A design method of polarization-insensitive large-size and large numerical aperture discrete achromatic superlens in mid-infrared waveband

Abstract

This invention relates to a design method for large-size, high numerical aperture discrete achromatic superlenses that are polarization-insensitive in the mid-infrared band. This invention relates to the field of micro / nano photonic metasurface technology. Based on the superlens's diameter, numerical aperture, and operating frequency band, this invention obtains the required phase delay and dispersion at different positions of the achromatic lens; constructs a corresponding polarization-insensitive cell library; selects the required cells from the cell library according to the required phase and group delay at each position; and arranges these cells in a square with the superlens center as the origin, along the x and y directions at periodic intervals of P, thereby obtaining the designed superlens. The achromatic superlens proposed in this invention has the characteristic of being polarization-insensitive, and compared with PB phase-type lenses that are only sensitive to circular polarization, it has a wider range of applications.

Description

Technical Field

[0001] This invention relates to the field of micro-nano photonic metasurface technology, and is a design method for large-size and large numerical aperture discrete achromatic metalenses that are insensitive to polarization in the mid-infrared band. Background Technology

[0002] Infrared lenses provide imaging information in conditions of low visibility, such as darkness. The infrared spectrum is generally defined as 2.5μm to 25μm, with 3μm to 8μm being the mid-infrared band. Within the mid-infrared band, 3μm to 5μm is an atmospheric window where infrared loss is relatively low. Mid-infrared lenses have important applications in industrial manufacturing, environmental monitoring, gas measurement, and target recognition. Traditional infrared achromatic lenses are lens groups composed of several lenses, which are large, heavy, power-consuming, and difficult to integrate. The emergence of superlenses solves these problems. Superlenses achieve focusing by manipulating the wavefront information of electromagnetic waves at the subwavelength level.

[0003] Furthermore, achromatic superlenses can be achieved by controlling the dispersion of the unit at the subwavelength scale. However, the size of the achromatic superlens is limited by the achromatic bandwidth and numerical aperture. Large apertures are necessary for optical systems that collect weak or rapidly changing signals, such as in astronomical imaging, remote airborne surveillance, and high-power laser applications, where large-sized superlenses are required to reduce the demand for incident light density. In optical systems, especially those requiring the collection of weak or rapidly changing signals, higher incident light density means more light energy entering the system. This typically helps improve image brightness and signal-to-noise ratio. However, if the aperture of the lens or objective is small, a higher incident light density may be needed to obtain sufficient signal, placing higher demands on the light source and potentially introducing more noise or causing system overload.

[0004] Discrete achromatic theory can relax the restrictions on the size, numerical aperture and achromatic bandwidth of achromatic superlenses. However, existing superlenses constructed using discrete achromatic theory are polarization sensitive and have a limited range of applications, while the present invention is polarization insensitive and has a wide range of applications. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a design method for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band. The large-size and large numerical aperture discrete achromatic superlens of this invention, which is insensitive to polarization in the mid-infrared band, has the characteristics of large size, large numerical aperture, and insensitivity to polarization, and can eliminate chromatic aberration within the working bandwidth, thereby improving imaging quality.

[0006] This invention provides the following technical solutions:

[0007] A method for designing a large-size, high-numerical-aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band, the method comprising the following steps:

[0008] Step 1: Based on the diameter, numerical aperture, and operating frequency band of the superlens, obtain the phase delay and dispersion required at different positions of the achromatic lens;

[0009] Step 2: Construct the corresponding polarization-insensitive cell library;

[0010] Step 3: Select the required elements from the element library according to the required phase and group delay at each position, and arrange these elements in a square with the center of the superlens as the origin and a period of P along the x and y directions to obtain the designed superlens.

[0011] Preferably, step 1 specifically comprises:

[0012] A plane wave with wavelength λ is incident normally on a metasurface lens and converges to its focal point A. The focal length of the metasurface lens is designed to be f. The phase distribution function of the metasurface should satisfy the following formula:

[0013]

[0014] in, Let (x, y) be the distribution function, representing the position of any point unit structure on the metasurface lens; the goal of achromatic correction is set to be at an angular frequency ω. c Centered on, with bandwidth Δω all The angular frequency range will In ω c Expanding to a Taylor series:

[0015]

[0016] Where φ(x, y, ω) c ) represents the center frequency ω c The phase distribution below, This represents the group delay phase distribution, where For group delay distribution, O(ω) 2 ) is the higher-order modulus, which is taken as 0. The group delay is a constant independent of ω.

