Tunable device and method for forming the same

Abstract

In some embodiments, a tunable lens is provided. The tunable lens includes a substrate; at least one layer of ferroelectric material disposed over the substrate; and a first electrode disposed on the at least one layer of ferroelectric material; wherein a refractive index of the at least one layer of ferroelectric material is tunable by applying an electric field through the first electrode.

Description

TUNABLE DEVICE AND METHOD FOR FORMING THE SAMETECHNICAL FIELD

[0001] The present disclosure generally relates to a tunable lens and a method for forming a tunable lens.BACKGROUND

[0002] Tunable 2D flat lenses, or planar metalenses, offer a compact and aberration -free alternative to traditional optical lenses by controlling the phase and amplitude of light through nanoantenna arrays. Electrical tuning, particularly using materials like graphene and WS2, has garnered significant attention for its potential in enabling fast, reconfigurable devices suitable for optoelectronic integration. In graphene, applying high voltages alters its Fermi energy and carrier density, modulating optical transmittance, while in WS2, electrostatic gating adjusts excitonic resonance, providing control over light properties. However, the intrinsic tuning effect of these materials is typically weak, and enhancements such as integrating optical cavities are needed to amplify this effect and achieve more efficient and practical tunable metalenses for dynamic light manipulation.

[0003] Therefore, there exists a need to provide an improved tunable lens and an improved method for forming a tunable lens.SUMMARY

[0004] According to a first aspect of the present disclosure, a tunable lens is provided. The tunable lens may include a substrate; at least one layer of ferroelectric material disposed over the substrate; and a first electrode disposed on the at least one layer of ferroelectric material; wherein a refractive index of the at least one layer of ferroelectric material is tunable by applying an electric field through the first electrode.

[0005] According to a second aspect of the present disclosure, a method for forming a tunable lens is provided. The method may include forming at least one layer of ferroelectric material disposed over a substrate; and forming a first electrode on the at least one layer of ferroelectric material; wherein a refractive index of the at least one layer of ferroelectric material is tunable by applying an electric field through the first electrode.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] FIG. l is a block diagram showing a tunable lens according to various embodiments of the present disclosure.

[0007] FIG. 2 is a block diagram showing a tunable lens according to various embodiments of the present disclosure.

[0008] FIG. 3 shows an optical image of the tunable lens of FIG. 2 according to various embodiments of the present disclosure.

[0009] FIG. 4 is a block diagram showing an optical setup for characterizing the focusing effect and the performance of a tunable lens according to various embodiments of the present disclosure.

[0010] FIGS. 5A to 5D show the focusing effect and the performance of a tunable lens obtained by the optical setup of FIG. 4 according to various embodiments of the present disclosure.

[0011] FIGS. 6A and 6B show calculated x-component of the light field of a tunable lens before and after applying electric field thereto, respectively, according to various embodiments of the present disclosure; FIG. 6C shows the peak intensity of the focal spot of the tunable lens as a function of the DC voltage, according to various embodiments of the present disclosure.

[0012] FIGS. 7Ato 7F show anisotropy in a tunable lens according to various embodiments of the present disclosure.

[0013] FIGS. 8A to 8F show linear electro-optic effect in a tunable lens according to various embodiments of the present disclosure.

[0014] FIGS. 9A to 9H show the atomic structure, electronic, optical, and electro-optic properties of a 2D ferroelectric layer of a tunable lens by first-principle calculation, according to various embodiments of the present disclosure.

[0015] FIG. 10 shows a flow chart of a method 1000 for forming a tunable lens according to various embodiments of the present disclosure.DETAILED DESCRIPTION

[0016] Embodiments described below in the context of a method are analogously valid for the respective element, device, apparatus, or system, and vice versa. Furthermore, it will be understood that the embodiments described below may be combined, for example, a part of one embodiment may be combined with a part of another embodiment, and a part of one implementation may be combined with a part of another implementation.

[0017] It should be understood that the singular terms "a", "an", and "the" include plural references unless context clearly indicates otherwise. Similarly, the word "or" is intended to include "and" unless the context clearly indicates otherwise.

[0018] It will be farther understood that the terms “comprise” (and any form of comprise, such as “comprises” and “comprising”), “have” (and any form of have, such as “has” and “having”), “include” (and any form of include, such as “includes” and “including”), and “contain” (and any form of contain, such as “contains” and “containing”) are open-ended linking verbs. As a result, a method or device that “comprises,” “has,” “includes” or “contains” one or more steps or elements possesses those one or more steps or elements, but is not limited to possessing only those one or more steps or elements. Likewise, a step of a method or an element of a device that “comprises,” “has,” “includes” or “contains” one or more features possesses those one or more features, but is not limited to possessing only those one or more features. Furthermore, a device or structure that is configured in a certain way is configured in at least that way, but may also be configured in ways that are not listed.

[0019] Approximating language, as used herein throughout the specification and claims, may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as “about,” “substantially”, is not limited to the precise value specified but within tolerances that are acceptable for operation of the embodiment for an application for which it is intended. In some instances, the approximating language may correspond to the precision of an instrument for measuring the value.

[0020] The term “tunable lens” may be used herein to refer to an optical element that allows for real-time adjustments to its optical properties, such as focal length or shape or focal spot. This dynamic capability may be achieved through various mechanisms, including electro-optic effects, liquid crystal adjustments, mechanical alterations, acousto-optic modulation, or microelectromechanical systems (MEMS). Tunable lenses may be highly versatile and find applications in imaging systems, augmented reality (AR), optical communication, and adaptive optics. They may offer significant advantages such as flexibility, compactness, and ease of integration into different devices, allowing for on-the-fly adjustments to meet varying conditions.

