A quadratic phase-modulated double-layer metasurface wide-angle imaging lens with monochromatic aberration elimination

Abstract

The present invention discloses a double-layer metasurface wide-angle imaging lens with quadratic phase modulation and monochromatic aberration elimination. The double-layer wide-angle imaging lens comprises: a substrate L1, a nano-cylinder array structure layer M1 arranged on the upper surface of L1, and a nano-cylinder array structure layer M2 on the lower surface. M1 is established according to the binary optical surface 2 formula of ZEMAX and has the function of correcting spherical aberration; M2 is modulated by the quadratic phase formula and can eliminate the coma generated after the angled light source is incident and focused. When the imaging lens is working, the angled light source is incident from the dielectric cylinder array structure layer on the top surface of the substrate, passes through L1 and M2, and focuses the light onto the sensor. The present invention uses a nano-cylinder array structure layer, which can be used to focus incident light at a large angle, and can minimize the volume and weight of the system, thereby improving the practical application effect of the imaging lens.

Description

Technical Field

[0001] The present invention relates to the field of optical imaging, and in particular to a double-layer wide-angle imaging lens based on a quadratic phase metasurface, which can utilize the metasurface to achieve a wide-angle imaging effect with monochromatic aberration eliminated. Background Art

[0002] Most traditional optical lenses are realized by constructing curved surfaces, so the size and weight of the optical system are relatively large. In addition, the field of view (FOV) of traditional optical lenses is strictly limited. It is well known that the field of view angle of a lens determines the visual range in various imaging and detection equipment. Therefore, the limitations of the field of view angle may affect the performance of the lens in scientific research and engineering practice. It is crucial to expand the FOV of lenses through various methods, especially in eliminating monochromatic aberrations. There are currently some special optical systems, such as using fisheye lenses to achieve a large field of view, but this type of lens is bulky and complex in structure.

[0003] Traditional optical components are manufactured by cutting and grinding lenses, then combining them together to form lens groups. However, as optical devices shrink in size and become lighter, the precision requirements of traditional processing are rapidly increasing. Maintaining sufficient imaging quality while reducing the size of traditional lenses means that the cost is rising.

[0004] In recent years, a new class of micro-nano two-dimensional materials, metasurfaces, has emerged that can control the phase and amplitude of light propagating through arrays of subwavelength structures. Metasurface-based designs have been applied to numerous imaging devices, such as tunable terahertz focusing lenses and broadband achromatic imaging systems. Metasurfaces have become a viable alternative to traditional optical components. However, in reported wide-angle imaging metasurfaces, coma and spherical aberration remain uncorrected, and the introduction of these monochromatic aberrations can significantly offset the imaging field of view. Summary of the Invention

[0005] The purpose of the present invention is to address the above-mentioned existing problems and provide a double-layer metasurface wide-angle imaging lens with a large field of view, small size, and easy processing, with a secondary phase modulation and monochromatic aberration elimination.

[0006] The technical solution for achieving the purpose of the present invention is: a double-layer metasurface with quadratic phase modulation and monochromatic aberration elimination wide-angle imaging lens, wherein the double-layer metasurface with monochromatic aberration elimination wide-angle imaging lens includes a substrate L1 and metasurface structures for adjusting phase and correction arranged on the upper and lower surfaces of the substrate, wherein the metasurface structure is a rectangular array of cylinders, wherein the cylinders are TiO2 nanocylinders, the upper metasurface structure M1 is used to eliminate spherical aberration, and the lower metasurface structure M2 is used to correct coma of obliquely incident light.

[0007] Preferably, the radius of the cylinder in the metasurface structure is determined by the following formula:

[0008]

[0009] Where R is the radius of the cylinder, is the phase of TiO2 nanocylinders.

[0010] Preferably, the phase of the TiO2 nanocylinder in M1 is obtained using the following formula:

[0011]

[0012] in, is the phase of the TiO2 cylinder in M1, i is the number of TiO2 nanocylinders, r is the coordinate position of the TiO2 nanocylinders on M1, D is the diameter of M1, a n In order to optimize the coefficient, n=1-5 is selected here. After optimization, it is sufficient to eliminate the influence of spherical aberration, and the subsequent coefficients have little effect on the results.