[0017] The first measure is to introduce phase compensation, thereby ensuring that the frequency at any position of the superlens is ω. c The electromagnetic waves arrive at the focal point simultaneously;

[0018] The second term is achieved by introducing dispersion compensation, thereby ensuring that within the bandwidth Δω all Electromagnetic waves within a certain range can reach the focal point simultaneously.

[0019] Preferably, step 1 further includes:

[0020] Substituting the hyperbolic phase distribution that the lens should satisfy, we obtain the conditions that must be met to achieve an achromatic metalens:

[0021] 1) Angular frequency ω c phase distribution

[0022]

[0023] 2) Group delay distribution

[0024]

[0025] By setting the frequency to satisfy the equal frequency interval condition Δω, equal intervals can be achieved. The extension utilizes a finite phase delay to fit phase delay dispersion requirements of arbitrary magnitude.

[0026] Preferably, the group delay distribution GD is set as follows:

[0027]

[0028] In quasi-achromatic superlenses, a group delay ΔGD is used for the remainder calculation. The required dispersion of the superlens is in the range of 0 to ΔGD, and the magnitude of the dispersion is independent of the numerical aperture radius, thus enabling the construction of large-size achromatic superlenses.

[0029] For ΔGD, we have:

[0030]

[0031] For the dispersion of a superlens, we have:

[0032] GD1 = mod(GD, ΔGD) + m * ΔGD

[0033] For frequency ω c At +NΔω, the phase required by the quasi-achromatic superlens is:

[0034]

[0035] In the above formula, m*2π is ignored, and light of different frequencies does not arrive at the focal plane simultaneously. The above formula can be written as:

[0036]

[0037] In Δω all Within the range, at different positions of the superlens, light of different frequencies satisfies the phase distribution described above, at Δω all Discrete achromatic color difference can be achieved within the range.

[0038] Preferably, step 2 specifically comprises:

[0039] There are seven types of dielectric pillars for superlenses: square pillars, air, square rings, square ring pillars, cross-shaped pillars, square ring crosses, and square cross rings. All pillars have the same height H and period P. The structural parameters of the square pillars include the side length W1. The air structure is the case where the side length W1 = 0. The structural parameters of the square rings include the outer ring side length W... 21 And the inner ring side length W 22 The structural parameters of the square ring cylinder include the side length W of the outer ring of the square ring. 31 The side length W of the inner ring 32 The side length W of the square prism 33 The structural parameters of the cross-shaped column include the long side L4 and the short side W4, while the structural parameters of the square ring cross-shaped column include the side length W of the outer ring of the square ring. 51 The side length W of the inner ring 52 The short side W of the cross-shaped prism 53 The long side L5 of the cross-shaped prism is equal to W. 52 The structural parameters of the square ring include the side length W of the outer ring. 61 The inner cross short side W 62 With the long side L6, all the medium pillars of the superlens satisfy the principle of central symmetry, thus achieving polarization insensitivity.

[0040] Preferably, the phase and dispersion modulation provided by each unit structure are calculated in FDTD using the finite-difference time-domain method. By determining the period P and height H of each unit, the phase and dispersion modulation of each unit is obtained by changing the structural parameters of each unit, thereby completing the construction of a unit library. Through these seven units, the dispersion phase of the constructed unit library covers 6π to 23π.

[0041] Preferably, considering the cell transmittance, the cell period P = 1.7 μm and the height H = 6.5 μm are selected. Then, different structures are scanned to obtain a cell library. It can be seen that the ratio of the height to the period of all cells is 3.83:1.

[0042] A design system for a large-size and high numerical aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band, the system comprising:

[0043] The calculation module obtains the phase delay and dispersion required by the achromatic lens at different positions of the lens based on the diameter, numerical aperture and operating frequency band of the superlens.

[0044] A building module that constructs a corresponding polarization-insensitive cell library;

[0045] The design module selects the required units from the unit library based on the phase and group delay required at each position, and arranges these units in a square with the center of the superlens as the origin and a period of P along the x and y directions, thereby obtaining the designed superlens.

