a two-dimensional plane, the metasurface lens of the present application is a single-layer metasurface lens, that is, the present application uses a single metasurface to realize the construction of a continuous broadband achromatic metasurface lens within the target band, overcoming the shortcomings of the traditional achromatic lens design, which mostly relies on the traditional lens cascade, is bulky, heavy and difficult to integrate. The embodiment of the present invention is based on a single metasurface, and realizes achromatism by ingeniously designing the micro-nano structural units of the metasurface, so that the achromatic lens system is thinner and lighter, and is conducive to integration.

[0061] According to an embodiment of the present invention, since a variety of structural units with 90° rotational symmetry (C4 symmetry) in cross section are used, the constructed metasurface lens is insensitive to the polarization state of the incident light, is applicable to various polarization states, and is easy to process and manufacture.

[0062] According to an embodiment of the present invention, the target waveband is the mid-wave infrared waveband of 3-5 μm, such as Figure 3 As shown, the columnar structure includes: a square column, a rectangular frame column, a concentric rectangular column, a cross column and a cross column with a rectangular frame. The constructed metasurface lens achieves broadband continuous achromatism within a bandwidth of 2μm.

[0063] According to an embodiment of the present invention, the target waveband is the long-wave infrared waveband of 8-14 μm. Figure 4As shown, the columnar structures include square columns, rectangular frame columns, concentric rectangular columns, cross-shaped columns, cross-shaped columns with rectangular frames, cylindrical columns, circular ring columns, and concentric cylindrical columns. The constructed metasurface lens achieves broadband continuous achromatism within a bandwidth of 6 μm.

[0064] According to an embodiment of the present invention, in the existing research work on metasurface lenses, most of the work is in the visible light and near-infrared bands, and only discrete wavelengths and narrow bandwidth achromatism can be achieved. The embodiment of the present invention can achieve broadband continuous achromatism, which has certain advantages.

[0065] According to an embodiment of the present invention, the material of the substrate is one of silicon, germanium, CaF2, and MgF2. The material of the columnar structure is silicon or germanium.

[0066] According to an embodiment of the present invention, the materials of the substrate and the columnar structure are both high refractive index and low loss materials, and are compatible with the CMOS process for integrated circuit manufacturing. They can be processed by photolithography and etching, and are easy to manufacture.

[0067] According to an embodiment of the present invention, in operation S2, according to the ideal distribution relationship between the spatial position of the metasurface lens and the spectral phase, the lowest frequency phase and phase dispersion at any spatial position on the surface of the metasurface lens operating in the target band and target focal length in the ideal state are determined, including operations S21 - S23.

[0068] In operation S21, according to the ideal distribution relationship, the optimal structural units at different spatial positions on the surface of the metasurface lens corresponding to multiple sets of phase compensation parameters are determined by using different sampling wavelengths within the target band.

[0069] In operation S22, the figure of merit corresponding to each set of phase compensation parameters is determined according to the optimal structural units at different spatial positions corresponding to each set of phase compensation parameters.

[0070] In operation S23, the optimal parameters among the multiple sets of phase compensation parameters are determined according to the figure of merit corresponding to each set of phase compensation parameters, where the optimal parameters are used to determine the lowest frequency phase and phase dispersion at any spatial position on the surface of the metasurface lens operating in the target band and target focal length in the ideal state.

[0071] According to an embodiment of the present invention, in operation S21, the ideal distribution relationship between the spatial position of the metasurface lens and the spectral phase is expressed as follows:

[0072]

[0073] where r is the distance between the spatial position and the center of the lens, f is the target focal length, c is the speed of light, ω is the angular frequency of the incident light, and r0 and C0 are parameters.

[0074] According to an embodiment of the present invention, incident light with different angular frequencies ω within the target wavelength band has a fixed phase value C0 at the position of the lens where r = r0. The aperture of the metasurface lens is taken as the value of r0, and C0 is the phase value at the edge of the lens. r0 and C0 are the lens parameters of the metasurface lens.

[0075] Φ0 = Φ(r, ω1) (2)

[0076] ω1 is the lowest angular frequency within the target wavelength band, and Φ0 represents the lowest-frequency phase within the working wavelength band.