[0013] Preferably, the phase of the TiO2 nanocylinder in M2 is obtained using the following formula:

[0014]

[0015] Among them, the plane where M2 is located is regarded as the xy plane, and the normal axis of M2 is regarded as the z axis. is the phase of the TiO2 nanocylinder in M2, i is the number of TiO2 nanocylinders, k0 is the wave vector, and k0 = 2π / λ, λ represents the working wavelength, f is the focal length, r 2 =x 2 +y 2 , x and y are the coordinate positions of each TiO2 nanocylinder arranged on M2. It is assumed that the incident light beam is located in the xz plane and forms an arbitrary angle θ with the z axis, that is, θ is the angle of oblique incidence of the incident light.

[0016] Preferably, the height h of the TiO2 nanocylinder should be greater than Where λ represents the operating wavelength, is the refractive index of TiO2.

[0017] Preferably, the lattice constant p should be less than λ / 2NA, and at the same time, p should be less than the equivalent working wavelength λ / n of the incident light in the substrate. L1 And greater than the diffraction condition λ / 2n L1 , where n L1 is the refractive index of the substrate, and NA is the numerical aperture.

[0018] Preferably, the diameter d of the base L1 and the focal length f of the lens should satisfy d>f.

[0019] Preferably, the thickness t and diameter d of the base L1 should satisfy t<(df) / tan80°.

[0020] Compared with the prior art, the present invention has the following significant advantages: 1) the optical metalens used is a special lens that arranges micro-nano TiO2 cylinders on a planar substrate to achieve the functions of a traditional lens (the doublet lens has micro-nano TiO2 cylinder arrays on both sides), which can achieve the functions of a complex traditional lens group in a very limited volume. Its functionality mainly relies on the arrangement structure of the micro-nano TiO2 cylinders. Different arrangement structures can achieve different functions and have great expansion space, while improving the coma aberration of the curved lens; 2) when the incident light has a certain incident angle, the doublet metalens used can still maintain good focusing; 3) while ensuring the above two capabilities, the lens with a micro-nano structure is used to improve imaging efficiency, minimize the volume and weight of the lens system, and reduce costs.

[0021] The present invention is further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a quadratic phase-modulated double-layer metasurface aberration-eliminating wide-angle imaging lens in the embodiment.

[0023] Figure 2 These are example diagrams of the relationship between the radius of the TiO2 cylindrical structure and its phase and transmittance in the embodiments, where (a) is an example diagram of the relationship between the radius of the TiO2 cylindrical structure and its phase, and (b) is an example diagram of the relationship between the radius of the TiO2 cylindrical structure and its transmittance.

[0024] Figure 3 The simulation results of M2 in the embodiment are obtained when the incidence angle is 70°, where (a) is the xz plane result of vertical incidence when M2 is working, and (b) is the xy plane result of vertical incidence when M2 is working.

[0025] Figure 4 The simulation results of M2 in the embodiment are obtained when the incidence angle is 80°, where (a) is the xz plane result of vertical incidence when M2 is working, and (b) is the xy plane result of vertical incidence when M2 is working.

[0026] Figure 5 The simulation results of M2 in the embodiment are obtained by using ZEMAX for focusing simulation at vertical incidence, where (a) is the simulation result of ZEMAX for focusing simulation at vertical incidence, and (b) is a partial enlarged view of the result.

[0027] Figure 6 The simulation results of the joint action of M1 and M2 in the embodiment are as follows: (a) is a simulation result of the joint action of M1 and M2, and the focusing simulation result of ZEMAX at vertical incidence is obtained; (b) is a partial enlarged view of the result.

[0028] Figure 7 This is a double-layer metasurface wide-angle imaging lens model established in the embodiment. DETAILED DESCRIPTION

[0029] To facilitate understanding of the present invention, the present invention will be described more fully below with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the drawings. However, the present invention may be embodied in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive disclosure of the present invention.

[0030] It should be noted that if the embodiments of the present invention involve directional indications such as up, down, left, right, front, back, etc., then the directional indications are only used to explain the relative position relationship, movement status, etc. between the various components under a certain specific posture as shown in the accompanying drawings. If the specific posture changes, the directional indication will also change accordingly.

