Design method of 3D nonlinear optical non-reciprocal diffraction element and application thereof

Abstract

The design method of the 3D nonlinear optical non-reciprocal diffraction element discloses a method for determining the discrete phase distribution at different spatial positions of a holographic plane according to the asymmetric target second harmonic light field distribution corresponding to the forward transmission and reverse transmission; a single 3D basic unit module is determined according to a single discrete phase, that is, the position of the inverted ferroelectric domain module in the 3D basic unit module is controlled by setting the moving distance of the inverted ferroelectric domain module along the light beam propagation direction, and the position of the inverted ferroelectric domain module in the 3D basic unit module is determined by the discrete phase, and the value range of the discrete phase is -pi to +pi; the 3D basic unit module distribution corresponding to the discrete phase distribution constitutes the 3D nonlinear optical non-reciprocal diffraction element. The application can be used for designing non-reciprocal nonlinear photonic crystal devices, solving the problem of asymmetric light field regulation and second harmonic twin image of the nonlinear photonic crystal device.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear photonics, specifically a design method for 3D nonlinear optical nonreciprocal diffraction elements and its application. Background Technology

[0002] Introducing different physical responses, such as optical loss and phase shift, into forward and reverse propagating light using non-reciprocal devices to generate asymmetric wavefront shaping dependent on the propagation direction is of great significance in optical communication, optical information processing, fundamental physics research, and interdisciplinary research. Asymmetric optical field manipulation is typically achieved through three methods: introducing a magnetic field, temporal control of the dielectric constant, or introducing nonlinearity. Nonlinear metasurfaces and nonlinear photonic crystals are two important media for achieving nonlinear manipulation. Existing research shows that nonlinear metasurfaces have already achieved asymmetric optical field manipulation, but work on achieving asymmetric optical field manipulation using nonlinear photonic crystals has not yet been reported. This is mainly because the design of non-reciprocal nonlinear photonic crystal devices is currently not feasible.

[0003] Nonlinear photonic crystals possess spatially modulated second-order nonlinear coefficients χ. (2) It plays an important role in second-order nonlinear wavefront shaping and nonlinear holographic imaging. Spatially modulated χ... (2) The distribution provides a set of reciprocal lattice vectors to satisfy quasi-phase matching between interacting waves during optical frequency conversion, thereby achieving high-efficiency energy conversion. Furthermore, positive and negative χ... (2) Microstructures can generate nonlinear polarized waves with a phase difference of π. Therefore, by modulating χ in a plane perpendicular to the direction of incident light propagation... (2) By understanding the spatial distribution of nonlinear wavefronts, effective nonlinear wavefront shaping can be achieved. In recent years, there have been two main methods for achieving nonlinear wavefront shaping using nonlinear photonic crystals. The first method is nonlinear computer-generated holograms (Opt. Lett. 36(15):3015-3017(2011)), but the nonlinear photonic crystals designed using this method have complex shapes and are difficult to fabricate in practice. The second method is detour phase holograms (Light: Science & Applications 10,146(2021); Nanoscale, 13,2693(2021)). Although the nonlinear photonic crystals designed using this method are easy to fabricate experimentally, they still have two drawbacks in achieving second harmonic optical field manipulation: first, the problem of second harmonic twins caused by non-collinear quasi-phase matching, which greatly reduces the efficiency of optical field manipulation; second, the inability to achieve asymmetric optical field manipulation, which seriously limits the development of non-reciprocal imaging devices and non-reciprocal filtering devices.

[0004] In summary, eliminating second-harmonic twins to improve wavefront shaping efficiency, and achieving asymmetric optical field manipulation to advance the development of non-reciprocal imaging devices and non-reciprocal filtering devices, have significant research and practical application value. Summary of the Invention

[0005] The technical problem this invention aims to solve is the inability of existing nonlinear photonic crystal devices to achieve asymmetric wavefront shaping and the problem of second harmonic twinning. This invention provides a design method and application for 3D nonlinear optical nonreciprocal diffraction elements to address the limitations of existing nonlinear photonic crystal devices in achieving asymmetric optical field manipulation and the second harmonic twinning problem. This invention determines the arrangement of different 3D basic unit modules at corresponding spatial locations by using discrete phase values ​​at different spatial positions. This allows for arbitrary manipulation of the generated second harmonic phase, ensuring that the second harmonic phases generated in forward and reverse propagation are opposite, thereby achieving asymmetric optical field manipulation of the second harmonic.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problem is as follows: a design method for a 3D nonlinear optical non-reciprocal diffraction element, wherein the 3D nonlinear optical non-reciprocal diffraction element comprises multiple 3D basic unit modules arranged in space, and the design method for the 3D nonlinear optical non-reciprocal diffraction element is as follows:

[0007] Based on the asymmetric target second harmonic light field distribution corresponding to the forward and reverse transmission cases, the discrete phase distribution at different spatial locations of the holographic plane is determined, and then the 3D basic unit module corresponding to each discrete phase is determined.

