Optical response electromagnetic simulation method and system for dynamic evolution of nano array structure

Abstract

The invention discloses an optical response electromagnetic simulation method and system for dynamic evolution of a nano-array structure, and the method comprises the following steps: carrying out the geometric modeling of the nano-array structure, dispersing the periodic units in the nano-array structure into dipole arrays at equal intervals, and distributing a corresponding polarizability to each dipole; initializing a simulation condition, and setting an incident light condition, a medium environment and a periodic boundary condition; establishing a dipole interaction matrix meeting a periodic boundary condition, calculating an inverse matrix, and further calculating a polarization vector of a dipole; updating the inverse matrix based on a rank-one or low-rank inverse updating method; and calculating an optical response parameter of the nano array based on the updated polarization vector. On the premise of ensuring the calculation accuracy, the optical response change of the nano array structure in the dynamic evolution process can be efficiently tracked, and the method is suitable for electromagnetic simulation and optical optimization calculation scenes involving a large number of intermediate states.

Description

Technical Field

[0001] This invention relates to the fields of electromagnetic simulation and nano-optical computing technology, and in particular to an electromagnetic simulation method and system for the optical response of dynamic evolution of nanoarray structures. Background Technology

[0002] The Discrete Dipole Approximation (DDA) method is a classic electromagnetic simulation technique. Its basic principle is to discretize a continuous geometric structure into an array of equally spaced dipoles, thereby calculating its optical response. Existing DDA software mainly includes DDSCAT (Draine BT, Flatau PJ, J. Opt. Soc. Am. A, 1994, 11:1491-1499) and ADDA (Yurkin MA, Hoekstra AG, J. Quant. Spectrosc. Radiat. Transfer, 2007, 106:558-589). These software programs typically employ solvers combining Fast Fourier Transform (FFT) and Complex Conjugate Gradient (CCG), thus demonstrating wide applicability and good computational performance in optical calculations of static geometries.

[0003] However, existing technologies still have significant limitations in simulating the optical response of nanoarray structures during dynamic evolution. On the one hand, as the structure dynamically changes, traditional methods require repeatedly constructing and solving the complete matrix for each intermediate structure, resulting in high computational cost and low efficiency. On the other hand, existing technologies lack efficient real-time update strategies for the coupling relationship between local structures and the overall optical response, making it difficult to accurately capture the evolutionary characteristics of nanoarrays. Therefore, existing technologies cannot meet the needs of large-scale dynamic evolution simulation and also limit the ability to perform detailed analysis and prediction of the optical behavior of nanoarrays. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of large computational load, low efficiency of solving repeated matrices, and insufficient coupling between local structure and optical response in the existing technology for simulating the optical response of the dynamic evolution process of nanoarray structures.

[0005] The technical solution adopted by this invention to solve its technical problem is: to provide an electromagnetic simulation method for the dynamic evolution of optical response of a nanoarray structure, comprising the following steps:

[0006] The structural modeling step involves geometrically modeling the nanoarray structure, discretizing the periodic units in the nanoarray structure into an array of equally spaced dipoles, and assigning a corresponding polarizability to each dipole.

[0007] The matrix construction steps include initializing the simulation conditions, setting the incident light conditions, medium environment, and periodic boundary conditions; establishing the dipole interaction matrix that satisfies the periodic boundary conditions, calculating the inverse matrix, and then calculating the polarization vector of the dipole point.

[0008] The structural dynamic evolution steps involve updating the inverse matrix based on the rank-one or low-rank inverse update method;

[0009] The optical response calculation steps are based on the updated polarization vector to calculate the optical response parameters of the nanoarray, including the absorption cross section, scattering cross section, extinction cross section, and local electromagnetic field enhancement.

[0010] Preferably, the structural dynamic evolution step includes the following steps:

[0011] The dipole interaction matrix satisfying the periodic boundary conditions is decomposed into a geometrically dependent part and a polarizability dependent part.

[0012] When a dipole replacement occurs in a nanoarray structure, the geometric dependence remains unchanged, while only the polarizability dependence changes. The dipole response of the new structure is calculated using a rank-one update inverse matrix algorithm.

[0013] Preferably, in the structural dynamic evolution step, when a dipole point j is updated from the first polarizability αj to the second polarizability αj', the update of the diagonal matrix A(α) is equivalent to updating the diagonal elements at indices (3j−2), (3j−1), and (3j) respectively, and obtaining the updated inverse matrix A' through at least three rank-one inverse updates. -1 .

[0014] Preferably, for scenarios involving dipole addition and removal caused by geometric evolution, a polarizability approximation method is used to keep the dimension of the dipole interaction matrix unchanged. The polarizability approximation includes setting the polarizability of the removed dipole point to a preset polarizability value so that dipole removal is equivalent to dipole replacement, and updating the inverse matrix based on a rank-one or low-rank inverse update method.

