A terahertz wide-angle broadband meta-lens and its preparation method

Abstract

The present invention discloses a terahertz wide-angle broadband meta-lens and a preparation method thereof. The meta-lens comprises a substrate and a meta-unit on the substrate, wherein a plurality of meta-units are evenly arranged on the substrate; the meta-units comprise five types: cylindrical structure, circular ring structure, square column structure, cross structure, and square ring structure; by changing the proportions of the five types of meta-units, the phase, dispersion phase, and transmittance of the meta-unit at the center frequency are obtained. The design method is as follows: first, a "phase-dispersion" unit library is constructed; then, based on the corrected quadratic aspheric phase profile formula, group delay formula, and unit simulated transmittance, appropriate units are selected to arrange the meta-lens. The preparation method is as follows: first, silicon wafer-glass anodic bonding is performed, followed by exposure and development, and finally deep silicon etching is performed. The meta-lens prepared by the present invention has the advantages of planarization, polarization insensitivity, the ability to achieve convergence within a large field of view and broadband, and stable focal length.

Description

Technical Field

[0001] The present invention relates to the field of terahertz imaging technology, and in particular to a terahertz wide-angle, broadband meta-lens and a preparation method thereof. Background Art

[0002] Terahertz (THz) waves are electromagnetic waves with a frequency range of 0.1-10 THz, located between microwaves and far infrared in the electromagnetic spectrum. Their wide spectrum, strong penetration, security, and "fingerprint" characteristics give them broad application prospects in communications, imaging, sensing, and other fields. With the development of THz technology, discrete devices commonly used in THz wave applications, such as beam splitters, lenses, attenuators, and reflectors, have played a vital role. Traditional THz discrete devices are mostly composed of materials such as high-density polyethylene, silicon, and quartz, which often require a thick thickness to complete the accumulation of propagation phase, seriously hindering the miniaturization of THz devices.

[0003] A metasurface is a two-dimensional array composed of periodically arranged subwavelength units. It not only has the function of locally controlling the phase, amplitude, polarization and other characteristics of electromagnetic waves, but also has the characteristics of thin thickness and easy processing, which helps to achieve the miniaturization of terahertz devices.

[0004] Metalenses are flat lenses based on metasurfaces that can manipulate electromagnetic wavefronts within the subwavelength range. This overcomes the drawback of traditional lenses that rely on curved surfaces to reshape the wavefront and significantly reduces the thickness of terahertz lenses. In 2015, Zhang Weili et al. designed a terahertz superlens using a C-type split ring resonator unit. When x-polarized terahertz waves are incident vertically, the superlens exhibits broadband focusing characteristics from 0.5 to 0.9 THz, but the focal length varies with frequency. In 2017, Yu Xiaomei et al. designed a dielectric superlens composed of subwavelength cross-shaped silicon pillars and experimentally demonstrated that the superlens can focus linearly polarized terahertz waves with a wavelength of 630 μm. These terahertz superlenses generally suffer from high loss and low efficiency. To improve the focusing efficiency of terahertz superlenses, researchers have proposed all-dielectric superlenses and multilayer superlenses composed of high-refractive-index, low-loss materials. In 2018, Zhang Weili et al. designed a polarization-insensitive, transmissive all-dielectric terahertz superlens; in 2017, Chen HouTong et al. designed a transmissive multilayer terahertz superlens with an operating frequency of 0.4 THz.

[0005] Like traditional lenses, the imaging quality of terahertz metalenses is also affected by aberrations. To eliminate these aberrations—monochromatic and chromatic—researchers have proposed terahertz wide-angle metalenses and terahertz achromatic metalenses. In 2018, Gang Chen et al. designed a metalens operating at 118.8 μm with a numerical aperture of 0.707, capable of imaging within a range of -48° to 48°. In 2019, Songlin Zhuang et al. used C-type silicon pillar units to design and verify a polarization-sensitive achromatic metalenses with a bandwidth of 0.3-0.8 THz and a numerical aperture of 0.385. In 2020, Gang Chen et al. proposed a polarization-sensitive achromatic metalenses operating in the 2.29-2.7 THz band with a peak efficiency of 32.6%. However, research in the terahertz band that combines broadband achromaticity with large-field-of-view imaging is rare. Summary of the Invention

[0006] The purpose of the present invention is to provide a meta-lens with a small aperture, being polarization-insensitive, being able to achieve convergence within a large field of view and a broadband, and having a stable focal length, and a preparation method thereof.

