Design method of large-size and large-numerical-aperture discrete achromatic superlens insensitive to middle-infrared band polarization

Abstract

The invention relates to a design method of a large-size and large-numerical-aperture discrete achromatic superlens insensitive to middle-infrared band polarization. The invention relates to the technical field of micro-nano photon metasurfaces. Phase delay and dispersion required by an achromatic lens at different positions of the lens are obtained according to the diameter, the numerical aperture and the working frequency band of the metasurface; constructing a corresponding unit library insensitive to polarization; and screening required units in the unit library according to the phase and group delay required by each position, and arranging the units in a square manner by taking the center of the super lens as an original point and taking a period P as an interval in x and y directions, so as to obtain the designed super lens. The achromatic superlens provided by the invention has the characteristic of polarization insensitivity, and has a wider application scene compared with a PB phase type lens only sensitive to circular polarization.

Description

Technical Field

[0001] The invention relates to the technical field of micro-nano photonic supersurfaces, and is a method for designing a large-size and large-numerical-aperture discrete achromatic superlens that is polarization-insensitive in the mid-infrared band. Background Art

[0002] Infrared lenses can provide imaging information in conditions of poor visibility such as darkness. The range of the infrared spectrum is generally defined as 2.5μm to 25μm, of which 3μm to 8μm is the mid-infrared band. In the mid-infrared band, 3μm to 5μm is an atmospheric window, and in this band, the infrared loss is relatively small. Mid-infrared lenses have important applications in industrial manufacturing, environmental monitoring, gas measurement, target identification, etc. The traditional infrared achromatic lens is a lens group composed of several lenses. It is large in size, heavy, and has high power consumption and is not easy to integrate. The emergence of superlens can solve the above problems. Superlens can achieve focusing function by manipulating the wavefront information of electromagnetic waves at subwavelength size.

[0003] In addition, by regulating the dispersion of the unit on a subwavelength scale, the achromatic function of the metalens can be achieved, but the size of the metalens achromatism is limited by the achromatic bandwidth and numerical aperture. Large apertures are necessary for optical systems that collect weak or rapidly changing signals. For example, in astronomical imaging, remote airborne monitoring, and in high-power laser applications, large-sized meta-lenses are required to reduce the demand for incident light source density. In optical systems, especially those that need to collect weak or rapidly changing signals, the higher the incident light source density, the more light energy enters the system. This generally helps to improve the brightness and signal-to-noise ratio of the image. However, if the aperture of the lens or objective is small, a higher incident light source density may be required to obtain sufficient signal, which will place higher requirements on the light source and may introduce more noise or cause system overload.

[0004] The discrete achromatism theory can relax the restrictions on the size, numerical aperture and achromatism bandwidth of the achromatism metalens, but the existing metalens constructed by the discrete achromatism theory is polarization sensitive and has a small scope of application, while the present invention is polarization insensitive and has a wide scope of application. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a design method for a large-size and large-numerical-aperture discrete achromatic superlens that is polarization-insensitive in the mid-infrared band. The large-size and large-numerical-aperture discrete achromatic superlens that is polarization-insensitive in the mid-infrared band of the present invention has the characteristics of large size, large numerical aperture, and polarization insensitivity, and can eliminate chromatic aberration within the working bandwidth to improve imaging quality.

[0006] The present invention provides the following technical solutions:

[0007] A method for designing a large-size and large-numerical-aperture discrete achromatic metalens in the mid-infrared band, the method comprising the following steps:

[0008] Step 1: Obtain an achromatic lens according to the diameter, numerical aperture and working frequency band of the metalens to obtain the required phase delay and dispersion at different positions of the lens;

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

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

[0011] Preferably, the step 1 is specifically:

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

[0013]

[0014] in, is the distribution function, (x, y) represents the position of the unit structure at any point on the metasurface lens; the achromatic target is set to be the angular frequency ω c is the center and the bandwidth is Δω all The angular frequency range is In ω c The surrounding expands into a Taylor series:

