A design method for broadband planar thin-film metalens

Abstract

The present invention discloses a method for designing a broadband planar thin-film metalens, comprising the following steps: 1) determining the phase function, broadband group delay function, and group delay dispersion function of the target metalens needle, and dividing the target metalens into three segments of 0-π, π-2π, and 2π-3π along the radial direction at intervals of π; 2) determining a microstructure library of the target metalens; 3) dividing the 0-π segment and the 2π-3π segment of the target metalens into a plurality of grid points according to the microstructure arrangement period, finding the microstructure with the highest matching degree with the phase, group delay, and group delay dispersion value required by the grid point in the microstructure library, and filling it into the grid point to obtain the far-field focusing results of the 0-π and 2π-3π segments of the metalens; 4) filling the π-2π segment of the metalens and optimizing the microstructure arrangement to obtain the best result. The present invention can achieve a metalens with a larger aperture and a larger numerical aperture, and maintain polarization independence, focusing efficiency, and focal length consistency.

Description

Technical Field

[0001] The present invention relates to the fields of optical imaging and optical device integration, and in particular to a new design method for a broadband thin-film superlens. Background Art

[0002] Optical imaging is widely used in aerospace, military, industrial robotics, and medical imaging. Optical refractive lenses are key components of imaging systems. They use the light refraction effect generated by the curved interface of the lens material to converge light emitted from a point back to an image point. Due to limitations such as imaging principles and material dispersion, the imaging effect of a single refractive lens is limited. Therefore, high-performance imaging systems often contain a variety of complex combinations of lenses and optical elements. With the development of modern production and life, people's demand for high-performance, miniaturized, and high-density optical imaging systems has posed new challenges to the development of imaging technology. With the advancement of micro-nano processing technology in recent years, super lenses are a very promising solution to replace traditional lenses for miniaturization. They can reduce the thickness of traditional glass lenses from centimeters to micrometers or even nanometers. At the same time, the planar structure of super lenses is its natural advantage, which solves the problems of difficult alignment between traditional lenses and complex alignment equipment.

[0003] The commonly used design method for broadband metalenses currently consists of three steps: the first step is to obtain the phase, group delay, and group delay dispersion functions required for focusing. Using geometric optics methods, the function of phase variation with radius is obtained, and the Taylor expansion of this function is then performed to obtain the group delay and group delay dispersion functions. The second step is to obtain the metalens microstructure group and determine the relationship between the microstructure size and the phase, group delay, group delay dispersion, and higher-order terms. The third step is to find a microstructure unit that matches the function. The various indicators of the broadband metalenses designed using this design method are mutually constrained, primarily between polarization dependence and broadband characteristics, between numerical aperture and metalens radius, and between numerical aperture and focusing efficiency. This restricts further improvement in metalens performance.

[0004] Designing an optical metalens with large numerical aperture, high diffraction efficiency, high transmittance, high resolution, polarization independence, and large radius is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] In response to the problems existing in existing design methods, the purpose of the present invention is to provide a π-phase design method for broadband planar thin-film metalens design. The present invention can achieve a metalens with a larger aperture, a larger numerical aperture, and maintain the polarization independence, focusing efficiency and focal length consistency of the lens.

[0006] The technical solution of the present invention is:

[0007] A method for designing a broadband planar thin-film metalens comprises the following steps:

[0008] 1) Based on the initial period and initial focal length of the target metalens, the phase function, broadband group delay function, and group delay dispersion function corresponding to the target metalens for incident light with a central wavelength within a broadband are determined; the radius of the target metalens is determined based on the radial coordinates of the outermost microstructure within the target metalens that causes a phase jump difference of 3π. Then, based on the phase jump difference between the microstructure and the central microstructure at different radial coordinates within the target metalens, the target metalens is divided into three radial segments at intervals of π: 0-π, π-2π, and 2π-3π. Light focusing through the metalens involves two phase accumulation stages: the first stage is the phase jump caused by light passing through the metalens microstructure, and the second stage is the phase accumulation from the microstructure to the set focal point. Assuming that the incident light wave is a plane wave with the same initial phase at the front surface of the metalens, the sum of the two phase accumulation stages caused by light passing through different microstructures is equal and can be any value C. The second phase accumulation stage is the optical path difference from the different microstructures to the focal point. Subtracting the second phase accumulation stage from the sum of the phase accumulation stages C yields the phase jump value required to be satisfied by the metalens microstructure. The functional relationship between the metalens radial coordinate and the phase jump value is the phase function required for metalens focusing. The metalens phase function is then used to perform a Taylor expansion of the incident light frequency to obtain the group delay and group delay dispersion functions, which are used to subsequently arrange the metalens microstructures and improve the broadband focal length consistency of the metalens. As the radial coordinate increases, the second-stage phase accumulation also increases, and therefore the difference in phase jump values between the central microstructure and the outermost microstructure of the metalens also increases. When the phase jump value difference is limited to 3π, the radial coordinate of the outermost microstructure is the radius of the metalens. Based on the phase jump value difference between the microstructure and the central microstructure at different radial coordinates, the metalens is divided into 0-π, π-2π, and 2π-3π segments at intervals of π.

[0009] 2) Select various microstructure shapes within the metalens plane that are polarization-independent for incident light of the target wavelength. Then, based on the preset microstructure period of the target metalens, determine the relationship between the size of each microstructure shape and the phase change, group delay, and group delay dispersion when the microstructure size varies within a microstructure arrangement period, and determine the microstructure library. To ensure the polarization independence of the metalens, select isotropic microstructure shapes within the metalens plane. Based on the preset metalens microstructure arrangement period, determine the relationship between the size of the microstructure shape and the phase change, group delay, and group delay dispersion when the microstructure size varies within a period, and form a three-dimensional database of microstructure size, phase, group delay, and group delay dispersion.

[0010] 3) The 0-π and 2π-3π segments of the target metalens are divided into a plurality of grid points according to the microstructure arrangement period, and the radial coordinates of each grid point are substituted into the phase function, group delay function, and group delay dispersion function to obtain the required phase, group delay, and group delay dispersion values. Then, the microstructure with the highest matching degree with the required phase, group delay, and group delay dispersion values of the grid point is found in the microstructure library and filled into the grid point to obtain the focusing results of the 0-π and 2π-3π segments of the metalens. The 0-π and 2π-3π segments of the metalens are divided into a plurality of grid points according to the pre-set microstructure period, and filled with different microstructures. The radial coordinates of each grid point are substituted into the above-mentioned phase, group delay, and group delay dispersion functions to obtain the required phase, group delay, and group delay dispersion values. Then, the microstructure size with the highest matching degree with the above-mentioned phase, group delay, and group delay dispersion values is found in the microstructure library. The microstructure is filled into the corresponding grid point to obtain the far-field focusing results of the 0-π and 2π-3π segments of the metalens. The phase adjustment capability of the microstructure itself is superimposed on the inherent 2π phase difference of the two segments of the lens, and the lens has two main focusing peaks.

[0011] 4) The design radius and focal length of the π-2π segment of the target metalens are set as variables to obtain multiple sets of phase functions, group delay functions, and group delay dispersion functions. The range of microstructure sizes and microstructure periods used in each of the three segments (0-π, π-2π, and 2π-3π) are then set as variables to obtain multiple sets of microstructure arrangements that satisfy the phase function, group delay function, and group delay dispersion function described in step 1). Among all arrangements, the arrangement with the highest focusing efficiency, maximum numerical aperture, and highest focal length consistency is then found to obtain the structural design of the target metalens. The π-2π segment of the metalens is then filled in, and the microstructure arrangement is optimized to obtain the optimal result. The π-2π segment uses different phase, group delay, and group delay dispersion functions than the 0-π and 2π-3π segments. The design radius and focal length of the π-2π segment metalens are set as variables to obtain multiple sets of phase, group delay, and group delay dispersion functions. For the same phase, group delay, and group delay dispersion functions, multiple sets of arrangements are obtained if different microstructure library regions are selected. The researchers then set the microstructure size range and period of each region as variables to obtain multiple microstructure arrangements that satisfy the phase, group delay, and group delay dispersion functions. Among all these arrangements, they found the one that maximized focusing efficiency, numerical aperture, and focal length consistency.