[0021] The advent of 2D ferroelectrics, characterized by their spontaneous polarization states in layer-by-layer domains without the limitation of a finite size effect, may bring enormous promise for applications in integrated optoelectronic devices. Comparing withsemiconductor / insulator devices, ferroelectric devices may show natural advantages such as non-volatility, low energy consumption and high response speed. The linear electro-optic modulation of light in 2D ferroelectrics (e.g. in CuInP2S6film) and electrically tunable 2D ferroelectric metalens are present in this disclosure. The in-plane phase retardation may be continuously tuned by a transverse DC electric field, yielding an effective electro-optic coefficient rcof 20.28 pm / V. The CuInP2S6crystal exhibits birefringence with the fast axis oriented along its (010) plane. Birefringence is the optical property of certain materials that causes a single ray of light to split into two rays when it passes through. The birefringence is quantified as the difference between maximum refractive index and minimum refractive index exhibited by the material. The 2D ferroelectric Fresnel metalens shows efficacious focusing ability with an electrical modulation efficiency of the focusing exceeding 34%. The theoretical analysis and first principle calculations uncover the origin of the birefringence and unveil its ultralow light absorption across a wide wavelength range in this non-excitonic system. The van der Waals ferroelectrics may enable room-temperature electrical modulation of light and offer the freedom of heterogenous integration with silicon and other material system for highly compact and tunable photonics and metaoptics. Owing to ordered spontaneous polarization states that may be re-oriented under an external electric field, ferroelectrics have unique advantages as compared with common semiconductors / insulators and have found distinct applications in optoelectronic devices like nonvolatile memories, electro-optic modulators, and phase shifter. The ferroelectrics may be epitaxial oxides with strong covalent / ionic bonds in the perovskite crystal structures.

[0022] Although ferroelectricity-induced controllable polarization has been achieved, it is limited by several fundamental issues. One significant challenge is the high sensitivity of thin- film ferroelectricity to boundary conditions, which stems from the presence of dangling bonds inherent to the perovskite structure and the difficulties in controlling oxygen stoichiometry during the thin-film epitaxial deposition process. When the film thickness is reduced to the nanometer scale or a critical thickness, depolarization can lead to a substantial decrease in the Curie temperature or even the complete loss of the ferroelectric response. Despite extensive research, the underlying microscopic mechanisms behind critical thickness and size effects remain unresolved, due to competing factors such as dead layers and imperfect charge screening. Additionally, integrating different materials heterogeneously for multifunctional, high-density circuits remains a key goal in modern optoelectronics. As such, materials thatoffer high stability down to the 2D limit and facilitate easy integration are essential for advancing future optoelectronic devices and circuits.

[0023] The recent advancements in 2D materials have sparked interest in the ferroelectric field, with the discovery of layer-by-layer domain walls down to atomic thickness. 2D ferroelectrics offer several advantageous properties, such as the absence of dangling bonds, mechanical flexibility, and clean van der Waals interfaces, which are not present in their bulk counterparts. These materials may enable the creation of electric-field-tunable heterostructures with other 2D materials, like semimetal graphene and semiconductor transition -metal dichalcogenides (TMDCs), facilitating the development of innovative beyond-Moore electronic devices, such as ferroelectric field-effect transistors and tunnel junctions. The low switching barriers of 2D ferroelectrics may result in high-speed data writing with minimal power consumption. Additionally, they have led to the exploration of new phenomena, including Moire ferroelectricity, interlayer sliding ferroelectricity, and multiferroic coupling. While the application of 2D ferroelectrics in optoelectronics and photonics is still limited, their exceptional properties have the potential to drive significant progress in nanophotonics. Moreover, 2D ferroelectrics may provide a promising avenue for heterogeneous integration, eliminating the interfacial challenges associated with rigid materials, which have long hindered progress in integrated photonics.

[0024] Dielectric and metallic metasurfaces may control the amplitude, phase, and polarization of light through nanoscale features arranged in a subwavelength pattern. These ultrathin, flat structures may hold great promise for replacing traditional bulky optical components, offering a compact solution for miniaturizing optical systems and enabling entirely new devices. By selecting the shape, size, and orientation of the nanoscale elements, metasurfaces may precisely manipulate light-matter interactions. Metalenses, or flat lenses, may be an example of such devices that revolutionize optical design by providing compact solutions for applications such as imaging and augmented or virtual reality. The refractive index of 2D ferroelectrics may be modulated by an electric field, offering a simple and effective way to manipulate metasurfaces, compared to other variables like temperature, pressure, or magnetic fields. The present approach may allow for precise, layer-by-layer control of light properties. Moreover, the present 2D ferroelectrics may present a promising material family with potential for CMOS-compatible fabrication, low energy consumption, high robustness, and flexible integration, paving the way for advanced, energy-efficient optoelectronic devices.

[0025] The present 2D CuInP2S6may exhibit spontaneous in-plane optical birefringence with its fast axis along the (010) crystal plane. Its optical birefringence may be linearly modulated by applying an electric field, with an effective electro-optic coefficient rcto be 20.28 pm / V, an inaugural electro-optic value observed in 2D ferroelectrics. The flat lens, designed to include a CuInP2S6layer embedded between a bottom gold reflector and top gold rings, shows diffraction limit focusing at the designed focal length. Due to linear electro-optic effect, the focusing spot may be continuously tuned through application of voltages, realizing a high modulation efficiency of 34% and a focusing efficiency of 6.5%. Theoretical calculation and first principle simulation are conducted to study the retardation, fast axis orientation and Pockels coefficient rcof the material and show good agreement with the experiment. The findings suggest that CuInP2S6, as a 2D ferroelectrics with transparency across a broad spectrum range from visible to near-IR, is a viable and promising platform for future active metaoptics applications.

[0026] The following examples pertain to various aspects of the present disclosure.

[0027] Example 1 is a tunable lens, comprising: a substrate; at least one layer of ferroelectric material disposed over the substrate; and a first electrode disposed on the at least one layer of ferroelectric material; wherein a refractive index of the at least one layer of ferroelectric material is tunable by applying an electric field through the first electrode.

[0028] In Example 2, the subject matter of Example 1 may optionally include a second electrode disposed between the substrate and the at least one layer of ferroelectric material, wherein the electric field is applied through the first electrode and the second electrode.

[0029] In Example 3, the subject matter of Example 2 may optionally include that the second electrode is made of conductive material.

[0030] In Example 4, the subject matter of Example 2 or Example 3 may optionally include that the substrate and the second electrode are both transparent and the lens is configured to operate in transmission mode.

[0031] In Example 5, the subject matter of Example 2 may optionally include that the second electrode is made of metal as back reflector and the lens is configured to operate in reflection mode.

[0032] In Example 6, the subject matter of any of Examples 1 to 5 may optionally include that the at least one layer of ferroelectric material comprises at least one layer of Van der Waals material.

[0033] In Example 7, the subject matter of Example 6 may optionally include that the Van der Waals material comprises CuInP2S6, In2Se3. WTe2, MoTe2, 3R MoS2, 3R WS2, and twisted ABN.

[0034] In Example 8, the subject matter of any of Examples 1 to 7 may optionally include that the first electrode comprises a ring structure.

