A Nonlinear Beam Shaping Method Based on Stacked Moiré Metasurfaces

Abstract

This invention relates to the field of metasurface technology, specifically disclosing a nonlinear beam shaping method based on stacked moiré metasurfaces. The method includes: obtaining the frequency harmonic wavelength of the fundamental light and the target emission angle of the nonlinear beam; calculating the quasi-period of the moiré lattice of the stacked moiré metasurface; calculating the correspondence between the lattice period and the twist angle of the stacked moiré metasurface; obtaining a stacked moiré metasurface with the stated correspondence; and forming a nonlinear beam by irradiating the fundamental light onto the stacked moiré metasurface, wherein the emission angle of the nonlinear beam is the target emission angle. This invention calculates the correspondence between the lattice period and the twist angle of the stacked moiré metasurface based on the target emission angle of the nonlinear beam, fabricates stacked moiré metasurfaces with different lattice periods and twist angles, and forms rich momentum components through the combination of reciprocal lattice vectors of multiple basic metasurfaces, thereby precisely modulating the nonlinear beam.

Description

Technical Field

[0001] This invention relates to the field of metasurface technology, and in particular to a nonlinear beam shaping method based on stacked moiré metasurfaces. Background Technology

[0002] Momentum transfer plays a crucial role in controlling the interaction between photons and matter. This effect has been significantly observed in the diffraction of periodic structures (such as gratings), where momentum associated with the reciprocal lattice vector is transferred to the photon, thereby altering the direction of light propagation. The concept of momentum transfer is essential for designing optical elements that control and manipulate light, contributing to applications such as beam steering, beam splitting, information processing, and multichannel communication. It is fundamental to the development of optical technology and has a wide-ranging impact on various scientific and engineering fields.

[0003] To enhance the flexibility of optical manipulation, a flexible reciprocal space needs to be established, capable of generating customizable momentum component spectra. The Mohr effect, arising from the superposition of two or more periodic lattices with twist angles or mismatched lattice constants, has emerged as a general strategy for generating various lattices with variable symmetry and periodicity. This variability is achieved by directly manipulating the twist angles or lattice constant mismatches. The Mohr effect, with its inherent capabilities, offers a promising pathway to creating new Brillouin bands, forming rich momentum spaces.

[0004] The field of metasurfaces is renowned for its flexibility in manipulating light, providing a fascinating framework for designing real and reciprocal lattices. The fusion of metasurface concepts with moiré photonics has already yielded substantial progress in the linear domain. However, this research has yet to extend into the nonlinear domain.

[0005] Furthermore, the fabrication of photonic moiré metasurfaces requires complex techniques compared to the unique engineering methods used for twisted bilayer two-dimensional materials. Generally, photonic moiré structures fall into two main strategies. On one hand, optical moiré metasurfaces can incorporate two sets of lattices into the same layer, forming a single-layer moiré superlattice; this fabrication process is relatively simple. On the other hand, by controlling the twist angle and interlayer distance, twisted bilayer moiré metasurfaces offer greater optical manipulation freedom and higher mechanical strength, demonstrating excellent application potential in tunable systems, but they are more difficult to fabricate. The difficulty in etching typical nonlinear crystals (such as lithium niobate) further limits the expansion of moiré metasurfaces into the nonlinear domain. Summary of the Invention

[0006] This invention aims to address the lack of research on nonlinear optical modulation utilizing stacked moiré metasurfaces. To this end, this invention provides a nonlinear beam shaping method based on stacked moiré metasurfaces. According to the target emission angle of the nonlinear beam, the correspondence between the lattice period and the twist angle of the stacked moiré metasurface is calculated. Stacked moiré metasurfaces with different lattice periods and twist angles are fabricated. By combining the reciprocal lattice vectors of multiple basic metasurfaces of the stacked moiré metasurface, rich momentum components are formed, thereby precisely modulating the nonlinear beam.

[0007] This invention provides a nonlinear beam shaping method based on stacked moiré metasurfaces, the technical solution of which includes:

[0008] Obtain the frequency harmonic wavelength of the fundamental light and the target emission angle of the nonlinear beam;

[0009] The quasi-period of the moiré lattice of the stacked moiré metasurface is calculated based on the frequency doubling wavelength of the fundamental light and the target emission angle of the nonlinear beam.

[0010] Based on the quasi-period of the moiré lattice of the stacked moiré metasurface, the correspondence between the lattice period and the twist angle of the stacked moiré metasurface is calculated.