[0012] Compared with the existing methods, the positive effects of the present invention are:

[0013] A metalens capable of achieving larger aperture and larger numerical aperture while maintaining polarization independency, focusing efficiency, and focal length consistency. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1Schematic diagram of the segmented design method of the superlens π phase.

[0015] Figure 2 is the far-field distribution corresponding to microstructures with different periods;

[0016] (a) Far-field distribution when the microstructure period is 0.8 times the initial period, (b) Far-field distribution when the microstructure period is 0.9 times the initial period, (c) Far-field distribution when the microstructure period is the initial period.

[0017] Figure 3 The phase distribution of the output field corresponding to different periods;

[0018] (a) Phase distribution of the outgoing field when the microstructure period of the outer ring segment is the initial period, (b) Phase distribution of the outgoing field when the microstructure period of the outer ring segment is 0.8 times the initial period.

[0019] Figure 4 The microstructure arrangement of lithium niobate thin film superlens is designed using the π phase design method.

[0020] Figure 5 This is a comparison of focusing between the superlens π phase design method and the traditional method;

[0021] (a) Focusing of the lens designed using the traditional method, (b) Focusing of the superlens designed using the π-phase design method.

[0022] Markings in the figure: 1-base layer, 2-superlens, 3-superlens 2π-3π segment, 4-superlens π-2π segment, 5-superlens 0-π segment. DETAILED DESCRIPTION

[0023] To make the above features and advantages of the present invention more clearly understood, the following embodiments are given and described in detail with reference to the accompanying drawings. These embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention in any way.

[0024] The π phase segmentation method of the present invention is shown in the attached Figure 1 The initial period of the lens microstructure was set to 230nm, and the initial focal length was set to 100μm. The phase function corresponding to incident light with a wavelength of 500nm was calculated according to the method for determining the phase function required for focusing described in the technical solution, and the phase at the edge of the metalens was limited to zero phase. The lens design was then divided into three segments, 0-π, π-2π, and 2π-3π, with a phase difference of π as the spacing, for segmented design. The Taylor expansion of the metalens phase function with respect to frequency was performed to obtain the group delay function and group delay dispersion function that the metalens must satisfy.

[0025] Using lithium niobate as the microstructure material, after comprehensively considering the transmittance and phase change range, pillars with rectangular cross-sections and their complementary structures were selected. The phase, group delay, and group delay dispersion values corresponding to pillars of different widths and complementary structures were obtained to construct a microstructure library.

[0026] According to the obtained phase, group delay, and group delay dispersion functions, the arrangement of the 0-π and 2π-3π segments of the metalens is completed. The 0-π segment uses a column structure with a rectangular cross section, and the 2π-3π segment uses a complementary structure. First, the 0-π and 2π-3π segments of the metalens are divided into several grid points according to the pre-set microstructure period, and filled with different microstructures. For the microstructure on each grid point in each segment, a compromise is made between the phase, group delay, and group delay dispersion. At the same time, the continuity of the overall microstructure width change must be ensured to obtain the size of the microstructure on each grid point. The far-field distribution of these two segments of the lens will form two focusing peaks with similar light intensities, such as Figure 2 (c) One of them is the focus peak corresponding to the designed focal length, and the other is the focus peak with a smaller focal length.

[0027] Based on the focusing results of the two-segment lens, the middle ring area of the metalens, namely the π-2π segment of the metalens, is filled in to suppress the peak with larger focal length and enhance the effect of the peak with smaller focal length. For the middle segment lens, it is necessary to find a microstructure arrangement whose far-field peak is near the peak with smaller focal length and whose phase can match the far-field phase of the two-segment lens. The focusing function (phase, group delay, group delay dispersion function) used in the π-2π segment of the metalens is different from that of the 0-π and 2π-3π segments. The design radius and focal length of the π-2π segment focusing function are set as variables to obtain multiple sets of focusing function relationships.

