Multi-beam optical antenna based on reverse design and optimization method

Abstract

The invention relates to a multi-beam optical antenna based on reverse design and an optimization method, and the method comprises the steps: S1, segmenting a to-be-optimized radiation structure into a plurality of pixel units, carrying out the initialization assignment of dielectric constants of all pixel units, obtaining a first dielectric constant distribution matrix, and initializing a current smoothing parameter; s2, optimizing the first dielectric constant distribution matrix by combining an adjoint method with a gradient descent method to obtain a second dielectric constant distribution matrix; s3, processing and updating the second dielectric constant distribution matrix based on the current smoothing parameter to obtain a third dielectric constant distribution matrix; s4, judging whether dispersion in the dielectric constant distribution matrix reaches a pre-configured first threshold value or not, if yes, executing the step S5, and if not, executing the step S6; s5, processing the third dielectric constant distribution matrix to obtain an etching matrix; and S6, taking the third dielectric constant distribution matrix as the updated first dielectric constant distribution matrix, increasing the smoothing parameter, and returning to the step S2. Compared with the prior art, the multi-beam antenna has the advantages of realizing multiple beams on a single antenna and the like.

Description

Technical Field

[0001] The present invention relates to the field of multi-beam optical antennas, and in particular to a multi-beam optical antenna based on inverse design and an optimization method thereof. Background Art

[0002] With the rapid development of photonic integration technology, optical phased array (OPA), as a key technology for achieving high integration, high stability and low-cost beam control, has shown great application potential in the fields of lidar, free-space communication, three-dimensional imaging, etc. Traditional mechanical beam control systems are limited by inherent defects such as large size and slow response speed. OPA-based solid-state beam control technology is gradually becoming the core technology route of the new generation of beam control systems due to its advantages such as no mechanical components, fast response speed and high integration. Traditional optical phased array technology achieves beam deflection by controlling the phase of multiple optical antennas, and has important applications in solid-state lidar and optical communication systems. However, the existing technology has the following limitations:

[0003] 1. Limited scanning range: Traditional OPAs rely on wavelength tuning or electrically controlled phase shifters to achieve beam deflection. The scanning range is usually limited by the antenna spacing, making it difficult to achieve large field of view coverage.

[0004] 2. High system complexity: One-dimensional OPA requires a fast tunable laser, while two-dimensional OPA requires N 2 The large-scale phase shifter network results in high power consumption and complex control.

[0005] 3. Difficulty in implementing multi-beams: Traditional phased arrays require multi-channel sub-arrays or time-division multiplexing to implement multi-beams, which increases system size and cost.

[0006] Furthermore, traditional optical antenna design primarily relies on forward design, which relies on physical principles and empirical formulas to improve device performance through parameter sweeps and local optimization. This approach has significant limitations: first, the design process relies heavily on the designer's expertise and experience; second, when the optimization goal changes, the entire design process often needs to be restarted; and most importantly, forward design methods struggle to break through the performance limits of traditional structures and cannot achieve multi-beam implementation on a single antenna.

[0007] In recent years, inverse design methods have demonstrated groundbreaking potential in the field of photonic devices. These methods, through algorithm-driven optimization, generate non-intuitive structures, potentially breaking through the limitations of traditional empirical design. Furthermore, existing optical antennas primarily focus on improving single-beam performance, while achieving high efficiency and multi-beam radiation within a limited aperture remains a challenge.

[0008] For example, Chinese patent CN116449488A discloses an optical antenna that emits at any angle based on reverse design. It optimizes the optical antenna by cutting the area to be optimized into multiple pixel units and assigning them 0 or 1. However, this method uses discrete assignments, and the computational complexity of direct binary search (DBS) is high through pixel-by-pixel brute force search, and only a limited number of parameters are optimized each time. As the functional complexity of the device increases, it becomes necessary to expand the parameter space to find a device structure that meets all functional requirements. This determines the increase in the overall size of the device and the number of pixels. Therefore, using the above algorithm will greatly increase the computational cost and design efficiency. Summary of the Invention

[0009] The purpose of the present invention is to provide a multi-beam optical antenna and optimization method based on inverse design in order to solve the above technical problems.

