CN115236851B - Planar metalens and its design method based on global control principle - Google Patents

Abstract

The invention provides a design method of a planar superlens based on a global regulation principle, which comprises the steps of presetting topological charge number, expected focal length and diameter data of the planar superlens to design a structural pattern of the planar superlens; selecting a substrate and a metal layer, wherein the substrate is made of a light-transmitting material with complete transmission property for light, and the metal layer is made of a metal material with complete reflection or complete absorption property for light; manufacturing a substrate layer with a proper size according to the diameter of the planar superlens, and depositing a metal layer on the substrate layer; and etching the designed structural pattern of the planar superlens on the metal layer to ensure that the hole pattern grating array of the pattern on the metal layer is completely transparent and the rest part is completely light-blocking, thus obtaining the planar superlens.

Description

Planar metalens and its design method based on global control principle

Technical Field

The present invention relates to the field of optoelectronic technology, and more specifically to a planar metalens based on a global control principle and a design method thereof.

Background technique

Lenses, as an important component of optical systems, have attracted extensive attention from researchers in terms of their structural design and performance improvement. However, traditional optical lenses and Fresnel lenses are limited by their physical mechanisms, are large in size, and have single functions, and cannot meet the requirements of miniaturization, integration, and multi-performance of optical devices in modern optical systems. In order to solve this problem, researchers have designed a device that can realize the function of a lens based on a metasurface, namely a metalens. A metalens is composed of an array of artificial unit structures at a sub-wavelength scale. Through the local interaction between light and the unit structure, the wavefront of the incident light is divided into several sub-wave sources to achieve phase modulation, thereby realizing the functions of a lens such as focusing. It has the advantages of ultra-thin thickness, small size, and multi-dimensional regulation. The introduction of a metalens provides a new idea for regulating the light field in micro-nano integrated optical systems.

At present, the design of metalenses is to achieve local phase control by the resonant and non-resonant effects of subwavelength scatterers on light. The resonant effect type metalens is a resonant cavity structure designed to cause a sudden change in phase through surface plasmon resonance or Mie resonance. However, the resonance effect is related to the wavelength. Therefore, the metalens designed based on this principle can only work within a narrow band; non-resonant effect type metalens such as propagation phase or geometric phase method can effectively expand the working bandwidth. For propagation phase type metalens, it is necessary to design the unit structure with a large aspect ratio to meet the change of accumulated phase to change the wavefront of the light wave. For geometric phase type metalens, the wavefront is controlled by the relationship between the rotation angle and phase of the nanostructure unit. Its performance strongly depends on the precise rotation angle of the unit structure and the polarization state of the incident light. This method has mode selection for the incident light and can only control the incident light of a specific polarization or topological state. It is necessary to introduce additional optical devices to pre-process the light source; the hybrid metalens based on geometric phase and propagation phase modulation combines the advantages of the two control mechanisms, but such a lens structure design is more complex, and the processing difficulty and cost are greater.

In summary, there are still the following deficiencies in the design of planar metalens:

(1) The current research on superlenses all starts from the metasurface and is based on the local regulation of the unit structure, which makes the superlens a local regulation element and lacks a clear connection between the local unit and the whole. All methods inevitably involve the design combination of the geometric morphology, size and spatial arrangement of a single micro-nano structure. It is necessary to design a reasonable period corresponding to the nano-unit structure so that the scattering of light waves in the structural unit is only a local effect, and the coupling and crosstalk between the scattering units can be ignored. The process from design to manufacturing is relatively complicated, and the processing technology requirements are strict, which makes the cost of superlenses high and greatly limits the development of its application industrialization;

(2) Each unit structure in the metasurface array plays an important role in regulating the response to incident light. Therefore, a single metalens cannot achieve the regulation of any complex structured light field. After the structure is fixed, it can only act on a specific mode of light.

(3) Although reconfigurable metasurfaces make it possible to realize multifunctional metalenses, the functions of current single metalenses are still relatively limited, making it difficult to realize multifunctional planar metalenses.