[0077] ΔΦ = Φ(r, ω2) - Φ(r, ω1) (3)

[0078] ω2 is the highest angular frequency within the target wavelength band, and the phase dispersion ΔΦ is the difference between the highest-frequency phase and the lowest-frequency phase within the working wavelength band. Combining equations (1)-(3), it can be seen that after r0 and C0 are determined, the ideal phase Φ and the ideal phase dispersion ΔΦ at each position of the metalens can be determined.

[0079] According to an embodiment of the present invention, the specific steps for determining the optimal structural units at different spatial positions on the surface of the metasurface lens corresponding to multiple sets of phase compensation parameters by using different sampling wavelengths within the target wavelength band include operations S221 - S225.

[0080] In operation S221, multiple sets of metasurface lens parameters are obtained. Each set of metasurface lens parameters includes r0 and C0. The aperture of the metasurface lens is a fixed value designed according to actual needs, and C0 takes values within the range of 0 - 2π at a fixed step. Therefore, the r0 values of each set of metasurface lens parameters are the same, and the C0 value is a value within the range of 0 - 2π.

[0081] In operation S222, for each set of metasurface lens parameters, the target vectors corresponding to different sampling wavelengths at each spatial position of the metasurface lens are determined, where the target vectors are used to characterize the phase and transmittance distributions of the metasurface lens.

[0082] In operation S223, the simulation vectors corresponding to different sampling wavelengths for each structural unit are determined through simulation, where the simulation vectors are used to characterize the phase and transmittance distributions of the structural units.

[0083] In operation S224, the cross-wavelength error sum at each spatial position of each structural unit is determined according to the difference between the target vectors and the simulation vectors at each sampling wavelength, where the cross-wavelength error sum is the sum of the differences at each sampling wavelength.

[0084] In operation S225, according to the cross-wavelength error sum at each spatial position of each structural unit, the structural unit with the minimum cross-wavelength error sum is determined as the optimal structural unit.

[0085] According to an embodiment of the present invention, the lowest-frequency phase is the phase of the lowest-frequency incident light at each spatial position on the surface of the metasurface lens or each structural unit within the target wavelength band. Phase dispersion is the difference between the phase of the highest-frequency incident light and the phase of the lowest-frequency incident light at each spatial position on the surface of the metasurface lens or each structural unit within the target wavelength band.

[0086] According to an embodiment of the present invention, in operation S23, determining the optimal parameters among multiple sets of metasurface lens parameters according to the figure of merit corresponding to each set of metasurface lens parameters includes: selecting the metasurface lens parameters corresponding to the minimum value of the figure of merit as the optimal parameters according to the figure of merit corresponding to each set of metasurface lens parameters.

[0087] According to the design principle of the embodiment of the present invention, the metasurface lens of the present invention can achieve continuous broadband achromatism. In related research work, only discrete wavelengths and narrow-bandwidth achromatism can be achieved.

[0088] According to an embodiment of the present invention, in operation S3, each structural unit in the structural unit library is simulated, and the lowest-frequency phase and phase dispersion provided by each structural unit are extracted.

[0089] According to an embodiment of the present invention, the method further includes: simulating the metasurface lens to obtain the near-field light field distribution and far-field light field distribution of the metasurface lens. As Figure 5 shown, the constructed metasurface lens, that is, the gds layout file, is imported into the optical simulation software Lumerical FDTD to establish a simulation model, and the near-field and far-field light field distributions of the lens are calculated to determine the performance indicators of the metasurface lens.

[0090] According to an embodiment of the present invention, the lowest-frequency phase is the phase of the lowest-frequency incident light at each spatial position on the surface of the metasurface lens or each structural unit within the target wavelength band; phase dispersion is the difference between the phase of the highest-frequency incident light and the phase of the lowest-frequency incident light at each spatial position on the surface of the metasurface lens or each structural unit within the target wavelength band.

[0091] According to an embodiment of the present invention, simulating each structural unit in the structural unit library includes:

[0092] Simulating each structural unit using optical simulation software to obtain the transmittance and phase information of each structural unit within the target wavelength band, and extracting the lowest-frequency phase and phase dispersion of each structural unit.

[0093] According to an embodiment of the present invention, a metasurface lens is provided, which adopts the above-mentioned construction method.