[0010] The purpose of the present invention can be achieved by the following technical solutions:

[0011] A multi-beam optical antenna optimization method based on inverse design, comprising:

[0012] Step S1: Divide the radiation structure to be optimized into multiple pixel units, initialize and assign the dielectric constants of all pixel units, and use the dielectric constant distribution matrix obtained after the initialization and assignment as the first dielectric constant distribution matrix, and initialize the smoothing parameter as the current smoothing parameter, wherein the dielectric constant distribution matrix is ​​composed of the dielectric constants of each pixel unit;

[0013] Step S2: Optimizing the first dielectric constant distribution matrix using the adjoint method combined with the gradient descent method to obtain a second dielectric constant distribution matrix that meets the multi-beam target;

[0014] Step S3: Projecting and assigning values ​​to the dielectric constants in the second dielectric constant distribution matrix based on the current smoothing parameter, and updating to obtain a third dielectric constant distribution matrix;

[0015] Step S4: determining whether the dispersion in the dielectric constant distribution matrix reaches a pre-configured first threshold; if so, executing step S5; otherwise, executing step S6;

[0016] Step S5: performing a second binarization process on the third dielectric constant distribution matrix to obtain an etching matrix;

[0017] Step S6: Use the third dielectric constant distribution matrix as the updated first dielectric constant distribution matrix, increase the smoothing parameter, and then return to step S2.

[0018] The dielectric constant has a value range of:

[0019] [εmin , ε max ]

[0020] Among them, ε min is the lower limit of the dielectric constant, ε max is the upper limit of the dielectric constant;

[0021] During the process of initializing and assigning values ​​to the dielectric constants of all pixel units in step S1 , the dielectric constants of all pixel units are assigned a value of / 2.

[0022] The step S2 specifically includes:

[0023] Step S2-1: determining multiple beam directions according to the multi-beam target, and performing forward simulation based on each beam direction to obtain a second electric field distribution corresponding to each beam direction within the radiation structure;

[0024] Step S2-2: obtaining a first electric field distribution within the radiation structure through reverse simulation;

[0025] Step S2-3: obtaining, based on the first electric field distribution and the second electric field distribution corresponding to each beam direction, the influence of the objective function corresponding to each beam direction on the dielectric constant of each pixel unit in the radiation structure as a sub-gradient corresponding to each beam direction;

[0026] Step S2-4: Obtain the gradient of the total objective function corresponding to the sub-gradients of each beam direction;

[0027] Step S2-5: Use the gradient descent method to update the dielectric constant of each pixel unit, and repeat steps S2-1 to S2-4 until the objective function converges, and use the dielectric constant of each pixel unit at this time as the second dielectric constant distribution matrix.

[0028] The forward simulation method is as follows: a Gaussian source is set above the antenna and inputted in reverse to the antenna's radiation structure, wherein the reverse input direction matches the corresponding beam direction;

[0029] The reverse simulation method is: the beam is input in a forward direction along an input waveguide, wherein the output end of the input waveguide is connected to a radiation structure.

[0030] The first threshold is 0.99.

[0031] In step S3, the dielectric constant after projection assignment is:

[0032]

[0033] Where: ε i is the dielectric constant after projection assignment, is the density of nodes in the physical field, specifically a function of the smoothing parameter and the dielectric constant before projection.

[0034] The step S5 comprises:

[0035] Step S5-1: Determine a dielectric constant cutoff value;

[0036] Step S5-2: determining the etching parameters of all pixel units with dielectric constants greater than the dielectric constant cutoff value to be 1, and determining the etching parameters of all pixel units with dielectric constants less than the dielectric constant cutoff value to be 0, to obtain an etching matrix.

[0037] A multi-beam optical antenna based on reverse design includes a silicon substrate, a dielectric buried oxide layer, and an optical antenna arranged in sequence from bottom to top. The optical antenna includes an input waveguide and a radiation structure. The optical antenna is arranged above the dielectric buried oxide layer along the length direction of the waveguide layer. A light source is injected from the input waveguide and enters the radiation structure through the input waveguide. The radiation structure is optimized by the method described above.