[0031] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features specified as "first" and "second" may explicitly or implicitly include at least one of such features. In addition, the technical solutions between the various embodiments can be combined with each other, but this must be based on the fact that ordinary technicians in this field can implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0032] In order to ensure that the phase change of the TiO2 nanocylinder unit structure of the upper metasurface structure M1 and the lower metasurface structure M2 can cover 0 to 2π when the radius changes within a certain range, the height h of the TiO2 nanocylinder should be greater than λ / (n M1 -1).

[0033] The present invention uses glass as the substrate, the diameter d of the substrate L1 and the focal length f of the lens should satisfy d>f, and the thickness t of the substrate L1 should satisfy t<(df) / tan80°.

[0034] In order to ensure high efficiency, the geometric parameters of the TiO2 nanocylinder unit structure need to meet the following restrictions: according to the Nyquist sampling theorem, the lattice constant p should be less than λ / 2NA, and at the same time, in order to ensure that only the 0th order diffraction occurs at normal incidence, p should be less than the equivalent working wavelength of the incident light in the substrate (λ / n L1 ) is greater than the diffraction condition (λ / 2n L1 ).

[0035] TiO2 was chosen as the material for the nanocylinders because its refractive index has a large real part and a negligible imaginary part in the visible light band, resulting in a high refractive index and almost negligible absorption loss. The metasurface structure parameters were set. The parameters were: a SiO2 glass layer, 75μm diameter disk, 18μm thickness; an upper metasurface structure M1 with a diameter of 75μm; and a lower metasurface structure M2 with a diameter of 75μm, with all three concentric. The simulated wavelength was 532nm. The preferred TiO2 cylinder height h was 600nm, and the lattice constant p was 250nm.

[0036] Combine Figure 1 The present invention discloses a quadratic phase-modulated double-layer metasurface wide-angle imaging lens, comprising a glass substrate (L1), a micro-nano dielectric cylinder array structure layer (M1) disposed on the upper surface of the glass, and a micro-nano dielectric cylinder array structure layer (M2) disposed on the lower surface of the glass. M1 and M2 have the same structure, and TiO2 nanocylinders are disposed on the glass in a rectangular array. M1 is established according to the binary optical surface 2 formula of ZEMAX and has the function of correcting spherical aberration. M2 is modulated by the quadratic phase formula and can eliminate coma generated by angled light source incident and focusing. Therefore, the radius of the cylinder in M1 is different from the radius of the cylinder in M2 and is determined by the following formula:

[0037]

[0038] In the formula, R is the radius of the cylinder, is the phase of the cylinder.

[0039] The relationship between the phase of the TiO2 cylinder unit structure and the radius (R) of the TiO2 cylinder is as follows: Figure 2 As shown in the figure, a suitable radius is selected so that the phase change of the cylinder meets the design requirements, and the phase change can achieve a phase coverage of 0 to 2π to achieve discrete phase control.

[0040] Here, M1 is used to eliminate spherical aberration, and M2 is used to correct coma caused by large-angle oblique incident light, and they are respectively arranged on the upper and lower surfaces of the substrate L1.

[0041] M2 can be arranged according to the formula. The relationship between the phase and radius of the nanocylinder has been obtained, so the phase can be manipulated by controlling the radius of the nanocylinder accordingly. Formula (2) represents the quadratic phase formula, which can be achieved by locally and independently changing the radius of the nanocylinder.

[0042]

[0043] In the formula, the plane where M2 is located is regarded as the xy plane, and the normal axis of M2 is regarded as the z axis. is the phase of each TiO2 nanocylinder, k0 is the wave vector, and k0 = 2π / λ, λ (532nm) represents the operating wavelength, f is the focal length, r 2 =x 2 +y 2 , x and y are the coordinate positions of each TiO2 nanocylinder arranged on M2. It is assumed that the incident light beam is located in the xz plane and forms an arbitrary angle θ with the z axis, that is, θ is the angle of oblique incidence of the incident light.

[0044] M1 can be arranged according to the formula. The relationship between the phase and radius of the nanocylinder has been obtained, so the phase can be manipulated by controlling the radius of the nanocylinder accordingly. Formula (3) represents the phase formula of the binary optical surface 2 in ZEMAX, which can be achieved by locally and independently changing the radius of the nanocylinder.