[0008] Each of the aforementioned 3D basic unit modules includes an inverted ferroelectric domain module and a ferroelectric domain background substrate module. The position of the inverted ferroelectric domain module in the 3D basic unit module is controlled by setting the moving distance of the inverted ferroelectric domain module along the beam propagation direction, and the position of the inverted ferroelectric domain module in the 3D basic unit module is determined by discrete phase, the value range of which is -π to +π.

[0009] The 3D basic unit modules that correspond one-to-one with the discrete phase distribution constitute the 3D nonlinear optical non-reciprocal diffraction element.

[0010] Preferably, in each of the 3D basic unit modules, the thickness of the inverted ferroelectric domain module in the beam propagation direction is designed to be half the thickness of the 3D basic unit module in the beam propagation direction; the length and width of the inverted ferroelectric domain module perpendicular to the beam propagation direction are designed to be equal to the length and width of the 3D basic unit module perpendicular to the beam propagation direction, respectively. This technical solution optimizes the nonlinear diffraction efficiency, ensuring that the duty cycle of the inverted ferroelectric domain module in each 3D basic unit module is 50%, thereby generating the highest nonlinear diffraction efficiency.

[0011] Furthermore, each of the aforementioned inverted ferroelectric domain modules includes multiple inverted ferroelectric domain units. The thickness of each of the aforementioned inverted ferroelectric domain units in the beam propagation direction is designed as σy / Nu, where Nu is an integer, taking Nu≥4. Nu represents the number of discrete phase types after discretizing the continuous phase [-π,+π], which is also the number of types of all 3D basic unit modules in the aforementioned 3D nonlinear optical nonreciprocal diffraction element; σy=2π / (k2-2k1), where k1 and k2 are the magnitudes of the fundamental frequency wave vector and the second harmonic wave vector, respectively.

[0012] Furthermore, in each of the 3D basic unit modules, if the relationship between the number of inverted ferroelectric domain units Nd and the number of types Nu of all 3D basic unit modules in the 3D nonlinear optical nonreciprocal diffraction element satisfies: Nu = 2 * Nd, where Nu represents the number of discrete phase types that can be realized by all 3D basic unit modules;

[0013] The number Nd of inverted ferroelectric domain units in each of the 3D basic unit modules is determined based on the complexity of the asymmetric target second harmonic optical field distribution corresponding to the forward and reverse transmission cases.

[0014] In the above technical solution, the relationship between the number of inverted ferroelectric domain units Nd in each 3D basic unit module and the number of types Nu of all 3D basic unit modules in the 3D nonlinear optical nonreciprocal diffraction element satisfies Nu = 2 * Nd. This can maximize the information capacity carried per unit area of ​​the nonlinear optical nonreciprocal diffraction element while ensuring imaging quality.

[0015] Furthermore, in each of the aforementioned 3D basic unit modules, the ratio of the distance between the center of the inverted ferroelectric domain module and the center of the 3D basic unit module to the thickness of the 3D basic unit module in the beam propagation direction is denoted as P. nm Then P nm Phase with the second harmonic accumulated after the incident light passes through this 3D basic unit module The relationship between them satisfies a linear relationship, which can be expressed as:

[0016] Based on the aforementioned linear relationship, the position of the inverted ferroelectric domain module in the 3D basic unit module is determined by discrete phase.

[0017] In the above technical solution, The proposed method directly converts the phase of each pixel at the holographic plane. A one-to-one correspondence is established between the specific structure of each 3D basic unit module in the optical element (i.e., the positional relationship between the inverted ferroelectric domain module and the ferroelectric domain background substrate module). Therefore, after obtaining the phase distribution on the holographic plane using the asymmetric target second harmonic optical field distribution corresponding to the forward and reverse propagation cases, a linear relationship is established. This allows for the reconstruction of the 3D basic unit modules at the corresponding pixels in a 3D nonlinear optical element, thereby reconstructing the entire 3D nonlinear optical nonreciprocal diffraction element.

[0018] Preferably, the process of determining the discrete phase distribution at different spatial locations on the holographic plane based on the asymmetric target second harmonic light field distribution corresponding to the forward and reverse transmission cases is as follows: the continuous phase distribution on the holographic plane required to generate the asymmetric target second harmonic light field is discretized into Nu equal parts to obtain the discrete phase distribution, where Nu is the number of types of all 3D basic unit modules in the 3D nonlinear optical nonreciprocal diffraction element, and Nu represents the number of discrete phase types that can be realized by all 3D basic unit modules.

[0019] Preferably, the inverted ferroelectric domain module and the ferroelectric domain background substrate module of each of the 3D basic unit modules are obtained by direct writing on the original ferroelectric domains using femtosecond laser.

[0020] Furthermore, the original ferroelectric domains are made of uniformly polarized or naturally grown lithium niobate crystals, or uniformly polarized or naturally grown barium strontium niobate crystals, or uniformly polarized or naturally grown barium calcium niobate crystals.

[0021] The above-mentioned design method for 3D nonlinear optical nonreciprocal diffraction elements is applied to the generation of second harmonics and the manipulation of the optical field of second harmonic asymmetric target optical fields, specifically as follows:

[0022] Based on the asymmetric target second harmonic optical field distribution corresponding to the forward and reverse transmission cases, the continuous phase distribution at different spatial locations of the holographic plane is determined, and then the discrete phase distribution at different spatial locations of the holographic plane is determined.