[0094] According to an embodiment of the present invention, the substrates of the structural units of the metasurface lens are connected and arranged periodically.

[0095] According to an embodiment of the present invention, when the target band is the mid-wave infrared band of 3-5 μm, the numerical aperture of the structural unit is 0.20-0.32, the height of the structural unit is 2.5-3.4 μm, and the offset of the average focal length at each wavelength within the target band compared to the target focal length is 2.67-4.67%, and the focal spot size is close to the diffraction limit. When the target band is the long-wave infrared band of 8-14 μm, the numerical aperture of the structural unit is 0.32-0.71, the height of the structural unit is 7-16.5 μm, and the maximum offset of the focal length at each wavelength within the target band relative to the average focal length is 2.48%-5.02%, and the focal spot size is close to the diffraction limit.

[0096] The following lists specific embodiments to illustrate the case where the target band is the mid-wave infrared band of 3-5 μm.

[0097] In this embodiment, the working band range of the metasurface lens design capable of achieving achromatism is 3-5 μm, the period of the structural unit (i.e., the period of the substrate of the structural unit) and the height are both 2.5 μm, the lens diameter is 100 μm, the target focal length is 200 μm, the numerical aperture (NA)=0.24, and the structural unit is as Figure 3 shown.

[0098] Figure 6 shows the focal spot light field distribution diagram of the far-field x-z plane of the incident light of different wavelengths passing through the metasurface lens according to the embodiment of the present invention.

[0099] As Figure 6 shown, for the focal spot light field distribution diagrams of the far-field X-Z plane of the incident light with wavelengths of 3 μm, 3.5 μm, 4 μm, 4.5 μm, and 5 μm passing through the metasurface lens, it can be seen that the focal points of the incident light of different wavelengths (or different frequencies) after focusing are basically located on a horizontal line near 200 μm, achieving achromatism.

[0100] Figure 7 shows the light field distribution of the focal plane of the incident light of different wavelengths passing through the metasurface lens and the corresponding electric field distribution diagrams in the x and y directions according to the embodiment of the present invention.

[0101] As Figure 7 shown, for the light field distribution of the focal plane of the incident light with wavelengths of 3 μm, 3.5 μm, 4 μm, 4.5 μm, and 5 μm passing through the metasurface lens and the corresponding electric field distribution diagrams in the x and y directions, it can be seen that the light field distributions of the focused light spots in the x-axis and y-axis are almost coincident, and near-diffraction-limited focusing is achieved.

[0102] Figure 8 It shows a schematic diagram of the normalized electric field distribution of incident light at different wavelengths on the z-axis according to an embodiment of the present invention.

[0103] As Figure 8 shown, the Z-axis coordinates corresponding to the peaks of the electric field intensities of incident light at different wavelengths (3μm, 3.5μm, 4μm, 4.5μm, and 5μm respectively) are almost the same, that is, incident light with different frequencies in the target band can be focused on the same focal plane.

[0104] Keeping the height and period of the structural unit unchanged and the aperture of the metasurface lens unchanged, four metasurface lenses with focal lengths of 225μm, 250μm, and 150μm respectively, that is, numerical apertures NA of 0.22, 0.20, and 0.32 respectively, were designed in the same way.

[0105] Figure 9 It shows a schematic diagram of the change of the focal length of a metasurface lens with different numerical apertures according to an embodiment of the present invention with respect to the incident light wavelength.

[0106] As Figure 9 shown. When NA = 0.20, the maximum deviation of the focal length of the metasurface lens at each wavelength with respect to the average focal length is 4.04%, the average deviation is 2.51%, and the deviation of the average focal length compared to the designed focal length (target focal length) is 2.67%; when NA = 0.22, the maximum deviation of the focal length at each wavelength with respect to the average focal length is 7.65%, the average deviation is 2.28%, and the deviation of the average focal length compared to the designed focal length is 4.40%; when NA = 0.24, the maximum deviation of the focal length at each wavelength with respect to the average focal length is 7.22%, the average deviation is 3.65%, and the deviation of the average focal length compared to the designed focal length is 3%; when NA = 0.32, the maximum deviation of the focal length at each wavelength with respect to the average focal length is 6.37%, the average deviation is 2.10%, and the deviation of the average focal length compared to the designed focal length is 4.67%. Generally speaking, the deviation of the average focal length compared to the designed focal length is limited to 2.67% - 4.67%, achieving axial achromatism, which proves the universality of the aforementioned achromatic metasurface lens construction method.