[0007] The technical solution for achieving the purpose of the present invention is: a terahertz wide-angle broadband meta-lens, comprising a substrate and a meta-unit on the substrate;

[0008] A plurality of meta-structure units are evenly arranged on the substrate; the meta-structure units include five types: cylindrical structure, circular ring structure, square column structure, cross structure, and square ring structure; by changing the cross-sectional dimensions of the five types of meta-structure units, the phase, dispersion phase, and transmittance of the meta-structure units at the center frequency are obtained.

[0009] Furthermore, the substrate is made of silicon dioxide, the meta-unit is made of silicon, and the size and period of the meta-unit are smaller than the maximum operating wavelength;

[0010] The superstructure unit is any one of a cylindrical structure, a circular ring structure, a square column structure, a cross structure, and a square ring structure;

[0011] The meta-units are arranged in a C4 symmetrical structure to ensure that the meta-lens is insensitive to the polarization of the incident light.

[0012] The period of the meta-unit is less than the Nyquist sampling rate λ / 2NA, where λ is the operating wavelength and NA is the numerical aperture of the meta-lens;

[0013] The metastructure unit is a truncated waveguide, and the phase changes linearly with the frequency within the working bandwidth. The phase and transmittance are independent of the incident angle within the working field. where n eff (ω) is the effective refractive index, h is the height of the metacell, c is the speed of light in vacuum, and ω is the frequency.

[0014] Furthermore, the phase distribution of the metalens is:

[0015]

[0016] Where F = f*ω n , for an achromatic lens, n = 0; ω is the angular frequency, c is the speed of light, f is the preset focal length of the metalens, and r is the distance from any metaunit to the center of the metalens;

[0017] At ω=ω p Taylor expansion at:

[0018]

[0019] Among them, ω p is the operating frequency, F is the focal length related to the frequency, is the phase distribution of the metalens at the center frequency, are the group delay and group delay dispersion of the metalens respectively;

[0020] For an achromatic lens, F = f is a constant, and the higher-order terms of the phase distribution are ignored. Therefore, the phase distribution is a linear function of ω:

[0021]

[0022] In order to avoid the group delay at the center of the lens r = 0 is 0, the phase should be added with a linear correction δ*(ω-ω min ) / Δω, where δ is the maximum phase compensation, Δω=ω max -ω min is the working bandwidth, ω max 、ω min are the maximum and minimum operating frequencies respectively;

[0023] Therefore, the corrected phase distribution and dispersion phase distribution are:

[0024]

[0025]

[0026] In order to realize a wide-angle broadband achromatic meta-lens, the meta-unit at position r should simultaneously satisfy the corrected phase Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ).

[0027] A method for preparing a terahertz wide-angle broadband metalens comprises the following steps:

[0028] Step 1: By changing the duty cycle of five metacells, the phase, dispersion phase, and transmittance of the metacells at the center frequency are obtained to construct a phase-dispersion cell library;

[0029] Step 2: Determine the numerical aperture of the quadratic aspheric meta-lens and select the element with the corrected phase Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ) are arranged with matching units, and the transmittance of the selected units is greater than 70%;

[0030] Step 3: Calculate the focusing efficiency of the metalens within the working bandwidth and working field of view;

[0031] Step 4: Based on the metalens constructed in steps 1 to 3, perform silicon wafer-glass anodic bonding: Use a wafer bonder to anodically bond the cleaned glass and silicon wafer.

[0032] Step 5, exposure and development: first pre-treat the surface of the silicon wafer, spin-coat the photoresist, and pre-bake to remove the organic solvent in the photoresist; use a UV photolithography machine and a chrome-plated mask to expose the photoresist, and develop to remove the exposed part of the photoresist;

[0033] Step 6: Deep silicon etching: Use plasma etching equipment to perform deep silicon etching on the sample, and use organic cleaning to remove residual glue to obtain a meta-lens sample.

[0034] Furthermore, the phase, dispersion phase, and transmittance of the meta-units at the center frequency are obtained by changing the duty cycle of the five meta-units as described in step 1, and a phase-dispersion unit library is constructed, as follows:

[0035] Step 1.1: Perform broadband scans on the five meta-units with different cross-sectional shapes one by one. Through scanning, the relationship between the phase and frequency of the meta-unit under specific structures and specific parameters is obtained. After linear fitting, the linear fitting coefficient R is obtained. 2 ;

[0036] Step 1.2, select the linear fitting coefficient R 2 Larger superstructure units, to obtain their phase at the center frequency Dispersion Phase and transmittance T i ,composition Phase-dispersion unit library, where the dispersion phase is the corrected group delay multiplied by the bandwidth, i represents the i-th simulated meta-unit;

[0037] Step 1.3: Obtain the relationship between the phase of the meta-unit and the source incident angle under the set structure and specific parameters through angle scanning.

