Planar Distorting Mirror Based on Gradient Metasurface and Method for Manipulating and Predicting Object Imaging

Abstract

The present invention proposes a planar funhouse mirror based on a gradient metasurface, and further analyzes the distortion of the macroscopic virtual image of an arbitrary object generated by the planar funhouse mirror based on this reflective metasurface by means of ray optics, and manipulates the shape, direction, and position of the virtual image by changing the additional wave vector function.

Description

Technical Field

[0001] The present invention belongs to the technical field of optics, and particularly relates to a planar distorting mirror based on a gradient metasurface and a method for manipulating and predicting object imaging. Background Art

[0002] In classical optics, an interesting application is based on the deformation of virtual images, namely, distorting mirrors or magic mirrors. Different from a plane mirror that produces an undistorted virtual image in a reverse-symmetric manner, a distorting mirror uses an uneven mirror surface to produce a desired distorted illusion. Its working principle is that the curved mirror surface is equivalent to many concave and convex mirrors, thus forming a distorted image. The limitation of this traditional distorting mirror is that it is necessary to manufacture an uneven mirror surface, which poses relatively high requirements for the design and manufacture of the mirror surface. In addition, it is very difficult to predict in advance the virtual image formed by a macroscopic object based on a traditional distorting mirror.

[0003] In the past decade or so, people have found that metamaterials have novel functions for forming optical illusions (such as invisibility). Recently, metasurfaces composed of ultrathin resonant units have attracted a great deal of attention due to their unprecedented electromagnetic wave manipulation capabilities and manufacturing feasibility. Based on metasurfaces, scientists have proposed and realized various novel phenomena such as the generalized laws of reflection and refraction, the conversion from propagating waves to evanescent waves, high-efficiency holograms, spin and orbital angular momentum control, invisibility cloaks, vector light field generation, and planar superlenses. In particular, extensive discussions have been carried out on the imaging capabilities of metasurfaces in research such as high-efficiency holography and planar superlenses. Among them, great progress has been made in improving the efficiency of holographic imaging and in improving some functions of superlenses, such as achromatic and aberration-free superlenses. However, most previous studies have focused on how to avoid rather than cause image distortion, and for reflective metasurfaces, the problem of virtual image distortion of macroscopic finite-size objects has rarely been discussed.

[0004] Since metasurfaces have the ability to almost arbitrarily control the reflected light, this characteristic makes it show the possibility of realizing a planar distorting mirror (FDM) without using a curved surface. Moreover, with the rapid development of advanced manufacturing technologies, it can be foreseen that large-sized metasurfaces will ultimately be realized in the future, which makes it possible to realize macroscopic optical devices such as distorting mirrors. Summary of the Invention

[0005] The present invention proposes a planar distorting mirror (FDM) based on a gradient metasurface and a method for manipulating and predicting object imaging. By means of ray optics, the shape, direction, and position of the macroscopic virtual image generated by this FDM are studied, and the macroscopic virtual image of any object can be manipulated by changing the distribution of the additional wave vector function K(x) of the metasurface.

[0006] The present invention proposes a planar funhouse mirror (FDM) based on a gradient metasurface, and analyzes the distortion of the macroscopic virtual image of any object generated by the FDM based on this reflective metasurface through ray optics, as well as manipulates the shape, direction, and position of the virtual image by changing the additional wave vector function.

[0007] The specific technical solution of the present invention is as follows:

[0008] Solution 1: A planar funhouse mirror based on a gradient metasurface, including a metal substrate and a dielectric layer formed on the metal substrate. The dielectric layer is composed of a plurality of sequentially connected block structure units; several air holes are provided on the surface of the block structure unit, and the pore filling rate on the surface of the block structure unit is obtained by calculation according to the effective medium theory based on the additional wave vector function given for the planar funhouse mirror.

[0009] Preferably, the material of the dielectric layer is selected according to the given additional wave vector function.

[0010] Preferably, the dielectric layer is made of Ge, Si, or TiO2.

[0011] Preferably, the thickness of the dielectric layer is not greater than half of the working wavelength.

[0012] Preferably, the metal substrate is made of a perfect electric conductor.

[0013] Preferably, the metal substrate is Ag, Au, or Al.