[0035] Tn Example 9, the subject matter of Example 8 may optionally include that the first electrode is made of metal or conductive materials.

[0036] Tn Example 10, the subject matter of Example 7 or Example 8 may optionally include that the first electrode is a Fresnel zone lens.

[0037] In Example 11, the subject matter of any of Examples 1 to 10 may optionally include that the substrate comprises a rigid or flexible substrate, made of glass, quartz, SiO2 / Si, sapphire, Polycarbonate (PC) or Polyethylene (PE).

[0038] Example 12 is a method for forming a tunable lens, comprising: forming at least one layer of ferroelectric material disposed over a substrate; and forming a first electrode on the at least one layer of ferroelectric material; wherein a refractive index of the at least one layer of ferroelectric material is tunable by applying an electric field through the first electrode.

[0039] In Example 13, the subject matter of Example 12 may optionally include forming a second electrode between the substrate and the at least one layer of ferroelectric material, wherein the electric field is applied through the first electrode and the second electrode.

[0040] In Example 14, the subject matter of Example 13 may optionally include that the second electrode is made of conductive oxide, and wherein the substrate and the second electrode are both transparent and the lens is configured to operate in transmission mode.

[0041] In Example 15, the subject matter of Example 13 may optionally include that the second electrode is made of metal as back reflector and the lens is configured to operate in reflection mode.

[0042] In Example 16, the subject matter of any of Examples 12 to 15 may optionally include that the at least one layer of ferroelectric material comprises at least one layer of Van der Waals material including CuInP2S6In2Se3, WTe2, MoTe2, 3RMoS2, 3R WS2, and twisted hBN.

[0043] In Example 17, the subject matter of any of Examples 12 to 16 may optionally include that the first electrode comprises a ring structure.

[0044] In Example 18, the subject matter of Example 17 may optionally include that the first electrode is made of metal.

[0045] In Example 19, the subject matter of Example 17 or Example 18 may optionally include that the first electrode is a Fresnel zone lens.

[0046] In Example 20, the subject matter of any of Examples 12 to 19 may optionally include that the substrate comprises a rigid or flexible substrate, made of glass, quartz, SiO2 / Si, sapphire, Polycarbonate (PC) or Polyethylene (PE).

[0047] FIG. 1 is a block diagram showing a tunable lens 100 according to various embodiments of the present disclosure. The tunable lens 100 may include a substrate 110, at least one layer of ferroelectric material 120 disposed over the substrate 1 10; and a first electrode 130 disposed on the at least one layer of ferroelectric material 120. A refractive index of the at least one layer of ferroelectric material 120 may be tunable by applying an electric field through the first electrode 130. The first electrode 130 may be arranged in a specific way through alternated rings or fingers or interdigitated structure.

[0048] According to various non-limiting embodiments, the tunable lens 100 may include the at least one layer of (electrically tunable) ferroelectric material 120 having the (electrically tunable) refractive index. Different voltages may be so applied to the first electrode 130 to determine a respective refractive index of the at least one layer of (electrically tunable) ferroelectric material 120 and consequently the focal spot of the tunable lens 100. In other words, a varying voltage may be applied to the at least one layer of (electrically tunable) ferroelectric material 120 in a manner that the refractive index of the at least one layer of (electrically tunable) ferroelectric material 120 varies accordingly, whereby the focal spot of the tunable lens 100 is (continuously) tuned by the varying voltages. That is, the tunable focal spot of the tunable lens 100 may be tunable by changing the voltages applied to the tunable lens 100.

[0049] According to various non-limiting embodiments, the at least one layer of ferroelectric material 120 may include at least one layer of Van der Waals material. Van der Waals materials may include, but not limited to, CuInP2S6, In2Se3, WTe2, MoTe2, 3R (3- rhombohedral phase) M0S2, 3R WS2, and twisted hBN. The Van der Waals materials may exhibit switchable spontaneous electric and optical polarization, controllable by an external electric field in electronic and optoelectronic applications, including electro-optic modulators and non-volatile memories. The 2-dimensional (2D) Van der Waals materials including CuInP2S6, ImSe;, WTe2, MoTe2, 3R M0S2, 3R WS2and twisted hBN , with intrinsic ferroelectric polarity at atomic thickness, may offer the advantage of no dangling bonds which facilitate easier heterogeneous integration. Integrating of 2D Van der Waals materials likeCuInP2S6, In2Se3, WTe2, MoTe2, 3R M0S2, 3R WS2and twisted hBN with silicon (e.g. a substrate) and III-V photonic circuits may overcome the crystalline-matching epitaxial challenges often encountered with conventional epitaxial oxides that have perovskite crystal structures, offering promising pathways for the development of advanced optoelectronic devices. In other words, the present tunable lens may be compatible to various substrates, mitigating the lattice mismatch restriction. The Van der Waals electro-optic material, e g. CuInP2S6, with abroad wavelength transparency from visible to near-IR, may be used for wide- range light focusing.

[0050] According to various non-limiting embodiments, the first electrode 130 may be configured to have lens effects (e.g. a Fresnel zone lens or metasurfaces based flat lens). In an example, the first electrode 130 may include a ring structure, e.g., a Fresnel zone lens. The first electrode may be made of metal or conductive materials. As used herein, the term “Fresnel zone lens” may refer to an optical lens designed to focus light using concentric rings, known as Fresnel zones, which are based on the principles of Fresnel diffraction. The Fresnel lens may be constructed from flat, stepped surfaces arranged in these circular zones. Each ring may correspond to a specific zone of Fresnel diffraction, where light waves are redirected and combined to converge at a common focal point. This design may enable the lens to achieve the same focal length as a conventional lens while being significantly thinner and lighter, making it particularly suitable for applications where size and weight are critical, such as in cameras, projectors, and solar concentrators. The ability to manipulate light using the diffraction pattern of these zones may allow the lens to efficiently focus light with minimal material.

[0051] According to various non-limiting embodiments, the tunable lens 100 may further include a second electrode (not shown) disposed between the substrate 110 and the at least one layer of ferroelectric material 120, wherein the electric field is applied through the first electrode 130 and the second electrode. In some embodiments, the second electrode may be made of conductive oxide (e g. Indium Tin Oxide (ITO)). The substrate 110 and the second electrode may be both transparent when the lens 100 is configured to operate in transmission mode. In some embodiments, the second electrode may be made of metal (e.g. gold (Au), or titanium (Ti)) as back reflector when the lens 100 is configured to operate in reflection mode.