[0015] Preferably, dipole addition is considered the reverse process of dipole removal, and is achieved by updating the polarizability of the newly added dipole from the preset polarizability value to the target polarizability value.

[0016] Preferably, the inverse matrix update and polarization vector calculation are performed in parallel on a graphics processing unit (GPU) for accelerated execution.

[0017] This invention also provides an electromagnetic simulation system for the dynamic evolution of optical response of nanoarray structures, comprising:

[0018] The structural modeling module performs geometric modeling of the nanoarray structure, discretizing the periodic units in the nanoarray structure into an array of equally spaced dipoles, and assigning a corresponding polarizability to each dipole.

[0019] The matrix construction module initializes the simulation conditions, sets the incident light conditions, medium environment, and periodic boundary conditions; establishes the dipole interaction matrix that satisfies the periodic boundary conditions, calculates the inverse matrix, and then calculates the polarization vector of the dipole point;

[0020] The structural dynamic evolution module updates the inverse matrix based on the rank-one or low-rank inverse update method;

[0021] The optical response calculation module calculates the optical response parameters of the nanoarray based on the updated polarization vector, including the absorption cross section, scattering cross section, extinction cross section, and local electromagnetic field enhancement.

[0022] The present invention also provides an electronic device, comprising:

[0023] One or more processors;

[0024] A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to perform the method as described in any one of claims 1-6.

[0025] The present invention also provides a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements any of the methods described above.

[0026] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements any of the methods described above.

[0027] The present invention has the following beneficial effects:

[0028] (1) Improved computational efficiency: By using the inverse matrix update algorithm, the large linear optical system does not need to be solved repeatedly for each evolution step during the dynamic evolution of the nanoarray structure, which significantly reduces the amount of computation and improves the overall efficiency of large-scale optical simulation.

[0029] (2) Accurate capture of dynamic evolution: It can update the electric field response of each dipole in real time, realize high-precision coupling between the geometric changes of the nanoarray structure and the optical response, and the optical response can be accurate to the dipole resolution.

[0030] (3) Enhanced interactivity: The simulation system supports interactive operation with the Large Language Model (LLM), which can realize functions such as parameter adjustment, simulation scheme recommendation and result analysis, thereby reducing the complexity of user operation and improving the ease of use.

[0031] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the embodiments. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the steps of an electromagnetic simulation method for the dynamic evolution of a nanoarray structure according to an embodiment of the present invention.

[0033] Figure 2 This is a flowchart illustrating an electromagnetic simulation method for the dynamic evolution of a nanoarray structure according to an embodiment of the present invention.

[0034] Figure 3 This is a comparison chart showing the efficiency of tracking the dynamic evolution of the optical response of a nanoarray structure according to an embodiment of the present invention.

[0035] Figure 4 This is a schematic diagram of the optical response electromagnetic simulation system for the dynamic evolution of a nanoarray structure according to an embodiment of the present invention.

[0036] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0038] Figure 1 This embodiment illustrates the method steps of an electromagnetic simulation method for the dynamic evolution of an optical response of a nanoarray structure, including:

[0039] S101, structural modeling step, geometric modeling of the nanoarray structure, discretizing the periodic units in the nanoarray structure into an array of equally spaced dipoles, and assigning a corresponding polarizability to each dipole.

[0040] S102, Matrix construction steps: Initialize simulation conditions, set incident light conditions, medium environment and periodic boundary conditions; establish the dipole interaction matrix that satisfies the periodic boundary conditions, calculate the inverse matrix, and then calculate the polarization vector of the dipole point;

[0041] S103, the structural dynamic evolution step, updates the inverse matrix based on the rank-one or low-rank inverse update method;

[0042] S104, Optical Response Calculation Step, calculates the optical response parameters of the nanoarray based on the updated polarization vector, including absorption cross section, scattering cross section, extinction cross section, and local electromagnetic field enhancement.

[0043] Specifically, in this embodiment, in S101, the following was selected: Using rectangular blocks as periodic units, these blocks are discretized into equally spaced dipoles with a lattice spacing of 1 nm, resulting in a total of 3000 dipoles. Their three-dimensional coordinates are denoted as... .

[0044] Specifically, the initialization simulation conditions in S102 of this embodiment include:

[0045] An incident light field is set up such that the incident light forms a normal vector with respect to the plane constituting the two-dimensional periodic nanoarray. The included angle propagates from the negative z-axis direction to the positive z-axis direction. Set the scanning wavelength mode, from... Scanned ,interval One sample is taken.