[0046] A computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a design method for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to mid-infrared polarization.

[0047] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement a design method for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to mid-infrared polarization.

[0048] The present invention has the following beneficial effects:

[0049] Compared with the prior art, the present invention:

[0050] Compared to existing technologies, this invention designs a large-size, high numerical aperture discrete achromatic superlens that is polarization-insensitive in the mid-infrared band. This lens has a diameter of 5 mm, a numerical aperture of 0.42, and an achromatic bandwidth of 3 μm to 5 μm, featuring large size, high numerical aperture, and wide-bandwidth achromaticity. Furthermore, the achromatic superlens proposed in this invention is polarization-insensitive, which allows for a wider range of applications compared to PB phase-type lenses that are only sensitive to circular polarization. Attached Figure Description

[0051] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0052] Figure 1 The diagram shown is a schematic of the unit library constructed according to the present invention;

[0053] Figure 2 The diagram shown is a schematic representation of the model constructed according to this invention.

[0054] Figure 3 The diagram shows the distribution of the lens with a diameter of 3 mm and a numerical aperture of 0.42 constructed according to the present invention at focal lengths of 3 μm to 5 μm.

[0055] Figure 4 The diagram shows the energy distribution in the XZ plane and the energy distribution in the XY plane at the focal point according to the present invention.

[0056] Figure 5 This invention includes the MTF of continuous achromatic lens theory, the MTF of discrete achromatic lens theory, and the MTF of discrete achromatic lens simulation. Detailed Implementation

[0057] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0059] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0060] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0061] The present invention will be described in detail below with reference to specific embodiments. Specific Implementation Example 1:

[0063] To address the shortcomings of existing technologies, this invention provides a design method for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band. The large-size and large numerical aperture discrete achromatic superlens of this invention, which is insensitive to polarization in the mid-infrared band, has the characteristics of large size, large numerical aperture, and insensitivity to polarization, and can eliminate chromatic aberration within the working bandwidth, thereby improving imaging quality.

[0064] according to Figures 1 to 5As shown, the specific optimized technical solution adopted by the present invention to solve the above-mentioned technical problems is: The present invention relates to a design method for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band.

[0065] A method for designing a large-size, high-numerical-aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band, the method comprising the following steps:

[0066] Step 1: Based on the diameter, numerical aperture, and operating frequency band of the superlens, obtain the phase delay and dispersion required at different positions of the achromatic lens;

[0067] Step 2: Construct the corresponding polarization-insensitive cell library;

[0068] Step 3: Select the required elements from the element library according to the required phase and group delay at each position, and arrange these elements in a square with the center of the superlens as the origin and a period of P along the x and y directions to obtain the designed superlens. Specific Implementation Example 2:

[0070] The only difference between Embodiment 2 and Embodiment 1 of this application is that:

[0071] Step 1 specifically involves:

[0072] A plane wave with wavelength λ is incident normally on a metasurface lens and converges to its focal point A. The focal length of the metasurface lens is designed to be f. The phase distribution function of the metasurface should satisfy the following formula:

[0073]

[0074] in, Let (x, y) be the distribution function, representing the position of any point unit structure on the metasurface lens; the goal of achromatic correction is set to be at an angular frequency ω. c Centered on, with bandwidth Δω all The angular frequency range will In ω c Expanding to a Taylor series:

[0075]

[0076] Where φ(x, y, ω) c ) represents the center frequency ω c The phase distribution below, This represents the group delay phase distribution, where For group delay distribution, O(ω) 2 ) is the higher-order modulus, which is taken as 0. The group delay is a constant independent of ω.