[0038] Furthermore, the numerical aperture of the quadratic aspheric meta-lens is determined as described in step 2, and the corrected phase Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ) are arranged with matching units, and the selected units have a transmittance greater than 70%, as follows:

[0039] Step 2.1. Determine the focal length and diameter of the metalens and obtain the center frequency ω p The modified phase distribution Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ):

[0040]

[0041]

[0042] Where c is the speed of light in vacuum, f is the focal length of the metalens, r is the distance from any metacell to the center of the metalens, δ is the maximum phase compensation, and Δω = ω max -ω min is the working bandwidth, ω max 、ω min is the maximum and minimum operating frequency, ω p is the center frequency;

[0043] The above results are combined into (Φ j ,Ψ j ) target library, j represents the metacell at the jth position of the metalens, and the maximum is the total number of metalenses with determined focal length and diameter;

[0044] Step 2.2: From the established phase-dispersion unit library, i.e. In the cell library, select the cell with (Φ j ,Ψ j ) The target library matches the unit array, first calculate the phase of the i-th simulation unit Dispersion Phase and transmittance T i The phase Φ corrected by the meta-unit at the jth position on the meta-lens j , dispersion phase Ψ j and the Euclidean distance d between the transmittance T (assuming it is always equal to 1) ij :

[0045]

[0046] Among them, w1 and w2 are weight factors to balance the weights between dimensions;

[0047] Step 2.3: Calculate the d value of the metacell at the jth position on the metalens. ij The minimum value is taken to obtain the meta-units at each position, and then the array is arranged to obtain the discretized terahertz wide-angle broadband meta-lens based on the quadratic aspheric surface.

[0048] Furthermore, the focusing efficiency of the meta-lens described in step 3 within the working bandwidth and working field of view is as follows:

[0049] The focusing efficiency η is defined as the ratio of the optical power in the focusing area to the incident optical power, where the incident optical power is defined as the optical power transmitted through the aperture diaphragm, which is the same size as the metasurface lens and is at a distance of λ / 2 from the exit plane of the metasurface lens. The focusing area is defined as the circular aperture area near the focus, where the circular aperture size is the size of the Airy disk.

[0050] Furthermore, in step 5, the photoresist used is AZ4620 photoresist, the spin coating speed is 750r / 30s, and the thickness is 15um.

[0051] Furthermore, in step 5, the pre-baking temperature is 100° C., the time is 15 minutes, the exposure time is 70 seconds, and the development time is 120 seconds.

[0052] Furthermore, the deep silicon etching in step 6 adopts the Bosch process, and the etching depth is 900 μm.

[0053] Compared with the prior art, the present invention has the following significant advantages: (1) By using a modified quadratic aspheric phase profile and dispersion control method, a 10 mm aperture, polarization-insensitive, wide-angle, broadband terahertz meta-lens is designed, with a field of view of ±50°, an operating frequency band of 0.3 THz to 0.5 THz, a numerical aperture of 0.707, and a convergence efficiency of up to 21%; (2) The use of a quadratic aspheric meta-lens can achieve convergence of incident plane electromagnetic waves within a larger field of view, and ensure that the electromagnetic waves transmitted through the meta-lens can maintain a symmetrical distribution about the main light at the focus within a larger range of incident angles; (3) Combined with the dispersion control of the meta-lens, convergence can be achieved within a large field of view and a broadband, and the focal length is stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a schematic structural diagram of a terahertz wide-angle broadband meta-lens of the present invention, wherein (a) is an overall view, and (b) is an enlarged top-view SEM image of a partial area.

[0055] Figure 2Schematic diagrams of the structures of the superstructure unit in the present invention, wherein (a) is a schematic diagram of a cylindrical superstructure unit, (b) is a schematic diagram of a circular ring superstructure unit, (c) is a schematic diagram of a square column superstructure unit, (d) is a schematic diagram of a cross superstructure unit, and (e) is a schematic diagram of a square ring superstructure unit.

[0056] Figure 3 3 is a graph showing the relationship between transmittance, relative phase delay, frequency and unit duty cycle of a uniform periodic array corresponding to a cylindrical meta-unit in an embodiment of the present invention, wherein (a) is a graph showing the relationship with frequency, and (b) is a graph showing the relationship with unit duty cycle.

[0057] Figure 4 3 is a graph showing the relationship between the relative phase delay, transmittance, source incident angle, and unit duty cycle of the uniform periodic array corresponding to the cylindrical meta-unit in an embodiment of the present invention, where (a) is the relationship diagram corresponding to the phase delay, and (b) is the relationship diagram corresponding to the transmittance.