[0015]

[0016] where φ(x, y, ω c ) represents the center frequency ω c The phase distribution under represents the group delay phase distribution, where is the group delay distribution, O(ω 2 ) is the high-order modulus, taking the high-order modulus as 0, the group delay is a constant that has nothing to do with ω;

[0017] The first is to introduce phase compensation to ensure that the frequency at any position of the metalens is ω c The electromagnetic waves reach the focus at the same time;

[0018] The second term is to introduce dispersion compensation to ensure that the bandwidth Δω all Electromagnetic waves within the range can reach the focus at the same time.

[0019] Preferably, the step 1 further comprises:

[0020] Substituting the hyperbolic phase distribution that the lens should satisfy, we can obtain the conditions that must be met to realize the achromatic meta-lens:

[0021] 1) Angular frequency ω c Phase distribution

[0022]

[0023] 2) Group delay distribution

[0024]

[0025] By setting the frequency to meet the equal frequency interval condition Δω, equal interval can be achieved. The extension of the method uses finite phase delay to fit the phase delay dispersion requirements of arbitrary size.

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

[0027]

[0028] In quasi-achromatism, a group delay ΔGD is used for modulus. The dispersion required by the superlens is in the range of 0 to ΔGD. The size of the dispersion is independent of the radius numerical aperture, thus realizing the construction of a large-size achromatic superlens:

[0029] For ΔGD, we have:

[0030]

[0031] The dispersion of the metalens is:

[0032] GD1=mod(GD,ΔGD)+m*ΔGD

[0033] For the frequency ω c +NΔω, the phase required for the quasi-achromatic metalens is:

[0034]

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

[0036]

[0037] In Δω all Within the range, at different positions of the superlens, light of different frequencies satisfies the above phase distribution, in Δω all Discrete achromatization is achieved within the range.

[0038] Preferably, the step 2 is specifically:

[0039] There are seven types of superlens dielectric columns: square column, air, square ring, square ring column, cross, square ring cross, square cross ring. The height H and period P of all dielectric columns are the same. The structural parameters of the square column include the side length W1. The air structure is the case where the side length W1=0 of the square. The structural parameters of the square ring include the side length W of the outer ring. 21 and the inner ring side length W 22 The structural parameters of the square ring column include the side length W of the outer ring of the square ring 31 , the side length of the inner ring is W 32 , the side length of the square column is W 33 The structural parameters of the cross column include the long side L4 and the short side W4, and the structural parameters of the square ring cross column include the side length W of the outer ring of the square ring 51 , the side length of the inner ring is W 52 , the short side W of the cross column 53 , the long side of the cross column L5 = W 52 The structural parameters of the square ring include the side length W of the outer ring of the square ring 61 , inner cross short side W 62 , long side L6, all superlens dielectric columns satisfy the principle of central symmetry, thereby achieving polarization insensitivity.

[0040] Preferably, the phase control and dispersion control that each unit structure can provide are calculated in FDTD by the finite difference time domain method. After determining the period P and height H of each unit, the control of phase and dispersion by 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~23π.

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

[0042] A mid-infrared band polarization-insensitive large-size and large-numerical-aperture discrete achromatic metalens design system, the system comprising:

[0043] A calculation module, wherein the calculation module obtains the phase delay and dispersion required at different positions of the lens by obtaining the achromatic lens according to the diameter, numerical aperture and working frequency band of the metalens;

[0044] Building blocks that construct a corresponding polarization-insensitive cell library;

[0045] The design module selects the required units in the unit library according to the phase and group delay required at each position, and arranges these units in a square with a period P along the x and y directions with the center of the super lens as the origin, so as to obtain the designed super lens.

[0046] A computer-readable storage medium stores a computer program, which is executed by a processor to implement a method for designing a large-size and large-numerical-aperture discrete achromatic metalens in the mid-infrared band that is polarization-insensitive.