Summary of the invention

In view of this, the first purpose of the present invention is to provide a design method of a planar metalens based on the global control principle, by overall designing the lens structure pattern, so as to realize focusing control of a spatial structure light beam with arbitrary spatial phase and polarization structure.

Based on the same inventive concept, a second object of the present invention is to provide a planar metalens based on the global control principle.

The first object of the present invention can be achieved by adopting the following technical solutions:

A design method of a planar metalens based on a global control principle comprises the following steps:

Designing a structural pattern of a planar metalens according to a preset topological charge, an expected focal length, and diameter data of the planar metalens, wherein the structural pattern includes a plurality of non-periodically distributed hole-type grating arrays;

Selecting materials for the substrate and the metal layer, wherein the substrate material is a light-transmitting material having a completely light-transmitting property, and the metal layer material is a metal material having a total reflection or total absorption property for light;

According to the diameter of the planar metalens, a base layer with an adapted size is manufactured, and a metal layer is deposited on the base layer;

The structural pattern of the designed planar superlens is etched on the metal layer, so that the hole-type grating array part of the pattern on the metal layer is completely light-transmissive and the rest of the pattern is completely light-blocking, thereby obtaining a planar superlens.

Furthermore, the deposition thickness of the deposited metal layer is no more than one tenth of the working wavelength.

Furthermore, the substrate material is glass, and the metal layer material is gold.

Furthermore, the pre-set structural pattern of the planar metalens is designed according to the topological charge, the expected focal length and the diameter of the planar metalens, including:

The angle cosine wave related to the topological charge is used as the reference light to interfere with the spherical wave carrying the expected focal length information to obtain the amplitude hologram.

The amplitude hologram is represented by a transmittance function, and the transmittance function is processed using a threshold truncation function related to the amplitude to obtain a transmittance function expression related to the topological charge and carrying the expected focal length information.

The pattern corresponding to the transmittance function expression is calculated to obtain the structural pattern of the planar metalens.

Furthermore, the angular cosine wave associated with the topological charge has a cosine periodic profile (circular grating) along the azimuth angle, and its expression is cos(mθ), where m is a non-zero integer representing the topological charge of the oscillation frequency of the angular cosine wave, and θ is the azimuth angle.

Furthermore, the expression of the spherical wave carrying the expected focal length information is: Where/> is the phase distribution of the spherical wavefront, expressed as/> In the expression, λ is the operating wavelength, x and y are the spatial coordinates of the spherical wavefront, and _zf is the expected focal length.

Furthermore, the amplitude hologram is represented by a transmittance function, and the transmittance function is processed using a threshold truncation function related to the amplitude, so as to obtain a transmittance function expression related to the topological charge and carrying the expected focal length information, including:

Assume t(x,y) represents the transmittance function of the amplitude hologram at the position (x,y), which can be expressed as:

Define an amplitude-dependent threshold cutoff function q(x, y), q = arcsin(A(x, y))/π, where A(x, y) is a bias function that can adjust the non-uniform distribution of the incident amplitude. Using the Signal sign function, set the values of t(x, y) that are less than and greater than the threshold to 0 and 1, respectively, that is:

Because the hologram is produced by the interference of two waves in the transverse plane, based on the paraxial approximation, Simplified to:

After sorting and derivation, the transmittance function expression is:

The second object of the present invention can be achieved by adopting the following technical solutions:

A planar metalens based on the global control principle, comprising:

The metal layer is made of a metal material having total reflection or total absorption characteristics for light, and has a structural pattern including a plurality of non-periodically distributed hole-type grating arrays; the structural pattern carries focal length information of the metalens; in the structural pattern, the hole-type grating array portion is completely light-transmissive, and the remaining portion is completely light-blocking;

The substrate is made of a light-transmitting material with a completely light-transmitting property and is used to carry the metal layer.

Furthermore, the substrate is a glass substrate, the metal layer is a gold film, and the thickness of the gold film is no more than one tenth of the working wavelength.