[0028] Changing the period of each microstructure can change the far-field focusing peak and improve the fitting degree between the target phase function and the actual phase value. Figure 2 These are the far-field focusing effects of the 0-π and 2π-3π metalenses at different periods. The periods from left to right are 0.8 times the initial period, 0.9 times the initial period, and 1 times the initial period, indicating that changing the period can change the peak values of the two focusing peaks. Figure 3 The degree of fit between the target phase function and the actual phase value under different periods of the 0-π segment metalens is given. It shows that the degree of fit between the target phase and the actual phase can be improved by changing the period. Therefore, the selection range of the structural size used in each microstructure period and each area is set as a variable, and multiple groups of microstructure arrangements that meet the focusing function (phase, group delay, group delay dispersion function) are obtained. Further, among all the arrangements, the arrangement with the highest focusing efficiency, the largest numerical aperture, and the highest focal length consistency is found. The final focusing microstructure distribution is shown in the figure below. Figure 4 As shown, the vertical axis corresponds to the width of the column and the width of the complementary structure cavity.

[0029] Figure 5 The far-field focusing results of the traditional design method and the π-phase design method are compared. In the figure, the Z axis is the axis perpendicular to the surface of the metalens and passes through the center of the metalens. Figure 5 (a) Metalens designed by traditional method, Figure 5 (b) Metalens designed using the π-phase design method. This shows that the π-phase design method can design a metalens with a larger radius and a larger numerical aperture while maintaining polarization indifference, focusing efficiency, and focal length consistency.

[0030] Although the foregoing disclosure illustrates embodiments of the present invention, it should be noted that various changes and modifications may be made without departing from the scope of the present invention as defined in the claims. The embodiments and specific parameters therein are provided solely for the purpose of clearly describing the inventor's invention verification process and are not intended to limit the scope of patent protection of the present invention. The lithium niobate thin film material used in this example can also be applied to other materials. Therefore, the scope of protection of the present invention should be determined by the contents of the appended claims.

Claims

1. A method for designing a broadband planar thin-film metalens, comprising: 1) Determining the phase function, broadband group delay function, and group delay dispersion function corresponding to the target metalens for incident light of a central wavelength within a broadband according to the initial period and initial focal length of the target metalens; The radius of the target metalens is determined according to the radial coordinates of the outermost microstructure that causes a phase mutation value difference of 3π in the target metalens, and then the target metalens is divided into three sections along the radial direction at intervals of π: 0-π, π-2π, and 2π-3π according to the phase mutation value differences between the microstructures and the central microstructure at different radial coordinates in the target metalens; 2) selecting various microstructure shapes that are polarization-independent for incident light of a target wavelength within the metalens plane, and then, based on a preset microstructure period of the target metalens, obtaining the relationship between the size of each microstructure shape and phase change, group delay, and group delay dispersion when the microstructure size varies within a microstructure arrangement period, thereby obtaining a microstructure library; 3) The 0-π segment and 2π-3π segment of the target metalens are divided into a number of grid points according to the microstructure arrangement period, and the radial coordinates of each grid point are substituted into the phase function, group delay function, and group delay dispersion function to obtain the required phase, group delay, and group delay dispersion values. Then, the microstructure with the highest matching degree with the phase, group delay, and group delay dispersion values required for the grid point is found in the microstructure library, and the microstructure is filled into the grid point to obtain the far-field focusing results of the 0-π and 2π-3π segment metalens; 4) setting the design radius and focal length of the π-2π segment of the target metalens as variables to obtain multiple sets of phase functions, group delay functions, and group delay dispersion functions; then setting the selection range of the microstructure size used in each of the three segments 0-π, π-2π, and 2π-3π and the microstructure period as variables to obtain multiple sets of microstructure arrangements that satisfy the phase function, group delay function, and group delay dispersion function described in step 1); then finding the arrangement with the highest focusing efficiency, the largest numerical aperture, and the highest focal length consistency among all arrangements to obtain the structural design of the target metalens.

2. The method according to claim 1, characterized in that The microstructures in the microstructure library are in the form of columns with rectangular cross sections and their complementary structures.

3. The method according to claim 2, characterized in that The material of the microstructure is lithium niobate.

4. The method according to claim 1, 2 or 3, characterized in that: The phase function is obtained according to the functional relationship between the radial coordinate of the target metalens and the phase mutation value, and then Taylor expansion is performed on the frequency of the phase function to obtain the group delay function and the group delay dispersion function.

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