[0014] Solution 2: A method for predicting object imaging, based on the planar funhouse mirror described in any one of Solution 1 and its preferred solutions. When a given additional wave vector function K(x) is provided, for an object point S(l, h) located at (l, h) in front of the planar funhouse mirror, the virtual image point formed after reflection by the planar funhouse mirror is S′(x0, y0), where:

[0015]

[0016] In the formula, x represents the position on the planar funhouse mirror where reflection occurs, that is, the reflection point, k0 is the wave number in free space, represents the vertical component of the wave vector of the reflected wave, is the parallel component of the wave vector of the reflected wave, r represents the reflected wave, and i represents the incident wave;

[0017] For a given observation point O(x d , y d ), the reflection point x is obtained by solving from Equation (3) through the wave vector matching method:

[0018]

[0019] For any object composed of multiple points, the virtual image points corresponding to each point on the object are calculated, so as to obtain the shape, direction and position of the virtual image corresponding to the object formed by each virtual image point.

[0020] Solution 3: A method for controlling object imaging, based on the planar distorting mirror described in any one of Solution 1 and its preferred solutions, controls the imaging shape, direction and position of the object by changing the additional wave vector function on the planar distorting mirror.

[0021] For the object point S at the given position (l, h), the virtual image points obtained after reflection at any position of the planar distorting mirror are all at the specified position (x0, y0), and the additional wave vector function conforms to the difference between the parallel components of the wave vectors of the incident light and the reflected light, that is:

[0022]

[0023] In the formula, x represents the position where reflection occurs on the planar distorting mirror, that is, the reflection point, is the parallel component of the wave vector of the reflected wave, is the parallel component of the wave vector of the incident wave, r represents the reflected wave, and i represents the incident wave.

[0024] Beneficial effects:

[0025] Traditional distorting mirrors use uneven mirror surfaces to produce the desired distorted illusions, which puts relatively high requirements on the design and manufacture of the mirror surfaces. The present invention proposes a planar distorting mirror with low manufacturing cost and strong operability, and can generate fixed virtual image points at any position by adjusting K(x).

[0026] Furthermore, the present invention also starts from ray optics, analyzes the characteristics of the macroscopic virtual images generated by FDM, predicts the distortion of the virtual images of macroscopic objects, such as shape, direction and position, by incorporating the functions of the metasurface into the ray optics theory. And this method conforms to Fermat's principle, which is convenient for predicting the shape, direction and position of the macroscopic virtual images of finite-size objects. Description of the drawings

[0027] Figure 1 is a schematic structural diagram of FDM, and the reference numerals in the drawings: 1 - metal substrate, 2 - dielectric layer, 21, 22, 23 respectively represent different block structural units, 3 - air holes.

[0028] Figure 2 Among them: Figure 2 A is a schematic ray diagram of the object point image generated by FDM; Figure 2 B is a schematic diagram of the image point positions corresponding to the object points located at (0, 2a) for three different K(x).

[0029] Figure 3 Schematic diagram of forming a distorted virtual image of a finite-sized real object by FDM with different K(x).

[0030] Figure 4 FDM design process diagram and numerical simulation verification diagram for generating image points at arbitrarily selected positions. Detailed implementation mode

[0031] As Figure 1 shown, in the embodiment, we disclose an FDM. The structure of the FDM mainly consists of a metal substrate 1 and a dielectric layer 2 formed on the metal substrate. The dielectric layer 2 is composed of a plurality of successively connected block structure units. Among them, the metal substrate can be a metal material such as Ag, Au, Al, or a perfect electric conductor at low frequencies. The thickness of the metal substrate layer only needs to be greater than the skin depth of the metal material. The dielectric layer 2 can be made of materials such as Ge, Si, TiO2, etc., and is specifically determined according to the additional wave vector function K(x) to be designed, where x represents the position where reflection occurs on the FDM. The relative dielectric constant ε (abbreviation "dielectric constant") of the plurality of block structure units included in the dielectric layer 2 can be determined by the effective medium theory according to the specific required additional wave vector function K(x), which will not be elaborated here. Among them, the numbers 21, 22, and 23 respectively represent block structure units with different dielectric constants. The specific distribution of different dielectric constants can be realized by opening air holes on the surface of the block structure units. The number and diameter of the air holes are related to the final dielectric constant and can be calculated by the effective medium theory according to the specific required additional wave vector function K(x) (the specific design method can refer to Figure 4 and its related descriptions). For example, when the relative dielectric constant ε of the material selected for the dielectric layer 2 is 18, at this time, according to the effective medium theory, any dielectric constant distribution within the range of 1 - 18 can be realized on the dielectric layer 2. The thickness of the dielectric layer 1 can be calculated by the transfer matrix theory according to the required additional wave vector function K(x), and is generally distributed within one-half of the working wavelength, that is, ≤λ / 2.