Furthermore, the structural pattern is a plurality of non-periodically distributed hole grating arrays having rotational symmetry and axial symmetry.

Further, the structural pattern is obtained by the following method:

The angle cosine wave related to the topological charge is used as the reference light to interfere with the spherical wave carrying the expected focal length information to obtain an amplitude hologram; the expression of the angle cosine wave is cos(mθ), where m is a non-zero integer representing the topological charge of the oscillation frequency of the angle cosine wave, and θ is the azimuth angle; the expression of the spherical wave carrying the expected focal length information is in is the phase distribution of the spherical wavefront, expressed as/> In the expression, λ is the operating wavelength, x and y are the spatial coordinates of the spherical wavefront, and z _f is the expected focal length;

The amplitude hologram is represented by a transmittance function, and the transmittance function is processed using a threshold truncation function related to the amplitude to obtain a transmittance function expression related to the topological charge and carrying the expected focal length information.

The pattern corresponding to the transmittance function expression is calculated to obtain the structural pattern of the planar metalens.

Furthermore, the transmittance function expression is:

The pattern corresponding to the transmittance function expression is calculated, and the obtained structural pattern of the planar metalens has |m|-fold rotational symmetry and |m|-root symmetry axes.

The present invention has the following beneficial effects compared with the prior art:

1. Different from the traditional planar metalens based on local unit regulation, the present invention proposes an ultra-thin planar metalens based on a global regulation mechanism with a thickness less than the sub-wavelength level, which realizes Fourier transform, imaging, broadband response, scalar and vector light field regulation and other functions on a single lens structure.

2. The planar metalens proposed in the present invention can add a converging spherical wavefront to incident light with arbitrary spatial structure by designing the structural pattern. When the incident light is diffracted by the planar metalens structure, the output light can be focused at the expected focus and maintain the initial phase and polarization characteristics. Therefore, the incident light is mode-free, and the focusing requirements of plane waves (scalar light fields) and light beams with arbitrary spatial phase and polarization structures can be met.

3. Compared with traditional optical lenses, the planar metalens proposed in the present invention is ultra-thin (the thickness can be less than one-tenth of the working wavelength) and can be applied to miniaturized modern optical application scenarios; compared with the metalens, this planar metalens has a simple structure, reduces the cost of processing and manufacturing, and greatly expands the application prospects of planar metalens.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a planar superlens structure pattern of Example 1 of the present invention.

FIG. 2 is a diagram of a plane wave focusing experimental device according to Embodiment 2 of the present invention.

FIG3 is a diagram showing the plane wave focusing experiment results of the planar metalens of Example 2 of the present invention.

Figure 4 is a focusing experiment result diagram of the structured light field of the planar metalens of Example 2 of the present invention, wherein (a) is a light field intensity distribution diagram of the x-z plane after the vector light field passes through the planar lens sample, (b) is a light field distribution diagram of the focal plane corresponding to (a), (c) is a schematic diagram of the focal plane x component corresponding to (b) obtained using a polarizer, (d) is a light field intensity distribution diagram of the x-z plane after the vortex light field passes through the planar lens sample, (e) is a light field distribution diagram of the focal plane corresponding to (d), and (f) is an interference pattern obtained by interfering the vortex light in the focal plane with the plane wave.

FIG5 is a diagram of a Fourier transform performance verification experimental device according to Embodiment 3 of the present invention.

FIG6 is a diagram showing the Fourier transform performance verification experiment results of the planar metalens of Example 3 of the present invention.

FIG7 is a diagram showing the experimental results of the imaging performance of the planar metalens of Example 3 of the present invention, wherein FIGS. a and c are imaging results, and FIG. b is a schematic diagram of the imaging target.