[0047] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a method for designing a large-size and large-numerical-aperture discrete achromatic metalens in the mid-infrared band is implemented.

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

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

[0050] Compared with the prior art, the present invention designs a large-size, large numerical aperture discrete achromatic metalens that is polarization-insensitive in the mid-infrared band. The diameter of the lens is 5 mm, the numerical aperture is 0.42, and the achromatic bandwidth is 3 μm to 5 μm. It has the characteristics of large size, large numerical aperture, and wide-band achromatism. In addition, the achromatic metalens proposed in the present invention has the characteristic of being polarization-insensitive, and compared with the PB phase-type lens that is only sensitive to circular polarization, it has a wider range of application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0052] Figure 1 Shows a schematic diagram of a cell library constructed for the present invention;

[0053] Figure 2 Showing a schematic diagram of a model diagram constructed for the present invention;

[0054] Figure 3 The distribution diagram of the lens with a diameter of 3 mm and a numerical aperture of 0.42 constructed according to the present invention at a focal length of 3 μm-5 μm is shown;

[0055] Figure 4 Shown is the XZ plane energy distribution of the present invention and the XY plane energy distribution diagram at the focus;

[0056] Figure 5 The present invention shows the MTF of the continuous achromatic lens theory, the MTF of the discrete achromatic lens theory, and the MTF of the discrete achromatic lens simulation. DETAILED DESCRIPTION

[0057] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0059] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0060] In addition, 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 is described in detail below in conjunction with specific embodiments. Specific embodiment one:

[0063] In view of the shortcomings of the prior art, the present invention provides a design method for a large-size and large-numerical-aperture discrete achromatic superlens that is polarization-insensitive in the mid-infrared band. The large-size and large-numerical-aperture discrete achromatic superlens that is polarization-insensitive in the mid-infrared band of the present invention has the characteristics of large size, large numerical aperture, and polarization insensitivity, and can eliminate chromatic aberration within the working bandwidth to improve imaging quality.

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

[0065] A method for designing a large-size and large-numerical-aperture discrete achromatic metalens in the mid-infrared band, the method comprising the following steps:

[0066] Step 1: Obtain an achromatic lens according to the diameter, numerical aperture and working frequency band of the metalens to obtain the required phase delay and dispersion at different positions of the lens;

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

[0068] Step 3: Select the required units in the unit library according to the phase and group delay required at each position, and arrange these units in a square with a period P along the x and y directions with the center of the super lens as the origin, so as to obtain the designed super lens. Specific embodiment 2:

[0070] The difference between the second embodiment of the present application and the first embodiment is that:

[0071] The step 1 is specifically as follows:

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

[0073]

[0074] in, is the distribution function, (x, y) represents the position of the unit structure at any point on the metasurface lens; the achromatic target is set to be the angular frequency ω c is the center and the bandwidth is Δω all The angular frequency range is In ω c The surrounding expands into a Taylor series:

[0075]

[0076] where φ(x, y, ω c ) represents the center frequency ω c The phase distribution under represents the group delay phase distribution, where is the group delay distribution, O(ω 2 ) is the high-order modulus, taking the high-order modulus as 0, the group delay is a constant that has nothing to do with ω;

[0077] The first is to introduce phase compensation to ensure that the frequency at any position of the metalens is ω c The electromagnetic waves reach the focus at the same time;

[0078] The second term is to introduce dispersion compensation to ensure that the bandwidth Δω all Electromagnetic waves within the range can reach the focus at the same time. Specific embodiment three:

[0080] The difference between the third embodiment of the present application and the second embodiment is that:

[0081] The step 1 also includes:

[0082] Substituting the hyperbolic phase distribution that the lens should satisfy, we can obtain the conditions that must be met to realize the achromatic meta-lens:

[0083] 1) Angular frequency ω c Phase distribution

[0084]

[0085] 2) Group delay distribution

[0086]

