Hybrid integrated superlens and design method and processing method thereof

Abstract

The application belongs to the field of simulation design of superlenses, and relates to a superlens with mixed integration of a multi-step structure and nano structures, a design method and a processing method of the superlens. The mixed integration superlens comprises a multi-step structure and nano structures. The multi-step structure comprises a plurality of phase design steps for changing the phase of incident light, and the height between adjacent phase design steps in the plurality of phase design steps is different. The height of the phase design step is related to the function realized by the mixed integration superlens. The nano structures are arranged on the other side of the same substrate as the multi-step structure. In the application, the multi-step structure and the nano structures of the mixed integration superlens are arranged on two different sides of the same substrate, and the processing technology of the two sides can be carried out separately without affecting each other. The nano structures arranged on the plane have more uniform etching depth, higher precision, higher arrangement freedom and stronger phase control ability.

Description

Technical Field

[0001] This invention belongs to the field of superlens simulation design, and more specifically, relates to a hybrid integrated superlens and its design and fabrication methods. Background Technology

[0002] Metasurfaces are two-dimensional array structures composed of subwavelength-scale electromagnetic resonant units. By artificially designing the shape and size of these units and the macroscopic order of the two-dimensional array, band selection, polarization control, and wavefront modulation of electromagnetic radiation can be achieved on an ultrathin scale at the order of electromagnetic wavelengths. Superlenses, on the other hand, are planar lenses that utilize metasurfaces to manipulate light. Compared to planar substrate superlenses, superlenses that integrate metasurfaces with other structures offer significant advantages in miniaturization and chromatic aberration correction, making them a research trend in both academic and industrial fields.

[0003] Related technologies utilize multi-step structures as the substrate for metasurfaces, designing stepped-substrate metasurfaces. The fabrication method for these metasurfaces involves first performing grayscale etching on a planar substrate to obtain the stepped substrate, then depositing a structural layer on the stepped substrate, and finally using photolithography to form the nanostructures disposed on the stepped substrate. The substrate for this stepped-substrate metasurface is a plane of varying heights, which can be fabricated using existing semiconductor planar processing techniques.

[0004] However, this method involves depositing the structural layer on a stepped substrate, which may result in uneven thickness of the structural layer at different heights on the substrate. This can lead to inconsistent etching depths of the nanostructures during photolithography, increasing the processing difficulty and affecting the optical performance of the superlens. Furthermore, the stepped substrate may restrict the degree of freedom in arranging the nanostructures, thus affecting the phase modulation capability of the superlens. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a hybrid integrated superlens and its design and fabrication methods. The hybrid integrated superlens of the present invention comprises a multi-step structure and a nanostructure. The multi-step structure includes multiple phase-designed steps that alter the phase of incident light rays, with adjacent phase-designed steps having different heights. The nanostructure has a uniform height and is disposed on another surface of the same substrate as the multi-step structure. The hybrid integrated superlens of the present invention disposes the multi-step structure and the nanostructure on two different surfaces of the same substrate, allowing for separate fabrication processes on both surfaces without interference. Furthermore, the nanostructure disposed on the plane exhibits more uniform etching depth, higher precision, greater arrangement freedom, and stronger phase control capabilities.

[0006] According to a first aspect of the present invention, a hybrid integrated superlens is provided, comprising a multi-step structure and a nanostructure; the multi-step structure includes a plurality of phase design steps for changing the phase of incident light, wherein adjacent phase design steps have different heights; the nanostructure has a uniform height and is disposed on another surface of the same substrate as the multi-step structure, the nanostructure being used to modulate the phase of the incident light.

[0007] Preferably, the nanostructure is a columnar structure, a hollow structure, or a nested structure.

[0008] Preferably, the column structure is a cylinder or a square column;

[0009] The hollow structure is a hollow cylinder or a hollow square prism;

[0010] The nested structure is either a cylinder nested within a cylinder or a square prism nested within a square prism.

[0011] According to another aspect of the present invention, a method for designing a hybrid integrated superlens as described in any one of the claims is provided, comprising the following steps:

[0012] (1) Determine the working band of the hybrid integrated superlens, and take the middle wavelength of the working band as the main wavelength of the working band. The middle wavelength of the working band is the average of the minimum and maximum values ​​of the working band.

[0013] (2) The phase required for light with the dominant wavelength to pass through the phase design step in the substrate is calculated using the following formula:

[0014] φ c (x,y)=mod(φ design (x,y),2π)

[0015] Where (x, y) are coordinates determined by a coordinate system established with the base center as the origin, φ c (x,y) represents the phase required for light with the dominant wavelength to pass through the phase design step in the substrate, φ design (x,y) represents the phase required for the dominant wavelength of the operating band;

[0016] (3) The step height of the phase design staircase in the substrate is calculated using the following formula:

[0017]

[0018] Where h(x,y) represents the step height of the phase design step in the substrate; λ c φ represents the dominant wavelength of the operating band. c (x,y,λ c) represents a wavelength of λ c The phase required for light rays to pass through the phase design steps in the substrate; n c The substrate is represented by wavelength λ. c The refractive index of light;

[0019] (4) The phase required for light of other wavelengths in the operating band to pass through the phase design step in the substrate is calculated using the following formula:

[0020]

[0021] Where h(x,y) represents the step height of the phase design step in the substrate; n(λ) represents the refractive index of the substrate for light of other wavelengths in the working band; λ represents other wavelengths in the working band; φ substrate (x,y,λ) represents the phase required for light of other wavelengths in the working band to pass through the phase design step in the substrate;

[0022] (5) The required phase for the nanostructure is calculated using the following formula:

[0023] φ total (x,y,λ)=mod(φ substrate (x,y,λ)+φ nanostructure (x,y,λ),2π)

[0024] Where, φ total (x,y,λ) represents the design color difference phase; φ nanostructure (x,y,λ) represents the phase required for the nanostructure;

[0025] (6) Retrieve and select a set of nanostructures from the nanostructure database whose phases are closest to the required phase of the nanostructure and can cover the entire 2π phase; specifically: query the phases of each nanostructure from the nanostructure database; calculate the difference between each nanostructure phase and the required phase of the nanostructure, and determine the nanostructure corresponding to the nanostructure phase with the smallest difference from the required phase of the nanostructure as the nanostructure whose phase is closest to the required phase of the nanostructure.