[0032] We can prepare the above simple structure of a single-layer dielectric attached to a metal by using a mature CMOS process. According to the effective medium theory, we can realize the distribution of the target dielectric constant on the dielectric layer by drilling corresponding air holes on the block structure units.

[0033] We call the proposed structure of different dielectric constant materials attached to a metal substrate FDM, that is, a reflective metasurface. According to the transfer matrix theory, we can calculate the reflection phase distribution on the FDM surface.

[0034] According to the generalized Snell's law in the metasurface, the inhomogeneity of the dielectric constant introduces a phase gradient between adjacent structural units, thus causing an additional parallel wave vector on the surface. The additional wave vector function is Therefore, we propose a planar funhouse mirror (FDM) based on the gradient metasurface, and further study the shape, direction, and position of the virtual image generated by this FDM through ray optics.

[0035] We find that the virtual image of any object can be manipulated by changing the distribution of the additional wave vector function K(x) of the metasurface (i.e., FDM). The specific method is as follows:

[0036] Set an object point S(l, h) in front of the metasurface. After reflection on the FDM, the corresponding image point (x0, y0) of the object point S(l, h) is:

[0037]

[0038] where x represents the position where reflection occurs on the FDM, k0 is the wave number in free space, represents the vertical component of the reflected wave vector, is the parallel component of the reflected wave vector, r represents the reflected wave, and i represents the incident wave.

[0039] Therefore, for an FDM with a given K(x) distribution, the position of the image point formed by the wave reflected from any position x on the FDM surface can be calculated by equations (1) and (2).

[0040] It can be seen that the adjustment parameter of this FDM is mainly the additional wave vector function K(x) of the FDM, and the additional wave vector function K(x) is determined by determined, the reflection phase is in turn determined by the dielectric constant ε(x) of the bulk structural unit. The distribution of ε(x) is determined by the background material (i.e., dielectric layer) selected in the effective medium theory and the pore filling rate f of the background material (related to the number and diameter of air holes). In other words, after selecting the background material, by adjusting the pore filling rate f of the background material, the adjustment of the additional wave vector function K(x) can be achieved, thereby manipulating the shape, direction, and position of the virtual image generated by the FDM.

[0041] In the following discussion, we will directly use the adjustment of the additional wave vector function K(x) to illustrate the working principle of the FDM. It can be seen from equations (1) and (2) that the image point (x0, y0) is a function of the position x on the FDM. According to equations (1) and (2), we give the distribution of the virtual image points (referred to as "image points") of point objects (referred to as "object points") under several different additional wave vector functions K(x), such as Figure 2 shown in B, Figure 2 Figure A is a ray diagram of the object point image generated based on the FDM.

[0042] As shown Figure 2 in the figure, after the fixed object point passes through the FDM of the given additional wave vector function K(x), the position of the imaged point will move with the reflection on the FDM. Figure 2 In A, the object point S is located at (l, h) in front of the FDM and can be expressed as S(l, h), S' m , S' n , S' p are different virtual image points corresponding to S for different K(x), and X m , X n , X p is the position where the reflection occurs on the FDM. Figure 2 In B, for three different K(x), the positions of the image points corresponding to the object point located at (0, 2a), where a is the unit of dimension, x0 represents the x-axis position of the virtual image point, and y0 represents the y-axis position of the virtual image point.

[0043] All the above discussions are about the case where a point object forms a certain virtual image based on the FDM. Next, we discuss the implementation method for the FDM to generate an arbitrarily distorted virtual image of a finite-size object.

[0044] As shown Figure 3 in the figure, a distorted virtual image of a finite-size actual object is formed through the FDM. Figure 3 In A, the ray schematic diagram shows that for an observer Observer located at O(x d , y d ), a virtual image of a finite-size actual object is formed by the FDM. Figure 3 B- Figure 3 I are the distorted virtual images formed by a horizontal line of finite size as the real object Object, with the observation point located at O(a, 2a). Each virtual image is generated by the FDM with a different additional wave vector function K(x), and the observation point remains unchanged, and the position of the horizontal line is exactly the same. Figure 3 B- Figure 3 I respectively adopt the functions K(x) as K(x) = -0.2(x / a)k0, K(x) = 0.2(x / a)k0, K(x) = 0.1(x / a) 2 k0, K(x) = -0.1(x / a) 2 k0, K(x) = {-0.2(x / a)k0, x < 0; 0.2(x / a)k0, x ≥ 0}, K(x) = {0.2(x / a)k0, x < 0; 0.2(x / a)k0 - 0.2k0, x ≥ 0},