[0011] Obtain stacked moiré metasurfaces with the aforementioned correspondence;

[0012] The fundamental frequency light irradiates the stacked moiré metasurface to form the nonlinear beam. The emission angle of the nonlinear beam is the target emission angle, which achieves nonlinear beam shaping. The emission angle of the nonlinear beam is the angle between the beam path of the nonlinear beam and the normal of the stacked moiré metasurface.

[0013] Furthermore, the quasi-periodic moiré lattice of the stacked moiré metasurface... The calculation formula is:

[0014]

[0015] in, This is the harmonic wavelength of the fundamental frequency light. The target emission angle of the nonlinear beam.

[0016] Furthermore, based on the quasi-period of the moiré lattice of the stacked moiré metasurface, the formula for calculating the correspondence between the lattice period and the twist angle of the stacked moiré metasurface is as follows:

[0017]

[0018] in, For a moiré lattice quasi-periodic, For lattice period, For the angle of distortion.

[0019] Furthermore, the process of obtaining stacked moiré metasurfaces with the aforementioned correspondence is as follows:

[0020] Select one or more sets of values ​​for the lattice period and twist angle that conform to the corresponding relationship;

[0021] Based on the values ​​of the lattice period and twist angle, a nonlinear thin film is processed using a focused ion beam to obtain a stacked moiré metasurface.

[0022] Furthermore, the stacked moiré metasurface has two layers.

[0023] Furthermore, the processing procedure for the stacked moiré metasurface is as follows:

[0024] The nonlinear thin film without substrate support is fixed on the worktable;

[0025] Based on the value of the lattice period, a periodic array of basic metasurfaces A and B is fabricated on the nonlinear thin film using a focused ion beam.

[0026] A portion of the edge of the basic metasurface A is cut using a focused ion beam.

[0027] The tip of the nanomanipulator was welded to the edge of the basic metasurface A using platinum deposition.

[0028] Using a focused ion beam, the remaining connected portions of the edge of the basic metasurface A are cut off;

[0029] Move the nanomanipulator and rotate the stage by the value of the torsion angle so that the basic metasurface A covers the basic metasurface B;

[0030] The basic metasurface A and basic metasurface B are welded using platinum deposition.

[0031] The needle tip is cut off using a focused ion beam, and the edge of the basic metasurface B is cut to obtain the stacked moiré metasurface.

[0032] Furthermore, the nonlinear thin film is a metal film or a dielectric film.

[0033] Furthermore, the dielectric film is made of lithium niobate, lithium tantalate, zinc oxide, gallium arsenide, gallium phosphide, boron nitride, niobium oxide dihalide, or transition metal disulfide.

[0034] The above-described one or more technical solutions in the embodiments of the present invention have at least one of the following technical effects:

[0035] 1. This invention utilizes nonlinear materials to fabricate stacked moiré metasurfaces. By adjusting the lattice period and twist angle of the stacked moiré metasurfaces, the emission angle of a nonlinear beam is controlled, thereby precisely modulating the nonlinear beam. This invention designs stacked moiré metasurfaces composed of two or more layers of nonlinear periodic metasurfaces stacked at different angles. When excited by a fundamental frequency beam, nonlinear polarized dipoles are generated within the moiré metasurface through second-order magnetic susceptibility. These dipoles oscillate at twice the frequency of the fundamental field, acting as secondary sources for radiating second harmonic generation (SHG) waves to the far field. The array on the moiré metasurface forms a nonlinear photonic lattice with alternating zero and nonzero distributions. Furthermore, in addition to the inherent lattice momentum of each basic metasurface, moiré lattice momentum is also generated due to interlayer coupling between the stacked layers. This momentum is transferred to the SHG photons and modulates the propagation direction of the SHG wave. The spatial variation of moiré SHG diffraction corresponds to different emission directions of SHG. Therefore, the emission angle of SHG can be controlled by adjusting the lattice period and twist angle of the stacked moiré metasurface, thus achieving directional emission of SHG.

[0036] 2. This invention utilizes focused ion beam and platinum deposition technology to achieve precise processing of moiré metasurfaces. A matching nanomanipulator is used to release the metasurface from the original thin film and transfer it to another location. The rotation angle of the stage is controlled to stack two moiré metasurfaces at a specific angle. This stacked moiré metasurface processing method can achieve arbitrary twisting angles of multilayer basic metasurfaces. It is a high-quality, highly repeatable processing method. The processed stacked moiré metasurfaces have higher mechanical strength and greater degrees of manipulation freedom, and show excellent application potential in tunable systems.