[0045]

[0046] In the formula, is the phase of each TiO2 nanocylinder on M1, r is the coordinate position of each TiO2 nanocylinder on M1, and D is the diameter of M1. n Here, n=1-5 is selected as the optimization coefficient. After optimization, the spherical aberration effect is sufficiently eliminated, and the subsequent coefficients have little effect on the results.

[0047] The ZEMAX software was used to optimize the surface shape, and the phase profiles of the two metasurfaces that make up the doublet lens were obtained by ray tracing technology. Here, the optimization coefficient a n To minimize spherical aberration at normal incidence.

[0048] M1 is constructed by the binary optical surface 2 of ZEMAX software, and M1 is optimized by ZEMAX software. The phase profiles of the two metasurfaces that make up the doublet lens are obtained by ray tracing technology. Here, the optimization coefficient a n To minimize the spherical aberration at vertical incidence, the optimized coefficient a n As shown in Table 1 below:

[0049] Table 1 Optimized coefficient a n data

[0050]

[0051] The M2 layer is constructed using formula (1).

[0052] The phase of each cylinder of M1 and M2 is obtained by formula (2), (3) and Table 1, which is substituted into formula (1) to obtain the radius of the cylinder and establish the metasurface structure model.

[0053] The established model is simulated. X-polarized plane light is incident obliquely on the metasurface, and a monitor is set in the propagation direction to observe the intensity distribution, such as Figure 3 and Figure 4 As shown. Among them, Figure 3 is a simulation result diagram of an embodiment when the incident angle is 70°, wherein Figure 3 (a) is the xz plane result of vertical incidence when M1 is working, Figure 3 (b) is the xy plane result at vertical incidence when M1 is working. Figure 4 is a simulation result diagram of an embodiment when the incident angle is 80°, wherein Figure 4 (a) is the xz plane result of vertical incidence when M1 is working, Figure 4 (b) is the xy plane result at vertical incidence when M1 is working.

[0054] It can be seen that the designed double-layer metasurface with quadratic phase modulation and monochromatic aberration elimination wide-angle imaging lens has the obvious characteristic of focus displacement only in the focal plane in the intensity distribution of the propagation plane, and has a solid bright spot with good intensity in the xy plane.

[0055] Using the optimized a n The coefficient is established M2, and the simulation results are shown when focusing simulation is performed with ZEMAX. Figure 5 and Figure 6 As shown, Figure 5 FIG. 1 is a diagram showing the simulation results of focusing simulation using ZEMAX at vertical incidence obtained by simulating M1 in an embodiment. Figure 5 (a) is the simulation result of focusing simulation using ZEMAX at vertical incidence. Figure 5 (b) A local enlarged view of the results.

[0056] Figure 6 FIG. 1 is a diagram showing the simulation results of focusing simulation using ZEMAX at vertical incidence obtained by simulating the interaction of M1 and M2 in one embodiment. Figure 6 (a) is the simulation result of focusing simulation with ZEMAX at vertical incidence when M1 and M2 work together. Figure 6 (b) A local enlarged view of the results.

[0057] Figure 7 This is the double-layer metasurface wide-angle imaging lens model established in the embodiment. Here, the incident light is only set in the xz plane for simulation, so only a rectangular model in the xz plane is set.

[0058] When focusing with a traditional metasurface lens without spherical aberration, significant coma occurs as the normal angle of incidence increases. Through ZEMAX design and optimization, the present invention uses a doublet lens with TiO2 nanocylinder arrays on both sides, improving the coma of the curved lens and reducing spherical aberration at normal incidence.

[0059] The optical metalens used in this invention is a special lens composed of a two-dimensional array of micro-nano TiO2 cylinders fabricated on a substrate. It can modify optical wavefronts with subwavelength spatial resolution, achieving the functions of a traditional lens system with a complex but low-cost lens system. The doublet metalens maintains excellent focus even when incident light has a certain angle of incidence.