[0107] In addition, since the cross-sections of the designed structural units all have C4 symmetry, while being easy to manufacture, they have polarization insensitivity, that is, for incident light waves with different polarizations, their achromatic characteristics remain unchanged.

[0108] Figure 10 It shows the change of the focal length of a metasurface lens with a numerical aperture of 0.24 and a target focal length of 200μm according to an embodiment of the invention when the incident light is x-polarized and y-polarized.

[0109] As Figure 10As shown, whether the incident light is x-polarized (TE polarization) or y-polarized (TM polarization), the curves of the focal length of the metasurface lens in the present invention versus wavelength completely coincide, indicating that the achromatic metasurface lens designed in the present invention can be applied to both TE and TM polarizations simultaneously. Since various polarization states can be obtained by superposing TE and TM polarization states, the achromatic metalens designed in the present invention maintains the same focal position under various polarization states, including linearly polarized light, circularly polarized light, elliptically polarized light, and unpolarized light in any direction, and thus has polarization-insensitive characteristics.

[0110] According to an embodiment of the present invention, broadband achromatism in the mid-wave infrared band (3 - 5 μm) is achieved. Compared with the continuous achromatic bandwidth of 300 - 500 nm in previous research work, the achromatic bandwidth reaches 2000 nm.

[0111] The metasurface lens provided according to an embodiment of the present invention is based on the transmission phase principle, and five structural units provide appropriate phase and phase dispersion compensation to achieve achromatism.

[0112] The following lists specific embodiments to illustrate the case where the target band is the long-wave infrared band of 8 - 14 μm.

[0113] In this embodiment, the working band range of the designed achromatic metasurface lens is 8 - 14 μm, the structural unit period is 5 μm, the height is 7 μm, the lens diameter is 200 μm, the designed focal length is 300 μm, and NA = 0.32.

[0114] Figure 11 Shows the focal spot light field distribution diagrams of the far-field x-z plane of incident light with different wavelengths passing through the metasurface lens according to another embodiment of the present invention.

[0115] As Figure 11 shown, the focal spot light field distribution diagrams of the far-field X-Z plane of incident light with wavelengths of 8 μm, 9 μm, 10 μm, 11 μm, 12 μm, 13 μm, and 14 μm passing through the metasurface lens are presented. It can be seen that the focal points of incident light with different frequencies after focusing are basically on a horizontal line near 300 μm, achieving achromatism.

[0116] Figure 12 Shows the light field distribution of the focal plane of incident light with different wavelengths passing through the metasurface lens according to another embodiment of the present invention, as well as the corresponding electric field distribution diagrams in the x and y directions.

[0117] As Figure 12As shown, the light field distributions of the focal planes of incident light with wavelengths of 8μm, 9μm, 10μm, 11μm, 12μm, 13μm, and 14μm after passing through the metasurface lens, as well as the corresponding electric field distribution diagrams in the x and y directions, can be seen that the light field distributions of the focused spots on the x-axis and y-axis are almost coincident, and a nearly diffraction-limited focus is achieved.

[0118] Figure 13 The schematic diagram of the normalized electric field distribution of incident light at different wavelengths on the z-axis according to another embodiment of the present invention is shown.

[0119] As Figure 13 shown, the Z-axis coordinates corresponding to the peaks of the electric field intensities of incident light with different wavelengths (8μm, 9μm, 10μm, 11μm, 12μm, 13μm, and 14μm respectively) are almost the same, that is, incident light with different frequencies in the target band can be focused on the same focal plane.

[0120] Keeping the lens aperture and the period of the structural unit unchanged, the height of the structural unit is changed, and four other metasurface lenses with focal lengths of 100, 150, 200, and 250μm, that is, numerical apertures NA of 0.71, 0.55, 0.45, and 0.37 respectively, are designed in the same way.

[0121] Figure 14 The schematic diagram of the change of the focal length of the metasurface lens with different numerical apertures according to another embodiment of the present invention is shown.