[0026] (7) Determine the distribution of the multi-step structure according to the height of the multi-step structure calculated in step (3), and the shape and size of the nanostructure selected in step (6) to form the hybrid integrated superlens.

[0027] Preferably, in step (2), the phase required for the dominant wavelength of the operating band is calculated, including the following steps:

[0028] S1: Determine the focal length of the hybrid integrated superlens;

[0029] S2: Calculate the phase required for the main wavelength of the working band based on the main wavelength of the working band and the focal length of the hybrid integrated superlens;

[0030] The required phase φ for the dominant wavelength of the operating band is obtained using the following formula. design Calculate (x, y):

[0031]

[0032] Where f represents the focal length of the optical lens generated by the hybrid integrated superlens; λ c This indicates the dominant wavelength of the operating band.

[0033] Preferably, the method for establishing the nanostructure database includes the following steps:

[0034] (1) Based on the minimum wavelength λ of the operating band of the hybrid integrated superlens min and maximum wavelength λ max Determine the periodic range of the nanostructure database. and the height range of nanostructures Where λ0 is the dominant wavelength, n s Refractive index of substrate material, n p The refractive index of nanostructured materials;

[0035] (2) When the process reaches the minimum processable size CD, the cycle is determined as P = P0, where: the range of values ​​for P0 is... When the diameter of the nanostructure varies, Var_D = [CD, P0 - CD];

[0036] (3) Perform parameter scanning on the period P and the nanostructure diameter D and its height H under this period respectively. The number of scanning steps for the period, the nanostructure diameter and its height is not less than 10. Obtain the phase and transmittance of different nanostructure diameters at different wavelengths under this period and height, thereby establishing the nanostructure database.

[0037] Preferably, in step (1), the substrate material of the hybrid integrated superlens is determined according to the type of the working band.

[0038] Preferably, when the operating band is the wavelength range of infrared light, the substrate material is chalcogenide glass, zinc sulfide, zinc selenide, crystalline germanium, or crystalline silicon.

[0039] When the operating band is the wavelength range of visible light, the substrate material is silicon nitride, titanium oxide, gallium nitride, gallium phosphide, hydrogenated amorphous silicon, sapphire, or silicon oxide.

[0040] According to another aspect of the present invention, a method for fabricating a hybrid integrated superlens as described in any one of the claims is provided, comprising the following steps:

[0041] (1) The multi-step structure of the hybrid integrated superlens is obtained by grayscale exposure etching of the substrate;

[0042] (2) Coating photoresist on the other side of the same substrate as the multi-step structure;

[0043] (3) The nanostructure is formed by exposure on the photoresist;

[0044] (4) Etch and remove the remaining photoresist to obtain the hybrid integrated superlens.

[0045] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0046] (1) Compared to nanostructures set on stepped substrates, which require careful arrangement to avoid the edges of the steps, the nanostructures set on a flat substrate in this invention offer greater design freedom and can achieve smaller structural periods. Metasurfaces composed of such arranged nanostructures exhibit stronger phase modulation capabilities, better aberration correction in optical systems, and a wider range of applications.

[0047] (2) In this invention, the hybrid integrated superlens sets the multi-step structure and the nanostructure on two different surfaces of the same substrate. The grayscale exposure etching process of the multi-step structure and the photolithography process of the nanostructure can be performed separately without affecting each other, avoiding secondary processing on the same surface that would damage the existing structure. This allows the hybrid integrated superlens to use existing semiconductor processes, but the processing technology is simpler than that of stepped substrate metasurfaces, and it is easier to mass-produce and promote.

[0048] (3) Compared with the nanostructures set on the stepped substrate, the nanostructures set on the flat substrate surface of the present invention can be photolithographically processed without depositing a structural layer, avoiding the error caused by uneven thickness of the structural layer deposited on the stepped substrate, as well as the problem of uneven etching depth at various places that may be caused by photolithography on the stepped substrate, thus ensuring the accuracy and uniformity of the etching depth of the nanostructure. Attached Figure Description

[0049] Figure 1 A schematic diagram of the stepped substrate metasurface is shown.

[0050] Figure 2 In Figure 'a', a schematic diagram of the structure of the first implementation of the hybrid integrated superlens provided in Embodiment 1 of the present invention is shown.

[0051] Figure 2b in the figure shows a structural schematic diagram of the second implementation of the hybrid integrated superlens provided in Embodiment 1 of the present invention;

[0052] Figure 2 c in the figure shows a structural schematic diagram of the third implementation of the hybrid integrated superlens provided in Embodiment 1 of the present invention;

[0053] Figure 3 In Figure 'a', a schematic diagram of the cylindrical nanostructure in the hybrid integrated superlens provided in Embodiment 1 of the present invention is shown.