[0023] The 3D nonlinear optical nonreciprocal diffraction element designed using the design method of any one of claims 1-8 is used to arbitrarily adjust the phase of the second harmonic of the asymmetric target in the range of -π to +π for the forward and reverse propagation cases, respectively. That is, when plane light is incident on the 3D nonlinear optical nonreciprocal diffraction element, the phase of the second harmonic generated in the forward and reverse propagation cases is opposite, thereby realizing the asymmetric optical field control of the second harmonic.

[0024] For example, the design method of this invention can be used to generate asymmetric second harmonic vortex light. Specifically, based on the asymmetric target second harmonic vortex light corresponding to the forward and reverse transmission cases, the continuous phase distribution at different spatial positions of the holographic plane is determined, and then the discrete phase distribution at different spatial positions of the holographic plane is determined. The designed 3D nonlinear optical non-reciprocal diffraction element is used to generate asymmetric target second harmonic vortex light corresponding to the forward and reverse transmission cases.

[0025] For example, the design method of this invention can be used for dual-channel beam navigation and vortex light generation. Specifically, it determines the continuous phase distribution at different spatial positions of the holographic plane based on the beam navigation corresponding to forward transmission and the vortex light corresponding to reverse transmission, and then determines the discrete phase distribution at different spatial positions of the holographic plane. The designed 3D nonlinear optical non-reciprocal diffraction element is used to generate beam navigation for forward transmission and generate vortex light for reverse transmission.

[0026] Compared with existing technologies, the present invention has the following advantages: The 3D nonlinear optical nonreciprocal diffracting element designed by the method of the present invention is composed of multiple specific 3D basic unit modules arranged in space. Each 3D basic unit module consists of a reverse ferroelectric domain module and a ferroelectric domain background substrate module. When a fundamental frequency linearly polarized plane wave is incident on the 3D basic unit module, the position of the reverse ferroelectric domain module within the 3D basic unit module is controlled by setting the moving distance of the reverse ferroelectric domain module along the beam propagation direction. The position of the reverse ferroelectric domain module within the 3D basic unit module is determined by discrete phase, which allows for the modulation of the far-field second harmonic phase in the range of -π to +π. Furthermore, the second harmonic phases generated under forward and reverse propagation are opposite, thereby achieving asymmetric optical field modulation of the second harmonic. Therefore, when a fundamental frequency linearly polarized plane wave is incident on the 3D nonlinear optical nonreciprocal diffracting element, by arranging different 3D basic unit modules at different spatial positions, asymmetric modulation of the second harmonic phase generated under forward and reverse propagation can be achieved, thus realizing asymmetric second harmonic optical field modulation. The design method of this invention is highly practical and flexible in satisfying asymmetric optical field manipulation, and the types and number of 3D basic unit modules can be set according to the complexity of the target asymmetric nonlinear wavefront. This design method can solve the problems of existing nonlinear photonic crystal devices being unable to achieve asymmetric optical field manipulation and second harmonic twinning. Attached Figure Description

[0027] Figure 1 This is a design method and structural schematic diagram of a 3D nonlinear optical nonreciprocal diffraction element provided in Embodiment 1 of the present invention;

[0028] Figure 2 A schematic diagram of asymmetric second harmonic optical field manipulation of a 3D nonlinear optical nonreciprocal diffraction element and a schematic diagram of asymmetric second harmonic phase manipulation of a 3D basic unit provided in Embodiment 1 of the present invention.

[0029] Figure 3 This is a schematic diagram of the 3D nonlinear optical non-reciprocal diffraction element design and the generated asymmetric second harmonic light field corresponding to the asymmetric second harmonic beam navigation provided in Embodiment 2 of the present invention.

[0030] Figure 4 This is a schematic diagram of the 3D nonlinear optical non-reciprocal diffraction element design and the asymmetric second harmonic vortex light generated according to Embodiment 2 of the present invention.

[0031] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0032] 1 is the 3D basic unit module, 2 is the reverse ferroelectric domain module, 21 is the reverse ferroelectric domain unit, and 3 is the ferroelectric domain background substrate module. Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0034] Example 1: A design method for a 3D nonlinear optical nonreciprocal diffraction element and its application, such as... Figure 1 As shown, the 3D nonlinear optical nonreciprocal diffraction element comprises multiple 3D basic unit modules 1 arranged in space. The design method of the 3D nonlinear optical nonreciprocal diffraction element is as follows:

[0035] Based on the asymmetric target second harmonic light field distribution corresponding to the forward and reverse transmission cases, the discrete phase distribution at different spatial locations of the holographic plane is determined, and then the 3D basic unit module 1 corresponding to each discrete phase is determined.