[0122] As Figure 14 shown, when NA = 0.32, the maximum offset of the focal length at each wavelength relative to the average focal length is 4.37%, and the average offset is 1.83%; when NA = 0.37, the maximum offset of the focal length at each wavelength relative to the average focal length is 2.72%, and the average offset is 1.16%; when NA = 0.45, the maximum offset of the focal length at each wavelength relative to the average focal length is 5.02%, and the average offset is 2.88%; when NA = 0.55, the maximum offset of the focal length at each wavelength relative to the average focal length is 3.05%, and the average offset is 1.58%; when NA = 0.71, the maximum offset of the focal length at each wavelength relative to the average focal length is 2.48%, and the average offset is 0.94%. Generally speaking, the maximum offset of the focal length at each wavelength relative to the average focal length is limited to 2.48% - 5.02%, and the average offset is limited to 0.94% - 2.88%, achieving axial achromatism, which proves the universality of the aforementioned achromatic metasurface lens construction method.

[0123] In addition, since the designed structural units all have C4 symmetry, while being easy to manufacture, they have polarization insensitivity, that is, for incident light waves with different polarizations, their achromatic characteristics remain unchanged.

[0124] Figure 15 Shows the focal length change of a metasurface lens with a numerical aperture of 0.32 and a target focal length of 300 μm provided according to another embodiment of the present invention when the incident light is x-polarized and y-polarized.

[0125] As Figure 15 shown, whether the incident light is x-polarized or y-polarized, the curves of focal length versus wavelength in the present invention completely coincide, indicating that the infrared achromatic metalens designed in the present invention can be applied to both TE and TM polarizations. Since various polarization states can be obtained by superimposing TE and TM polarization states, the achromatic metalens designed in the present invention maintains the same focal position under various polarization states, including linearly polarized light, circularly polarized light, elliptically polarized light, and unpolarized light in any direction, and thus has polarization-insensitive characteristics.

[0126] The metasurface lens provided by the embodiment of the present invention realizes broadband achromatism in a continuous wavelength band based on a single metasurface. The working wavelength band is 8 - 14 μm (long-wave infrared) with a bandwidth of 6 μm, or the working wavelength band is 3 - 5 μm (mid-wave infrared) with a bandwidth of 2 μm.

[0127] The construction method of the metasurface lens provided by the embodiment of the present invention is universal. It can be used not only to design achromatic metasurface lenses with other numerical apertures but also to design achromatic metalenses in other spectral bands (such as visible light, near-infrared, mid-wave infrared, etc.).

[0128] The metasurface lens constructed according to the embodiment of the present invention can be applied to products such as imaging lenses, microscopes, and endoscopes.

[0129] According to the embodiment of the present invention, within the entire long-wave infrared band, the maximum deviation of the focal length at each wavelength realized by the metasurface lens from the average focal length is limited within 5.1%, achieving axial achromatism. The light field distributions in the x and y directions of the focal spot plane are almost coincident, and the focal spot size is close to the diffraction limit.

[0130] According to the embodiment of the present invention, the one-dimensional light field distributions in the x and y directions of the focal spot plane are almost coincident, achieving near-diffraction-limit focusing.

[0131] The metasurface lens provided by the embodiment of the present invention operates in the mid-wave infrared and long-wave infrared bands and has application prospects for infrared imaging systems.

[0132] According to the embodiment of the present invention, the construction method of the metasurface lens is universal, and the construction method can be directly applied to the design of metasurface lenses with other numerical apertures and other working wavelength bands.

[0133] The specific embodiments described above further elaborate on the objectives, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A construction method of a metasurface lens, comprising: Establishing a structural unit library, the structural unit library including a variety of structural units, the structural units including a substrate and columnar structures, the cross-sectional pattern of the columnar structures having 90° angular rotational symmetry, and the shapes and sizes of the cross-sections of any two structural units being different; Determining the lowest-frequency phase and phase dispersion at any spatial position on the surface of the metasurface lens operating in the target band and at the target focal length in an ideal state according to the ideal distribution relationship between the spatial position and spectral phase of the metasurface lens, wherein the incident light in the target band is focused at the target focal length, and the surface of the metasurface lens is a two-dimensional plane; the target band is the mid-wave infrared band of 3-5 μm, or the target band is the long-wave infrared band of 8-14 μm; Simulating each structural unit in the structural unit library and extracting the lowest-frequency phase and phase dispersion that each structural unit can provide; Traversing each spatial position on the surface of the metasurface lens, and screening the structural units in the structural unit library according to the lowest-frequency phase and phase dispersion that each structural unit can provide to determine the target structural unit at the spatial position, the lowest-frequency phase and phase dispersion of the target structural unit having the smallest error relative to the lowest-frequency phase and phase dispersion at the spatial position in the ideal state; Placing all the target structural units at their corresponding spatial positions respectively to complete the construction of the metasurface lens, and the constructed metasurface lens achieving continuous achromatism in the target band.