[0054] Figure 3 b in the figure shows a schematic diagram of the nanostructure of the square column of the hybrid integrated superlens provided in Embodiment 1 of the present invention;

[0055] Figure 3 c in the figure shows a schematic diagram of the nanostructure of the hollow cylinder in the hybrid integrated superlens provided in Embodiment 1 of the present invention;

[0056] Figure 3 The diagram 'd' in the figure shows a schematic diagram of the nanostructure of the hollow square prism in the hybrid integrated superlens provided in Embodiment 1 of the present invention;

[0057] Figure 3 The figure 'e' shows a schematic diagram of the nanostructure of a cylinder nested within a cylinder in the hybrid integrated superlens provided in Embodiment 1 of the present invention;

[0058] Figure 3 f in the figure shows a schematic diagram of the nanostructure of a square column nested in a square column in the hybrid integrated superlens provided in Embodiment 1 of the present invention;

[0059] Figure 4 A flowchart of a hybrid integrated superlens design method provided in Embodiment 2 of the present invention is shown;

[0060] Figure 5 A flowchart of a hybrid integrated superlens fabrication method provided in Embodiment 3 of the present invention is shown;

[0061] Figure 6 This diagram illustrates the height of the multi-step structure of the diverging lens designed according to the hybrid integrated superlens design method provided in Embodiment 2 of the present invention.

[0062] Figure 7 Figure 'a' shows a schematic diagram of the phase required by the nanostructure when the wavelength of the diverging lens designed according to the hybrid integrated superlens design method is 8 μm, in the design method of the hybrid integrated superlens provided in Embodiment 2 of the present invention.

[0063] Figure 7 Figure b shows a schematic diagram of the phase required by the nanostructure when the wavelength of the diverging lens designed according to the hybrid integrated superlens design method is 10 μm in the design method of the hybrid integrated superlens provided in Embodiment 2 of the present invention.

[0064] Figure 7 c in the figure shows a schematic diagram of the phase required by the nanostructure when the wavelength of the diverging lens designed according to the hybrid integrated superlens design method is 12 μm in the design method of the hybrid integrated superlens provided in Embodiment 2 of the present invention.

[0065] Figure 8 This diagram illustrates the structure of the refractive-superlens optical system, specifically the phase correction plate of the refractive-superlens optical system designed according to the hybrid integrated superlens design method provided in Embodiment 2 of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0067] This invention provides a hybrid integrated superlens, comprising: a multi-step structure and a nanostructure;

[0068] The multi-step structure includes: multiple phase design steps that change the phase of the incident light, wherein the heights of adjacent phase design steps are different; the height of the phase design steps is related to the function achieved by the superlens.

[0069] The nanostructures are highly uniform and are disposed on the other side of the same substrate as the multi-step structure. The nanostructures are used to modulate the phase of the incident light.

[0070] This invention discloses a design method for a hybrid integrated superlens, comprising:

[0071] The operating band of the hybrid integrated superlens is determined, and the substrate material of the hybrid integrated superlens is determined based on the operating band. At the same time, an intermediate wavelength is selected from the operating band as the dominant wavelength of the operating band.

[0072] The phase required for the dominant wavelength of the operating band is calculated, and this phase is related to the function achieved by the superlens.

[0073] Based on the phase required for the obtained dominant wavelength, the phase required for light with the dominant wavelength to pass through the phase design step in the substrate is calculated using the following formula:

[0074] φ c (x,y)=mod(φ design (x,y),2π)

[0075] Where, φ c (x,y) represents the phase required for light with the dominant wavelength to pass through the phase design step in the substrate, φ design (x,y) represents the phase required for the dominant wavelength of the operating band;

[0076] Based on the refractive index of the substrate material for light with the dominant wavelength, the phase required for light with the dominant wavelength to pass through the phase design step in the substrate, and the dominant wavelength of the operating band, the step height of the phase design step in the substrate is calculated using the following formula:

[0077]

[0078] Where h(x,y) represents the step height of the phase design step in the substrate; λ c φ represents the dominant wavelength of the operating band. c (x,y) represents the phase required for light with the dominant wavelength to pass through the phase design step in the substrate; n c This indicates the refractive index of the substrate for light rays having the dominant wavelength.

[0079] The step heights of adjacent phases in the substrate are different, thus forming the multi-step structure;

[0080] Based on other wavelengths in the operating band, the refractive index of the substrate for those other wavelengths in the operating band, and the step height of the phase design step in the substrate, the required phase for light of other wavelengths in the operating band to pass through the phase design step in the substrate is calculated using the following formula:

[0081]

[0082] Where h(x,y) represents the step height of the phase design step in the substrate; n(λ) represents the refractive index of the substrate for light of other wavelengths in the working band; λ represents other wavelengths in the working band; φ substrate (x,y,λ) represents the phase required for light of other wavelengths in the operating band to pass through the phase design steps in the substrate.

[0083] The design chromatic aberration phase of the hybrid integrated superlens is determined, and based on the phase required for light of other wavelengths in the operating band to pass through the phase design step in the substrate and the determined design chromatic aberration phase, the required phase of the nanostructure is calculated using the following formula:

[0084] φ total (x,y,λ)=mod(φ substrate (x,y,λ)+φ nanostructure (x,y,λ),2π)

[0085] Where, φ total (x,y,λ) represents the design color difference phase; φ nanostructure (x,y,λ) represents the phase required for the nanostructure.