[0052] According to various non-limiting embodiments, the substrate 110 may include, but not limited to, a rigid or flexible substrate, made of glass, quartz, SiO2 / Si, sapphire, Polycarbonate (PC) or Polyethylene (PE). The substrate 110 may be transparent, opaque or non-transparent. In some embodiments, the tunable lens 100 may be configured to be intransmission mode and, accordingly, the substrate 110 may be transparent so as to transmit the light incident on the tunable lens 100. In some embodiments, the tunable lens 100 may be configured to be in reflection mode and, accordingly, the substrate 100 may be opaque or nontransparent so as to reflect the light incident on the tunable lens 100. In some embodiments, the tunable lens 100 may be configured to be in reflection mode and include a second electrode (e g. 240 as described hereinafter) disposed between the substrate 1 10 and the at least one layer of ferroelectric material 120, and the second electrode (e.g. 240 as described hereinafter) may be as a back reflector, being opaque or non-transparent so as to reflect the light incident on the tunable lens 100. In these embodiments of the tunable lens 100 being configured to be in reflection mode and the second electrode (e.g. 240 as described hereinafter) being opaque or non-transparent, the substrate 110 may be in any form, including transparent, opaque and nontransparent. In some embodiments, the tunable lens 100 may be configured to be in reflection mode and include a second electrode (e g. 240 as described hereinafter) disposed between the substrate 110 and the at least one layer of ferroelectric material 120, the second electrode (e.g. 240 as described hereinafter) may be transparent, and the substrate 110 may be as a back reflector, being opaque or non-transparent so as to reflect the light incident on the tunable lens 100. In some embodiments, the tunable lens 100 may be configured to be in transmission mode and include a second electrode (e.g. 240 as described hereinafter) disposed between the substrate 110 and the at least one layer of ferroelectric material 120, and the substrate 110 and the second electrode (e g. 240 as described hereinafter) may be both transparent so as to transmit the light incident on the tunable lens 100.

[0053] FIG. 2 is a block diagram showing a tunable lens 200 according to various embodiments of the present disclosure. The tunable lens 200 may include a substrate (not shown); a second electrode 240 disposed on the substrate (not shown); at least one layer of ferroelectric material 220 disposed on the second electrode 240 (e g. over the substrate (not shown)); and a first electrode 230 disposed on the at least one layer of ferroelectric material 220. A refractive index of the at least one layer of ferroelectric material 220 may be tunable by applying an electric field (e.g. a voltage) through the first electrode 230 and the second electrode 240.

[0054] According to various non-limiting embodiments, the at least one layer of ferroelectric material 220 may include at least one layer of Van der Waals material. In one example, the Van der Waals material may include CuInP2S6(CIPS). The Van der Waals CuInP2S6membrane may exhibit strong in-plane optical anisotropy with its fast axis along the(010) crystal plane. The spontaneous polarity properties may be linearly modulated by applying a transverse electric field, resulting in an effective electro-optic coefficient rc(e.g. rc= 20.28 pm / V). The tunable lens 200, including the CuInP2S6layer embedded between the second electrode 240 (e g. a bottom gold reflector) and the first electrode 230 (e.g. top gold rings) may exhibit diffraction limit focusing at a designed focal length (e.g. 50 gm) and a DC modulation efficiency (e g. 34%). The room temperature Van der Waals electro-optic materials with large optical transparency window, high refractive index value, optical polarity, and electric-field switchable property may provide a promising platform for tunable metaoptics and photonic integrated circuits in light wave manipulation and optical information processing.

[0055] According to various non-limiting embodiments, the first electrode 230 may include a ring structure. In an example, the first electrode 230 may be a Fresnel zone lens. The first electrode may be made of metal (e.g. gold). The dimensions and spacings of the rings of the first electrode 230 (e.g. the top semi-transparent concentric annular gold rings ) may satisfy the condition of andwhere rm, r ’mare the outer and inner radii of the mthgold ring, respectively, λ is the wavelength, f is the focal length of the Fresnel zone lens 200. The proof-of-concept lens is designed by simulation to have a focal length of 49.56 gm at 632.8 nm, which corresponds to a total zone plate radius of r9~ 25 gm and a minimum zone width of Δr9~ 0.69 gm. The flat lens is designed to have an effective numerical aperture (NA) = 0.44 and the focal spot has a size with full width at half maximum (FWHM) = 0.76 gm.

[0056] The tunable lens 200 may include similar features of the tunable lens 100 as described above in connection to FIG. 1 , and therefore, features that are described in the context of the tunable lens 100 may correspondingly be applicable to the same or similar features in the tunable lens 200 and vice versa. Furthermore, additions and / or combinations and / or alternatives as described for a feature in the context of the tunable lens 100 may correspondingly be applicable to the same or similar feature in the tunable lens 200 and vice versa.

[0057] FIG. 3 shows an optical image of the tunable lens 200 with sandwiched C1PS layer 220 between the top semi-transparent concentric annular gold rings 230 and the bottom gold plate reflector 240 according to various embodiments of the present disclosure. The gold rings 230 are electrically connected by a 1 pm-wide wire 301 to be used as the top electrode 230. A vertical electric field is applied by using the top gold rings 230 and the bottom gold reflector 240 as the electrodes 240, 230, which enables electrical tunability via linear electro-optic modulation.

[0058] FIG. 4 is a block diagram showing an optical setup 400 for characterizing the focusing effect and the performance of a tunable lens (e.g. the tunable lens 100, 200, 700) according to various embodiments of the present disclosure.

[0059] According to various non-limiting embodiments, the optical setup 400 may include a motorized sample stage where sample 401 is placed, an (long working) objective lens 402, a beam splitter 403, the tunable lens 440 (e.g. the tunable lens 100, 200, 700), a (CMOS) camera 405, a laser 406 and an iris 407. The motorized sample stage may move along the Z axis around the focal plane of the objective lens 402. The laser 406 may be at 632.8 nm, collimated and guided onto the surface of the tunable lens 440 (e.g. the tunable lens 100, 200, 700).