2. The method according to claim 1, wherein, In the case where the target band is the mid-wave infrared band of 3-5 μm, the columnar structures include: square columns, rectangular frame columns, concentric rectangular columns, cross-shaped columns, and cross-shaped columns with rectangular frames, and the constructed metasurface lens achieves broadband continuous achromatism within a bandwidth of 2 μm. In the case where the target band is the long-wave infrared band of 8-14 μm, the columnar structures include square columns, rectangular frame columns, concentric rectangular columns, cross-shaped columns, cross-shaped columns with rectangular frames, cylindrical columns, circular ring columns, and concentric cylindrical columns, and the constructed metasurface lens achieves broadband continuous achromatism within a bandwidth of 6 μm.

3. The method according to claim 1, wherein, The material of the substrate is one of silicon, germanium, CaF2, and MgF2, and the material of the columnar structures is silicon or germanium.

4. The method according to claim 1, wherein Determining the lowest-frequency phase and phase dispersion at any spatial position on the surface of the metasurface lens operating in the target band and at the target focal length in an ideal state according to the ideal distribution relationship between the spatial position and spectral phase of the metasurface lens, including: According to the ideal distribution relationship, using different sampling wavelengths within the target band to determine the optimal structural units at different spatial positions on the surface of the metasurface lens corresponding to multiple groups of phase compensation parameters; Determining the figure of merit corresponding to each group of phase compensation parameters according to the optimal structural units at different spatial positions corresponding to each group of phase compensation parameters; Determine the optimal parameter among multiple groups of phase compensation parameters according to the quality factor corresponding to each group of phase compensation parameters, where the optimal parameter is used to determine the lowest-frequency phase and phase dispersion at any spatial position on the surface of the metasurface lens operating in the target band and at the target focal length under ideal conditions.

5. The method according to claim 2, wherein The method further includes: Simulate the metasurface lens to obtain the near-field light field distribution and far-field light field distribution of the metasurface lens.

6. The method according to claim 1, wherein The lowest-frequency phase is the phase of the lowest-frequency incident light at each spatial position on the surface of the metasurface lens or each structural unit within the target band; the phase dispersion is the difference between the phase of the highest-frequency incident light and the phase of the lowest-frequency incident light at each spatial position on the surface of the metasurface lens or each structural unit within the target band.

7. The method according to claim 6, wherein, Simulating each structural unit in the structural unit library includes: Using optical simulation software to simulate each structural unit to obtain the transmittance and phase information of each structural unit in the target band, and extracting the lowest-frequency phase and phase dispersion of each structural unit.

8. The method according to claim 1, wherein, The ideal distribution relationship between the spatial position and spectral phase of the metasurface lens is expressed as follows: where r is the distance between the spatial position and the center of the lens, f is the target focal length, c is the speed of light, ω is the angular frequency of the incident light, and r0 and C0 are parameters.

9. A metasurface lens constructed by the method according to any one of claims 1-8.

10. The surface lens according to claim 9, wherein The substrates of the structural units of the metasurface lens are connected and arranged periodically; When the target band is the mid-wave infrared band of 3-5 μm, the numerical aperture of the structural unit is 0.20-0.32, the height of the structural unit is 2.5-3.4 μm, and the offset of the average focal length at each wavelength within the target band compared to the target focal length is 2.67-4.67%; When the target band is the long-wave infrared band of 8-14 μm, the numerical aperture of the structural unit is 0.32-0.71, the height of the structural unit is 7-16.5 μm, and the maximum offset of the focal length at each wavelength within the target band relative to the average focal length is 2.48%-5.02%.

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