[0086] A set of nanostructures whose phases are closest to the required phase of the nanostructure and which cover the entire 2π phase were retrieved from the nanostructure database, including:

[0087] Retrieve the phases of each nanostructure from the nanostructure database;

[0088] Calculate the difference between the phase of each nanostructure and the required phase of the nanostructure, and determine the nanostructure whose phase has the smallest difference from the required phase of the nanostructure as the nanostructure whose phase is closest to the required phase of the nanostructure.

[0089] The nanostructure database stores the correspondence between nanostructures and their phases.

[0090] The hybrid integrated superlens is formed according to the calculated shape and size of the multi-step structure and the shape and size of the nanostructure;

[0091] Full-spectrum simulation was performed on the formed hybrid integrated superlens to obtain simulation results;

[0092] When the simulation results obtained can realize the functions that the optical lens generated by the hybrid integrated superlens can achieve, it is determined that the designed hybrid integrated superlens meets the functional requirements of the optical lens.

[0093] This invention discloses a method for fabricating a hybrid integrated superlens, used for fabricating any of the hybrid integrated superlenses described in the present invention, the method comprising:

[0094] The multi-step structure of the hybrid integrated superlens is obtained by grayscale exposure etching of the substrate;

[0095] Photoresist is coated on the other side of the same substrate as the multi-step structure;

[0096] The nanostructure is formed by exposure on the photoresist;

[0097] The remaining photoresist is etched and removed to obtain the superlens that integrates the multi-step structure and the nanostructure.

[0098] See Figure 1 The schematic diagram of the stepped substrate metasurface shown is provided, wherein the nanostructure 102 is disposed on the stepped substrate 101 of the stepped substrate metasurface; the stepped substrate metasurface has the disadvantages of being difficult to manufacture and having limited functions that can be realized by the metasurface.

[0099] Based on this, embodiments of this application propose a hybrid integrated superlens and related design and fabrication methods. A hybrid integrated superlens with a multi-step structure and a nanostructure is designed. The multi-step structure includes multiple phase-designed steps of different heights that alter the phase of incident light. The nanostructure is disposed on the other side of the same substrate as the multi-step structure, enabling the superlens integrating the multi-step structure and the nanostructure to function similarly to a stepped substrate metasurface. However, since the superlens places the multi-step structure and the nanostructure on two different sides of the same substrate, its fabrication process is easier to mass-produce and promote compared to stepped substrate metasurfaces. Moreover, compared to stepped substrate metasurfaces that can achieve the same effect, the superlens integrating the multi-step structure and the nanostructure has stronger phase modulation capabilities and can achieve more functions.

[0100] The following are specific embodiments.

[0101] Example 1

[0102] See Figure 2 The diagram shows a hybrid integrated superlens with different shapes. This embodiment proposes a hybrid integrated superlens, including a multi-step structure 103 and a nanostructure 102.

[0103] The multi-step structure 103 includes: multiple phase design steps that change the phase of the incident light, wherein the heights of adjacent phase design steps are different; the height of the phase design steps is related to the function achieved by the hybrid integrated superlens.

[0104] The nanostructure 102 has a uniform height and is disposed on the other side of the same substrate as the multi-step structure.

[0105] like Figure 2 The hybrid integrated superlens shown in figure 'a' can form an achromatic diverging lens in the far-infrared band (8μm to 12μm). The multi-step structure of the diverging lens is similar in shape to that of a concave lens.

[0106] like Figure 2 The hybrid integrated superlens shown in b in this embodiment can form an achromatic converging lens in the far-infrared band (8μm to 12μm). The multi-step structure of the achromatic negative lens is similar in shape to that of a convex lens.

[0107] like Figure 2 The hybrid integrated superlens shown in 'c' can form a phase compensation plate for a refractive-superlens hybrid optical system. The phase compensation plate has a multi-step structure.

[0108] In one embodiment, the nanostructure is a columnar structure, a hollow structure, or a nested structure.

[0109] The nanostructure is used to modulate the phase of the incident light.

[0110] See Figure 3 The diagram shows the structure of the nanostructure represented by 'a', which is a cylinder.

[0111] See Figure 3 The diagram shown in b is a schematic diagram of the nanostructure, which is a square prism.

[0112] See Figure 3 The diagram shown in Figure c illustrates the structure of the nanostructure, which is a hollow cylinder.

[0113] See Figure 3 The diagram shows the structure of the nanostructure d, which is a hollow square prism.

[0114] See Figure 3 The diagram shows the structure of the nanostructure, which is a nested cylinder structure.

[0115] See Figure 3 The diagram shown in f is a schematic diagram of the nanostructure, which is a nested square prism.

[0116] This embodiment proposes a hybrid integrated superlens, including the aforementioned multi-step structure and nanostructure.

[0117] In summary, this embodiment proposes a hybrid integrated superlens, which designs a superlens with a multi-step structure and a nanostructure. The multi-step structure includes multiple phase design steps of different heights that change the phase of the incident light. The nanostructure is disposed on the other side of the same substrate as the multi-step structure, thereby designing a hybrid integrated superlens that achieves the same function as the stepped substrate metasurface but with a simpler manufacturing process, making it easier to mass-produce and promote.