[0087] By setting the frequency to meet the equal frequency interval condition Δω, equal interval can be achieved. The extension of the method uses finite phase delay to fit the phase delay dispersion requirements of arbitrary size. Specific embodiment four:

[0089] The difference between the fourth embodiment of the present application and the third embodiment is that:

[0090] The group delay distribution GD is set as:

[0091]

[0092] In quasi-achromatism, a group delay ΔGD is used for modulus. The dispersion required by the superlens is in the range of 0 to ΔGD. The size of the dispersion is independent of the radius numerical aperture, thus realizing the construction of a large-size achromatic superlens:

[0093] For ΔGD, we have:

[0094]

[0095] The dispersion of the metalens is:

[0096] GD1=mod(GD,ΔGD)+m*ΔGD

[0097] For the frequency ω c+NΔω, the phase required for the quasi-achromatic metalens is:

[0098]

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

[0100]

[0101] In Δω all Within the range, at different positions of the superlens, light of different frequencies satisfies the above phase distribution, in Δω all Discrete achromatization is achieved within the range. Specific embodiment five:

[0103] The difference between the fifth embodiment of the present invention and the fourth embodiment is that:

[0104] The step 2 is specifically as follows:

[0105] There are seven types of superlens dielectric columns: square column, air, square ring, square ring column, cross, square ring cross, square cross ring. The height H and period P of all dielectric columns are the same. The structural parameters of the square column include the side length W1. The air structure is the case where the side length W1=0 of the square. The structural parameters of the square ring include the side length W of the outer ring. 21 and the inner ring side length W 22 The structural parameters of the square ring column include the side length W of the outer ring of the square ring 31 , the side length of the inner ring is W 32 , the side length of the square column is W 33 The structural parameters of the cross column include the long side L4 and the short side W4, and the structural parameters of the square ring cross column include the side length W of the outer ring of the square ring 51 , the side length of the inner ring is W 52 , the short side W of the cross column 53 , the long side of the cross column L5 = W 52 The structural parameters of the square ring include the side length W of the outer ring of the square ring 61 , inner cross short side W 62 , long side L6, all superlens dielectric columns satisfy the principle of central symmetry, thereby achieving polarization insensitivity. Specific embodiment six:

[0107] The difference between the sixth embodiment of the present invention and the fifth embodiment is that:

[0108] The phase control and dispersion control that each unit structure can provide are calculated in FDTD through the finite difference time domain method. After determining the period P and height H of each unit, the phase and dispersion control 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~23π. Specific embodiment seven:

[0110] The difference between the seventh embodiment of the present invention and the sixth embodiment is that:

[0111] Considering the unit transmittance, the unit period P = 1.7 μm and the height H = 6.5 μm are selected, and then different structures are scanned to obtain the unit cell library. It can be seen that the ratio of the height and period of all units is 3.83:1. Specific embodiment eight:

[0113] The difference between the eighth embodiment of the present invention and the seventh embodiment is that:

[0114] The present invention provides a mid-infrared band polarization-insensitive large-size and large numerical aperture discrete achromatic metalens design system, the system comprising:

[0115] A calculation module, wherein the calculation module obtains the phase delay and dispersion required at different positions of the lens by obtaining the achromatic lens according to the diameter, numerical aperture and working frequency band of the metalens;

[0116] Building blocks that construct a corresponding polarization-insensitive cell library;

[0117] The design module selects the required units in the unit library according to the phase and group delay required at each position, and arranges these units in a square with a period P along the x and y directions with the center of the super lens as the origin, so as to obtain the designed super lens. Specific embodiment nine:

[0119] The difference between the ninth embodiment of the present invention and the eighth embodiment is that:

[0120] The present invention provides a computer-readable storage medium on which a computer program is stored. The program is executed by a processor to implement a method for designing a large-size and large-numerical-aperture discrete achromatic metalens that is polarization-insensitive in the mid-infrared band. Specific embodiment ten:

[0122] The difference between the tenth embodiment of the present invention and the ninth embodiment is that:

[0123] The present invention provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, a method for designing a large-size and large-numerical-aperture discrete achromatic metalens that is polarization-insensitive in the mid-infrared band is implemented. Specific embodiment eleven:

[0125] The difference between the eleventh embodiment of the present invention and the tenth embodiment is that:

[0126] The technical solution of the present invention to realize the above lens is: the large-size, large numerical aperture discrete achromatic superlens in the mid-infrared band polarization insensitive includes two parts: a dielectric substrate and a dielectric column. The dielectric substrate plays a supporting role, and the dielectric column plays a role in modulating the wavefront of the electromagnetic wave. Since the material silicon has a good transmittance in the mid-infrared band, the dielectric substrate and the silicon column are both made of high-resistance silicon.

[0127] The diameter of the constructed achromatic superlens is 5mm, the working frequency range is 3μm-5μm, and the numerical aperture is 0.42. The maximum dispersion error of the focus that can be achieved by the lens within the working frequency range is 8.4%. The design method of the achromatic superlens is:

[0128] 1) Obtain the achromatic lens according to the diameter, numerical aperture and working frequency band of the metalens to obtain the phase delay and dispersion required at different positions of the lens

[0129] Assume that a plane wave with a wavelength of λ is incident on the metasurface lens and perfectly converges to the focus A of the metasurface lens. The focal length of the metasurface lens is designed to be f. Obviously, in order for the plane wave to be focused at the focus after passing through the metasurface unit structure, it means that the phase of the light transmitted through the metasurface lens unit structure at the focus point A is the same. That is, the metasurface phase distribution function should satisfy the formula:

[0130]

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

[0132] The above phase distribution is only a condition that needs to be met to construct a monochromatic metalens. Its focal length will change with the change of frequency, that is, the focal length is a function of the angular frequency ω. As mentioned above, the phase distribution of an ideal monochromatic focusing metalens is a hyperbolic distribution. If you want the focal length to be within a bandwidth Δω all If the angular frequency range of the achromatic aberration is to be kept constant, then the achromatic aberration work needs to be completed. Assuming that the goal of achromatic aberration is to keep the angular frequency ω c is the center and the bandwidth is Δω all The angular frequency range can be In ωc It expands into a Taylor series nearby.

[0133]

[0134] It can be seen that the expanded Taylor series is divided into three parts, where φ(x, y, ω c ) represents the center frequency ω c The phase distribution under represents the group delay phase distribution, where is the group delay distribution, O(ω 2 ) is the high-order modulus. Taking the high-order modulus as 0, the group delay is a constant that is independent of ω. It can be seen that the first term is to introduce phase compensation to ensure that the electromagnetic waves with a frequency of ωc at any position of the superlens reach the focus at the same time. The second term is to introduce dispersion compensation to ensure that the bandwidth Δω all Electromagnetic waves within the range can reach the focus at the same time.

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

[0136] 1) Phase distribution of angular frequency ωc

[0137]

[0138] 2) Group delay distribution

[0139]

[0140] The dispersion compensation requirements of continuous achromatic metalens will increase with the increase of aperture and NA. In traditional broadband achromatic metalenses, large dispersion requirements inevitably mean high thickness requirements for units. And units with too high aspect ratios are difficult to process. Quasi-achromatic metalenses based on time degrees of freedom can relax the restrictions on aperture and NA.

[0141] The phase delay based on the dispersion control characteristics can be extended according to the phase characteristics, thereby reducing the requirements for the large dispersion control capability of the unit. At the equally spaced frequency Δω, the original phase delay curve can be extended into multiple discrete phase delays with a difference of Therefore, as long as the design frequency satisfies the equal frequency interval condition Δω, equal interval can be achieved. The continuation of the phase delay can be used to fit the phase delay dispersion requirements of any size.