[0077] The first measure is to introduce phase compensation, thereby ensuring that the frequency at any position of the superlens is ω. c The electromagnetic waves arrive at the focal point simultaneously;

[0078] The second term is achieved by introducing dispersion compensation, thereby ensuring that within the bandwidth Δω all Electromagnetic waves within a certain range can reach the focal point simultaneously. Specific Implementation Example 3:

[0080] The only difference between Embodiment 3 and Embodiment 2 of this application is that:

[0081] Step 1 further includes:

[0082] Substituting the hyperbolic phase distribution that the lens should satisfy, we obtain the conditions that must be met to achieve an achromatic metalens:

[0083] 1) Angular frequency ω c phase distribution

[0084]

[0085] 2) Group delay distribution

[0086]

[0087] By setting the frequency to satisfy the equal frequency interval condition Δω, equal intervals can be achieved. The extension utilizes a finite phase delay to fit phase delay dispersion requirements of arbitrary magnitude. Specific Implementation Example 4:

[0089] The only difference between Embodiment 4 and Embodiment 3 of this application is that:

[0090] The group delay distribution (GD) is defined as follows:

[0091]

[0092] In quasi-achromatic superlenses, a group delay ΔGD is used for the remainder calculation. The required dispersion of the superlens is in the range of 0 to ΔGD, and the magnitude of the dispersion is independent of the numerical aperture radius, thus enabling the construction of large-size achromatic superlenses.

[0093] For ΔGD, we have:

[0094]

[0095] For the dispersion of a superlens, we have:

[0096] GD1 = mod(GD, ΔGD) + m * ΔGD

[0097] For frequency ω cAt +NΔω, the phase required by the quasi-achromatic superlens is:

[0098]

[0099] In the above formula, m*2π is ignored, and light of different frequencies does not arrive at the focal plane simultaneously. The above formula can be written as:

[0100]

[0101] In Δω all Within the range, at different positions of the superlens, light of different frequencies satisfies the phase distribution described above, at Δω all Discrete achromatic color difference can be achieved within the range. Specific Implementation Example 5:

[0103] The difference between Embodiment 5 and Embodiment 4 of the present invention lies only in:

[0104] Step 2 specifically involves:

[0105] There are seven types of dielectric pillars for superlenses: square pillars, air, square rings, square ring pillars, cross-shaped pillars, square ring crosses, and square cross rings. All pillars have the same height H and period P. The structural parameters of the square pillars include the side length W1. The air structure is the case where the side length W1 = 0. The structural parameters of the square rings include the outer ring side length W... 21 And the inner ring side length W 22 The structural parameters of the square ring cylinder include the side length W of the outer ring of the square ring. 31 The side length W of the inner ring 32 The side length W of the square prism 33 The structural parameters of the cross-shaped column include the long side L4 and the short side W4, while the structural parameters of the square ring cross-shaped column include the side length W of the outer ring of the square ring. 51 The side length W of the inner ring 52 The short side W of the cross-shaped prism 53 The long side L5 of the cross-shaped prism is equal to W. 52 The structural parameters of the square ring include the side length W of the outer ring. 61 The inner cross short side W 62 With the long side L6, all the medium pillars of the superlens satisfy the principle of central symmetry, thus achieving polarization insensitivity. Specific Implementation Example Six:

[0107] The difference between Embodiment Six and Embodiment Five of the present invention lies only in:

[0108] The phase and dispersion modulation provided by each unit structure are calculated in FDTD using the finite-difference time-domain method. By determining the period P and height H of each unit, the phase and dispersion modulation of each unit is obtained by changing the structural parameters of each unit, thereby completing the construction of a unit library. Through these seven units, the dispersive phase of the constructed unit library covers 6π to 23π. Specific Implementation Example 7:

[0110] The difference between Embodiment Seven and Embodiment Six of the present invention lies only in:

[0111] Considering the cell transmittance, we selected a cell period of P = 1.7 μm and a height of H = 6.5 μm. Then, we scanned different structures to obtain a cell library. We can see that the ratio of height to period for all cells is 3.83:1. Specific Implementation Example 8:

[0113] The difference between Embodiment 8 and Embodiment 7 of the present invention lies only in:

[0114] This invention provides a design system for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band, the system comprising:

[0115] The calculation module obtains the phase delay and dispersion required by the achromatic lens at different positions of the lens based on the diameter, numerical aperture and operating frequency band of the superlens.