[0118] Example 2

[0119] Before implementing the hybrid integrated superlens design method proposed in this embodiment, the following steps are required to establish a nanostructure database:

[0120] Based on the minimum wavelength λ of the operating band of the hybrid integrated superlens min and maximum wavelength λ max Determine the periodic range of the nanostructure database. and the height range of nanostructures Where λ0 is the dominant wavelength, n s Refractive index of substrate material, n p Let P be the refractive index of the nanostructure material. When the minimum processable size (Critical dimension, CD) can be achieved, the period is determined as P = P0 (where the value of P0 ranges from 1 to 1). When the period P is specified, the range of variation of the nanostructure diameter Var_D = [CD, P0 - CD]. Parametric scans are performed on the period P and the nanostructure diameter D and height H within this period, with a scan step count of no less than 10 for both the period and the nanostructure diameter and height. This yields the phase (λ) and transmittance (λ) of different nanostructure diameters at different wavelengths within this period and height, thus establishing a nanostructure database. This database records information such as the period (P), structural geometry, material, height, transmittance, and phase of each nanostructure.

[0121] The structural methods include, but are not limited to: nanocylinders, nanocubes, nanohollow cylinders, nanohollow cuboids, nanocylinders nested in cylinders, and nanocubes nested in cuboids.

[0122] For example, for the phase compensation plate of the refractive-superlens hybrid optical system, the operating wavelength is selected as 4.8 μm, and the substrate material is silicon. The nanostructure database selected includes nanocylinders, nanoprismatics, nanorings, and nanorings with P = 1.3 μm, H = 4.8 μm, and D from 0.7 μm to 1.2 μm.

[0123] After establishing the nanostructure database, the following hybrid integrated superlens design method can be implemented, see [link to documentation]. Figure 4 The flowchart shown illustrates a design method for a hybrid integrated superlens. This embodiment proposes a design method for a hybrid integrated superlens, including the following specific steps:

[0124] Step 400: Determine the operating band of the hybrid integrated superlens, and based on the operating band, determine the substrate material of the hybrid integrated superlens, while selecting an intermediate wavelength from the operating band as the dominant wavelength of the operating band.

[0125] When the operating band is the wavelength range of infrared light, the substrate materials that can be selected include, but are not limited to: chalcogenide glass, zinc sulfide, zinc selenide, crystalline germanium, and crystalline silicon.

[0126] When the operating wavelength is within the visible light range, the substrate can be made of materials including, but not limited to: silicon nitride, titanium oxide, gallium nitride, gallium phosphide, hydrogenated amorphous silicon, sapphire, and silicon oxide.

[0127] When the hybrid integrated superlens to be designed is used as a phase compensation plate in the mid-infrared band (3.7-4.8μm), since the working band is 3.7-4.8μm, then the middle wavelength (4.25μm) in 3.7-4.8μm can be selected as the main wavelength.

[0128] Step 401: Based on the obtained dominant wavelength of the working band, calculate the step shape and size of the multi-step structure, and determine the nanostructure that forms the metasurface.

[0129] In step 401 above, in order to calculate the step shape and size of the multi-step structure based on the obtained dominant wavelength of the working band, the following steps (1) to (4) can be performed:

[0130] (1) Calculate the phase required for the main wavelength of the operating band;

[0131] (2) Based on the phase required for the obtained dominant wavelength, calculate the phase required for light with the dominant wavelength to pass through the phase design step in the substrate;

[0132] (3) Based on the refractive index of the substrate for light with the dominant wavelength, the phase required for light with the dominant wavelength to pass through the phase design steps in the substrate, and the dominant wavelength of the working band, calculate the substrate height of the phase design steps in the substrate; wherein, the substrate heights of adjacent phase design steps in the substrate are different, thereby forming the multi-step structure;

[0133] (4) Based on other wavelengths in the working band, the refractive index of the substrate for light of other wavelengths in the working band, and the substrate height of the phase design step in the substrate, the phase required for light of other wavelengths in the working band to pass through the phase design step in the substrate is calculated.

[0134] In step (1) above, the phase required for the main wavelength of the operating band is calculated, including the following steps (11) to (12):

[0135] (11) Determine the focal length of the hybrid integrated superlens;

[0136] (12) Calculate the phase required for the main wavelength of the working band based on the main wavelength of the working band and the focal length of the hybrid integrated superlens;

[0137] The required phase φ for the dominant wavelength of the operating band is obtained using the following formula. design Calculate (x, y):

[0138]

[0139] Where f represents the focal length of the optical lens generated by the hybrid integrated superlens; λ c This indicates the dominant wavelength of the operating band.

[0140] Of course, any other existing phase calculation method can be used to calculate the phase required for the main wavelength of the operating band, which will not be elaborated here.

[0141] In step (2) above, the phase required for light with the dominant wavelength to pass through the phase design step in the substrate is calculated:

[0142] The phase required for light with the dominant wavelength to pass through the phase-designed step in the substrate is calculated using the following formula:

[0143] φ c (x,y)=mod(φ design (x,y),2π)

[0144] Where, φ c (x,y) represents the phase required for light with the dominant wavelength to pass through the phase design step in the substrate, φ design (x,y) represents the phase required for the dominant wavelength of the operating band.

[0145] The step height of the phase design staircase in the substrate is calculated using the following formula:

[0146]

[0147] Where h(x,y) represents the step height of the phase design step in the substrate; φ c (x,y) represents the phase required for light with the dominant wavelength to pass through the phase design step in the substrate; n c This represents the refractive index of the substrate for light with the dominant wavelength.

[0148] In step (4) above, the other wavelengths in the working band refer to the wavelengths remaining in the working band other than the wavelengths selected as the main wavelength.

[0149] Then, the phase required for light of other wavelengths in the operating band to pass through the phase design step in the substrate is calculated using the following formula:

[0150]

[0151] Where h(x,y) represents the step height of the phase design step in the substrate; n(λ) represents the refractive index of the substrate for light of other wavelengths in the working band; λ represents other wavelengths in the working band; φ substrate (x,y,λ) represents the phase required for light of other wavelengths in the operating band to pass through the phase design steps in the substrate.