FIG8 is a diagram showing the broadband performance experimental results of the planar metalens of Example 3 of the present invention, wherein FIGa shows the light field intensity distribution in the x-z plane after plane waves of different wavelengths are incident on the planar lens sample, and FIGb shows the light field distribution in the focal plane.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

Embodiment 1:

This embodiment provides a design method of a planar metalens based on a global control principle, comprising the following steps:

S10, designing a structural pattern of a planar metalens according to a preset topological charge, an expected focal length, and diameter data of the planar metalens, wherein the structural pattern comprises a plurality of non-periodically distributed hole-type grating arrays, including:

S11. In this embodiment, the expected focal length z _f is set to 50 μm, the diameter is set to 70 μm, and the topological charge number m is set to 8.

S12. Using the angle cosine wave expressed as cos(mθ) as the reference light, the phase distribution between the angle cosine wave and the spherical wavefront is Spherical waves/> Interference is performed to obtain an amplitude hologram.

S13. Let t(x,y) represent the transmittance function of the amplitude hologram at the position (x,y), which can be expressed as:

Define an amplitude-dependent threshold cutoff function q(x, y), q = arcsin(A(x, y))/π, where A(x, y) is a bias function that can adjust the non-uniform distribution of the incident amplitude. Using the Signal sign function, set the values of t(x, y) that are less than and greater than the threshold to 0 and 1, respectively, that is:

Because the hologram is produced by the interference of two waves in the transverse plane, based on the paraxial approximation, Simplified to:

After sorting and derivation, the transmittance function expression is:

S14. Calculate the pattern corresponding to the transmittance function expression, and obtain the structural pattern of the planar metalens as shown in FIG1.

S20, selecting materials for the substrate and the metal layer, wherein the substrate material is a light-transmitting material with a completely light-transmitting property, and the metal layer material is a metal material with a total reflection or total absorption property for light. In this embodiment, the substrate material is light-transmitting glass, and the metal layer material is gold.

S30. According to the diameter of the planar superlens, a base layer of an appropriate size is manufactured, and a metal layer is deposited on the base layer. In this embodiment, a gold film with a thickness not greater than one tenth of the working wavelength is deposited on a 0.3 mm glass substrate.

S40. Use focused ion beam technology to etch the structural pattern of the designed planar metalens on the gold film, so that the white part of the pattern on the metal layer is completely light-transmitting and the black part is completely light-blocking, thereby obtaining a planar metalens.

Embodiment 2:

This embodiment provides a planar metalens based on the global control principle and is used for focusing plane waves and structured light fields, specifically including:

S10, manufacturing a planar metalens sample, including:

S11, setting the expected focal length z _f = 50 μm, the diameter to 70 μm, the topological charge number m = 4, 6, 8, 10, and designing the structural pattern of the planar metalens;

S12. A gold film with a thickness not greater than one tenth of the working wavelength is deposited on a 0.3 mm glass substrate, and a structural pattern of the designed planar superlens is etched on the gold film, so that the hole-shaped grating array part of the pattern on the metal layer is completely light-transmitting, and the rest of the pattern is completely light-blocking, thereby obtaining four planar superlenses corresponding to m=4, 6, 8, and 10.

S20, build a plane wave focusing optical system, as shown in Figure 2. In this embodiment, the light source is a helium-neon laser (working wavelength is 632.8nm), which is collimated and expanded, and the light is incident on the plane metalens sample. The diffraction field after passing through the sample is collected by a 150× objective lens and a tube lens and projected onto a camera (CCD) to achieve the focusing of the plane wave.

S30. Build a structured light field focusing optical system based on the experimental device shown in Figure 2. After preparing the vector light and vortex light, make the vector light and vortex light incident on the plane metalens sample corresponding to m=8, respectively. Use a 150× magnification objective lens and a tube lens to collect the light field intensity distribution after passing through the sample and project it onto the CCD to achieve focusing of the structured light beam.

In this embodiment, the focusing experiment results of the plane wave focusing optical system are shown in Figure 3. It can be seen that the light modulated by the plane metalens produces a focusing effect near z = 50 μm, and the light field distribution on the focal plane is shown in Figure 3 (b). The half-height width of the focus measured in the experiment is about 540nm, achieving a sub-wavelength focusing effect.