[0036] Each 3D basic unit module 1 includes an inverted ferroelectric domain module 2 and a ferroelectric domain background substrate module 3. Each inverted ferroelectric domain module 2 includes multiple inverted ferroelectric domain units 21. The position of the inverted ferroelectric domain module 2 in the 3D basic unit module 1 is controlled by setting the moving distance of the inverted ferroelectric domain module 2 along the beam propagation direction. The position of the inverted ferroelectric domain module 2 in the 3D basic unit module 1 is determined by discrete phase. The value range of the discrete phase is from -π to +π.

[0037] The 3D basic unit modules 1, which correspond one-to-one with the discrete phase distribution, constitute 3D nonlinear optical non-reciprocal diffraction elements.

[0038] In the above design method, determining the discrete phase distribution at different spatial locations on the holographic plane, and then determining the 3D basic unit module 1 corresponding to each discrete phase, is essentially determining the type of 3D basic unit module 1. This type is determined based on the discrete phases that the specific structure of the 3D basic unit module 1 can generate. The specific structure refers to the positional relationship between the inverted ferroelectric domain module 2 and the ferroelectric domain background substrate module 3 within the 3D basic unit module 1. It should be noted that... Figure 1The 3D nonlinear optical nonreciprocal diffracting element shown is an example with eight types of 3D basic unit modules 1. Other types of 3D basic unit modules can also be determined based on the actual discrete phase. When the 3D nonlinear optical nonreciprocal diffracting element is working, a fundamental frequency linearly polarized plane wave (because linearly polarized plane waves have high coherence and are most widely used in laser-matter interaction processes) is incident on each 3D basic unit module 1. The position of the inverted ferroelectric domain module 2 in the 3D basic unit module 1 is controlled by setting the moving distance of the inverted ferroelectric domain module 2 along the beam propagation direction (that is, the positional relationship between the inverted ferroelectric domain module 2 and the ferroelectric domain background substrate module 3 in the 3D basic unit module 1). The position of the inverted ferroelectric domain module in the 3D basic unit module 1 is determined by the discrete phase. This allows the 3D basic unit module 1 to arbitrarily adjust the phase of the generated far-field second harmonic within the range of -π to +π, and to satisfy that the phases of the second harmonic generated in forward and reverse propagation are opposite, thereby achieving asymmetric optical field manipulation of the second harmonic. Therefore, when a fundamental frequency linearly polarized plane wave is incident on a 3D nonlinear optical nonreciprocal diffracting element, the second harmonic generated under forward and reverse propagation conditions can be independently controlled by arranging different 3D basic units 1 at different spatial positions, thereby realizing asymmetric second harmonic optical field control. Thus, the design method of the 3D nonlinear optical nonreciprocal diffracting element of this invention has high practicality and flexibility, and the types and number of 3D basic unit modules 1 can be set according to the complexity of the target second harmonic optical field.

[0039] It should be noted that the arrangement rule of different 3D basic unit modules 1 at different spatial positions satisfies the following: the discrete phase generated by the 3D basic unit module 1 at each spatial position is equal to the discrete phase at the corresponding spatial position on the holographic plane.

[0040] In Example 1, the thickness of the inverted ferroelectric domain module 2 in each 3D basic unit module 1 along the beam propagation direction is designed to be half the thickness of the 3D basic unit module 1 along the beam propagation direction; the length and width of the inverted ferroelectric domain module 2 perpendicular to the beam propagation direction are designed to be equal to the length and width of the 3D basic unit module 1 perpendicular to the beam propagation direction. Furthermore, in this example, the thickness of each inverted ferroelectric domain unit 21 along the beam propagation direction is designed to be σy / Nu, where Nu is an integer, taking Nu≥4. In Example 1, Nu=8, meaning that the number of discrete phase types after discretizing the continuous phase [-π,+π] in Example 1 is 8, which is also the number of types of all 3D basic unit modules 1 in the 3D nonlinear optical non-reciprocal diffraction element is 8; σy=2π / (k2-2k1), where k1 and k2 are the magnitudes of the fundamental frequency wave vector and the second harmonic wave vector, respectively.

[0041] As a preferred embodiment, in each 3D basic unit module 1, the relationship between the number Nd of the inverted ferroelectric domain units 21 and the number Nu of all types of 3D basic unit modules 1 in the 3D nonlinear optical non-reciprocal diffraction element satisfies: Nu = 2*Nd, where Nu represents the number of discrete phase types achievable by all 3D basic unit modules 1. For example, as mentioned above, if the thickness of the inverted ferroelectric domain units 21 in each 3D basic unit module 1 is designed to be σy / Nu, then the actual width of each inverted ferroelectric domain module 2 perpendicular to the beam propagation direction is Nd*σy / Nu; the length and width of the inverted ferroelectric domain module 2 perpendicular to the beam propagation direction are equal to the length and width of the 3D basic unit module 1, and their size depends on the processing accuracy and the optical field control accuracy. In Example 1, the corresponding length and width are selected to be 2μm. Based on this, according to the complexity of the target second harmonic optical field distribution and the information capacity carried per unit area of ​​the nonlinear optical non-reciprocal diffraction element, the number Nd of the inverted ferroelectric domain units 21 in each 3D basic unit module 1 is determined. In Example 1, we select 8 discrete phases (-3π / 4, -π / 2, -π / 4, 0, π / 4, π / 2, 3π / 4, π) to realize the reconstruction of the target light field. Therefore, Nd is selected as 4, and Nu = 2 * Nd = 8.