[0152] After calculating the shape and size of the multi-step structure based on the obtained dominant wavelength of the operating band, the following steps (41) to (42) can be performed to determine the nanostructure for forming the hybrid integrated superlens based on the obtained dominant wavelength of the operating band:

[0153] (41) Determine the design chromatic aberration phase of the hybrid integrated superlens, and calculate the required phase of the nanostructure based on the phase required when light of other wavelengths in the working band passes through the phase design step in the substrate and the determined design chromatic aberration phase;

[0154] (42) Retrieve from the nanostructure database and select a set of nanostructures whose phases are closest to the required phase of the nanostructure and can cover the full 2π phase, wherein the nanostructure database stores the correspondence between nanostructures and nanostructure phases.

[0155] In step (41) above, the design chromatic aberration phase of the hybrid integrated superlens corresponds to the function achieved by the designed optical lens.

[0156] In one embodiment, the correspondence between the design chromatic aberration phase of the hybrid integrated superlens and the optical lens formed by the hybrid integrated superlens can be expressed as follows:

[0157] Hybrid integrated superlens design: Chromatic phase 1 achromatic converging (positive) lens;

[0158] Hybrid integrated superlens design chromatic phase 2 achromatic divergence (negative) lens;

[0159] A phase compensation plate for a hybrid integrated superlens design chromatic aberration phase 3 refraction-superlens hybrid optical system.

[0160] Therefore, based on the optical lens to be formed by the hybrid integrated superlens, the design chromatic aberration phase of the hybrid integrated superlens corresponding to the optical lens to be formed can be determined.

[0161] To calculate the required phase for the nanostructure, the following formula is used:

[0162] φ total (x,y,)=mod(φ substrate (x,y,λ)+φ nanostructure (x,y,λ),2π)

[0163] Where, φ total (x,y,λ) represents the design color difference phase; φ nanostructure (x,y,λ) represents the phase required for the nanostructure.

[0164] In step (42) above, in order to find the nanostructure whose phase is closest to the required phase of the nanostructure from the nanostructure database, steps (421) to (422) can be performed.

[0165] (421) Retrieve the phases of each nanostructure from the nanostructure database;

[0166] (422) Calculate the difference between the phase of each nanostructure and the required phase of the nanostructure, and determine the nanostructure corresponding to the phase of the nanostructure with the smallest difference from the required phase of the nanostructure as the nanostructure whose phase is closest to the required phase of the nanostructure.

[0167] In step (422) above, when calculating the difference between the phase of each nanostructure and the required phase of the nanostructure, in one embodiment, the difference between the phase of each nanostructure and the required phase of the nanostructure can be calculated directly, that is: the phase of the nanostructure minus the required phase of the nanostructure to obtain the difference between the phase of the nanostructure and the required phase of the nanostructure.

[0168] In another implementation, the search for nanostructures can be performed using an optimization algorithm that minimizes the weighted error, the principle of which can be expressed by the following formula:

[0169]

[0170] Where Δ(x,y) represents the difference between the phase of each nanostructure and the required phase of the nanostructure.

[0171] (x,y,λ i ) represents a wavelength of λ i The phase required for nanostructures under certain conditions This indicates that the j-th nanostructure in the nanostructure database is at wavelength λ. i The nanostructure phase below, c i Indicates wavelength λ iThe weighting coefficient is usually 1.

[0172] Step 402: Form the hybrid integrated superlens according to the calculated shape and size of the multi-step structure and the shape and size of the nanostructure.

[0173] Step 403: Perform full-spectrum simulation on the formed hybrid integrated superlens to obtain simulation results.

[0174] Specifically, a full-spectrum simulation is performed on the designed hybrid integrated superlens, and the minimum wavelength λ in the working band of the hybrid integrated superlens is obtained. min up to the maximum wavelength λ max The wavelength interval is not less than (λ) max -λ min The light field propagation is performed by 10 / 10, and then all light fields are weighted and superimposed to obtain the full spectrum simulation result.

[0175] In this process, the weighting value used when weighting and superimposing all light fields is the relative amplitude of each wavelength in the working band (i.e., the square root of the intensity ratio of light). Generally, all weighting coefficients are 1. For example, when designing the resulting hybrid integrated superlens as a broadband converging lens, the condition for whether the light rays passing through the hybrid integrated superlens converge well to the same point is used as a criterion for whether the design meets the requirements.

[0176] Specifically, the convergence condition is that the half-width of the light focal point along the optical axis is less than or equal to twice the half-width defined by the diffraction limit, i.e. in, It is the average wavelength of light incident on the hybrid integrated superlens; NA is the numerical aperture of an optical system composed of a multi-step structure and nanostructures on the other side of the substrate; FWHM real Used to represent the half-width of the light focal point along the optical axis.

[0177] Step 404: When the simulation results obtained can realize the functions that the optical lens to be generated by the hybrid integrated superlens can achieve, it is determined that the designed hybrid integrated superlens meets the functional requirements of the optical lens.

[0178] Otherwise, if the simulation results fail to achieve the functions that the optical lens to be generated by the hybrid integrated superlens can achieve, then return to step 400 and try to use other wavelengths as the main wavelength to design the hybrid integrated superlens until it is determined that the designed hybrid integrated superlens meets the functional requirements of the optical lens.