In this embodiment, the focusing experiment results of the structured light field focusing optical system are shown in Figure 4. It can be seen that the planar metalens sample focuses the structured light field to the focal plane z = 50μm, the peak-to-peak value of the focal spot is 1.2μm, the half-height width of the central dark ring is close to 600nm, and the planar metalens does not change the phase and polarization characteristics of the incident light field.

Embodiment 3:

This embodiment provides a planar metalens based on the global control principle and is used for Fourier transform, specifically including:

S10, manufacturing a planar metalens sample, including:

S11, setting the expected focal length z _f = 18 cm, the diameter to 5 mm, the topological charge m to 8, and designing the structural pattern of the planar metalens;

S12. A gold film with a thickness not greater than one tenth of the working wavelength is deposited on a 0.3 mm glass substrate, and a structural pattern of the designed planar superlens is etched on the gold film, so that the hole-shaped grating array part of the pattern on the metal layer is completely light-transmitting and the rest of the pattern is completely light-blocking, thereby obtaining a planar superlens.

S20. Build an experimental system, as shown in Figure 5. The light emitted by the laser is collimated and incident on a reflective spatial light modulator (SLM) loaded with an Airy beam phase diagram, and then incident on the planar metalens sample. The diffraction field after passing through the lens is collected using a CCD. The cross-sectional view of the Airy beam experimentally photographed at different propagation distances is shown in Figure 6.

FIG7 illustrates the experimental results of imaging, where FIGS. a and c are the imaging results and FIG. b is a schematic diagram of the imaging target. It can be seen that the plane lens sample clearly displays the image of the highlighted area in the resolution plate.

The experimental results of broadband response are shown in Figure 8. Under illumination of light sources of different wavelengths, the plane lens can modulate and focus the incident light. Figure 8 (a) shows the light field intensity distribution in the xz plane after plane waves of different wavelengths are incident on the plane lens sample. When the wavelength is scanned from 430nm to 780nm, the visible light can be focused to different axial propagation positions (i.e., z _f ) of 28.9cm-15cm; the light field distribution in the focal plane is shown in Figure 8 (b). The half-height width of the focus measured in the experiment is about 30μm.

It can be seen that the planar metalens of this embodiment successfully converts the amplitude information of the Airy light field near the focal plane, and the Airy light beam converted using the phase information has the properties of diffraction-free transmission and self-acceleration.

In summary, the present invention proposes an ultra-thin planar metalens, which realizes multiple functions such as Fourier transform, imaging, broadband response, scalar and vector light field control on a single lens structure, and can meet the focusing requirements of plane waves (scalar light fields) and light beams with arbitrary spatial phase and polarization structures. Compared with traditional optical lenses and existing metalenses, they have their own advantages, which greatly expands the application prospects of planar metalenses.

Obviously, the embodiments described above are only part of the embodiments of the present invention, rather than all of the embodiments. The present invention is not limited to the details of the above embodiments, and any appropriate changes or modifications made by ordinary technicians in the relevant technical field are deemed to be within the patent scope of the present invention.

Claims (5)