[0060] The present invention is applicable to the fabrication of a double-layer metasurface with a monochromatic aberration-free wide-angle imaging lens with secondary phase modulation. The process involves first fabricating the micro-nanostructure on one side of the substrate. After cleaning the substrate, a 600nm thick layer of hydrogenated TiO2 is deposited on one side of the substrate using chemical vapor deposition (CVD) using a mixture of 5% silane and argon. The surface micro-nanostructure is then fabricated. A ZEP-520A electron beam photoresist approximately 300nm thick is applied to the substrate and baked at 180°C for five minutes. A water-soluble photolithography antistatic agent, aquaSAVE, is then applied approximately 60nm thick on the photoresist. The metasurface pattern is then drawn on the photoresist using electron beam lithography. The antistatic agent is then rinsed off with water, and the photoresist is developed in ZED-N50 photoresist developer. A 70nm thick layer of aluminum oxide is then deposited on the photoresist, and the photoresist is stripped in Remover PG solvent for patterning. The aluminum oxide layer, which already has the desired structure, is then used as a protective film for the TiO2 layer during the subsequent dry etching process to obtain the desired TiO2 structure. Ion etching is then performed in a mixture of SF6 and C4F8 plasma to etch the TiO2 into the desired structure. The aluminum oxide layer is then dissolved in a 1:1 solution of ammonium hydroxide and hydrogen peroxide at 80°C. A layer of SU-8 polymer approximately 2μm thick is applied to the structured side, baked at 90°C for 5 minutes, then baked at 200°C for 30 minutes to make the surface as smooth as possible. The surface is then exposed to ultraviolet light and baked at 200°C for 30 minutes to cure. Finally, it is polished and cut to ensure a smooth surface. The structure is made on the other side using the same method.

[0061] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A quadratic phase-modulated double-layer metasurface wide-angle imaging lens with monochromatic aberration elimination, characterized in that: The imaging lens includes a substrate L1 and metasurface structures disposed on the upper and lower surfaces of the substrate for phase adjustment and correction. The metasurface structure is a micro-nano dielectric cylindrical structure layer, wherein the cylinders are TiO2 nanocylinders. The upper metasurface structure M1 disposed on the upper surface of the substrate is used to eliminate spherical aberration, and the lower metasurface structure M2 disposed on the lower surface of the substrate is used to correct coma of obliquely incident light. The phase of TiO2 nanocylinders in M2 is obtained using the following formula: Among them, the plane where M2 is located is regarded as the xy plane, and the normal axis of M2 is regarded as the z axis. is the phase of the TiO2 nanocylinder in M2, i is the number of TiO2 nanocylinders, k0 is the wave vector, and k0 = 2π / λ, λ represents the working wavelength, f is the focal length, r 2 =x 2 +y 2 , x and y are the coordinate positions of each TiO2 nanocylinder arranged on M2, assuming that the incident light beam is in the xz plane, and θ is the angle of oblique incidence of the incident light.

2. The imaging lens according to claim 1, wherein: The substrate L1 is made of SiO2 glass.

3. The imaging lens according to claim 1, wherein: The radius of the TiO2 nanocylinder in the metasurface structure is determined by the following formula: Where R is the radius of the cylinder, is the phase of the cylinder.

4. The imaging lens according to claim 1, wherein: The phase of TiO2 nanocylinders in M1 is obtained using the following formula: in, is the phase of the TiO2 cylinder in M1, i is the number of TiO2 nanocylinders, r is the coordinate position of the TiO2 nanocylinders on M1, D is the diameter of M1, a n is the optimization coefficient, n=1-5.

5. The imaging lens according to claim 1, wherein: The height h of the TiO2 nanocylinder should be greater than Where λ represents the operating wavelength, is the refractive index of TiO2.

6. The imaging lens according to claim 1, wherein: The lattice constant p should be less than λ / 2NA. At the same time, p should be less than the equivalent working wavelength of the incident light in the substrate λ / n L1 And greater than the diffraction condition λ / 2n L1 , where n L1 is the refractive index of the substrate, and NA is the numerical aperture.

7. The imaging lens according to claim 1, wherein: The diameter d of the base L1 and the focal length f of the lens should satisfy d>f.

8. The imaging lens according to claim 1, wherein: The thickness t and diameter d of the base L1 should satisfy t<(df) / tan80°.

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