[0060] FIGS. 5 A to 5D show the focusing effect and the performance of the tunable lens 440 (e.g. the tunable 100, 200) obtained by the optical setup 400 according to various embodiments of the present disclosure. FIG. 5A is a camera image of the focal spot of the tunable lens 440 in the focal plane; FIG. 5B is an 3D surface plot of the intensity distribution of the focal spot, FIG. 5C shows cross-section intensity profile along the centre of the focal spot; and FIG. 5D is the Z distance scan showing a focal length of 48.75 μm

[0061] The focal spot as shown in FIG. 5C has a Gaussian line shape, and the cross- sectional intensity profile as shown in FIG. 5C has a FWHM of 1.38 pm and 0.76 μm from experiment and simulation, respectively. The side-lobes are almost negligible with intensity contrast between the focal spot and its surroundings > 28. The measured focal length is 48.75 pm as shown in FIG. 5D, which is very close to the designed value of 49.56 pm. The focusing efficiency, defined as the proportion of the incident light that is directed to the designed focal spot, is estimated to be 6.5%.

[0062] The linear electro-optic effect may enable tunability on the intensity of the focal spot of the present tunable lens. FIGS. 6A and 6B show calculated x-component of the light field of the present tunable lens 440 before and after applying electric field to the CuInP2S6film, respectively, according to various embodiments of the present disclosure. Due to electro-optic effect, applying voltage to the CuInP2S6film may result in a reduction in the refractive index. The tunable lens 440 is configured to have a diameter of 50 μm. The laser light wavelength is 632.8 nm. The refractive index is 2.7384 before applying electric field to the CuInP2S6film, and is 2.7084 after applying electric field to the CuInP2S6film. FIGS. 6A shows the simulated electric field distribution of light passing through the tunable lens 440, illustrating the focusing action at the focal plane. Applying an electric field induces a reduction in refractive index due to the electro-optic effect, subsequently resulting in an increase in focusing efficiency as shown in FIG. 6B. The gold rings are electrically connected by a 1 μm-wide wire 301 as shown in FIG. 3 to be used as the top electrode. FIG. 6C shows the peak intensity of the focal spot of the tunable lens 440 as a function of the DC voltage. An increase of the intensity is observed with increasing the electric field either positively or negatively, following the electro-optic effect as described hereinafter. The modulation efficiency is defined as1 - / min / 1max,where Imm and Imaxare the minimum and maximum light intensity of the focal spot without and with applying voltage, which is a measure to show the effectiveness of the electrical tunability of the flat lens by using the CuInP2S6ferroelectrics. The maximum modulation efficiency of our 2D CuInP2S6ferroelectric flat lens is as high as ~34.3%. The shaded area region as shown in FIG. 6C represents the error range between the upper envelope and lower envelope deduced from repeated measurements.

[0063] FIGS. 7A to 7F show anisotropy in a tunable lens 700 according to various embodiments of the present disclosure.

[0064] FIG. 7A shows a schematic diagram of the tunable lens 700. The tunable lens 700 may include a substrate 710 (e.g. glass); a second electrode 720 (e.g. graphene) disposed on the substrate 710; at least one layer of ferroelectric material 720 (e.g. CuInP2S6(CIPS)) disposed on the second electrode 740 (e.g. over the substrate 710), and a first electrode 730 (e g. graphene) disposed on the at least one layer of ferroelectric material 720. In other words, the CuInP2S6layer may be sandwiched between two graphene layers (i.e. the first electrode 730 and the second electrode 740). A refractive index of the at least one layer of ferroelectric material 720 may be tunable by applying an electric field (e g. a voltage) through the first electrode 730 and the second electrode 740. The CuInP2S6layer may be ferroelectric at room temperature. Below ferroelectric-paraelectric transition temperature Tc, CuInP2S6may exist in the monoclinic Cc phase, with polar C if and In'7' sublattices shifted in antiparallel directionsrelative to the midplane. The inherently low symmetry of CuInP2S6structure, where its unit cell lacks a point of inversion, may render CuInP2S6possess an in-plane anisotropy.

[0065] The tunable lens 700 may include similar features of the tunable lens 100, 200 as described above in connection to FIGS. 1 and 2, and therefore, features that are described in the context of the tunable lens 100, 200 may correspondingly be applicable to the same or similar features in the tunable lens 700 and vice versa Furthermore, additions and / or combinations and / or alternatives as described for a feature in the context of the tunable lens 100, 200 may correspondingly be applicable to the same or similar feature in the tunable lens 700 and vice versa.

[0066] It shall be appreciated that although the present disclosure is described with reference to CuInP2S6, the structure, ferroelectric and other properties of CuInP2S6are also applicable to other Van der Waals materials including, but not limited to, In2Se3, WTe2, MoTe2, 3R M0S2, 3R WS2and twisted hBN . Accordingly, the present tunable lenses 100, 200, 404, 700 may instead include at least one layer of any one of In2Se3, WTe2, MoTe2, and twisted hBN . Further, it shall be appreciated that although the present disclosure is described with reference to a single (e.g. one layer) of CuInP2S6, the present tunable lenses 100, 200, 404, 700 may include homostructures fabricated by combining two or more layers of a single Van der Waals material, or heterostructures formed by combining different Van der Waals materials, including but not limited to CuInP2S6, In2Se3, WTe2, MoTe2, 3R M0S2, 3R WS2and twisted hBN.

[0067] FIG. 7B shows refractive index of an example of the tunable lens 700 in the wavelength interval ranging from 400 nm to 900 nm. CuInP2S6has high refractive index values in wavelength range of 400 nm to 900 nm and the refractive index of 2.7384 is obtained at 632.8 nm as denoted in FIG. 7B. The linear electro-optic effect, or Pockels effect, describes a second-order interaction where applying a static electric field will alter a materials’ refractive index. Crystals with such effect may be used for controlling the phase, polarization, birefringence, and intensity of light passing through them.

[0068] FIGS. 7C and 7D show room-temperature (300 K) ferroelectricity of the example of FIG. 7B revealed by piezo response force microscopy (PFM) images with sub-μm spatial resolution, and show the out-of-plane PFM amplitude and phase signals, respectively. The ferroelectricity in CuInP2S6is confirmed by using PFM that has sub- μm spatial resolution under dual AC resonance tracking (DART) mode. The upward and downward polarizations are clearly observed in both amplitude and phase images, corresponding to the bright and darkareas in FIGS. 7C and 7D. Under electric field, the copper ions are displaced in an off-centered upward state that is coupled with a compensatory antiparallel shift of the In3+sublattice which in turn results in an out-of-plane polarization.