[0058] Figure 5 2 is a diagram showing the relationship between the dispersion phase, relative phase delay and transmittance of the meta-structure unit in an embodiment of the present invention, wherein (a) is a diagram showing the relationship between the dispersion phase and relative phase delay of the meta-structure unit, and (b) is a diagram showing the relationship between the dispersion phase and transmittance of the meta-structure unit.

[0059] Figure 6 Schematic diagram of the ideal phase, dispersion profile of the metalens in the embodiment of the present invention and the relative phase delay and dispersion phase corresponding to the metaunits taken in the actual array, wherein (a) is a schematic diagram of the ideal phase profile of the metalens in the embodiment and the relative phase delay corresponding to the metaunits taken in the actual array, and (b) is a schematic diagram of the ideal dispersion phase profile of the metalens in the embodiment and the dispersion phase corresponding to the metaunits taken in the actual array.

[0060] Figure 7 Schematic diagram of the ideal phase and dispersion profile in the radial direction of the metalens in an embodiment of the present invention and the relative phase delay and dispersion phase corresponding to the metaunits actually arranged. (a) is a schematic diagram of the ideal phase profile in the radial direction of the metalens and the relative phase delay corresponding to the metaunits actually arranged. (b) is a schematic diagram of the ideal dispersion phase profile in the radial direction of the metalens and the dispersion phase corresponding to the metaunits actually arranged.

[0061] Figure 8 Schematic diagram of the preparation process of the metalens in an embodiment of the present invention, wherein (a) is a bonding diagram, (b) is a spin coating diagram, (c) is an exposure diagram, (d) is a development diagram, and (e) is a deep silicon etching diagram.

[0062] Figure 9This is a schematic diagram of the distribution of the relative electric field amplitude in the longitudinal plane of the device at frequencies of 0.3THz, 0.35THz, 0.4THz, 0.45THz, and 0.5THz when a plane electromagnetic wave is irradiated onto the metalens at angles of 0°, 10°, 20°, 30°, 40°, and 50°, respectively, in an embodiment of the present invention, wherein (a) is a schematic diagram corresponding to 0°, (b) is a schematic diagram corresponding to 10°, (c) is a schematic diagram corresponding to 20°, (d) is a schematic diagram corresponding to 30°, (e) is a schematic diagram corresponding to 40°, and (f) is a schematic diagram corresponding to 50°.

[0063] Figure 10 This is a schematic diagram of the distribution of the relative electric field amplitude in the XOY plane of the device when plane electromagnetic waves with frequencies of 0.3THz, 0.35THz, 0.4THz, 0.45THz, and 0.5THz are vertically irradiated onto the terahertz wide-angle broadband metalens in an embodiment of the present invention.

[0064] Figure 11 This is a relationship diagram between the focal length, focusing efficiency, and frequency of the lens when a plane electromagnetic wave is irradiated onto the terahertz wide-angle broadband metalens at deflection angles of 0°, 10°, 20°, 30°, and 40° in the present invention, where (a) is a relationship diagram between the focal length and frequency, and (b) is a relationship diagram between the focusing efficiency and frequency. DETAILED DESCRIPTION

[0065] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0066] Combine Figure 1 (a) to (b) of the present invention, a terahertz wide-angle broadband meta-lens, comprising a substrate and a meta-unit on the substrate;

[0067] A plurality of superstructure units are evenly arranged on the substrate; Figure 2 In (a) to (e), the metastructure unit includes five types: cylindrical structure, circular ring structure, square column structure, cross structure, and square ring structure; by changing the cross-sectional dimensions of the five metastructure units, the phase, dispersion phase, and transmittance of the metastructure unit at the center frequency are obtained.

[0068] As a specific example, the substrate is made of silicon dioxide, the meta-unit is made of silicon, and the size and period of the meta-unit are smaller than the maximum operating wavelength;

[0069] The superstructure unit is any one of a cylindrical structure, a circular ring structure, a square column structure, a cross structure, and a square ring structure;

[0070] The meta-units are arranged in a C4 symmetrical structure to ensure that the meta-lens is insensitive to the polarization of the incident light.

[0071] The period of the meta-unit is less than the Nyquist sampling rate λ / 2NA, where λ is the operating wavelength and NA is the numerical aperture of the meta-lens;

[0072] The metastructure unit is a truncated waveguide, and the phase changes linearly with the frequency within the working bandwidth. The phase and transmittance are independent of the incident angle within the working field. where n eff (ω) is the effective refractive index, h is the height of the metacell, c is the speed of light in vacuum, and ω is the frequency.