[0179] For example, the hybrid integrated superlens design method proposed in this embodiment can be applied to design the following lenses:

[0180] 1) A superlens is needed as a far-infrared (8-12μm) converging lens with a focal length of -10mm and an aperture of 6mm, free from chromatic and spherical aberrations. A dominant wavelength of 10μm and a silicon substrate are selected. A database of nanostructures (P=3μm, H=8μm) including nanocylinders, nanoprismatics, nanorings, and nanorings is required.

[0181] According to the following formulas Eq-1 to Eq-3, the height of the corresponding multi-step structure can be obtained as follows: Figure 6 The chromatic phase difference at 8μm, 10μm, and 12μm corresponding to this substrate height is obtained from formula Eq-4, referencing... Figure 7 a in Figure 7 b and Figure 7 c in the text.

[0182] The phase φ required based on the dominant wavelength of the operating band design Then, the shape (x, y, h) of the multi-step structure on the substrate is calculated. The point on the substrate with coordinates (x, y) corresponds to the center wavelength λ. c Required phase φ c As shown in formula Eq-1:

[0183] φ c (x,y)=mod(φ design (x,y),2π)(Eq-1)

[0184] When the required phase is for a diverging lens (focal length f), the phase is designed as shown in formula Eq-2:

[0185]

[0186] In the formula, mod(, 2π) is the formula for the remainder when the specific value is taken as 2π. The phase φ required when designing the phase step in the substrate based on the light with the stated dominant wavelength is used. c The height h(x,y) at the base coordinates (x,y) can be determined using (x,y) and formula Eq-3:

[0187]

[0188] In the formula, n c Let be the refractive index of the substrate material at the dominant wavelength. The refractive index of the substrate at other wavelengths λ can be calculated based on the substrate thickness h(x,y). c Phase modulation, as shown in Eq-4:

[0189]

[0190] In the formula, n(λ) is the refractive index of the substrate material at wavelength λ.

[0191] To correct chromatic aberrations in the 8μm-12μm range, the phase of the nanostructure must satisfy the formula described above for calculating the required phase of the nanostructure. Furthermore, based on the formula for calculating the required phase of the nanostructure, the nanostructure units at different design locations of the entire hybrid integrated superlens can be obtained. Phase discretization can be performed using the formula described above for an optimization algorithm that minimizes the weighted error when searching for nanostructures.

[0192] Then, based on the formula for calculating the phase required for the nanostructure and the formula for the optimization algorithm that minimizes the weighted error for finding the nanostructure, the arrangement of the nanostructure is obtained.

[0193] Finally, the formed hybrid integrated superlens was subjected to full-spectrum simulation to obtain focusing effect diagrams in the full spectrum from 8μm to 12μm, thus verifying the focusing effect.

[0194] 2) Phase correction plate of refractive-superlens optical system

[0195] The phase correction plate of the refractive-superlens optical system consists of one superlens and two refractive lenses, operating in the 8-12μm wavelength range, with a half-field angle of view of 20°, an F-number of 0.8, and a total optical length of 85mm. The system configuration is as follows: Figure 8 As shown, the superlens is located in Figure 8 The middle; the refractive lens is located in the middle. Figure 8 The phase of the phase correction plate of the refractive-superlens optical system, with its multi-step structure, is shown in formula Eq-5.

[0196]

[0197] Where A, B, C, and D represent the phase distribution coefficients, respectively; ρ represents the radial coordinate of the phase correction plate surface of the refractive-superlens optical system, and R is the normalized radius.

[0198] Based on the above formulas Eq-1, Eq-3, Eq-4, and the formula for calculating the required phase of the nanostructure, the step height of the multi-step structure of the correction plate can be obtained. According to the formula for the optimization algorithm that minimizes the weighted error in finding the nanostructure, the required theoretical phase diagrams of the nanostructure at 8μm, 10μm, and 12μm can be obtained.

[0199] In summary, this embodiment proposes a design method for a hybrid integrated superlens. The method determines the operating wavelength of the hybrid integrated superlens and selects an intermediate wavelength as the dominant wavelength of the operating wavelength. Based on the obtained dominant wavelength of the operating wavelength, the shape and size of the multi-step structure and the nanostructure forming the hybrid integrated superlens are obtained. The hybrid integrated superlens is formed according to the obtained shape and size of the multi-step structure and the shape and size of the nanostructure. When the obtained simulation results can achieve the required functions of the hybrid integrated superlens, it is determined that the designed hybrid integrated superlens meets the functional requirements of an optical lens. Thus, a hybrid integrated superlens capable of achieving the target effect can be obtained based on the functional requirements of an optical lens.

[0200] Example 3

[0201] See Figure 5 The flowchart shown illustrates a hybrid integrated superlens fabrication method. This embodiment proposes an all-dielectric hybrid integrated superlens fabrication method for fabricating the hybrid integrated superlens proposed in Embodiment 1 above. The fabrication method includes the following specific steps:

[0202] Step 500: Perform grayscale exposure etching on the substrate to obtain the multi-step structure of the hybrid integrated superlens.

[0203] Step 501: Coat the other side of the same substrate as the multi-step structure with photoresist.

[0204] Step 502: Expose the photoresist to form the nanostructure.

[0205] Step 503: Etch and remove the remaining photoresist to obtain the superlens that integrates the multi-step structure and the nanostructure.

[0206] In summary, the hybrid integrated superlens fabrication method proposed in this embodiment is simpler and easier to mass-produce and promote than the fabrication process of a stepped substrate metasurface because the hybrid integrated superlens sets the multi-step structure and nanostructure on two different surfaces of the same substrate. The fabrication processes of the two surfaces can be carried out separately without affecting each other. At the same time, compared with the nanostructure set on the stepped substrate, the nanostructure set on the plane has a more uniform etching depth, higher precision, greater arrangement freedom, stronger phase control capability, more functions that can be realized, and a wider range of application scenarios.