[0042] As another preferred embodiment, in each 3D basic unit module 1, the ratio of the distance between the center of the inverted ferroelectric domain module 2 and the center of the 3D basic unit module 1 to the thickness of the 3D basic unit module 1 in the beam propagation direction is denoted as P. nm Then P nm Phase with the second harmonic accumulated after the incident light passes through this 3D basic unit module The relationship between them satisfies a linear relationship, which can be expressed as: Based on the linear relationship, the position of the inverted ferroelectric domain module 2 within the 3D basic unit module 1 is determined by discrete phase. For example... Figure 2 The diagram illustrates asymmetric second-harmonic optical field manipulation by a 3D nonlinear optical nonreciprocal diffracting element and asymmetric second-harmonic phase manipulation by a 3D basic unit. The 3D nonlinear optical nonreciprocal diffracting element consists of a series of 3D basic unit modules 1; the distance P is denoted as the distance between the center position of the inverted ferroelectric domain module 2 in 3D basic unit module 1 and the center position of 3D basic unit module 1. nm δy, where δy is the thickness of each 3D basic unit module 1 in the beam propagation direction. In Example 1, σy = 2π / (k2-2k1) is set to construct the collinear quasi-phase matching condition, which is used to solve the second harmonic twin problem in previous studies.

[0043] To construct the collinear quasi-phase matching condition, we set σy = 2π / (k2 - 2k1). Specifically, the quasi-phase matching relationship corresponding to the second harmonic generation process of the 3D nonlinear optical non-reciprocal diffracting element designed using the above method satisfies the collinearity condition 2k1 + G = k2, where G is the reciprocal lattice vector corresponding to the 3D nonlinear optical non-reciprocal diffracting element, and satisfies the relationship G = 2π / σy with the thickness σy of the 3D nonlinear optical non-reciprocal diffracting element. Collinear quasi-phase matching is as follows... Figure 2 (Top right) As shown. It should be noted that previous references (Light: Science & Applications 10, 146 (2021); Nanoscale, 13, 2693 (2021)) used nonlinear photonic crystal devices that could only perform nonlinear nonlinear Raman-Nass quasi-phase matching. The second harmonic generated by these previous nonlinear photonic crystal devices is not collinear with the fundamental incident light, but is symmetrically distributed on both sides of the fundamental wave, which is called a second harmonic twin. The collinear quasi-phase matching used in Example 1 overcomes the problem of existing second harmonic twins and can further improve the working efficiency of 3D nonlinear optical nonreciprocal diffracting elements.

[0044] In Example 1, the second harmonic phase is... Discretized into eight discrete phase elements, the number of types of 3D basic unit module 1, Nu = 8, as follows: Figure 2 The second row of the image shows eight basic 3D unit modules 1 (P). nm =-4 / 8, -3 / 8, -1 / 4, -1 / 8, 0, 1 / 8, 1 / 4, 3 / 8) provide 8 discrete phases respectively. Among them, P nm This represents the ratio of the distance between the center of the inverted ferroelectric domain module 2 in each 3D basic unit module 1 and the center of the 3D basic unit module 1 to the thickness of the 3D basic unit module 1. Figure 2 (Third line) and Figure 2 (Fourth row) represents the fundamental frequency incident light incident along the y-axis direction, as shown in the image. Figure 2 (The second row shows the amplitude and phase of the emitted second harmonic electric field from the eight 3D basic unit modules 1.) The results show that the eight 3D basic unit modules 1 produce equal second harmonic amplitudes; the eight 3D basic unit modules 1 produce eight discrete second harmonic phases, and these eight discrete phase values ​​form an increasing sequence with -π as the first term and π / 4 as the common difference; the SHG phase and P... nm The relational expression can be written as

[0045] It should be noted that in Example 1, the second harmonics generated by the fundamental frequency incident light during forward and reverse propagation through the same 3D basic unit have opposite phases. The specific analysis is as follows: In Example 1, the inverted ferroelectric domain module 2 in 3D basic unit module 1 detours along the beam propagation direction (y-axis) to generate the desired second harmonic phase. The second harmonic detour phase coding. This detour phase coding in the beam propagation direction, as described in Example 1, assigns P values ​​that are opposite for forward and reverse propagation. nm This value will further lead to the opposite. Value. The opposite second harmonic phases generated by forward and reverse transmission in Example 1. It forms the basis for constructing non-reciprocal diffraction elements to achieve asymmetric optical field manipulation.

[0046] Therefore, after obtaining the phase distribution on the holographic plane using the target asymmetric second harmonic optical field distribution corresponding to the forward and reverse propagation cases, this formula is used... This allows for the reconstruction of the 3D basic unit modules at corresponding pixels in a 3D nonlinear optical nonreciprocal diffraction element, thereby reconstructing the entire 3D nonlinear optical nonreciprocal diffraction element. This is based on this formula. The reconstructed 3D basic unit module has a 50% inverted domain duty cycle, and this detour phase encoding method in the propagation direction satisfies collinear quasi-phase matching, which can eliminate the second harmonic twin problem. Therefore, this encoding method can greatly improve the second harmonic conversion efficiency.