[0045] K(x) = {-0.2(x / a)k0, x < 0; 0.2(x / a)k0 - 0.2k0, x ≥ 0}, and

[0046] K(x) = {-0.2(x / a)k0 + 0.5k0, x < 0; 0.2(x / a)k0 - 0.5k0, x ≥ 0}。

[0047] As Figure 3 shown, we note that the situation of virtual images usually depends on the position of the observer (eye) (also called the "observation point"). For a given observation point O(x d , y d ), the analysis process of virtual image formation is as Figure 3 shown in A. We assume that only the light rays passing through the observation point O(x d , y d ) can be seen by the observer. For a point on the object, such as S(l, h), the light rays of this point pass through the point (x s , 0) on the FDM, are reflected to the observation point O(x d , y d ), and then, the object point S(l, h) will establish a virtual image point S′ according to Equations (1) and (2), and this virtual image point will be seen by the observer. Here, x s can be obtained by the method of wave vector matching, that is, substituting x into Equation (3) for solution: s Substitute it into Equation (3) and solve it:

[0048]

[0049] For an arbitrary object composed of many points, the virtual image of each point can be calculated by the above method, so as to obtain the shape, direction and position of the distorted image composed of each virtual image point.

[0050] From Figure 3 shown in B and 3C, we find that a linear K(x) with a negative slope or a positive slope can cause the virtual image to be enlarged or reduced. From Figure 3 D and Figure 3 E, we find that for a quadratic K(x), the sign change of its derivative at x = 0 will introduce a large distortion change along the virtual image direction. In Figure 3 F to Figure 3 I, we discuss the more general case of the distribution of the additional wave vector K(x) that is non-differentiable and discontinuous. When K(x) is non-differentiable, the virtual image will be split, as Figure 3 shown in F, K(x) = {-0.2(x / a)k0, x < 0; 0.2(x / a)k0, x ≥ 0}. When K(x) is discontinuous, the virtual image will also be split, as Figure 3 shown in G, K(x) = {0.2(x / a)k0, x < 0; 0.2(x / a)k0 - 0.2k0, x ≥ 0}; Figure 3As shown in H, \(K(x)=\begin{cases}-0.2(x / a)k_0, & x \lt 0 \\ 0.2(x / a)k_0 - 0.2k_0, & x\geq0\end{cases}\). We note that there are some overlapping parts in the segmented virtual images. Finally, Figure 3 I shows the process of forming two independent and different distorted virtual images by the additional wave vector function \(K(x)=\begin{cases}-0.2(x / a)k_0 + 0.5k_0, & x \lt 0 \\ 0.2(x / a)k_0 - 0.5k_0, & x\geq0\end{cases}\).

[0051] Next, we fix the position of an object point and then explore the possibility of generating the image point at any position by designing \(K(x)\) of the FDM. In addition, we try to find the condition that the image point is fixed at one point regardless of where the reflection occurs on the FDM. For a given object point \(S\) located at \((l, h)\), i.e., \(S(l, h)\), if its virtual image point is specified to be generated at \((x_0, y_0)\), the design of \(K(x)\) of the FDM naturally needs to conform to the difference in the parallel components of the wave vectors of the incident light and the reflected light, that is:

[0052]

[0053] Substituting the position of the object point \(S\), i.e., \((l, h)\) and the equation of \(K(x)\), i.e., Equation (4), into Equations (1) and (2), we find that the position of the image point obtained for any reflection point on the FDM is \((x_0, y_0)\). It can be noted that this powerful ability actually goes beyond traditional distorting mirrors, such as convex mirrors and concave mirrors. For traditional distorting mirrors, it is almost impossible to generate a fixed image point at any position. However, for the FDM designed here, the position of the image point can be easily controlled by adjusting \(K(x)\).