[0073] As a specific example, the phase distribution of the metalens is:

[0074]

[0075] Where F = f*ω n , for an achromatic lens, n = 0; ω is the angular frequency, c is the speed of light, f is the preset focal length of the metalens, and r is the distance from any metaunit to the center of the metalens;

[0076] At ω=ω p Taylor expansion at:

[0077]

[0078] Among them, ω p is the operating frequency, F is the focal length related to the frequency, is the phase distribution of the metalens at the center frequency, are the group delay and group delay dispersion of the metalens, respectively.

[0079] For an achromatic lens, F = f is a constant, and the higher-order terms of the phase distribution are ignored. Therefore, the phase distribution is a linear function of ω:

[0080]

[0081] In order to avoid the group delay at the center of the lens r = 0 is 0, the phase should be added with a linear correction δ*(ω-ω min ) / Δω, where δ is the maximum phase compensation, Δω=ω max -ω min is the working bandwidth, ω max 、ω min are the maximum and minimum operating frequencies respectively;

[0082] Therefore, the corrected phase distribution and dispersion phase distribution are:

[0083]

[0084]

[0085] In order to realize a wide-angle broadband achromatic meta-lens, the meta-unit at position r should simultaneously satisfy the corrected phase Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ).

[0086] The present invention provides a method for preparing a terahertz wide-angle broadband metalens, comprising the following steps:

[0087] Step 1: By changing the duty cycle of five metacells, the phase, dispersion phase, and transmittance of the metacells at the center frequency are obtained to construct a phase-dispersion cell library;

[0088] Step 2: Determine the numerical aperture of the quadratic aspheric meta-lens and select the element with the corrected phase Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ) are arranged with matching units, and the transmittance of the selected units is greater than 70%;

[0089] Step 3: Calculate the focusing efficiency of the metalens within the working bandwidth and working field of view;

[0090] Step 4: Based on the metalens constructed in steps 1 to 3, perform silicon wafer-glass anodic bonding: Use a wafer bonder to anodically bond the cleaned glass and silicon wafer.

[0091] Step 5, exposure and development: first pre-treat the surface of the silicon wafer, spin-coat the photoresist, and pre-bake to remove the organic solvent in the photoresist; use a UV photolithography machine and a chrome-plated mask to expose the photoresist, and develop to remove the exposed part of the photoresist;

[0092] Step 6: Deep silicon etching: Use plasma etching equipment to perform deep silicon etching on the sample, and use organic cleaning to remove residual glue to obtain a meta-lens sample.

[0093] As a specific example, the phase, dispersion phase, and transmittance of the meta-units at the center frequency are obtained by changing the duty cycle of the five meta-units in step 1, and a phase-dispersion unit library is constructed as follows:

[0094] Step 1.1: Perform broadband scans on the five meta-units with different cross-sectional shapes one by one. Through scanning, the relationship between the phase and frequency of the meta-unit under specific structures and specific parameters is obtained. After linear fitting, the linear fitting coefficient R is obtained. 2 ;

[0095] Step 1.2, select the linear fitting coefficient R 2Larger superstructure units, to obtain their phase at the center frequency Dispersion Phase and transmittance T i ,composition Phase-dispersion unit library, where the dispersion phase is the corrected group delay multiplied by the bandwidth, i represents the i-th simulated meta-unit;

[0096] Step 1.3: Obtain the relationship between the phase of the meta-unit and the source incident angle under the set structure and specific parameters through angle scanning.

[0097] As a specific example, in step 1.1, the phase, dispersion phase, and transmittance of the metacell at the center frequency are obtained by changing the duty cycle of the five metacells, and a phase-dispersion cell library is constructed as follows:

[0098] Step 1.1.1. Perform broadband scans on the five meta-units with different cross-sectional shapes one by one. Through scanning, the relationship between the phase and frequency of the meta-unit under specific structures and specific parameters is obtained. After linear fitting, the linear fitting coefficient R is obtained. 2 ;

[0099] Step 1.1.2, select the linear fitting coefficient R 2 Larger superstructure units, to obtain their phase at the center frequency Dispersion Phase and transmittance T i ,composition Phase-dispersion unit library, where the dispersion phase is the corrected group delay multiplied by the bandwidth, i represents the i-th simulated meta-unit;

[0100] Step 1.1.3: Obtain the relationship between the phase of the meta-unit and the source incident angle under specific structures and parameters through angle scanning.