[0069] FIGS. 7E and 7F show polarization-dependent Raman intensity spectra of the example of FIG. 7B for angle dependence of cross and parallel polarization configurations, respectively. The inset curves 701 , 702 show the Raman spectrum. The incident polarization is fixed, and the scattered signal is analysed by the second polarizer with either parallel or perpendicular polarization in reference to the incident laser light. The example is placed at a degree aligned with below birefringence measurement. The Raman peak at 521 cm is due to Si substrate. The modes at wavenumbers of ~70 cm-1and ~100 cm-1are attributed to variations of cations (Cu+, In3+ions) and anions (P2S64-ions), respectively. While the peaks at ~ 157 cm-1and ~260 cm-1correspond to deformations of the S-P-P [ δ(SPP)], S-P-S [ (SPS)] bonds within the octahedra, respectively. The modes at ~312 cm-1, ~371 cm-1, and ~446 cm-1are attributed to distortions of Cu+within the S6, cage, P-P stretching [v(PP)], and PS3stretching [^(PSi)], respectively. The mode at ~553 cm-1is influenced by cations. The in-plane optical anisotropy of CuInP2S6is revealed by polarization-resolved Raman spectroscopy. FIGS. 7E and 7E illustrate 8 active phonon vibrational modes. All the modes exhibit 4-lobed shapes, with maximum intensity at angles of 10°, 100°, 190°, and 280° for cross polarization configuration, and 65°, 155°, 245°, and 335°for parallel polarization configuration. These results indicate that the polarized Raman spectra strongly depend on the phonon symmetry, confirming the structural anisotropy of the optical anisotropy in the in-plane direction.

[0070] FIGS. 8 A to 8F show linear electro-optic effect in CuInP2S6(CIPS) of a tunable lens according to various embodiments of the present disclosure.

[0071] FIG. 8 A is a schematic diagram of the electro-optic measurement system using photo elastic modulator (PEM) to measure the retardation of CuInP2S6micro-sized flakes. The optical axis of the PEM is set to be zero degree. The angle resolved phase retardation when rotating the sample with angles relative to the optical axis of the PEM is measured and shown in FIG. 8B.

[0072] FIG. 8B shows intrinsic in-plane phase retardance and birefringence of the van der Waals ferroelectric membrane. Two maxima and two minima can be seen from FIG. 8B. The birefringence value is determined by using angle-resolved phase retardationΦ = Φ - Φywhich describes the phase difference between the transmitted light fields polarized in parallel to the x and y axis, respectively. A He-Ne CW laser at 632.8 nm wavelength is selected as the light source, as CuInP2S6, is optically transparent at this wavelength.

[0073] The first peak value of 0.08 radians is observed at the angle of 51°, which corresponds to the orientation of the fast axis and is generally used to define the direction of retardation. The birefringence txn = nx- nyis calculated to be 0 0149 usingwhere B, λ and t are phase retardation, wavelength of the probe light and thickness of the CuInP2S6, respectively. The thickness of the CuInP2S6flake is 549.3 nm. The isotropic glass substrates and graphene electrode layers do not have birefringence; therefore no differences are observed in their angle-resolved retardation curves.

[0074] FIG. 8C shows cross-sectional transmission electron microscopy (TEM) image of the CuInP2S6layer. The inset 801 shows the Fourier transform of the cross-sectional TEM image. FIG. 8D shows the enlarged image in the white rectangular area 802 of FIG. 8C. The CuInP2S6flake is cleaved by using focused ion beam (FIB) along the zero-degree direction in the phase retardation measurement. The direction perpendicular to the plane of TEM image corresponds to the atomic arrangement projected along the direction near to

[0110] , The crystal orientation associated to the optical fast axis is verified via the cross-sectional TEM image. The 2d-spacing is 1.26 nm as shown in FIG. 8C and accordingly, the d-spacing is estimated to be 0.63 nm. CuInP2S6has a monoclinic structure with lattice parameters of a = 6.0956(4) A°, b = 10.5645(6) A’, c = 13.6230(8) A°. When the lattice rotates clockwise through 51° around the c axis, it is then projected along the

[0010] direction, which indicates that the fast optical axis is parallel to its (010) plane.

[0075] FIG. 8E shows phase retardation as a function of the out-of-plane electric field (i.e. voltage) between the top and bottom few-layer graphene. The birefringence of the ferroelectric CuInP2S6film may be tuned by applying electric field, which in turn will tune the phase of the light passing through it. The change of phase retardation of light passing through the CuInP2S6is measured by applying a DC out-of-plane electric field. The voltage applied to the device is lower than the coercive voltage that is around 5 V. As guided by the arrows 803, 804, the voltage sweeps from 5 V to -5V. FIG. 8F shows linear phase shift and birefringence difference (Pockels effect). The curves are calculated by subtracting the value of voltage = 0 V. The transverse electric field induced birefringence shift δ (Δn) is expressed by the formula ofwhere n is the refractive index of the material, rcis the effective electro-optic coefficient, and E is the electric field. The dashed line 805 is the fitting result to the data of the curve, based on the above linear fitting formula. The linear electro-optical coefficient rcis determined to be 20.28 pm / V. A linear electro-optic response is observed from the phase and birefringence shift.

[0076] Numerical modeling using a simulator based on first-principle calculations has been performed to understand the electro-optic property of CuInP2S6, and its potentials for metaoptics applications. FIGS. 9A to 9H show the atomic structure, electronic, optical, and electro-optic properties of 2D ferroelectric CuInP2S6of a tunable lens by first-principle calculation, according to various embodiments of the present disclosure.

[0077] FIGS. 9A and 9B show the fully relaxed atomic structure of CuInP2S6obtained through density functional theory (DFT) calculations, viewed along the a- and c-axis, respectively. The solid lines 901, 902 denote the unit cell boundaries. A 3x3x 1 supercell is used to facilitate visual orientation The relaxed atomic structure is characterized by in-plane lattice vectors a and b arranged in a hexagonal pattern, forming an angle of 120° (y). The out- of-plane lattice vector c is positioned such that the a and β angles measure 98.7° each. The inset of FIG. 9B is the mapping of experimental optical axes to the lattice vectors. The triclinic unit cell used in the theoretical calculations is mapped to the monoclinic conventional cell used in the experimental analyses to facilitate spatial orientation. The dashed lines 903 indicate the conventional cell used in experiments. The relationships among the primitive lattice vectors, the fast optical axis 904 and slow optical axis 905 are also illustrated.