[0038] A multi-beam optical antenna optimization device based on inverse design includes a memory, a processor, and a program stored in the memory. When the processor executes the program, the method as described above is implemented.

[0039] A storage medium stores a program, which implements the above method when executed.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1. By setting a dielectric constant matrix, the dielectric constants of all pixel units are taken within a range, and an adjoint method combined with a gradient descent method is used for iterative optimization. A smoothing parameter is used to successively project and assign values ​​to each dielectric constant in the second dielectric constant distribution matrix. This allows the realization of complex multi-beam optical antennas within a larger parameter space, achieving breakthroughs in control accuracy, efficiency, and compactness.

[0042] 2. Compared with traditional optical antennas, this invention achieves multi-beam synchronous radiation through an innovative reverse design method, breaking through the technical limitations of traditional phased arrays that rely on phase modulation. Secondly, the use of an SOI structure that is fully compatible with CMOS processes not only ensures the manufacturability of the device, but also achieves miniaturization and high integration, facilitating large-scale system integration. Thirdly, the optical structure designed through topological optimization has excellent beam control capabilities, can accurately achieve a preset far-field radiation pattern, and has strong beam directivity and a small spot size. Finally, the optimized radiation structure has low processing difficulty while ensuring performance, meeting the processing requirements of existing semiconductor processes. These advantages make this invention of great application value in fields such as lidar and free-space communications.

[0043] 3. During the initialization and assignment of the dielectric constants of all pixel units, the dielectric constants of all pixel units are assigned intermediate values, thereby avoiding the occurrence of non-physical strong scattering in the initial design and achieving faster convergence and higher performance robustness in the design.

[0044] 4. A gradually increasing smoothing parameter is used to successively project and assign values ​​to each dielectric constant in the second dielectric constant distribution matrix. Compared with the method of directly binarizing according to the boundary value, the performance upper limit of the multi-beam optical antenna is significantly improved through an optimization path with greater degrees of freedom. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of the main steps of the method of the present invention;

[0046] Figure 2 A top view of a dual-beam optical antenna based on inverse design provided by an embodiment of the present invention;

[0047] Figure 3 Schematic side view of the multi-beam optical antenna based on reverse design of the present invention;

[0048] Figure 4 A far-field distribution diagram of a dual-beam optical antenna based on inverse design provided in one embodiment of the present invention.

[0049] Figure 5 The topological structure and far-field distribution diagram of a three-beam optical antenna based on inverse design provided in one embodiment of the present invention;

[0050] Figure 6 The topological structure and far-field distribution diagram of a four-beam optical antenna based on inverse design provided in one embodiment of the present invention;

[0051] Among them: 1. Silicon substrate; 2. Dielectric buried oxide layer; 3. Input waveguide; 4. Radiation structure. DETAILED DESCRIPTION

[0052] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0053] A multi-beam optical antenna optimization method based on inverse design, such as Figure 1 As shown, including:

[0054] Step S1: Divide the radiation structure 4 to be optimized into a plurality of pixel units, initialize and assign the dielectric constants of all pixel units, and use the dielectric constant distribution matrix obtained after the initialization and assignment as the first dielectric constant distribution matrix, and initialize the smoothing parameter as the current smoothing parameter, wherein the dielectric constant distribution matrix is ​​composed of the dielectric constants of each pixel unit;

[0055] In this embodiment, the width of the input waveguide 3 is 0.4 μm, and the size of the radiation module in the reverse-engineered radiation structure 4 is 8 μm × 8 μm. At the same time, the design area is discretized into pixel units of size 20 nm × 20 nm, resulting in a total of 160,000 pixel units. In this application, the dielectric constant range is:

[0056] [ε min , ε max ]

[0057] Among them, ε min is the lower limit of the dielectric constant, ε max is the upper limit of the dielectric constant;

[0058] In the process of initializing the dielectric constants of all pixel units, different methods can be used in different embodiments, for example, all can be set to the maximum value, all can be set to the minimum value, or random assignment can be performed. However, in this embodiment, the dielectric constants of all pixel units are assigned to ε min +ε max / 2, thus avoiding the unphysical strong scattering in the initial design and achieving faster convergence and higher performance robustness in the design.