[0047] As a preferred embodiment, in Example 1, the discrete phase distribution at different spatial locations on the holographic plane is determined based on the asymmetric target second harmonic light field distribution corresponding to the forward and reverse transmission cases. Specifically, the continuous phase distribution on the holographic plane required to generate the asymmetric target second harmonic light field is discretized into Nu equal parts to obtain the discrete phase distribution. Here, Nu is the number of types of all 3D basic unit modules in the 3D nonlinear optical nonreciprocal diffraction element, and Nu represents the number of discrete phase types that can be realized by all 3D basic unit modules.

[0048] The arrangement of the 3D basic unit module 1 in a 3D nonlinear optical nonreciprocal diffraction element is based on the phase it generates. The discrete phase values ​​corresponding one-to-one with the discrete phase values ​​that generate the target asymmetric light field are arranged in sequence. The determination of the discrete phases required for the target asymmetric light field involves two steps: first, obtaining the continuous phase distribution, and then discretizing the obtained continuous phase distribution into eight discrete phases according to actual needs. When using a 3D nonlinear optical non-reciprocal diffraction optical element with fundamental frequency line polarized light incident, the transmitted second harmonic light field distribution is consistent with the target asymmetric light field under both forward and reverse propagation conditions.

[0049] Preferably, each 3D basic unit module is fabricated by femtosecond laser direct writing onto the original ferroelectric domains to obtain inverted ferroelectric domain modules and ferroelectric domain background substrate modules. The original ferroelectric domains are uniformly polarized or naturally grown lithium niobate crystals, or uniformly polarized or naturally grown barium strontium niobate crystals, or uniformly polarized or naturally grown barium calcium niobate crystals. Naturally grown barium strontium niobate crystals or naturally grown barium calcium niobate crystals contain (180-degree) antiparallel needle-like ferroelectric domains, and these needle-like antiparallel ferroelectric domains are easily inverted using laser direct writing. Furthermore, using such naturally grown barium strontium niobate crystals or naturally grown barium calcium niobate crystals facilitates the fabrication of 3D nonlinear optical nonreciprocal diffraction elements.

[0050] Example 2: An application of the design method for a 3D nonlinear optical nonreciprocal diffraction element of Example 1 for asymmetric second harmonic beam navigation, specifically:

[0051] Based on the continuous phase distribution on the holographic plane of the target pattern, multiple discrete phases are determined;

[0052] A 3D nonlinear optical nonreciprocal diffraction optical element was designed using the design method of Example 1 above, and used for asymmetric second harmonic beam navigation.

[0053] The continuous phase of the target light field refers to the continuous phase distribution on the holographic plane, which is obtained through the target's asymmetric second harmonic light field distribution and the generalized law of refraction.

[0054] like Figure 3 The figure shows a schematic diagram of the design of a 3D nonlinear optical nonreciprocal diffraction element and the resulting asymmetric second harmonic beam navigation corresponding to asymmetric ±2.79° beam navigation. Figure 3 The top left image shows the target second harmonic phase distribution required to achieve asymmetric ±2.79° beam navigation, which is obtained from the generalized law of refraction. Specifically, the asymmetric ±2.79° beam navigation refers to: achieving +2.79° second harmonic beam navigation in forward propagation and -2.79° second harmonic beam navigation in reverse propagation. To facilitate subsequent encoding, the continuous phase distribution is first discretized into eight equal parts. Based on the principle of equal phase and the discrete phase distribution diagram, eight 3D basic unit modules are arranged sequentially to obtain the theoretically designed 3D nonlinear optical non-reciprocal diffraction optical element, forming a 3D hologram (e.g., ...). Figure 3 (As shown in the upper middle figure). 3D nonlinear optical non-reciprocal diffraction optical elements are composed of an eight-domain structure, such as... Figure 3The figure below shows the design method of the proposed 3D nonlinear optical non-reciprocal diffraction element. Numerical calculations verified the asymmetric second harmonic beam navigation function of the designed 3D nonlinear optical non-reciprocal diffraction element. Based on the stepwise fast Fourier transform beam propagation method, when the fundamental frequency linearly polarized light is transmitted forward and backward into the designed 3D nonlinear optical non-reciprocal diffraction element, the numerically calculated second harmonic light field intensity distribution is as follows: Figure 3 As shown in the upper right figure, the numerically calculated asymmetric beam navigation angle is ±2.8°, which matches the theoretical value of ±2.79°.

[0055] Example 3: An application of the design method of the 3D nonlinear optical nonreciprocal diffraction element of Example 1 for the generation of asymmetric second harmonic vortex light, specifically:

[0056] Based on the continuous phase distribution on the holographic plane of the target pattern, multiple discrete phases are determined;

[0057] A 3D nonlinear optical nonreciprocal diffraction optical element was designed using the design method of Example 1 above, and used for the generation of asymmetric second harmonic vortex light.