[0037] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0039] Figure 1 This is a flowchart provided by the present invention.

[0040] Figure 2 This is a diagram illustrating the manufacturing process of the stacked moiré metasurface provided by the present invention.

[0041] Figure 3This is the shaping beam pattern of the nonlinear beam provided by the present invention.

[0042] Figure 4 This is a SEM image of the stacked moiré metasurface provided by the present invention.

[0043] Figure 5 This is a schematic diagram of the moiré lattice of the stacked moiré metasurface provided by the present invention.

[0044] Figure 6 This is the SHG spot distribution diagram provided by the present invention.

[0045] Figure 7 This is a schematic diagram showing how the SHG spot changes with the torsion angle, provided by the present invention.

[0046] Figure 8 This is a curve of the torsion angle versus the emission angle provided by the present invention.

[0047] Figure 9 This is a curve of lattice period versus emission angle provided by the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but should not be used to limit the scope of this invention.

[0049] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0050] Nonlinear moiré metasurfaces, composed of multiple layers of periodic lattices with twisted or mismatched lattice constants, have attracted considerable attention in the field of electronics, especially in the context of twisted bilayer two-dimensional (2D) materials. Research on the properties of 2D materials has gradually extended to the field of photonics, and has progressed to moiré metasurfaces with greater degrees of tunability. Stacking two or more periodic structures to form moiré patterns is becoming a promising platform for confining and manipulating light. Compared to the unique engineering methods of 2D materials, the fabrication of photonic moiré metasurfaces requires complex techniques. Generally, photonic moiré structures are mainly divided into two strategies. On the one hand, optical moiré metasurfaces can write two sets of lattices into the same layer to form a monolayer moiré superlattice; this fabrication process is relatively simple. On the other hand, by controlling the twist angle and interlayer distance, twisted bilayer moiré metasurfaces provide greater degrees of freedom for optical manipulation, have higher mechanical strength, and show excellent application potential in tunable systems. In recent years, although moiré superlattices have made significant progress in the linear domain, nonlinear moiré metasurfaces remain an unexplored experimental frontier. Manipulating light propagation at the nanoscale through moiré metasurfaces provides a new platform for nonlinear optical modulation.

[0051] The following is combined Figures 1 to 9 The present invention will be further described in detail below, providing a nonlinear beam shaping method based on stacked moiré metasurfaces:

[0052] In this embodiment, as Figure 1 As shown, a nonlinear beam shaping method based on stacked moiré metasurfaces is provided, including the following steps:

[0053] Step 1: Obtain the frequency harmonic wavelength of the fundamental light and the target emission angle of the nonlinear beam.

[0054] Step 2: Calculate the quasi-period of the moiré lattice of the stacked moiré metasurface based on the frequency harmonic wavelength of the fundamental light and the target emission angle of the nonlinear beam.

[0055] Quasi-periodic moiré lattice of the stacked moiré metasurface The calculation formula is:

[0056]

[0057] in, This is the harmonic wavelength of the fundamental frequency light. The target emission angle of the nonlinear beam.

[0058] Step 3: Based on the quasi-period of the moiré lattice of the stacked moiré metasurface, calculate the correspondence between the lattice period and the torsion angle of the stacked moiré metasurface. The calculation formula is as follows:

[0059]

[0060] in, For a moiré lattice quasi-periodic, For lattice period, For the angle of distortion.

[0061] Step 4: Obtain the stacked moiré metasurfaces with the aforementioned correspondence. The specific process is as follows:

[0062] Select one or more sets of values ​​for the lattice period and twist angle that conform to the aforementioned correspondence; the experimenter selects values ​​for the lattice period and twist angle that are conducive to equipment processing based on personal experience.

[0063] Based on the values ​​of the lattice period and twist angle, a nonlinear thin film is processed using a focused ion beam to obtain a stacked moiré metasurface. A stacked moiré metasurface is obtained for each set of lattice period and twist angle values.

[0064] The nonlinear thin film is a metal film, such as gold; or a dielectric film, such as lithium niobate (LiNbO3), lithium tantalate (LiTaO3), zinc oxide (ZnO), gallium arsenide (GaAs), gallium phosphide (GaP), boron nitride (BN), niobium oxide dihalide (NbOX2), transition metal disulfide (MX2), etc.