[0059] Step S2: Optimizing the first dielectric constant distribution matrix using the adjoint method combined with the gradient descent method to obtain a second dielectric constant distribution matrix that meets the multi-beam target, specifically including:

[0060] Step S2-1: determining multiple beam directions according to the multi-beam target, and performing forward simulation based on each beam direction to obtain a second electric field distribution corresponding to each beam direction in the radiation structure 4;

[0061] Step S2-2: obtaining a first electric field distribution within the radiation structure 4 through reverse simulation;

[0062] Step S2-3: Based on the first electric field distribution and the second electric field distribution corresponding to each beam direction, the influence of the objective function corresponding to each beam direction on the dielectric constant of each pixel unit in the radiation structure 4 is obtained as a sub-gradient corresponding to each beam direction;

[0063] Step S2-4: Obtain the gradient of the total objective function corresponding to the sub-gradients of each beam direction;

[0064] Step S2-5: Use the gradient descent method to update the dielectric constant of each pixel unit, and repeat steps S2-1 to S2-4 until the objective function converges, and use the dielectric constant of each pixel unit at this time as the second dielectric constant distribution matrix.

[0065] During the iterative optimization process, the L-BFGS optimization algorithm is used to automatically adjust the dielectric constant of each pixel unit along the negative direction of the gradient, and the iterative process is repeated until the optimal dielectric constant distribution is obtained.

[0066] In this embodiment, the objective function is specifically T TE0 , that is, the mode transmission efficiency of light incident on the radiating structure at the expected angle and coupled to the TE0 mode in the waveguide, thereby ensuring the high efficiency and low crosstalk of the multi-beam optical antenna.

[0067] In addition, in this embodiment, the forward simulation method is: by setting a Gaussian source above the antenna, reverse input is input to the antenna's radiation structure 4, wherein the reverse input direction matches the corresponding beam direction. Specifically, in this embodiment, the reverse input direction is opposite to the corresponding beam direction, and the reverse simulation method is: the beam is forward input along the input waveguide 3, wherein the output end of the input waveguide 3 is connected to the radiation structure 4.

[0068] Step S3: Projecting and assigning values ​​to the dielectric constants in the second dielectric constant distribution matrix based on the current smoothing parameter, and updating to obtain a third dielectric constant distribution matrix;

[0069] In step S3, the dielectric constant after projection assignment is:

[0070]

[0071] Where: ε i is the dielectric constant after projection assignment, is the density of nodes in the physical field, specifically a function of the smoothing parameter and the dielectric constant before projection.

[0072] Step S4: determining whether the dispersion in the dielectric constant distribution matrix reaches a pre-configured first threshold; if so, executing step S5; otherwise, executing step S6;

[0073] In this embodiment, specifically, the first threshold is 0.99.

[0074] Step S5: performing a second binarization process on the third dielectric constant distribution matrix to obtain an etching matrix, specifically comprising:

[0075] Step S5-1: Determine a dielectric constant cutoff value. The cutoff point can be an average value or other values.

[0076] Step S5-2: determining the etching parameters of all pixel units with dielectric constants greater than the dielectric constant cutoff value to be 1, and determining the etching parameters of all pixel units with dielectric constants less than the dielectric constant cutoff value to be 0, to obtain an etching matrix.

[0077] Step S6: Use the third dielectric constant distribution matrix as the updated first dielectric constant distribution matrix, increase the smoothing parameter, and then return to step S2.

[0078] A multi-beam optical antenna based on reverse design includes a silicon substrate 1, a dielectric buried oxide layer 2, and an optical antenna arranged in sequence from bottom to top. The optical antenna includes an input waveguide 3 and a radiation structure 4. The optical antenna is arranged above the dielectric buried oxide layer 2 along the length direction of the waveguide layer. The light source is injected from the input waveguide 3 and enters the radiation structure 4 through the input waveguide 3. The radiation structure 4 is optimized by the method as described above.

[0079] Specifically, after the etching matrix is ​​obtained, the corresponding radiation structure 4 can be obtained by etching.