[0116] A building module that constructs a corresponding polarization-insensitive cell library;

[0117] The design module selects the required units from the unit library based on the phase and group delay required at each position, and arranges these units in a square with the center of the superlens as the origin and a period of P along the x and y directions, thereby obtaining the designed superlens. Specific Implementation Example Nine:

[0119] The difference between Embodiment Nine and Embodiment Eight of the present invention lies only in:

[0120] The present invention provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a design method for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band. Specific Implementation Example 10:

[0122] The only difference between Embodiment 10 and Embodiment 9 of the present invention is that:

[0123] The present invention provides a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a design method for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band. Specific Implementation Example Eleven:

[0125] The only difference between Embodiment Eleven and Embodiment Ten of this invention is that:

[0126] The technical solution for achieving the above-mentioned lens in this invention is as follows: This large-size, high numerical aperture discrete achromatic superlens, which is insensitive to polarization in the mid-infrared band, comprises two parts: a dielectric substrate and a dielectric pillar. The dielectric substrate provides support, while the dielectric pillar modulates the wavefront of the electromagnetic wave. Since silicon has good transmittance in the mid-infrared band, both the dielectric substrate and the silicon pillar are made of high-resistivity silicon.

[0127] The constructed achromatic superlens has a diameter of 5 mm, an operating frequency range of 3 μm-5 μm, and a numerical aperture of 0.42. The maximum chromatic dispersion error at the focal point achievable by this lens within the operating frequency range is 8.4%. The design method of the achromatic superlens is as follows:

[0128] 1) Based on the diameter, numerical aperture, and operating frequency band of the superlens, obtain the phase delay and dispersion required at different positions of the achromatic lens.

[0129] Suppose a plane wave with wavelength λ is incident normally on a metasurface lens and perfectly converges to its focal point A. The focal length of the metasurface lens is designed to be f. Clearly, for the plane wave to be focused at the focal point after passing through the metasurface unit structure, the light rays transmitted through the metasurface lens unit structure must have the same phase at focal point A. That is, the metasurface phase distribution function should satisfy the formula:

[0130]

[0131] Let be the distribution function, where (x,y) represents the position of any point unit structure on the metasurface lens.

[0132] The phase distribution described above is merely a condition required for constructing a monochromatic superlens; its focal length changes with frequency, meaning it is a function of angular frequency ω. As mentioned above, an ideal monochromatic focusing superlens exhibits a hyperbolic phase distribution. If you want the focal length to be within a bandwidth Δω all If the frequency remains constant within the angular frequency range, then achromatic aberration needs to be performed. Assume the goal of achromatic aberration is to maintain the desired frequency at angular frequency ω. c Centered on, with bandwidth Δω all The angular frequency range can be In ωc The surrounding area expands into a Taylor series.

[0133]

[0134] As can be seen, the expanded Taylor series is divided into three parts, where φ(x, y, ω) c ) represents the center frequency ω c The phase distribution below, This represents the group delay phase distribution, where For group delay distribution, O(ω) 2 Let ω be the higher-order modulus. Taking the higher-order modulus as 0, the group delay is a constant independent of ω. It can be seen that the first term introduces phase compensation, thus ensuring that electromagnetic waves of frequency ωc at any position of the superlens arrive at the focal point simultaneously. The second term introduces dispersion compensation, thus ensuring that within the bandwidth Δω... all Electromagnetic waves within a certain range can reach the focal point simultaneously.

[0135] Substituting the hyperbolic phase distribution that the lens should satisfy, we can obtain the conditions that must be met to achieve a perfectly achromatic metalens:

[0136] 1) Phase distribution of angular frequency ωc

[0137]

[0138] 2) Group delay distribution

[0139]

[0140] The dispersion compensation requirement of continuous achromatic metalenses increases with the aperture and NA (nanometer). In traditional broadband achromatic metalenses, a large dispersion requirement inevitably means a high element thickness requirement. Excessively high element aspect ratios are difficult to manufacture. Quasi-achromatic metalenses based on time-degree-of-freedom can relax the limitations on aperture and NA.

[0141] Phase delay based on dispersion modulation characteristics can be extended according to phase properties, thereby reducing the requirement for large dispersion modulation capability of the unit cell. At equally spaced frequencies Δω, the original phase delay curve can be extended into multiple discrete phase delays, which differ in phase from each other. Therefore, as long as the design frequency satisfies the equal frequency spacing condition Δω, equal spacing can be achieved. The extension of the phase delay allows for fitting phase delay dispersion requirements of arbitrary magnitudes using a finite phase delay.