[0065] Taking the fabrication of a two-layer stacked moiré metasurface as an example, the fabrication method of the stacked moiré metasurface used in this method is explained in detail as follows:

[0066] Step 4.1: Fix the substrate-free nonlinear thin film onto the worktable.

[0067] Step 4.2: Based on the value of the lattice period, using a focused ion beam, a periodic array of fundamental metasurfaces A and B is fabricated on the nonlinear thin film, as follows: Figure 2 (a) and Figure 2 As shown in (e).

[0068] Step 4.3: Using a focused ion beam, cut a portion of the edge of the basic metasurface A.

[0069] Step 4.4: The tip of the nanomanipulator is welded to the edge of the basic metasurface A using platinum deposition, such as... Figure 2 (b) and Figure 2 As shown in (f).

[0070] Step 4.5: Using a focused ion beam, cut the remaining connecting portion of the edge of the basic metasurface A; at this point, the basic metasurface A is completely cut off from the film.

[0071] Step 4.6: Move the nanomanipulator hand, as follows Figure 2 (c) and Figure 2 As shown in (g), the stage is rotated with the value of the twist angle so that the basic metasurface A covers the basic metasurface B; when the stage rotates, it drives the nonlinear film to rotate together.

[0072] Step 4.7: Weld the basic metasurface A and the basic metasurface B using platinum deposition; weld at the edges of the basic metasurface A and the basic metasurface B.

[0073] Step 4.8: Using a focused ion beam, cut off the needle tip and the edge of the basic metasurface B to obtain the stacked moiré metasurface. At this point, the basic metasurface B is completely cut off from the film, as shown below. Figure 2 (d) and Figure 2 As shown in (h).

[0074] This invention employs a stacked moiré metasurface fabrication method to process two or more layers of stacked moiré metasurfaces. In step 4.2, more sets of periodic arrays of basic metasurfaces are fabricated, and steps 4.3-4.7 are repeated to increase the number of stacked layers. This invention utilizes focused ion beams to achieve precise metasurface fabrication and uses a matching nanomanipulator to release the metasurface from the original thin film and transfer it to another location. The rotation angle of the stage is controlled to stack two metasurfaces at a specific angle. The stacked moiré metasurface fabrication method used in this invention can achieve arbitrary twist angle stacking of multiple layers of basic metasurfaces, and is a high-quality, highly repeatable fabrication method. The fabricated stacked moiré metasurfaces have higher mechanical strength and greater degrees of manipulation freedom, and show excellent application potential in tunable systems.

[0075] Step 5: The fundamental frequency light irradiates the stacked moiré metasurface to form the nonlinear beam. The emission angle of the nonlinear beam is the target emission angle, thereby achieving nonlinear beam shaping. The emission angle of the nonlinear beam is the angle between the beam path of the nonlinear beam and the normal of the stacked moiré metasurface.

[0076] The following experiments verify the shaping effect of the stacked moiré metasurface of the present invention on nonlinear beams.

[0077] 1. Shaping optical path for nonlinear beams

[0078] like Figure 3As shown, the shaping optical path includes, in sequence, a tunable Ti:sapphire femtosecond laser (Maitai, Spectra-Physics, 80MHz, 230fs), a Glan-Taylor prism (GTP), a half-wave plate (HWP), a 10x objective lens (Obj1 10x, NA=0.25), a stacked moiré metasurface, a 100x objective lens (Obj2 100x, NA=0.90), a short-pass filter (BG40 colored glass), and a semi-transparent plastic screen. A camera (CCD) is positioned behind the plastic screen. The pump laser beam is focused onto the stacked moiré metasurface through the 10x objective lens, forming a focused spot with a diameter of approximately 10µm. The SHG wave transmitted from the other side of the stacked moiré metasurface is collected by the 100x objective lens and the fundamental frequency light is filtered out by the short-pass filter, forming an SHG pattern on the semi-transparent plastic screen. The SHG pattern is captured by the camera.

[0079] In the experiment, the pump wavelength was chosen to be 950 nm, corresponding to an SHG wavelength of 475 nm, which is shorter than the lattice period of the moiré metasurface (600 nm), thus facilitating effective diffraction of the SHG light. Due to the short interaction length of the beam within the studied moiré metasurface, the SHG diffraction follows a Raman-Natt mechanism. In this case, transverse lattice momentum transfer dominates, thereby modulating the propagation direction of the SHG wave.