[0142] The group delay distribution GD is:

[0143]

[0144] In the quasi-achromatic metalens, ideal achromatism is performed at N points, and the remaining points are approximately achromatism. In the quasi-achromatic, a group delay ΔGD is used to take the remainder, so that the dispersion required by the metalens is within the range of 0 to ΔGD, and the size of the dispersion is independent of the radius numerical aperture, so that the construction of a large-scale achromatic metalens can be realized.

[0145] For ΔGD, we have:

[0146]

[0147] Therefore, the dispersion of the metalens is:

[0148] GD1=mod(GD,ΔGD)+m*ΔGD

[0149] For the frequency ω c +NΔω, the phase required for the quasi-achromatic metalens 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 at the same time. The quasi-achromatic superlens uses the fact that light of the same frequency can reach the focal plane at the same time, while light of different frequencies does not reach the focal plane at the same time. 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 above phase distribution, and can be in Δω all Discrete achromatization is achieved within the range.

[0154] 2) Constructing a corresponding polarization-insensitive cell library

[0155] After completing the above work, the unit library was constructed next. There are seven types of superlens dielectric columns: square column, air, square ring, square ring column, cross, square ring cross, and square cross ring. The height H and period P of all dielectric columns are the same. The structural parameters of the square column include the side length W1. The air structure is the case where the side length W1=0 of the square. 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 column include the side length W of the outer ring of the square ring 31 , the side length of the inner ring is W 32 , the side length of the square column is W 33The structural parameters of the cross column include the long side L4 and the short side W4. The structural parameters of the square ring cross column include the side length W of the outer ring of the square ring 51 , the side length of the inner ring is W 52 , the short side W of the cross column 53 , the long side of the cross column L5 = W 52 The structural parameters of the square ring include the side length W of the outer ring of the square ring 61 , inner cross short side W 62 , long side L6. All superlens dielectric columns satisfy the principle of central symmetry, thus achieving polarization insensitivity. The phase control and dispersion control that each unit structure can provide can be calculated in FDTD by the finite difference time domain method. After determining the period P and height H of each unit, by changing the structural parameters of each unit, the control of phase and dispersion by each unit can be obtained, thereby completing the construction of a unit library. Through these seven units, the dispersion phase of the constructed unit library can cover 6π~23π.

[0156] Considering the unit transmittance, the unit period P = 1.7 μm and the height H = 6.5 μm are selected, and then different structures are scanned to obtain the unit cell library. It can be seen that the ratio of the height and period of all units is 3.83:1.

[0157] 3) Select the required units in the unit library according to the phase and group delay required at each position, and arrange these units in a square with a period P along the x and y directions with the center of the super lens as the origin, so as to obtain the designed super lens.

[0158] Figure 1 The cell library constructed is shown in the figure. There are seven types of cells in total. The constructed cell library is also given. The dispersion phase can cover 6π~23π in the range of 3μm-5μm, which meets the design requirements.

[0159] Figure 2 The diagram of the constructed model, where a is a lens with a diameter of 3 mm, b is the 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 distribution of focal lengths of a lens with a diameter of 3mm and a numerical aperture of 0.42 at 3μm-5μm. The horizontal line is the focal length of the continuous achromatic lens, and its value is 3.241mm. The red dotted line is the focal length of the discrete achromatic lens, and its maximum error with the continuous achromatic lens is 8.4%.

[0161] Figure 4 is the energy distribution in the XZ plane and the energy distribution in the XY plane at the focus.