1. A design method for a planar metalens based on a global control principle, characterized in that it comprises the following steps: Designing a structural pattern of a planar metalens according to a preset topological charge, an expected focal length, and diameter data of the planar metalens, wherein the structural pattern includes a plurality of non-periodically distributed hole-type grating arrays; Selecting materials for the substrate and the metal layer, wherein the substrate material is a light-transmitting material having a completely light-transmitting property, and the metal layer material is a metal material having a total reflection or total absorption property for light; According to the diameter of the planar metalens, a base layer with an adapted size is manufactured, and a metal layer is deposited on the base layer; Etching a designed planar metalens structure pattern on the metal layer so that the hole-shaped grating array portion of the pattern on the metal layer is completely light-transmissive and the rest of the pattern is completely light-blocking, thereby obtaining a planar metalens; The method of designing a structural pattern of the planar metalens according to a preset topological charge, an expected focal length, and a diameter of the planar metalens comprises: The angle cosine wave related to the topological charge is used as the reference light to interfere with the spherical wave carrying the expected focal length information to obtain the amplitude hologram. The amplitude hologram is represented by a transmittance function, and the transmittance function is processed using a threshold truncation function related to the amplitude to obtain a transmittance function expression related to the topological charge and carrying the expected focal length information. Calculate the pattern corresponding to the transmittance function expression to obtain the structural pattern of the planar metalens; The angular cosine wave associated with the topological charge has a cosine periodic profile along the azimuth angle, and its expression is cos(mθ), where m is a non-zero integer representing the topological charge of the oscillation frequency of the angular cosine wave, and θ is the azimuth angle; The expression of the spherical wave carrying the expected focal length information is: Where/> is the phase distribution of the spherical wavefront, expressed as/> In the expression, λ is the operating wavelength, x and y are the spatial coordinates of the spherical wavefront, and z _f is the expected focal length; Assume that the transmittance function t(x,y) of the amplitude hologram at the position (x,y) is: Define an amplitude-dependent threshold cutoff function q(x,y), q = arcsin(A(x,y))/π; A(x,y) is a bias function used to adjust the non-uniform distribution of the incident amplitude; use the Signal sign function to set the t(x,y) value less than the threshold to 0, and the t(x,y) value greater than the threshold to 1, that is: Phase distribution of spherical wavefront Simplified to: After sorting and derivation, the transmittance function expression is: 2. The design method of a planar metalens based on the global control principle according to claim 1 is characterized in that the deposition thickness of the deposited metal layer is not greater than one tenth of the working wavelength. 3. The design method of a planar metalens based on the global control principle according to claim 1 is characterized in that the substrate material is glass and the metal layer material is gold. 4. A planar metalens based on the global control principle, characterized by comprising: The metal layer is made of a metal material having total reflection or total absorption characteristics for light, and has a structural pattern including a plurality of non-periodically distributed hole-type grating arrays; the structural pattern carries focal length information of the metalens; in the structural pattern, the hole-type grating array portion is completely light-transmissive, and the remaining portion is completely light-blocking; The substrate is made of a light-transmitting material with a completely light-transmitting property and is used to carry the metal layer; The structural pattern is a plurality of non-periodically distributed hole-type grating arrays with rotational symmetry and axial symmetry; the structural pattern is obtained by the following method: The angle cosine wave related to the topological charge is used as the reference light to interfere with the spherical wave carrying the expected focal length information to obtain the amplitude hologram. The amplitude hologram is represented by a transmittance function, and the transmittance function is processed using a threshold truncation function related to the amplitude to obtain a transmittance function expression related to the topological charge and carrying the expected focal length information. Calculate the pattern corresponding to the transmittance function expression to obtain the structural pattern of the planar metalens; The angular cosine wave associated with the topological charge has a cosine periodic profile along the azimuth angle, and its expression is cos(mθ), where m is a non-zero integer representing the topological charge of the oscillation frequency of the angular cosine wave, and θ is the azimuth angle; the expression of the spherical wave carrying the expected focal length information is Where/> is the phase distribution of the spherical wavefront, expressed as/> In the expression, λ is the working wavelength, x and y are the spatial coordinates of the spherical wavefront, and z _f is the expected focal length; let the transmittance function t(x,y) of the amplitude hologram at the position (x,y) be: Define an amplitude-dependent threshold cutoff function q(x,y), q = arcsin(A(x,y))/π; A(x,y) is a bias function used to adjust the non-uniform distribution of the incident amplitude; use the Signal sign function to set the t(x,y) value less than the threshold to 0, and the t(x,y) value greater than the threshold to 1, that is: Phase distribution of spherical wavefront Simplified to: After sorting and derivation, the transmittance function expression is: 5. The planar metalens based on the global control principle according to claim 4 is characterized in that the substrate is a glass substrate, the metal layer is a gold film, and the thickness of the gold film is not more than one tenth of the working wavelength.