[0080] like Figure 2 、 Figure 3 A multi-beam optical antenna structure based on reverse design is shown, including a silicon substrate 1, a dielectric buried oxide layer 2, and an optical antenna.

[0081] The optical antenna consists of an input waveguide 3 and a reverse-engineered radiation structure 4. The incident light propagates along the x-direction and, after passing through the optical antenna structure, is emitted in the far field in the target direction.

[0082] like Figure 2 In the reverse-designed dual-beam optical antenna shown, in this embodiment, the radiation module in the radiation structure is made of silicon, and the other parts are made of air.

[0083] As an example, considering only the fundamental mode of the waveguide and the injection light source at a wavelength of 1550 nm, multiple optical antennas were designed, including dual-beam, triple-beam, and quad-beam optical antennas, and the following graphical results were obtained.

[0084] like Figure 4The far-field distribution diagram of the reverse-engineered dual-beam optical antenna is shown in Figure 1. The beam energy is concentrated in two preset directions, and the background stray field is weak, which fully demonstrates the good control ability of the optical antenna for the dual beams. The widths of the individual beams in the direction are 14.7° and 23° respectively, and the final far-field beam pointing is: θ=8.2°, and θ = 8.2°, In addition, the antenna radiation efficiency reaches 51.3%, and the calculated adjacent beam crosstalk (the ratio of the adjacent beam intersection power to the peak power) is -11.5dB.

[0085] like Figure 5 The topology of the reverse-engineered three-beam optical antenna is shown ( Figure 5 (a)) and far-field distribution diagram ( Figure 5 (b)), in this embodiment, the radiation structure includes a radiation module made of silicon and a silicon dioxide cladding layer covering it. Figure 5 As shown in (b), the beam energy is concentrated in three preset directions, the background stray field is weak, and the optical antenna can achieve the control of the three beams. The beam radiated at the middle angle of the optical antenna is far-field along the θ direction and along the The beam widths in the two directions are 16° and 22° respectively, and the final far-field beam pointing is approximately: θ=6°, θ=48°, θ=48°, The intensity of the beam with the larger angle is approximately 0.8 times that of the middle beam. Furthermore, the antenna's radiation efficiency is 33.4%, which is somewhat lower than that of a dual-beam antenna. As the number of beams generated by a finite aperture increases, the overlap between beams inevitably increases, resulting in a calculated adjacent beam crosstalk of -8dB.

[0086] like Figure 6 The topology of the inversely designed four-beam optical antenna is shown ( Figure 6 (a)) and far-field distribution diagram ( Figure 6 (b)), in this embodiment, the radiation structure includes a radiation module made of silicon and a silicon dioxide cladding layer covering it. Figure 6 As shown in (b), the beam energy is concentrated in four preset directions, and the background stray field is slightly significant, but the optical antenna can still effectively control the four beams. The beam radiated at the middle angle of the optical antenna is in the far field along the θ direction and along the The beam widths in the two directions are 12° and 23° respectively, and the final far-field beam pointing is approximately: θ=23°, θ=23°, θ=54°, θ=54°, The intensity distribution of the four beams exhibits high uniformity. Furthermore, the antenna achieves a radiation efficiency of 12.7%, which is somewhat lower than that of the dual-beam and triple-beam antennas. The calculated adjacent beam crosstalk is -5.5 dB, reflecting the inherent challenges of multi-beam energy dispersion within a limited aperture.

[0087] The above examples demonstrate that the inverse design method has significant potential in achieving multi-beam directional transmission, providing a high-performance, low-cost solution for solid-state lidar and optical communication systems.