[0101] As a specific example, in step 2, the numerical aperture of the quadratic aspheric meta-lens is determined, and the corrected phase Φ(r,ω) is selected from the unit library. p ) and the corrected dispersion phase Ψ(r,ω p ) are arranged with matching units, and the selected units have a transmittance greater than 70%, as follows:

[0102] Step 2.1. Determine the focal length and diameter of the metalens and obtain the center frequency ω p The modified phase distribution Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ):

[0103]

[0104]

[0105] Where c is the speed of light in vacuum, f is the focal length of the metalens, r is the distance from any metacell to the center of the metalens, δ is the maximum phase compensation, and Δω = ω max -ω min is the working bandwidth, ω max 、ω min is the maximum and minimum operating frequency, ω p is the center frequency;

[0106] The above results are combined into (Φ j ,Ψ j ) target library, j represents the meta-unit at the j-th position of the meta-lens, and the maximum is the total number of units of the meta-lens with determined focal length and diameter.

[0107] Step 2.2: From the established phase-dispersion unit library, i.e. In the cell library, select the cell with (Φ j ,Ψ j ) The target library matches the unit array, first calculate the phase of the i-th simulation unit Dispersion Phase and transmittance T i The phase Φ corrected by the meta-unit at the jth position on the meta-lens j , dispersion phase Ψ j and the Euclidean distance d between the transmittance T (assuming it is always equal to 1) ij :

[0108]

[0109] Among them, w1 and w2 are weight factors to balance the weights between dimensions;

[0110] Step 2.3: Calculate the d value of the metacell at the jth position on the metalens. ij The minimum value is taken to obtain the meta-units at each position, and then the array is arranged to obtain the discretized terahertz wide-angle broadband meta-lens based on the quadratic aspheric surface.

[0111] As a specific example, the calculation of the convergence efficiency of the metalens within the working bandwidth and working field of view described in step 3 is as follows:

[0112] The focusing efficiency η is defined as the ratio of the optical power in the focusing area to the incident optical power, where the incident optical power is defined as the optical power transmitted through an aperture stop that is the same size as the metasurface lens and is at a distance of λ / 2 from the exit plane of the metasurface lens; the focusing area is defined as the circular aperture area near the focus, where the circular aperture size is the size of the Airy disk.

[0113] Combine Figure 8 In (a) to (e), in the method for preparing the terahertz wide-angle broadband metalens:

[0114] Step 4 specifically includes: performing silicon wafer-glass anodic bonding based on the metalens constructed in steps 1 to 3: using a wafer bonder to anodic bond the cleaned glass and silicon wafer;

[0115] Step 5 is specifically as follows: exposure and development: first, pre-treat the surface of the silicon wafer, spin-coat the photoresist, and pre-bake to remove the organic solvent in the photoresist; use a UV photolithography machine and a chrome-plated mask to expose the photoresist, and develop to remove the exposed part of the photoresist;

[0116] The photoresist adopts AZ4620 photoresist, the spin coating speed is 750r / 30s, the thickness is 15um; the pre-baking temperature is 100°C, the time is 15 minutes; the exposure time is 70s; and the development time is 120s.

[0117] Step 6 is specifically as follows: deep silicon etching: using plasma etching equipment to perform deep silicon etching on the sample, and organic cleaning to remove residual glue to obtain a meta-lens;

[0118] The deep silicon etching adopts the Bosch process, and the etching depth is 900um.

[0119] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0120] Example 1

[0121] In this embodiment, a 10 mm aperture, polarization-insensitive terahertz wide-angle broadband meta-lens is designed and manufactured. Its field of view is ±50°, the operating frequency band is 0.3 THz to 0.5 THz, the numerical aperture is 0.707, and the focusing efficiency can reach 21%.

[0122] Figure 3 (a) shows the relationship between transmittance, relative phase delay and frequency for the uniform periodic array corresponding to the cylindrical meta-unit. Figure 3 (b) is a graph showing the relationship between transmittance, relative phase delay, and unit duty cycle for a uniform periodic array of cylindrical metaunits.

[0123] Figure 4(a) shows the relationship between the relative phase delay of the uniform periodic array corresponding to the cylindrical meta-unit and the source incident angle and the unit duty cycle; Figure 4 (b) is a graph showing the relationship between the transmittance of the uniform periodic array corresponding to the cylindrical meta-unit and the source incident angle and the unit duty cycle;

[0124] Figure 5 (a) is a diagram showing the relationship between the dispersion phase and relative phase delay of the adopted meta-unit; Figure 5 (b) is a diagram showing the relationship between the transmittance and dispersion phase of the meta-unit used.

[0125] Figure 6 (a) is a schematic diagram of the ideal phase profile of the metalens and the relative phase delay corresponding to the metaunits used in the actual array; Figure 6 (b) is a schematic diagram of the ideal dispersion phase profile of the metalens and the dispersion phase corresponding to the metaunits used in the actual array;

[0126] Figure 7 (a) is a schematic diagram of the relative phase delay between the ideal phase profile in the radial direction of the meta-lens and the meta-units in the actual array. Figure 7 (b) is a schematic diagram of the ideal dispersion phase profile in the radial direction of the metalens and the dispersion phase corresponding to the metalens units in the actual array.