[0080] 2. Stacked Moiré metasurfaces

[0081] Two factors influence the emission angle of SHG waves related to stacked moiré metasurfaces: the lattice period of the moiré metasurface and the twist angle between the layers. To facilitate the experiment, three stacked moiré metasurfaces were fabricated. The nonlinear film was a lithium niobate (LN) film with a thickness of 210 nm; the area of ​​the moiré metasurface was 25 × 25 µm. 2 The diameter of the pores in the periodic array is 225 nm, and the lattice period is 600 nm; the twist angles are 15°, 30° and 45° respectively.

[0082] The stacked moiré metasurface was fabricated using focused ion beam (FIP) and platinum deposition. The FIP beam used gallium cations at 30 kV and 24 pA. SEM images of the stacked moiré metasurface are shown below. Figure 4 As shown. Figure 4 (a) is a representative cross-sectional SEM image of the moiré metasurface, showing the periodic structure of the moiré lattice with a quasi-period of 600 nm and a pore diameter of 225 nm. Figure 4(a) It was confirmed that the fabricated metasurface has uniform pore size and steep sidewalls, and the suspended structure enhances the refractive index contrast between the film and the substrate environment, which can effectively promote optical field confinement in the vertical direction, which is the key to achieving high-quality optical performance. Figure 4 (b) is a top-view SEM image of the Mohr metasurface, showing the twist angle. It is a 30° double-layer stacked moiré metasurface.

[0083] Moiré lattices formed by stacked moiré metasurfaces with twist angles of 15°, 30°, and 45° are as follows: Figure 5 As shown. Figure 5 The three sets of images in the image, from left to right, have distortion angles of 15°, 30°, and 45°, respectively. Figure 5 (a)- Figure 5 (c) is a schematic diagram of a stacked moiré metasurface formed by identical square lattices; Figure 5 (d)- Figure 5 (f) is the theoretical calculation result of the moiré lattice pattern of the stacked moiré metasurface; Figure 5 (g)- Figure 5 (i) Experimental observations of the moiré lattice patterns of stacked moiré metasurfaces captured by a microscope. The stacking process of the moiré metasurfaces introduces new quasi-periodic features, particularly the enlarged moiré lattice generated by 15° and 30° twists. Figure 5 (d) and Figure 5 The black dashed squares in (e) highlight this feature. This invention incorporates disproportionate twist angles, resulting in aperiodic moiré patterns. Quasi-periodicity of the moiré lattice can be achieved through the formula... Confirmed. Furthermore, the moiré lattice formed by the 45° twist is consistent with the Ammann-Beenker jigsaw puzzle and exhibits remarkable 8-fold rotational symmetry. Figure 5 (g)- Figure 5 (i) The actual pattern shown under a microscope is very close to the theoretical pattern, which visually confirms the stacked moiré metasurface constructed in this invention.

[0084] 3. Shaping nonlinear beams using stacked moiré metasurfaces

[0085] The distribution of SHG light spots captured by the camera is as follows Figure 6 As shown. Figure 6 (a) shows the SHG spot measured from a single-layer moiré metasurface, with the dashed circle indicating the aperture of the 100x objective lens. Figure 6 (b) shows the reciprocal lattice corresponding to the monolayer moiré metasurface. The momentum transfer of the SHG spot generates the peripheral first-order diffraction spot, which in turn... Figure 6 (a) is marked with a blue circle. Figure 6 (c)- Figure 6 (n) shows the SHG spot and reciprocal lattice of the stacked moiré metasurfaces with twist angles of 15°, 30° and 45°. Figure 6 (c) Figure 6 (g) and Figure 6 (k) represents the measured SHG spot. Figure 6 (d) Figure 6 (h) and Figure 6 (l) are the reciprocal lattices of the blue, undistorted moiré metasurface and the red, distorted moiré metasurface, respectively. Figure 6 (e) Figure 6 (i) Figure 6 (m) Figure 6 (f) Figure 6 (j) and Figure 6 (n) describes the reciprocal lattice vectors, which are composed of combinations of the reciprocal lattice vectors of the moiré metasurface. Based on different vector combinations, these vectors are divided into four groups, including... , , and ,exist Figure 6 The colors are represented by dark green, light green, dark yellow, and light yellow, respectively.