[0088] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

Claims

1. A multi-beam optical antenna optimization method based on inverse design, characterized in that: include: Step S1: dividing the radiation structure to be optimized (4) into a plurality of pixel units, and initializing and assigning the dielectric constants of all pixel units, and using the dielectric constant distribution matrix obtained after the initialization and assignment as the first dielectric constant distribution matrix, and initializing the smoothing parameter as the current smoothing parameter, wherein the dielectric constant distribution matrix is ​​composed of the dielectric constants of each pixel unit; Step S2: Optimizing the first dielectric constant distribution matrix using the adjoint method combined with the gradient descent method to obtain a second dielectric constant distribution matrix that meets the multi-beam target; Step S3: Projecting and assigning values ​​to the dielectric constants in the second dielectric constant distribution matrix based on the current smoothing parameter, and updating to obtain a third dielectric constant distribution matrix; Step S4: determining whether the dispersion in the dielectric constant distribution matrix reaches a pre-configured first threshold; if so, executing step S5; otherwise, executing step S6; Step S5: performing a second binarization process on the third dielectric constant distribution matrix to obtain an etching matrix; Step S6: Use the third dielectric constant distribution matrix as the updated first dielectric constant distribution matrix, increase the smoothing parameter, and then return to step S2.

2. The multi-beam optical antenna optimization method based on inverse design according to claim 1, characterized in that: The dielectric constant has a value range of: [e min ,he max ] Among them, ε min is the lower limit of the dielectric constant, ε max is the upper limit of the dielectric constant; In the process of initializing the dielectric constants of all pixel units in step S1, the dielectric constants of all pixel units are assigned to (ε min +ε max ) / 2.

3. The multi-beam optical antenna optimization method based on inverse design according to claim 1, characterized in that: The step S2 specifically includes: Step S2-1: determining a plurality of beam directions according to a multi-beam target, and performing forward simulation based on each beam direction to obtain a second electric field distribution corresponding to each beam direction in the radiation structure (4); Step S2-2: obtaining a first electric field distribution within the radiation structure (4) through reverse simulation; Step S2-3: Based on the first electric field distribution and the second electric field distribution corresponding to each beam direction, the influence of the objective function corresponding to each beam direction on the dielectric constant of each pixel unit in the radiation structure (4) is obtained as a sub-gradient corresponding to each beam direction; Step S2-4: Obtain the gradient of the total objective function corresponding to the sub-gradients of each beam direction; Step S2-5: Use the gradient descent method to update the dielectric constant of each pixel unit, and repeat steps S2-1 to S2-4 until the objective function converges, and use the dielectric constant of each pixel unit at this time as the second dielectric constant distribution matrix.

4. The multi-beam optical antenna optimization method based on inverse design according to claim 3, characterized in that: The forward simulation method is as follows: a Gaussian source is set above the antenna and inputted in reverse to the radiation structure (4) of the antenna, wherein the reverse input direction matches the corresponding beam direction; The reverse simulation method is as follows: the beam is input in a forward direction along the input waveguide (3), wherein the output end of the input waveguide (3) is connected to the radiation structure (4).

5. The multi-beam optical antenna optimization method based on inverse design according to claim 1, characterized in that: The first threshold is 0.

99.

6. The multi-beam optical antenna optimization method based on inverse design according to claim 2, characterized in that: In step S3, the dielectric constant after projection assignment is: Where: i is the dielectric constant after projection assignment, is the density of nodes in the physical field, specifically a function of the smoothing parameter and the dielectric constant before projection.

7. The multi-beam optical antenna optimization method based on inverse design according to claim 1, characterized in that: The step S5 comprises: Step S5-1: Determine a dielectric constant cutoff value; Step S5-2: determining the etching parameters of all pixel units with dielectric constants greater than the dielectric constant cutoff value to be 1, and determining the etching parameters of all pixel units with dielectric constants less than the dielectric constant cutoff value to be 0, to obtain an etching matrix.

8. A multi-beam optical antenna based on reverse design, comprising a silicon substrate (1), a dielectric buried oxide layer (2), and an optical antenna arranged in sequence from bottom to top, the optical antenna comprising an input waveguide (3) and a radiation structure (4), characterized in that: The optical antenna is arranged above the dielectric buried oxide layer (2) along the length direction of the waveguide layer. The light source is injected from the input waveguide (3) and enters the radiation structure (4) through the input waveguide (3). The radiation structure (4) is optimized by the method described in any one of claims 1 to 7.

9. A multi-beam optical antenna optimization device based on inverse design, comprising a memory, a processor, and a program stored in the memory, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

10. A storage medium having a program stored thereon, characterized in that: When the program is executed, the method according to any one of claims 1 to 7 is implemented.

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