[0078] FIG. 9C shows electronic band structures obtained using DFT (dashed lines) and Green's function (G) and screened Coulomb interaction (W) GW (solid lines) for CuInP2S6. A direct GW band gap of 2.41 eV at the T point of the Brillouin Zone is observed, which is larger than the direct DFT gap of 1.82 eV. The topmost valence band of CuInP2S6is relative flat, whereas the lowest unoccupied band is significantly more dispersive, echoing the findings based on DFT calculations.

[0079] FIG. 9D shows energy-dependent real (ei) and imaginary (£2) parts of the CuInP2S6dielectric function along different optical polarization directions. The dotted lines 906, 907,908 mark the wavelengths at 378 nm, 441 nm, and 632.8 nm, respectively. The column plot909 in the right panel presents (in atomic units) the square of the magnitude of the optical transition matrix elements along the fast axis. vais the velocity vector in the direction a, |0> and |S> refer to the many-body ground state and excitonic wavefunctions, respectively. The real (1) and imaginary (ε2) parts of the CuInP2S6, dielectric functions are calculated using GWplus Bethe-Salpeter equation (BSE) approach along a, a + 2b, a - b, and a + b directions of the unit cell, which approximately correspond to the 0°, 90°, fast, and slow experimental optical axes, respectively (as shown in the inset of FIG. 9B). In < 0|v«|S >, vαis the velocity vector in the direction a, < 0| and |S > refer to the many-body ground state and excitonic wavefunctions, respectively. Varying the polarization direction of the incident photon does not lead to noticeable change in energy of the first exciton. The magnitudes of the first non-zero optical transition matrix element along the directions of interest are also small, suggesting that CuInP2S6is not an excitonic system. The optical band gap of CuInP2S6is larger than the energy of the incident photon wavelength of 632.8 nm, indicating that the electro-optic effect and flat lens results shown above are applicable to the whole wide transmittance spectrum. For energies below the optical band gap, no incident photons of these energies are absorbed and ε2 is zero. The relationship between the refractive index and the dielectric functions of CuInP2S6can be simplified to n = √ε1for incident beam energies below the optical band gap. FIG 9D shows that £1 along the fast polarization axis is smaller than that of the slow axis at 632.8 nm. On the other hand, 1 along the 0° axis closely matches the value along the 90° axis. The birefringence (Δn = nα+90° - na) at 632.8 nm is large along the fast axis and is smaller for the 0° axis (nslow- nfast> n90 °- n0°). The present theoretical results of the birefringence and phase retardation in CuInP2S6correspond well to the experimental observations, reflecting the maxima and minima at approximately the experimental fast and slow optical axes, respectively. The optical band gap is determined to be about 2.37 eV, where the first non-zero optical transition matrix element is observed at 523 nm.

[0080] FIG. 9E shows theoretical values of phase retardation and birefringence at different polarization angles with = 632.8 nm. The theoretical magnitudes of birefringence and phase retardation at the experimental fast axis, where the quantities are expected to reach their maxima, are determined to be 2.45* 10-2and 13.4x 10-2radians, respectively.

[0081] FIG. 9F shows energy dependent phase retardation (solid lines) and birefringence (dotted lines) along the 90° and slow axes. Along the fast axis, a minimum of -0.11 × 10-2and a maximum of 0.13x l0-2in birefringence occur at 378 nm and 441 nm, respectively. These wavelengths correspond to energies beyond the optical band gap, and the birefringence at these energies involve variations in both £1 and £2. It is observed that £2 of the fast and slow axes at these energies are approximately the same. Therefore, the birefringence and phase retardation at these energies are still predominantly influenced by the differences in £1. To simulate the linear electro-optic effect, the Pockels effect susceptibility tensor is calculated. The latter isobtained from second-order perturbation theory using the single-particle energies and wave functions from a DFT calculation (thus excitonic effects are not accounted for). From the relevant components of the Pockels effect tensor, the effective linear electro-optic coefficient as a function of frequency, rcω ), is determined.

[0082] FIG. 9G shows the simulated (linear) electro-optic coefficient rcin wavelength range of 540 nm to 1000 nm, predicting rc= 9.87 pm / V at 632.8 nm, which is within an order of magnitude from the observed value. Higher rcvalues are observed at shorter wavelengths, suggesting a greater degree of tunability for larger adaptability in this region. With rcknown, the phase retardation can be calculated.

[0083] FIG. 9H shows phase retardation spectrum as a function of photon energy and applied voltage. Phase retardation increases with increasing the voltage, showing linear electrooptic effect. With the broadband light transmittance, the electrical switchable spontaneous polarity, the linear electric-field modulation of light, and the flexibility to integrate with other substrates and structures, the electrically tunability of van der Waals CuInP2S6ferroelectric holds tremendous potentials for applications in various fields such as imaging, sensing, and communication.

[0084] Linear electrical modulation of light is demonstrated by applying transverse electric field to the CuInP2S6film, which has highly orientated ferroelectric domains and optical anisotropy with the fast axis along (010) crystal plane. The effective electro-optic coefficient rcis measured to be 20.28 pm / V. To fabricate the flat lens, CuInP2S6is sandwiched between concentric gold circles and a gold reflector, which also act as two electrodes to apply voltage. The flat lenses exhibit an electrical modulation efficiency > 34%. The first-principle calculations unveil the interplay between crystal orientation and optical birefringence, underscoring the high transparency exhibited across a wide wavelength range and the large linear electro-optic coefficient in shorter wavelength region, harmonizing with experimental observations. The electrically tunable CuInP2S6, ferroelectrics may find applications in metalens and metaoptics for compact optical development, and prompt the exploration of other 2D ferroelectric materials for future electrically tunable and reconfigurable flat optics and photonics.

[0085] FIG. 10 shows a flow chart of a method 1000 for forming a tunable lens (e.g. tunable lens 100, 200, 404, 700). The method 1000 for forming a tunable lens may include: forming at least one layer of ferroelectric material (e.g. CuInP2S6) disposed over a substrate (e.g. SiC>2 / Si) (at step 1010); and forming a first electrode (e.g. gold) on the at least one layer of ferroelectricmaterial (at step 1020); wherein a refractive index of the at least one layer of ferroelectric material is tunable by applying an electric field through the first electrode.