[0086] like Figure 6 (a) and Figure 6 As shown in (b), due to the conservation of momentum in the light spot, a perpendicularly incident beam will produce an SHG light spot with zero transverse momentum, thus revealing a prominent central light spot. Four distinct peripheral light spots (marked with four blue circles) can also be seen in the far field, indicating that the transverse momentum is not zero. The presence of these peripheral light spots indicates that momentum has been transferred from the reciprocal lattice to the SHG light spot. The reciprocal lattice of the Mohr metasurface exhibits a square lattice, which is... ,in, and It is an integer. and It is a unit vector in reciprocal space. SHG wave and zero reciprocal lattice vector. The interaction between the origins of the reciprocal lattice produces the central spot in the experiment. This central spot is referred to as the zeroth-order SHG diffraction. It originates from the reciprocal lattice vectors. and The momentum transfer results in four peripheral light spots, i.e., first-order diffraction.

[0087] When two moiré metasurfaces are stacked together, interlayer coupling introduces the superposition of reciprocal lattices from the individual moiré metasurfaces. The reciprocal lattice of the twisted layer is represented as... ,in, and It is an integer. and It is the unit vector in the reciprocal space of the twisted element surface. , Therefore, the reciprocal vector of the stacked moiré metasurface, i.e., the sum of the reciprocal vectors of each layer, can be expressed as: .

[0088] like Figure 6 As shown in (c), in addition to the central fourth-order diffraction spot, we also obtained two different sets of first-order peripheral spots, distinguished by blue and red circles, respectively. These two sets of spots correspond to two layers of moiré metasurfaces, and the two sets exhibit a relative angular offset of 15°. Figure 6 (d) shows the basic reciprocal lattice of the two-layer moiré metasurface, represented by red and blue dots, respectively. The monolayer moiré metasurface exhibits only zero-order and first-order diffraction, while the interlayer-twisted bilayer moiré metasurface displays additional SHG spots. These spots are composed of the reciprocal lattice vectors of the two basic lattices. Figure 6 As shown in (e), the vector (Blue horizontal arrow) and The combination of (red arrows) produces a vector. (Dark green short arrow). The momentum transfer of these vectors forms an SHG spot tightly surrounding the zeroth-order spot, such as... Figure 6 As shown by the dark green circle in (c), this group of light spots is classified as Similarly, vectors (Blue vertical arrow) and Generate a vector (Light green arrow) This group of light spots is classified as Because this set of light spots is close to the edge of the objective lens aperture, two light spots were missing in the experiment, such as... Figure 6 (c) shows the dashed circles. These light spots are formed by the combination of two reciprocal lattice unit vectors, called second-order diffraction. Furthermore, as... Figure 6 As shown in (f), the vector and Further combining, a vector is generated. (Dark yellow arrow) This forms a set of third-order SHG diffraction spots, marked as ,exist Figure 6 (c) is marked with a dark yellow circle. These diffraction spots confirm the presence of abundant higher-order diffraction in the non-periodic stacked moiré metasurface.

[0089] Figure 6 (g)- Figure 6(n) shows the SHG spots of stacked moiré metasurfaces with twist angles of 30° and 45°, including diffraction components from zero to third order. It visually demonstrates that the twist angle has a significant impact on the position and symmetry of the SHG spots. Furthermore, the stacked moiré metasurface with a 45° twist angle exhibits two different sets of third-order diffraction spots. Figure 6 (k) are respectively in dark yellow ( ) and light yellow ( (Use circles to distinguish)

[0090] To visually illustrate the complex adjustment of the torsion angle to SHG emission, Figure 7 The trajectory of the SHG spot as a function of the torsion angle is described. For example... Figure 7 As shown in (a), as the twist angle increases, The SHG spot migrates outward from the origin of the reciprocal space to the four corners along a quarter arc. For example... Figure 7 As shown in (b), The SHG spots also move along a quarter arc, but their trajectories are similar to... The trajectories exhibit mirror symmetry along the diagonal of the reciprocal grid. As the torsion angle increases, these spots shift inward from the corners towards the center, a unique dynamic feature of SHG emission. (Example: ...) Figure 7 As shown in (c), with the change of the torsion angle, The SHG spot moves along a unique, four-leaf-shaped path. These intricate trajectories demonstrate that the twist angle directly affects the spatial distribution of the SHG spot. Changing the twist angle between layers of the stacked moiré metasurface can shape the SHG.

[0091] like Figure 8 As shown, the torsion angle affects the emission angle of the SHG. The effect of the launch angle. The angle between the beam path of the SHG and the normal to the stacked moiré metasurface. The emission angle of the SHG. The emission direction of SHG can be controlled by changing the twist angle between the layers of the stacked moiré metasurface.