[0054] Next, we use finite element simulation to prove this inference. Here, the FDM is a dielectric layer with a different dielectric constant distribution attached to the plane of a perfect conductor along the x-axis direction, as Figure 1 shown in the structure, and the thickness of the dielectric layer is \(0.1\lambda\), where \(\lambda\) is the wavelength in free space, and the relative magnetic permeability of the dielectric layer is set to 1. Considering that the object point is located at \((0, 10\lambda)\), according to Equation (4), we can obtain the \(K(x)\) distribution of six image points at different positions. The six image points are \((0, -2\lambda)\), \((0, -10\lambda)\), \((0, -15\lambda)\), \((5\lambda, -10\lambda)\), \((-5\lambda, -10\lambda)\) and \((2\lambda, -4\lambda)\), as Figure 4 shown in B. The phase distribution can be obtained through where \(C\) is a constant, and then the \(\varepsilon(x)\) distribution of the actual structure can be obtained from the transfer matrix theory, as Figure 4As shown in C. Assuming that the electric field phase of the image point is the same as that of the object point, C can be uniquely determined. For convenience, we take two examples where the image points are located at (-5λ, -10λ) and (2λ, -4λ) respectively. The derived phase distribution and the calculated relative permittivity ε distribution of the dielectric layer are as Figure 4 shown in B and 4C. The field pattern distribution of the FDM designed based on the image point located at (-5λ, -10λ) is as Figure 4 shown in D. The field pattern distribution is proved to be consistent with the interference field of two point sources located at (-5λ, -10λ) and (0, 10λ), as Figure 4 shown in E. In Figure 4 F and 4G, the field pattern distribution of the FDM designed based on the image point located at (2λ, -4λ) is consistent with the interference field of two point sources located at (0, 10λ) and (0, 10λ). The results of the above simulations prove that the ray-optics method we proposed is correct and effective, and, in fact, the ray-optics method is also consistent with the Fermat's principle method. Interestingly, the ray-optics method can conveniently predict the virtual image of any finite-size object generated by the FDM.

[0055] Finally, it should be noted that although the embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields. The above specific embodiments are merely illustrative and guiding, rather than restrictive. Those of ordinary skill in the art, under the inspiration of this specification, can also make many forms without departing from the scope protected by the claims of the present invention, and these all belong to the scope of protection of the present invention.

Claims

1. A planar funhouse mirror based on a gradient metasurface, characterized in that, It includes a metal substrate and a dielectric layer formed on the metal substrate. The dielectric layer is composed of a plurality of sequentially connected block structure units; there are a number of air holes on the surface of the block structure units, and the pore filling rate on the surface of the block structure units is obtained by calculation according to the effective medium theory based on a given additional wave vector function. The additional wave vector function is determined by and the reflection phase is in turn determined by the dielectric constant ε(x) of the block structural unit. The additional wave vector function conforms to the difference in the parallel components of the wave vectors of the incident light and the reflected light, where x represents the position where reflection occurs on the planar funhouse mirror.

2. The planar distorting mirror according to claim 1, wherein The material of the dielectric layer is selected according to a given additional wave vector function.

3. The planar distorting mirror according to claim 1, characterized in that, The dielectric layer is made of Ge, Si or TiO2.

4. The planar distorting mirror according to claim 1, wherein The thickness of the dielectric layer is not greater than one-half of the working wavelength.

5. The planar distorting mirror according to claim 1, wherein The metal substrate is made of a perfect electric conductor at low frequencies.

6. The planar distorting mirror according to claim 1, characterized in that, The metal substrate is Ag, Au or Al.

7. A method for predicting the imaging of an object based on the planar distorting mirror according to any one of claims 1 to 6, characterized in that when a given additional wave vector function K(x) is provided, for an object point S(l, h) located at (l, h) in front of the planar distorting mirror, the virtual image point formed after reflection by the planar distorting mirror is S′(x0, y0), where: In the formula, x represents the position on the planar distorting mirror where reflection occurs, that is, the reflection point, and k0 is the wave number in free space. is the parallel component of the reflected wave vector, represents the perpendicular component of the reflected wave vector, r represents the reflected wave and i represents the incident wave, is the parallel component of the wave vector of the incident wave; For a given observation point O(x d , y d ), the reflection point x is obtained by solving Equation (3) through the wave vector matching method:

8. The method according to claim 7, wherein For an arbitrary object composed of multiple points, the virtual image points corresponding to each point on the object are calculated, so as to obtain the shape, direction and position of the virtual image corresponding to the object formed by each virtual image point.

9. A method for controlling an object to form an image by a planar funny mirror according to any one of claims 1 to 6, characterized in that, The imaging shape, direction and position of the object are controlled by changing the additional wave vector function on the planar distorting mirror.

10. The method according to claim 9, characterized in that, For an object point S at a given position (l, h), the virtual image points obtained after reflection at any position on the planar distorting mirror are all at a specified position (x0, y0), and the additional wave vector function K(x) conforms to the difference between the parallel components of the wave vectors of the incident light and the reflected light, that is: Wherein, x represents the position where reflection occurs on the planar distorting mirror, i.e., the reflection point. is the parallel component of the wave vector of the reflected wave. is the parallel component of the wave vector of the incident wave, r represents the reflected wave, and i represents the incident wave.

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