[0058] The continuous phase of the target light field refers to the continuous phase distribution on the holographic plane, which is obtained by the topological charge of the target asymmetric vortex light.

[0059] like Figure 4 The figure shows a schematic diagram of the design of a 3D nonlinear optical nonreciprocal diffraction element corresponding to the generation of asymmetric second harmonic vortex light and the generated asymmetric second harmonic light field. Figure 4 The first row of the diagram shows the phase of the vortex beam with a topological charge of 2 and the eight-domain structure corresponding to the 3D nonlinear optical nonreciprocal diffracting element (3D hologram) encoded by this phase. To verify the asymmetric vortex beam generation capability of the designed 3D nonlinear optical nonreciprocal diffracting element, we calculated the second harmonic light field under forward and reverse propagation conditions using the step-by-step fast Fourier transform beam propagation method. Specifically, when fundamental Gaussian linearly polarized light (where the vortex beam component is 0, i.e., topological charge LC_FF = 0) is input to the 3D nonlinear optical nonreciprocal diffracting element in both forward and reverse propagation, the numerically calculated second harmonic light field intensity distribution is as follows: Figure 4 As shown in the second row; when the fundamental frequency vortex (topological charge LC_FF = 2) linearly polarized light is transmitted in both the forward and reverse directions into a 3D nonlinear optical nonreciprocal diffraction element, the numerically calculated second harmonic light field intensity distribution is as follows: Figure 4As shown in the third row. Column 1 shows the phase distribution of the fundamental frequency incident light; columns 2-4 show the second harmonic electric fields generated after the fundamental frequency incident light propagates forward through a 3D nonlinear optical non-reciprocal diffraction element, where columns 2-3 show the near-field amplitude and phase distribution of the second harmonic, and column 4 shows the far-field intensity distribution of the second harmonic; columns 5-7 show the second harmonic electric fields generated after the fundamental frequency incident light propagates backward through a 3D nonlinear optical non-reciprocal diffraction element, where columns 5-6 show the near-field amplitude and phase distribution of the second harmonic, and column 7 shows the far-field intensity distribution of the second harmonic. Based on the fact that the number of phase changes of 2π around a circle is the topological charge, we can deduce that: the topological charge of the second harmonic generated by the forward propagation of high-frequency light with a topological charge of 0 (LC_FF=0) is 2 (LC_SHG=2), and the topological charge of the second harmonic generated by the reverse propagation is -2 (LC_SHG=-2); the topological charge of the second harmonic generated by the forward propagation of vortex fundamental frequency light with a topological charge of 2 (LC_FF=2) is 6 (LC_SHG=6), and the topological charge of the second harmonic generated by the reverse propagation is 2 (LC_SHG=2). The results show that when the same fundamental frequency light propagates forward and backward through the designed 3D nonlinear optical nonreciprocal diffracting element, it will generate asymmetric second harmonic vortex light, and the nonlinear process can be expressed by the optical orbital angular momentum conservation law as LC_SHG=2*LC_FF±LC_HOLO. Wherein, "+" sign corresponds to the forward transmission case; "-" sign corresponds to the reverse transmission case; LC_SHG, LC_FF, and LC_HOLO are the optical orbital angular momentum topological charges carried by the outgoing second harmonic, the fundamental frequency incident light, and the 3D nonlinear optical nonreciprocal diffraction element, respectively.

[0060] In summary, the design method and application of the 3D nonlinear optical nonreciprocal diffracting element disclosed in this invention aim to achieve asymmetric second harmonic optical field manipulation. The 3D nonlinear optical nonreciprocal diffracting element designed by this invention consists of multiple specific 3D basic unit modules arranged in space. Each 3D basic unit module comprises a reverse ferroelectric domain module and a ferroelectric domain background substrate module. When a fundamental frequency linearly polarized plane wave is incident on the 3D basic unit module, the position of the reverse ferroelectric domain module within the 3D basic unit module is controlled by setting the movement distance of the reverse ferroelectric domain module along the beam propagation direction. The position of the reverse ferroelectric domain module within the 3D basic unit module is determined by discrete phase, which allows for the manipulation of the far-field second harmonic phase within the range of -π to +π. Furthermore, the second harmonic phases generated in forward and reverse propagation are opposite, thereby achieving asymmetric optical field manipulation of the second harmonic. This invention's design method possesses high practicality and flexibility in satisfying asymmetric optical field manipulation, and the types and number of 3D basic unit modules can be set according to the complexity of the target asymmetric nonlinear wavefront.