[0092] In this experiment, multiple stacked moiré metasurfaces with different lattice periods were fabricated under a twist angle of 45° and a frequency doubling wavelength of 475 nm for the fundamental frequency light. The emission angle of the SHG was then measured. The results obtained are as follows Figure 9 As shown. From Figure 9 As can be seen from this, the SHG's launch angle As the lattice period changes, altering the lattice period of the stacked moiré metasurface can also shape the SHG.

[0093] 4. Conclusion

[0094] In summary, this invention delves into the potential of moiré metasurfaces for modulating nonlinear optical processes, with a focus on SHG wave shaping. We fabricated high-performance stacked moiré metasurfaces characterized by extended aperiodic patterns, generating complex diffraction points and directional SHG waves controlled by both torsion angle and lattice period. This invention demonstrates the complex modulation of SHG emission induced by different torsion angles and lattice periods. This invention marks a significant advancement in utilizing the unique properties of moiré lattices in nonlinear optics and beam shaping applications, representing a substantial step forward in advancing the frontiers of nonlinear optics and beam shaping by leveraging the unique properties of moiré lattices.

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A nonlinear beam shaping method based on stacked moiré metasurfaces, characterized in that, include: Obtain the frequency harmonic wavelength of the fundamental light and the target emission angle of the nonlinear beam; The quasi-period of the moiré lattice of the stacked moiré metasurface is calculated based on the frequency doubling wavelength of the fundamental light and the target emission angle of the nonlinear beam. Quasi-periodic moiré lattice of the stacked moiré metasurface The calculation formula is: in, This is the harmonic wavelength of the fundamental frequency light. The target emission angle of the nonlinear beam; Based on the quasi-period of the moiré lattice of the stacked moiré metasurface, the correspondence between the lattice period and the torsion angle of the stacked moiré metasurface is calculated; the calculation formula is: in, For a moiré lattice quasi-periodic, For lattice period, For the angle of distortion; Obtain stacked moiré metasurfaces with the aforementioned correspondence; The fundamental frequency light irradiates the stacked moiré metasurface to form the nonlinear beam. The emission angle of the nonlinear beam is the target emission angle, which achieves nonlinear beam shaping. The emission angle of the nonlinear beam is the angle between the beam path of the nonlinear beam and the normal of the stacked moiré metasurface.

2. The nonlinear beam shaping method based on stacked moiré metasurfaces as described in claim 1, characterized in that, The process of obtaining stacked moiré metasurfaces with the aforementioned correspondence is as follows: Select one or more sets of values ​​for the lattice period and twist angle that conform to the corresponding relationship; Based on the values ​​of the lattice period and twist angle, a nonlinear thin film is processed using a focused ion beam to obtain a stacked moiré metasurface.

3. The nonlinear beam shaping method based on stacked moiré metasurfaces as described in claim 2, characterized in that, The stacked moiré metasurface has two layers.

4. The nonlinear beam shaping method based on stacked moiré metasurfaces as described in claim 3, characterized in that, The fabrication process of the stacked moiré metasurface is as follows: The nonlinear thin film without substrate support is fixed on the worktable; Based on the value of the lattice period, a periodic array of basic metasurfaces A and B is fabricated on the nonlinear thin film using a focused ion beam. A portion of the edge of the basic metasurface A is cut using a focused ion beam. The tip of the nanomanipulator was welded to the edge of the basic metasurface A using platinum deposition. Using a focused ion beam, the remaining connected portions of the edge of the basic metasurface A are cut off; Move the nanomanipulator and rotate the stage by the value of the torsion angle so that the basic metasurface A covers the basic metasurface B; The basic metasurface A and basic metasurface B are welded using platinum deposition. The needle tip is cut off using a focused ion beam, and the edge of the basic metasurface B is cut to obtain the stacked moiré metasurface.

5. The nonlinear beam shaping method based on stacked moiré metasurfaces as described in claim 4, characterized in that, The nonlinear thin film is a metal film or a dielectric film.

6. The nonlinear beam shaping method based on stacked moiré metasurfaces as described in claim 5, characterized in that, The dielectric film is made of lithium niobate, lithium tantalate, zinc oxide, gallium arsenide, gallium phosphide, boron nitride, niobium oxide dihalide, or transition metal disulfide.

Images