[0086] In some embodiments, the at least one layer of ferroelectric material may be mechanically exfoliated from bulk single crystal and transferred onto the substrate. In these embodiments, the lattice-match limitation that is a common restriction for epitaxial thin films may be inapplicable or relaxed. In some embodiments, the at least one layer of ferroelectric material may be deposited / grown on the substrate by chemical or physical deposition / growth methods

[0087] According to various non-limiting embodiments, the method 1000 may further include forming a second electrode (e.g. titanium or gold) between the substrate and the at least one layer of ferroelectric material, wherein the electric field is applied through the first electrode and the second electrode. The second electrode may be deposited (e.g. Ti / Au = 3 / 50 nm) on the substrate (e g. SiO2 / Si) using e-beam evaporator. In some embodiments, the CuInPiSr, flakes may mechanically exfoliated from bulk single crystals and transferred onto the bottom Ti / Au layer. Then the structure may be annealed at 200 °C in Ar / l f = 95 / 5 for 10 hours. Subsequently, the first electrode (e g. top gold rings of 30 nm thick) may be patterned using electron beam lithography followed by lift-off.

[0088] In some embodiments, the second electrode may be made of conductive oxide, and the substrate and the second electrode may be both transparent and the lens is configured to operate in transmission mode. In some embodiments, the second electrode may be made of metal as back reflector and the lens is configured to operate in reflection mode.

[0089] According to various non-limiting embodiments, the at least one layer of ferroelectric material may include at least one layer of Van der Waals material including CuInP2S6, In2Se3, WTe2, MoTe2, 3R MoS2, 3R WS2, and twisted hBN.

[0090] According to various non-limiting embodiments, the substrate comprises a rigid or flexible substrate, made of glass, quartz, SiO2 / Si, sapphire, Polycarbonate (PC) or Polyethylene (PE).

[0091] According to various non-limiting embodiments, the first electrode may include a ring structure, e.g. a Fresnel zone lens. The first electrode may be made of metal.

[0092] According to non-limiting various embodiment, the manufacture of the present tunable lens may employ several fabrication techniques to create nanostructures for light manipulation, including electron beam lithography (e-beam lithography), which uses a focusedelectron beam to pattern a resist material with high resolution; nanoimprint lithography (NIL), where a mold with nanoscale features is pressed into a resist-coated substrate to imprint the desired pattern; and photolithography, which projects light through a photomask onto a photosensitive resist to create larger-area patterns. Chemical Vapor Deposition (CVD) and Physical Vapor Deposition (PVD) may be used to deposit thin films of materials that are then patterned through etching techniques like Reactive Ton Etching (RTE) Stamping and embossing methods may involve pressing patterned stamps onto substrates, while laser lithography uses focused laser beams to directly write patterns onto materials. Each of these techniques may be selected based on the required precision, material properties, and specific design needs of the lenses.

[0093] While the method described above is illustrated and described as a series of steps or events, it will be appreciated that any ordering of such steps or events are not to be interpreted in a limiting sense. For example, some steps may occur in different orders and / or concurrently with other steps or events apart from those illustrated and / or described herein. In addition, not all illustrated steps may be required to implement one or more aspects or embodiments described herein. Also, one or more of the steps depicted herein may be carried out in one or more separate acts and / or phases.

[0094] While this specification contains many details, these should not be understood as limitations on the scope of what may be claimed, but rather as descriptions of features specific to particular examples. Certain features that are described in this specification or shown in the drawings in the context of separate implementations can also be combined. Conversely, various features that are described or shown in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable sub-combination.

[0095] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single product or packaged into multiple products.

[0096] A number of implementations have been described. Nevertheless, it will be understood that various modifications can be made. Accordingly, other implementations are within the scope of the following claims.

Claims

CLAIMS1. A tunable lens, comprising: a substrate; at least one layer of ferroelectric material disposed over the substrate; and a first electrode disposed on the at least one layer of ferroelectric material; wherein a refractive index of the at least one layer of ferroelectric material is tunable by applying an electric field through the first electrode.

2. The lens of claim 1, further comprising: a second electrode disposed between the substrate and the at least one layer of ferroelectric material, wherein the electric field is applied through the first electrode and the second electrode.

3. The lens of claim 2, wherein the second electrode is made of conductive material.

4. The lens of claim 2 or claim 3, wherein the substrate and the second electrode are both transparent and the lens is configured to operate in transmission mode.

5. The lens of claim 2, wherein the second electrode is made of metal as back reflector and the lens is configured to operate in reflection mode.

6. The lens of any of claims 1 to 5, wherein the at least one layer of ferroelectric material comprises at least one layer of Van der Waals material.

7. The lens of claim 6, wherein the Van der Waals material comprises CuInP2S6, In2Se3, WTe2, MoTe2, 3R MoS2, 3R WS2, and twisted hBN.

8. The lens of any of claims 1 to 7, wherein the first electrode comprises a ring structure.

9. The lens of claim 8, wherein the first electrode is made of metal or conductive materials.

10. The lens of claim 7 or claim 8, wherein the first electrode is a Fresnel zone lens.

11. The lens of any of claims 1 to 10, wherein the substrate comprises a rigid or flexible substrate, made of glass, quartz, SiO2 / Si, sapphire, Polycarbonate (PC) or Polyethylene (PE).

12. A method for forming a tunable lens, comprising: forming at least one layer of ferroelectric material disposed over a substrate; and forming a first electrode on the at least one layer of ferroelectric material; wherein a refractive index of the at least one layer of ferroelectric material is tunable by applying an electric field through the first electrode.

13. The method of claim 12, further comprising: forming a second electrode between the substrate and the at least one layer of ferroelectric material, wherein the electric field is applied through the first electrode and the second electrode.

14. The method of claim 13, wherein the second electrode is made of conductive oxide, and wherein the substrate and the second electrode are both transparent and the lens is configured to operate in transmission mode.

15. The method of claim 13, wherein the second electrode is made of metal as back reflector and the lens is configured to operate in reflection mode.

16. The method of any of claims 12 to 15, wherein the at least one layer of ferroelectric material comprises at least one layer of Van der Waals material including CuInP2S6, In2Se3, WTe2, MoTe2, 3R MoS2, 3R WS2, and twisted hBN.

17. The method of any of claims 12 to 16, wherein the first electrode comprises a ring structure.

18. The method of claim 17, wherein the first electrode is made of metal.

19. The method of claim 17 or claim 18, wherein the first electrode is a Fresnel zone lens.

20. The method of any of claims 12 to 19, wherein the substrate comprises a rigid or flexible substrate, made of glass, quartz, SiO2 / Si, sapphire, Polycarbonate (PC) or Polyethylene (PE).

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