[0142] Group delay distributions (GDs) include:

[0143]

[0144] In a quasi-achromatic superlens, ideal achromaticity is achieved at N points, while approximate achromaticity is achieved at the remaining points. In quasi-achromatic superlens, a group delay ΔGD is used for the remainder, so the required dispersion of the superlens is within the range of 0 to ΔGD. The magnitude of the dispersion is independent of the radius numerical aperture, thus enabling the construction of large-size achromatic superlenses.

[0145] For ΔGD, we have:

[0146]

[0147] Therefore, for the dispersion of a superlens, we have:

[0148] GD1 = mod(GD, ΔGD) + m * ΔGD

[0149] For frequency ω c At +NΔω, the phase required by the quasi-achromatic superlens is:

[0150]

[0151] In the above formula, m*2π can be ignored; it only affects whether light of different frequencies can reach the focal plane simultaneously. A quasi-achromatic superlens utilizes the fact that light of the same frequency can reach the focal plane simultaneously, while light of different frequencies cannot reach the focal plane simultaneously. The above formula can be written as:

[0152]

[0153] Therefore, in Δω all Within the range, at different positions of the superlens, light of different frequencies satisfies the phase distribution described above, which allows us to achieve this at Δω. all Discrete achromatic color difference can be achieved within the range.

[0154] 2) Construct the corresponding polarization-insensitive cell library

[0155] After completing the above steps, the next step was to construct the unit library. There are seven types of superlens media pillars: square pillar, air, square ring, square ring pillar, cross, square ring cross, and square cross ring. All media pillars have the same height H and period P. The structural parameters of the square pillar include the side length W1. The air structure is the case where the square side length W1 = 0. The structural parameters of the square ring include the outer ring side length W... 21 And the inner ring side length W 22 The structural parameters of the square ring cylinder include the side length W of the outer ring of the square ring. 31 The side length W of the inner ring 32 The side length W of the square prism 33The structural parameters of the cross-shaped column include the long side L4 and the short side W4. The structural parameters of the square ring cross-shaped column include the side length W of the outer ring of the square ring. 51 The side length W of the inner ring 52 The short side W of the cross-shaped prism 53 The long side L5 of the cross-shaped prism is equal to W. 52 The structural parameters of the square ring include the side length W of the outer ring. 61 The inner cross short side W 62 The longest side is L6. All superlens dielectric pillars satisfy the principle of centrosymmetry, thus achieving polarization insensitivity. The phase and dispersion modulation provided by each unit structure can be calculated in FDTD using the finite-difference time-domain method. By determining the period P and height H of each unit, and changing the structural parameters of each unit, the phase and dispersion modulation of each unit can be obtained, thereby completing the construction of a unit library. Through these seven unit types, the dispersive phase of the constructed unit library can cover 6π to 23π.

[0156] Considering the cell transmittance, we selected a cell period of P = 1.7 μm and a height of H = 6.5 μm. Then, we scanned different structures to obtain a cell library. We can see that the ratio of height to period for all cells is 3.83:1.

[0157] 3) Select the required elements from the element library according to the phase and group delay required at each position, and arrange these elements in a square with the center of the superlens as the origin and the period P as the interval along the x and y directions to obtain the designed superlens.

[0158] Figure 1 The figure shows the types of elements used in the constructed element library, totaling seven. It also demonstrates that the constructed element library covers the dispersion phase from 6π to 23π within the 3μm-5μm range, meeting the design requirements.

[0159] Figure 2 The diagram shows the constructed model, where a is a lens diagram with a diameter of 3mm, b is a local size distribution of the lens, c is a local top view of the lens, 1 is a dielectric column, and 2 is a dielectric substrate.

[0160] Figure 3 The focal length distribution of a constructed lens with a diameter of 3 mm and a numerical aperture of 0.42 in the 3 μm-5 μm range is shown. The horizontal line represents the continuous achromatic focal length, which is 3.241 mm. The red dashed line represents the discrete achromatic focal length, with a maximum error of 8.4% compared to the continuous achromatic focal length.

[0161] Figure 4 Let X be the energy distribution in the XZ plane and the energy distribution in the XY plane at the focal point.

[0162] Figure 5 This includes the MTF of continuous achromatic lens theory, the MTF of discrete achromatic lens theory, and the MTF of discrete achromatic lens simulation.