[0162] Figure 5 It 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 the existing inventions, the advantages of the present invention are as follows: the present invention proposes a large-size, large numerical aperture discrete achromatic metalens that is polarization-insensitive in the mid-infrared band. The diameter of the lens is 5 mm, the numerical aperture is 0.42, and the achromatic bandwidth is 3 μm to 5 μm. It has the characteristics of large size, large numerical aperture, and wide-band achromatism. In addition, the achromatic metalens proposed by the present invention has the characteristic of being polarization-insensitive, and compared with the PB phase lens that is only sensitive to circular polarization, it has a wider range of application scenarios. Specific embodiment twelve:

[0165] The difference between the twelfth embodiment of the present invention and the eleventh embodiment is that:

[0166] The present invention designs a large-size, large numerical aperture discrete achromatic metalens that is polarization-insensitive in the mid-infrared band. To realize the design of the lens, the following steps are involved:

[0167] Firstly, according to the designed diameter D=5mm, numerical aperture NA=0.42 and working frequency band 3μm~5μm of the metalens, the phase compensation and dispersion compensation required to realize discrete achromatism at any position of the metalens are calculated.

[0168]

[0169] It is the phase distribution of any frequency in the working frequency band of 3μm to 5μm. At the center frequency ω c The amount of phase shift required. GD is the group delay required for the metalens to achieve achromatism, c is the speed of light, f is the focal length, and (x, y) is the coordinates of a point on the metalens surface. Δω=2*π*11.4285*10 12 rad / s, In addition, mod is a modulo function, and mod(GD, ΔGD) is the remainder after GD is divided by ΔGD.

[0170] Secondly, a cell library is constructed that can satisfy the phase required for dispersion phase and center frequency. As shown in the cell dispersion distribution, the dispersion phase of the constructed cell library ranges from 6π to 23π. Figure 1 shown.

[0171] Then, the units are screened, and an error function Error(x, y; n) is introduced when screening the units.

[0172]

[0173] (x, y) are the coordinates of a point on the surface of the metalens. Under ideal conditions, the frequency is ω k When the radius is r, the amplitude and phase distribution is: For all cells in the cell library, the frequency is ω k The amplitude and phase distribution at the time. N is the total number of frequency points selected in the frequency band, and k is the current frequency number. According to the strategy of minimum error function above, the unit is selected. For the sake of simplicity, N=15 frequency points within 60THz-100THz are used for calculation, and the result with the minimum error is taken.

[0174] Then, the screened results are simulated to obtain the achromatic results as shown in Figure 3 , Figure 4 In addition, the MTF that represents the imaging ability of the lens is obtained, as shown in Figure 5 shown.

[0175] In the description of this specification, the description of reference terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples without contradiction. In addition, the terms "first" and "second" are used only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" can explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined. Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present invention belong.

[0176] The above is only a preferred implementation of a method for designing a large-size and large-numerical-aperture discrete achromatic metalens that is polarization-insensitive in the mid-infrared band. The protection scope of a method for designing a large-size and large-numerical-aperture discrete achromatic metalens that is polarization-insensitive in the mid-infrared band is not limited to the above embodiments. All technical solutions under this idea belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, several improvements and changes without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A method for designing a large-size and large-numerical-aperture discrete achromatic metalens in the mid-infrared band, characterized by: The method comprises the following steps: Step 1: Obtain an achromatic lens according to the diameter, numerical aperture and working frequency band of the metalens to obtain the required phase delay and dispersion at different positions of the lens; Step 2: construct the corresponding polarization-insensitive cell library; Step 3: Select the required units in the unit library according to the phase and group delay required at each position, and arrange these units in a square with a period P along the x and y directions with the center of the super lens as the origin, so as to obtain the designed super lens.

2. The method according to claim 1, characterized in that: The step 1 is specifically as follows: Assume that a plane wave with a wavelength of λ is incident on the metasurface lens and converges to the focus A of the metasurface lens. The focal length of the metasurface lens is designed to be f, and the metasurface phase distribution function should satisfy the formula: in, is the distribution function, (x, y) represents the position of the unit structure at any point on the metasurface lens; The goal of setting achromaticity is to use an angular frequency ω c is the center and the bandwidth is Δω all The angular frequency range is In ω c The surrounding expands into a Taylor series: where φ(x, y, ω c ) represents the center frequency ω c The phase distribution under represents the group delay phase distribution, where is the group delay distribution, O(ω 2 ) is the high-order modulus, taking the high-order modulus as 0, the group delay is a constant that has nothing to do with ω; The first is to introduce phase compensation to ensure that the frequency at any position of the metalens is ω c The electromagnetic waves reach the focus at the same time; The second term is to introduce dispersion compensation to ensure that the bandwidth Δω all Electromagnetic waves within the range can reach the focus at the same time.