[0207] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A hybrid integrated superlens, characterized in that, The invention includes a multi-step structure and a nanostructure disposed on two different surfaces of the same flat substrate; the multi-step structure includes multiple phase design steps for changing the phase of incident light, and the heights of adjacent phase design steps are different; the nanostructure has a uniform height and is disposed on another surface of the same substrate as the multi-step structure, and is used to modulate the phase of incident light; the nanostructure is a columnar structure, a hollow structure, or a nested structure.

2. The hybrid integrated superlens as described in claim 1, characterized in that, The column structure is a cylinder or a square column; The hollow structure is a hollow cylinder or a hollow square prism; The nested structure is either a cylinder nested within a cylinder or a square prism nested within a square prism.

3. The design method of the hybrid integrated superlens as described in any one of claims 1-2, characterized in that, Includes the following steps: (1) Determine the working band of the hybrid integrated superlens, and take the middle wavelength of the working band as the main wavelength of the working band. The middle wavelength of the working band is the average of the minimum and maximum values ​​of the working band. (2) The phase required for light with the dominant wavelength to pass through the phase design step in the substrate is calculated using the following formula: in, The coordinates are determined by a coordinate system established with the center of the base as the origin. This indicates the phase required for light with the dominant wavelength to pass through the phase design steps in the substrate. This indicates the phase required for the dominant wavelength of the operating band; (3) The step height of the phase design staircase in the substrate is calculated using the following formula: in, This indicates the step height of the phase design steps in the substrate; This indicates the dominant wavelength of the operating band; Indicates wavelength as The phase required for light rays to pass through the phase design steps in the substrate; Indicates that the substrate is at wavelength. The refractive index of light; (4) The phase required for light of other wavelengths in the working band to pass through the phase design step in the substrate is calculated using the following formula: in, This indicates the step height of the phase design steps in the substrate; This indicates the refractive index of the substrate for light of other wavelengths in the operating band; Indicates other wavelengths within the operating band; This indicates the phase required for light of other wavelengths in the operating band to pass through the phase design steps in the substrate; (5) The phase required for the nanostructure is calculated using the following formula: in, Indicates the phase of the design color difference; The phase required to represent nanostructures; (6) Retrieve from the nanostructure database and select a set of nanostructure phases that are closest to the required phase of the nanostructure and can cover the entire The phase of the nanostructure; specifically: query the phase of each nanostructure from the nanostructure database; calculate the difference between each nanostructure phase and the required phase of the nanostructure, and determine the nanostructure corresponding to the nanostructure phase with the smallest difference from the required phase of the nanostructure as the nanostructure whose phase is closest to the required phase of the nanostructure. (7) Determine the distribution of the multi-step structure according to the height of the multi-step structure calculated in step (3), and the shape and size of the nanostructure selected in step (6) to form the hybrid integrated superlens.

4. The design method of the hybrid integrated superlens as described in claim 3, characterized in that, In step (2), the phase required for the dominant wavelength of the operating band is calculated, including the following steps: S1: Determine the focal length of the hybrid integrated superlens; S2: Calculate the phase required for the main wavelength of the working band based on the main wavelength of the working band and the focal length of the hybrid integrated superlens; The required phase of the dominant wavelength in the operating band can be determined using the following formula. Perform the calculation: Where f represents the focal length of the optical lens generated by the hybrid integrated superlens; This indicates the dominant wavelength of the operating band.

5. The design method of the hybrid integrated superlens as described in claim 3, characterized in that, The method for establishing the nanostructure database includes the following steps: (1) Based on the minimum wavelength of the operating band of the hybrid integrated superlens and maximum wavelength Determine the periodic range of the nanostructure database. and the height range of nanostructures ,in The main wavelength, The refractive index of the substrate material, The refractive index of nanostructured materials; (2) When the process reaches the minimum processable size CD, the cycle is determined as P = P0, where: the range of values ​​for P0 is When the diameter of the nanostructure varies, Var_D = [CD, P0] CD]; (3) Perform parameter scanning on the period P and the diameter D and height H of the nanostructure under this period respectively. The number of scanning steps for the period, the diameter and height of the nanostructure are not less than 10. Obtain the phase and transmittance of different nanostructure diameters at different wavelengths under this period and height, thereby establishing the nanostructure database.

6. The design method of the hybrid integrated superlens as described in claim 3, characterized in that, In step (1), the substrate material of the hybrid integrated superlens is determined according to the type of the working band.

7. The design method of the hybrid integrated superlens as described in claim 6, characterized in that, When the operating band is the wavelength range of infrared light, the substrate material is chalcogenide glass, zinc sulfide, zinc selenide, crystalline germanium, or crystalline silicon. When the operating band is the wavelength range of visible light, the substrate material is silicon nitride, titanium oxide, gallium nitride, gallium phosphide, hydrogenated amorphous silicon, sapphire, or silicon oxide.

8. The method for fabricating a hybrid integrated superlens as described in any one of claims 1-2, characterized in that, Includes the following steps: (1) The multi-step structure of the hybrid integrated superlens is obtained by grayscale exposure etching of the substrate; (2) On the other side of the same flat substrate as the multi-step structure, photoresist is applied without depositing a structural layer; (3) The nanostructure is formed by exposure on the photoresist; (4) Etch and remove the remaining photoresist to obtain the hybrid integrated superlens.

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