[0163] Compared with existing inventions, the advantages of this invention are as follows: This invention proposes a large-size, large numerical aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band. The lens has a diameter of 5 mm, a numerical aperture of 0.42, and an achromatic bandwidth of 3 μm to 5 μm, featuring large size, large numerical aperture, and wide-bandwidth achromaticity. Furthermore, the achromatic superlens proposed in this invention is polarization-insensitive, which allows for a wider range of applications compared to PB phase-type lenses that are only sensitive to circular polarization. Specific Implementation Example Twelve:

[0165] The only difference between Embodiment Twelve and Embodiment Eleven of the present invention is that:

[0166] This invention designs a large-size, high-numerical-aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band. The design of the lens involves the following steps:

[0167] First, based on the designed superlens with a diameter D = 5 mm, numerical aperture NA = 0.42, and operating frequency band of 3 μm to 5 μm, the phase compensation and dispersion compensation required to achieve discrete achromaticity at any position of the superlens are calculated.

[0168]

[0169] This represents the phase distribution at any frequency within the operating frequency band of 3μm to 5μm. For the center frequency ω c The required phase shift. GD is the group delay required for the superlens to achieve achromaticity, c is the speed of light, f is the focal length, and (x, y) are the coordinates of a point on the surface of the superlens. Δω=2*π*11.4285*10 12 rad / s, Additionally, mod is a modulo function, where mod(GD, ΔGD) is the remainder after dividing GD by ΔGD.

[0170] Secondly, a cell library is constructed that satisfies the required phase for both dispersion phase and center frequency. As shown in the cell dispersion distribution figure, the constructed cell library has a dispersion phase range of 6π to 23π. The cell library is as follows: Figure 1 As shown.

[0171] Then, the cells are filtered, and an error function Error(x, y; n) is introduced during the cell filtering process.

[0172]

[0173] (x, y) are the coordinates of a point on the surface of the superlens. For an ideal frequency ω k At that time, the amplitude and phase distribution at a radius of r, For all elements in the element library, the frequency is ω k The amplitude and phase distribution at that time. N is the total number of frequency points selected within the frequency band, and k is the current frequency. Following the strategy of minimizing the error function, the units are selected. For simplicity, N = 15 frequency points within the 60THz-100THz range are used for calculation, and the result with the smallest error is taken.

[0174] Then, the results obtained from the screening were simulated to obtain the achromatic color difference result as follows: Figure 3 , Figure 4 As shown. Additionally, the MTF, which represents the lens's imaging capability, was obtained, such as... Figure 5 As shown.

[0175] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or N embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification and the features of different embodiments or examples without contradiction. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of the present invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified. Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more N executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of the invention pertain.

[0176] The above description is merely a preferred embodiment of a design method for large-size and large numerical aperture discrete achromatic superlenses that are insensitive to mid-infrared polarization. The scope of protection for this design method is not limited to the above embodiments; all technical solutions falling within this conceptual framework are within the scope of protection of this invention. It should be noted that for those skilled in the art, any improvements and variations made without departing from the principles of this invention should also be considered within the scope of protection of this invention.