3. The method according to claim 2, characterized in that: The step 1 also includes: Substituting the hyperbolic phase distribution that the lens should satisfy, we can obtain the conditions that must be met to realize the achromatic meta-lens: 1) Angular frequency ω c Phase distribution 2) Group delay distribution By setting the frequency to meet the equal frequency interval condition Δω, equal interval can be achieved. The extension of the method uses finite phase delay to fit the phase delay dispersion requirements of arbitrary size.

4. The method according to claim 1, characterized in that: The group delay distribution GD is set as: In quasi-achromatism, a group delay ΔGD is used for modulus. The dispersion required by the superlens is in the range of 0 to ΔGD. The size of the dispersion is independent of the radius numerical aperture, thus realizing the construction of a large-size achromatic superlens: For ΔGD, we have: The dispersion of the metalens is: GD1=mod(GD,ΔGD)+m*ΔGD For the frequency ω c +NΔω, the phase required for the quasi-achromatic metalens is: In the above formula, m*2π is ignored, and light of different frequencies does not reach the focal plane at the same time. The above formula is written as: In Δω all Within the range, at different positions of the superlens, light of different frequencies satisfies the above phase distribution, in Δω all Discrete achromatization is achieved within the range.

5. The method according to claim 4, characterized in that: The step 2 is specifically as follows: There are seven types of superlens dielectric columns: square column, air, square ring, square ring column, cross, square ring cross, square cross ring. The height H and period P of all dielectric columns are the same. The structural parameters of the square column include the side length W1. The air structure is the case where the side length W1=0 of the square. The structural parameters of the square ring include the side length W of the outer ring. 21 and the inner ring side length W 22 The structural parameters of the square ring column include the side length W of the outer ring of the square ring 31 , the side length of the inner ring is W 32 , the side length of the square column is W 33 The structural parameters of the cross column include the long side L4 and the short side W4, and the structural parameters of the square ring cross column include the side length W of the outer ring of the square ring 51 , the side length of the inner ring is W 52 , the short side W of the cross column 53 , the long side of the cross column L5 = W 52 The structural parameters of the square ring include the side length W of the outer ring of the square ring 61 , inner cross short side W 62 , long side L6, all superlens dielectric columns satisfy the principle of central symmetry, thereby achieving polarization insensitivity.

6. The method according to claim 1, characterized in that: The phase control and dispersion control that each unit structure can provide are calculated in FDTD through the finite difference time domain method. After determining the period P and height H of each unit, the phase and dispersion control 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~23π.

7. The method according to claim 6, characterized in that: Considering the unit transmittance, the unit period P = 1.7 μm and the height H = 6.5 μm are selected, and then different structures are scanned to obtain the unit cell library. It can be seen that the ratio of the height and period of all units is 3.83:

1.

8. A mid-infrared polarization-insensitive large-size and large-numerical-aperture discrete achromatic metalens design system, characterized by: The system comprises: A calculation module, wherein the calculation module obtains the phase delay and dispersion required at different positions of the lens by obtaining the achromatic lens according to the diameter, numerical aperture and working frequency band of the metalens; Building blocks that construct a corresponding polarization-insensitive cell library; The design module selects the required units in the unit library according to the phase and group delay required at each position, and arranges these units in a square with a period P along the x and y directions with the center of the super lens as the origin, so as to obtain the designed super lens.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: The program is executed by a processor to implement the method according to claims 1-7.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the method of claims 1-7 is implemented.

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