Claims

1. A method of designing a 3D nonlinear optical non-reciprocal diffractive element, characterized in that, The 3D nonlinear optical non-reciprocal diffraction element comprises a plurality of 3D basic unit modules arranged in space, and a design method of the 3D nonlinear optical non-reciprocal diffraction element is as follows: According to the asymmetric target second harmonic light field distribution corresponding to the forward transmission and reverse transmission, the discrete phase distribution at different spatial positions of the holographic plane is determined, and then the 3D basic unit module corresponding to each discrete phase is determined; Each 3D basic unit module comprises an inverted ferroelectric domain module and a ferroelectric domain background substrate module, the position of the inverted ferroelectric domain module in the 3D basic unit module is controlled by setting the moving distance of the inverted ferroelectric domain module along the light beam propagation direction, and the position of the inverted ferroelectric domain module in the 3D basic unit module is determined by the discrete phase, and the value range of the discrete phase is -π to +π; in each 3D basic unit module, the thickness of the inverted ferroelectric domain module in the light beam propagation direction is designed to be half of the thickness of the 3D basic unit module in the light beam propagation direction; the length and width of the inverted ferroelectric domain module perpendicular to the light beam propagation direction are designed to be equal to the length and width of the 3D basic unit module perpendicular to the light beam propagation direction, respectively; The 3D basic unit module corresponding to the discrete phase distribution constitutes the 3D nonlinear optical non-reciprocal diffraction element.

2. The design method of a 3D nonlinear optical non-reciprocal diffractive element according to claim 1, characterized in that, Each of the described inverted ferroelectric domain modules comprises a plurality of inverted ferroelectric domain units, each of which is designed to have a thickness in the direction of light beam propagation of σ y / Nu wherein, Nu is an integer, and takes Nu ≥ 4, Nu represents the number of discrete phase types after the continuous phase [-π, +π] is discretized, that is, the number of types of all 3D basic unit modules in the 3D nonlinear optical non-reciprocal diffraction element; σ y=2π / (k 2 -2k 1 ) wherein k 1 and k 2 are the magnitudes of the fundamental wave vector and the second harmonic wave vector, respectively.

3. The method of designing a 3D nonlinear optical non-reciprocal diffractive element according to claim 2, wherein, In each of the aforementioned 3D basic unit modules, if the number of inverted ferroelectric domain units... Nd The number of types of all 3D basic unit modules in the aforementioned 3D nonlinear optical nonreciprocal diffraction element Nu The relationship between them satisfies: Nu =2* Nd ,in, Nu This represents the number of discrete phase types that can be realized by all 3D basic unit modules; The number of the reversed ferroelectric domain units in each 3D basic unit module is determined according to the complexity of the asymmetric target second harmonic light field distribution corresponding to the forward transmission and the backward transmission Nd .

4. The method of designing a 3D nonlinear optical non-reciprocal diffractive element according to claim 1, wherein, The ratio of the distance between the center of the inverted ferroelectric domain module and the center of the 3D basic unit module to the thickness of the 3D basic unit module in the direction of light beam propagation is denoted as P nm , then P nm The relationship between the phase of the second harmonic wave accumulated after the incident light passes through the 3D basic unit module and the phase of the incident light φ nm satisfies a linear relationship, which is expressed as: φ nm = 2π P nm ; According to the linear relationship, the position of the inverted ferroelectric domain module in the 3D basic unit module is determined by the discrete phase.

5. The method of designing a 3D nonlinear optical non-reciprocal diffractive element according to claim 1, wherein, The asymmetric target second harmonic light field distribution corresponding to the forward transmission and the backward transmission is used to determine the discrete phase distribution at different spatial positions of the holographic plane, and the specific process is as follows: the continuous phase distribution on the holographic plane required for generating the asymmetric target second harmonic light field is divided into discrete phase distributions by equal discrete, wherein, Nu The discrete phase distribution is obtained by equal discrete. Nu N is the number of all 3D basic unit modules in the 3D nonlinear optical non-reciprocal diffraction element, Nu N represents the number of discrete phases that can be achieved by all 3D basic unit modules.

6. The method of designing a 3D nonlinear optical non-reciprocal diffractive element according to claim 1, wherein, The inverted ferroelectric domain module and the ferroelectric domain background substrate module of each 3D basic unit module are machined on the original ferroelectric domain by femtosecond laser direct writing.

7. The method of designing a 3D nonlinear optical non-reciprocal diffractive element according to claim 6, wherein, The original ferroelectric domain adopts a uniformly polarized or naturally grown lithium niobate crystal or a uniformly polarized or naturally grown barium strontium niobate crystal or a uniformly polarized or naturally grown barium calcium niobate crystal.

8. Use of a method for designing a 3D nonlinear optical non-reciprocal diffractive element according to any one of claims 1 to 7, characterized in that, The 3D nonlinear optical non-reciprocal diffraction element is used for second harmonic generation and asymmetric target light field control of second harmonic, specifically as follows: According to the asymmetric target second harmonic light field distribution corresponding to the forward transmission and reverse transmission, the continuous phase distribution at different spatial positions of the holographic plane is determined, and then the discrete phase distribution at different spatial positions of the holographic plane is determined; The 3D nonlinear optical non-reciprocal diffraction element designed by the design method of the 3D nonlinear optical non-reciprocal diffraction element in any one of claims 1-7 is used for arbitrary control within the range of -π to +π of the asymmetric target second harmonic phase corresponding to the forward transmission and reverse transmission, that is, when the plane light is incident on the 3D nonlinear optical non-reciprocal diffraction element, the generated second harmonic phases under the conditions of forward transmission and reverse transmission are opposite, thereby realizing asymmetric light field control of the second harmonic.

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