[0046] Set the medium environment, and set the refractive index of the dipole to the refractive index of gold at the corresponding wavelength; set the medium environment to an aqueous solution with a refractive index of 1.33.

[0047] Define boundary conditions using direction vectors and Define two-dimensional periodic boundary conditions.

[0048] Specifically, in this embodiment, the dipole interaction matrix under periodic boundary conditions is constructed in S102, and then the inverse matrix under the initial geometry is solved. This allows us to obtain the polarization vector of the dipole. The dipole interaction matrix is ​​expressed as:

[0049]

[0050] in, It is consistent with the form of the dipole interaction matrix in free space in the classical discrete dipole approximation method; Let be the wave vector of the incident light; , represents the distance between the k-th dipole in the (m, n) periodic cell and the j-th dipole in the (0, 0) cell; As the cutoff factor, the summation of the series is truncated, and the cutoff condition is to consider all... The dipole interaction of periodic units.

[0051] Specifically, in this embodiment, the rank-one update algorithm is used in S104 to quickly obtain the new polarization vector, and the dipole interaction matrix under the periodic boundary conditions calculated in the previous step is decomposed into geometrically dependent parts. and polarization-dependent part , respectively represented as:

[0052]

[0053]

[0054]

[0055] Then, the pre-defined evolution path is read to determine if the number of dipoles in the structure has changed. If it remains unchanged, the process proceeds to the "dipole replacement branch." Specifically, if one of the gold dipoles is replaced by a silver dipole, meaning the polarizability of that dipole changes from... It became At this point, only the polarization-dependent part is updated. :

[0056]

[0057] Therefore, the new polarization vector can be obtained by updating it in the following four steps:

[0058]

[0059]

[0060]

[0061]

[0062] In this example, the evolution path is to move the periodic unit from... The rectangular block was etched as The cube's matrix dimensions change, leading to another branch. This branch additionally includes a polarizability approximation process, by setting the etched polarizability to... This effectively and uniquely controls the change in the dipole interaction matrix to the polarizability-dependent part. Then, it re-enters the "dipole replacement" branch. At this point, the updater can be further simplified to:

[0063]

[0064]

[0065]

[0066] Finally, for the case of "dipole addition", it can be regarded as the reverse process of "dipole removal", and the above process is followed.

[0067] Specifically, in S104 of this embodiment of the invention, the corresponding optical response is calculated by updating the polarization vector of the rank-one electromagnetic simulator, such as... Figure 3 The diagram illustrates the computational results for the optical responses of 2000 consecutive intermediates in this embodiment, where adjacent intermediates differ by only one dipole resolution unit. Comparative results show that, under the same computational accuracy requirements, the electromagnetic simulation system employed in this invention significantly outperforms the classic DDSCAT software and PyTorch-based general linear equation solvers in overall computational efficiency, achieving an acceleration of 10^6 times. These results clearly demonstrate that this invention can efficiently track the changes in the optical response of nanoarray structures during dynamic evolution while ensuring computational accuracy, making it suitable for electromagnetic simulation and optical optimization computation scenarios involving a large number of intermediate states.

[0068] Specifically, the method in this embodiment of the invention supports GPU acceleration to improve computational efficiency; the overall geometric modeling process of S101 can be embedded with a Model Context Protocol (MCP) Server, supporting interaction with a Large Language Model (LLM) to achieve rapid modeling; the full-process computation module for optical response calculation also supports interactive LLM calls.

[0069] See Figure 4 The diagram shown is a schematic representation of an electromagnetic simulation system for the dynamic evolution of a nanoarray structure according to an embodiment of the present invention, comprising:

[0070] The structural modeling module 401 performs geometric modeling of the nanoarray structure, discretizes the periodic units in the nanoarray structure into an array of equally spaced dipoles, and assigns a corresponding polarizability to each dipole.

[0071] The matrix construction module 402 initializes the simulation conditions, sets the incident light conditions, medium environment, and periodic boundary conditions; establishes the dipole interaction matrix that satisfies the periodic boundary conditions, calculates the inverse matrix, and then calculates the polarization vector of the dipole point;

[0072] The structural dynamic evolution module 403 updates the inverse matrix based on the rank-one or low-rank inverse update method;

[0073] The optical response calculation module 404 calculates the optical response parameters of the nanoarray based on the updated polarization vector, including the absorption cross section, scattering cross section, extinction cross section, and local electromagnetic field enhancement.

[0074] See Figure 5The diagram shown is a structural schematic of an electronic device provided in an embodiment of the present invention, including: a processor 501 and a memory 502; wherein the memory 502 is used to store computer execution instructions; and the processor 501 is used to execute the computer execution instructions stored in the memory to implement the various steps performed by the electronic device in the above embodiment. For details, please refer to the relevant descriptions in the foregoing method embodiments.