[0127] Figure 9 (a) to (f) are schematic diagrams of the distribution of the relative electric field amplitude in the longitudinal plane of the device at frequencies of 0.3THz, 0.35THz, 0.4THz, 0.45THz, and 0.5THz when plane electromagnetic waves are irradiated onto the terahertz wide-angle broadband meta-lens at angles of 0°, 10°, 20°, 30°, 40°, and 50°, respectively.

[0128] Figure 10 This is a schematic diagram of the distribution of the relative electric field amplitude in the XOY plane of the device when plane electromagnetic waves with frequencies of 0.3THz, 0.35THz, 0.4THz, 0.45THz, and 0.5THz are vertically irradiated onto the terahertz wide-angle broadband metalens.

[0129] Figure 11 (a) is a graph showing the relationship between the focal length of the lens and the frequency when a plane electromagnetic wave is irradiated onto the terahertz wide-angle broadband metalens at deflection angles of 0°, 10°, 20°, 30°, and 40°. Figure 11 (b) is a graph showing the relationship between the lens convergence efficiency and frequency when the plane electromagnetic wave is irradiated onto the terahertz wide-angle broadband meta-lens at deflection angles of 0°, 10°, 20°, 30°, and 40°.

[0130] The comparison of the key characteristic parameters of the existing terahertz metalens and the present invention is shown in Table 1:

[0131] Table 1

[0132]

[0133] Depend on Figures 3 to 11 As shown in Table 1, the terahertz wide-angle broadband metalens and its preparation method of the present invention can achieve the convergence of incident plane electromagnetic waves in a larger field of view, and ensure that the electromagnetic waves transmitted through the metalens can maintain their symmetrical distribution about the main light at the focus within a larger range of incident angles; at the same time, combined with the dispersion control of the metalens, it can achieve convergence in a large field of view and broadband, and the focal length remains stable.

Claims

1. A method for preparing a terahertz wide-angle broadband meta-lens, characterized in that: The following steps are involved: Step 1: By changing the duty cycle of the five metacells, the phase, dispersion phase, and transmittance of the metacells at the center frequency are obtained, and a phase-dispersion cell library is constructed, as follows: Step 1.1: Perform broadband scans on the five meta-units with different cross-sectional shapes one by one. Through scanning, the relationship between the phase and frequency of the meta-unit under the set structure and set parameters is obtained. After linear fitting, the linear fitting coefficient R is obtained. 2 ; Step 1.2, select the linear fitting coefficient R 2 The phase of the superstructure unit at the center frequency is obtained if the superstructure unit is greater than the set value. Dispersion Phase and transmittance T i ,composition Phase-dispersion unit library, where the dispersion phase is the corrected group delay multiplied by the bandwidth, i represents the i-th simulated meta-unit; Step 1.3: Obtain the relationship between the phase of the meta-unit and the source incident angle under the set structure and set parameters through angle scanning; Step 2: Determine the numerical aperture of the quadratic aspheric meta-lens and select the element with the corrected phase Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ) are arranged with matching units, and the transmittance of the selected units is greater than 70%; Step 3: Calculate the convergence efficiency of the metalens within the working bandwidth and working field of view as follows: The focusing efficiency η is defined as the ratio of the optical power in the focusing area to the incident optical power, where the incident optical power is defined as the optical power transmitted through the aperture stop, which is the same size as the metasurface lens and is at a distance of λ / 2 from the exit plane of the metasurface lens. The focusing area is defined as the circular aperture area near the focus, where the circular aperture size is the size of the Airy disk. Step 4: Based on the metalens constructed in steps 1 to 3, perform silicon wafer-glass anodic bonding: Use a wafer bonder to anodically bond the cleaned glass and silicon wafer. Step 5, exposure and development: first pre-treat the surface of the silicon wafer, spin-coat the photoresist, and pre-bake to remove the organic solvent in the photoresist; Use a UV lithography machine and a chrome-plated mask to expose the photoresist, and then develop and remove the exposed part of the photoresist; Step 6: Deep silicon etching: Use plasma etching equipment to perform deep silicon etching on the sample, and use organic cleaning to remove residual glue to obtain a meta-lens sample.

2. The method for preparing a terahertz wide-angle broadband metalens according to claim 1, wherein: Determine the numerical aperture of the quadratic aspheric meta-lens as described in step 2, and select the element with the corrected phase Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ) are arranged with matching units, and the selected units have a transmittance greater than 70%, as follows: Step 2.