Claims

1. A design method for a large-size, high-numerical-aperture discrete achromatic superlens that is insensitive to polarization in the mid-infrared band, characterized by: The method includes the following steps: Step 1: Based on the diameter, numerical aperture, and operating frequency band of the superlens, obtain the phase delay and dispersion required at different positions of the achromatic lens; Step 2: Construct the corresponding polarization-insensitive cell library; Step 3: Select the required cells from the cell library according to the required phase and group delay at each position, and arrange these cells in a square with the center of the superlens as the origin and a period of P along the x and y directions to obtain the designed superlens. Step 1 specifically involves: A plane wave with wavelength λ is incident normally on a metasurface lens and converges to its focal point A. The focal length of the metasurface lens is designed to be f. The phase distribution function of the metasurface should satisfy the following formula: in, Let (x, y) be the distribution function, and (x, y) represent the position of any point unit structure on the metasurface lens; The goal of setting achromaticity is to achieve an angular frequency ω c Centered on, with bandwidth Δω all The angular frequency range will In ω c Expanding to a Taylor series: Where φ(x,y,ω) c ) represents the center frequency ω c The phase distribution below, This represents the group delay phase distribution, where For group delay distribution, O(ω) 2 ) is the higher-order modulus, which is taken as 0. The group delay is a constant independent of ω, where ω is the angular frequency. The first measure is to introduce phase compensation, thereby ensuring that the frequency at any position of the superlens is ω. c The electromagnetic waves arrive at the focal point simultaneously; The second term is achieved by introducing dispersion compensation, thereby ensuring that within the bandwidth Δω all Electromagnetic waves within a certain range can simultaneously reach the focal point; Step 1 further includes: Substituting the hyperbolic phase distribution that the lens should satisfy, we obtain the conditions that must be met to achieve an achromatic metalens: 1) Angular frequency ω c phase distribution 2) Group delay distribution By setting the frequency to satisfy the equal frequency interval condition Δω, equal intervals can be achieved. The extension utilizes a finite phase delay to fit phase delay dispersion requirements of arbitrary magnitude; The group delay distribution (GD) is defined as follows: In quasi-achromatic superlenses, a group delay ΔGD is used for the remainder calculation. The required dispersion of the superlens is in the range of 0 to ΔGD, and the magnitude of the dispersion is independent of the numerical aperture radius, thus enabling the construction of large-size achromatic superlenses. For ΔGD, we have: For the dispersion of a superlens, we have: GD1 = mod(GD, ΔGD) + m * ΔGD For frequency ω c At +NΔω, the phase required by the quasi-achromatic superlens is: In the above formula, m*2π is ignored, and light of different frequencies does not arrive at the focal plane simultaneously. The above formula can be written as: In Δω all Within the range, at different positions of the superlens, light of different frequencies satisfies the phase distribution described above, at Δω all Discrete achromatic color difference can be achieved within the range.

2. The method according to claim 1, characterized in that: Step 2 specifically involves: There are seven types of dielectric pillars for superlenses: square pillars, air, square rings, square ring pillars, cross-shaped pillars, square ring crosses, and square cross rings. All pillars have the same height H and period P. The structural parameters of the square pillars include the side length W1. The air structure is the case where the side length W1 = 0. The structural parameters of the square rings include the outer ring side length W... 21 And the inner ring side length W 22 The structural parameters of the square ring cylinder include the side length W of the outer ring of the square ring. 31 The side length W of the inner ring 32 The side length W of the square prism 33 The structural parameters of the cross-shaped column include the long side L4 and the short side W4, while the structural parameters of the square ring cross-shaped column include the side length W of the outer ring of the square ring. 51 The side length W of the inner ring 52 The short side W of the cross-shaped prism 53 The long side L5 of the cross-shaped prism is equal to W. 52 The structural parameters of the square ring include the side length W of the outer ring. 61 The inner cross short side W 62 With the long side L6, all the medium pillars of the superlens satisfy the principle of central symmetry, thus achieving polarization insensitivity.

3. The method according to claim 1, characterized in that: The phase and dispersion modulation provided by each unit structure are calculated in FDTD using the finite-difference time-domain method. By determining the period P and height H of each unit, the phase and dispersion modulation of each unit is obtained by changing the structural parameters of each unit, thereby completing the construction of a unit library. Through these seven units, the dispersive phase of the constructed unit library covers 6π to 23π.

4. The method according to claim 3, characterized in that: Considering the cell transmittance, we selected a cell period of P = 1.7 μm and a height of H = 6.5 μm. Then, we scanned different structures to obtain a cell library. We can see that the ratio of height to period for all cells is 3.83:

1.

5. A design system for a large-size and large numerical aperture discrete achromatic superlens that is insensitive to mid-infrared polarization, the system operating based on the method of claim 1, characterized in that: The system includes: The calculation module obtains the phase delay and dispersion required by the achromatic lens at different positions of the lens based on the diameter, numerical aperture and operating frequency band of the superlens. A building module that constructs a corresponding polarization-insensitive cell library; The design module selects the required units from the unit library based on the phase and group delay required at each position, and arranges these units in a square with the center of the superlens as the origin and a period of P along the x and y directions, thereby obtaining the designed superlens.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the method as described in any one of claims 1-4.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the method according to any one of claims 1-4.

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