[0075] Alternatively, the memory 502 can be either standalone or integrated with the processor 501.

[0076] When the memory 502 is set up independently, the electronic device also includes a bus 503 for connecting the memory 502 and the processor 501.

[0077] This invention also provides a computer storage medium storing computer execution instructions, which, when executed by a processor, implement the method described above.

[0078] This invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0079] In the embodiments provided by this invention, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0080] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0081] Furthermore, the functional modules in the various embodiments of the present invention can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0082] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.

[0083] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules within the processor.

[0084] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0085] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0086] The aforementioned storage medium can be implemented from any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium accessible to general-purpose or special-purpose computers.

[0087] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. Both the processor and the storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic device or host device.

[0088] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0089] 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for electromagnetic simulation of the dynamic evolution of optical response of a nanoarray structure, characterized in that, Includes the following steps: The structural modeling step involves geometrically modeling the nanoarray structure, discretizing the periodic units in the nanoarray structure into an array of equally spaced dipoles, and assigning a corresponding polarizability to each dipole. The matrix construction steps include initializing the simulation conditions, setting the incident light conditions, medium environment, and periodic boundary conditions; establishing the dipole interaction matrix that satisfies the periodic boundary conditions, calculating the inverse matrix, and then calculating the polarization vector of the dipole point. The structural dynamic evolution steps involve updating the inverse matrix based on the rank-one or low-rank inverse update method; The optical response calculation steps are based on the updated polarization vector to calculate the optical response parameters of the nanoarray, including the absorption cross section, scattering cross section, extinction cross section, and local electromagnetic field enhancement.

2. The electromagnetic simulation method for the dynamic evolution of the optical response of a nanoarray structure according to claim 1, characterized in that, The structural dynamic evolution steps include the following steps: The dipole interaction matrix satisfying the periodic boundary conditions is decomposed into a geometrically dependent part and a polarizability dependent part. When a dipole replacement occurs in a nanoarray structure, the geometric dependence remains unchanged, while only the polarizability dependence changes. The dipole response of the new structure is calculated using a rank-one update inverse matrix algorithm.

3. The electromagnetic simulation method for the dynamic evolution of the optical response of a nanoarray structure according to claim 1, characterized in that, In the aforementioned structural dynamic evolution step, when a dipole point j is updated from the first polarizability αj to the second polarizability αj', the update of the diagonal matrix A(α) is equivalent to updating the diagonal elements at indices (3j−2), (3j−1), and (3j) respectively, and obtaining the updated inverse matrix A' through at least three rank-one inverse updates. -1 .

4. The electromagnetic simulation method for the dynamic evolution of the optical response of a nanoarray structure according to claim 1, characterized in that, For scenarios involving dipole addition and removal caused by geometric evolution, a polarizability approximation method is used to keep the dimension of the dipole interaction matrix unchanged. The polarizability approximation includes setting the polarizability of the removed dipole point to a preset polarizability value so that dipole removal is equivalent to dipole replacement, and updating the inverse matrix based on a rank-one or low-rank inverse update method.

5. The electromagnetic simulation method for the dynamic evolution of the optical response of a nanoarray structure according to claim 4, characterized in that, Adding a dipole is considered the inverse process of removing a dipole, and is achieved by updating the polarizability of the newly added dipole from the preset polarizability value to the target polarizability value.

6. The electromagnetic simulation method for the dynamic evolution of the optical response of a nanoarray structure according to claim 1, characterized in that, The inverse matrix update and polarization vector calculation are performed in parallel and accelerated on the graphics processing unit (GPU).

7. An electromagnetic simulation system for the dynamic evolution of an optical response of a nanoarray structure, characterized in that, include: The structural modeling module performs geometric modeling of the nanoarray structure, discretizing the periodic units in the nanoarray structure into an array of equally spaced dipoles, and assigning a corresponding polarizability to each dipole. The matrix construction module initializes the simulation conditions, sets the incident light conditions, medium environment, and periodic boundary conditions; establishes the dipole interaction matrix that satisfies the periodic boundary conditions, calculates the inverse matrix, and then calculates the polarization vector of the dipole point; The structural dynamic evolution module updates the inverse matrix based on the rank-one or low-rank inverse update method; The optical response calculation module calculates the optical response parameters of the nanoarray based on the updated polarization vector, including the absorption cross section, scattering cross section, extinction cross section, and local electromagnetic field enhancement.

8. An electronic device, characterized in that, include: One or more processors; A storage device for storing one or more programs that, when executed by one or more processors, cause the one or more processors to perform the method as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-6.

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