1. Determine the focal length and diameter of the metalens and obtain the center frequency ω p The modified phase distribution Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ): Where c is the speed of light in vacuum, f is the focal length of the metalens, r is the distance from any metacell to the center of the metalens, δ is the maximum phase compensation, and Δω = ω max -ω min is the working bandwidth, ω max 、ω min is the maximum and minimum operating frequency, ω p is the center frequency; The above results are combined into (Φ j ,Ψ j ) target library, j represents the metacell at the jth position of the metalens, and the maximum is the total number of metalenses with determined focal length and diameter; Step 2.2: From the established phase-dispersion unit library, i.e. In the cell library, select the cell with (Φ j ,Ψ j ) The target library matches the unit array, first calculate the phase of the i-th simulation unit Dispersion Phase and transmittance T i The phase Φ corrected by the meta-unit at the jth position on the meta-lens j , dispersion phase Ψ j and the Euclidean distance d between the transmittance T (assuming it is always equal to 1) ij , the transmittance T is assumed to be equal to 1, then: Among them, w1 and w2 are weight factors to balance the weights between dimensions; Step 2.3: Calculate the d value of the metacell at the jth position on the metalens. ij The minimum value is taken to obtain the meta-units at each position, and then the array is arranged to obtain the discretized terahertz wide-angle broadband meta-lens based on the quadratic aspheric surface.

3. The method for preparing a terahertz wide-angle broadband metalens according to claim 1, wherein: In step 5, the photoresist used is AZ4620 photoresist, the spin coating speed is 750r / 30s, and the thickness is 15um.

4. The method for preparing a terahertz wide-angle broadband metalens according to claim 1, wherein: In step 5, the pre-baking temperature is 100° C., the time is 15 minutes, the exposure time is 70 seconds, and the developing time is 120 seconds.

5. The method for preparing a terahertz wide-angle broadband metalens according to claim 1, wherein: The deep silicon etching in step 6 adopts the Bosch process, and the etching depth is 900 μm.

6. A terahertz wide-angle broadband meta-lens, characterized in that: The terahertz wide-angle broadband meta-lens is prepared by the preparation method according to any one of claims 1 to 5, and the terahertz wide-angle broadband meta-lens comprises a substrate and a meta-unit on the substrate; A plurality of meta-structure units are evenly arranged on the substrate; the meta-structure units include five types: cylindrical structure, circular ring structure, square column structure, cross structure, and square ring structure; by changing the cross-sectional dimensions of the five types of meta-structure units, the phase, dispersion phase, and transmittance of the meta-structure units at the center frequency are obtained.

7. The terahertz wide-angle broadband metalens according to claim 6, characterized in that: The substrate is made of silicon dioxide, the meta-unit is made of silicon, and the size and period of the meta-unit are smaller than the maximum operating wavelength; The superstructure unit is any one of a cylindrical structure, a circular ring structure, a square column structure, a cross structure, and a square ring structure; The superstructure unit is arranged in a C4 symmetrical structure; The period of the meta-unit is less than the Nyquist sampling rate λ / 2NA, where λ is the operating wavelength and NA is the numerical aperture of the meta-lens; The metastructure unit is a truncated waveguide, and the phase changes linearly with the frequency within the working bandwidth. The phase and transmittance are independent of the incident angle within the working field. where n eff (ω) is the effective refractive index, h is the height of the metacell, c is the speed of light in vacuum, and ω is the frequency.

8. The terahertz wide-angle broadband metalens according to claim 6, characterized in that: The phase distribution of the metalens is: Where F = f*ω n , for an achromatic lens, n = 0; ω is the angular frequency, c is the speed of light, f is the preset focal length of the metalens, and r is the distance from any metaunit to the center of the metalens; At ω=ω p Taylor expansion at: Among them, ω p is the operating frequency, F is the focal length related to the frequency, is the phase distribution of the metalens at the center frequency, are the group delay and group delay dispersion of the metalens respectively; For an achromatic lens, F = f is a constant, and the higher-order terms of the phase distribution are ignored. Therefore, the phase distribution is a linear function of ω: In order to avoid the group delay at the center of the lens r = 0 is 0, the phase should be added with a linear correction δ*(ω-ω min ) / Δω, where δ is the maximum phase compensation, Δω=ω max -ω min is the working bandwidth, ω max 、ω min are the maximum and minimum operating frequencies respectively; Therefore, the corrected phase distribution and dispersion phase distribution are: In order to realize a wide-angle broadband achromatic meta-lens, the meta-unit at position r should simultaneously satisfy the corrected phase Φ(r,ω p ) and the corrected dispersion phase Ψ(r,ω p ).

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