A VCSEL resonant cavity parameter prediction method and system for multimode suppression

Abstract

The present application relates to the technical field of optical device design, and particularly relates to a VCSEL resonant cavity parameter prediction method and system for multimode suppression. The method comprises the following steps: obtaining surface relief microstructure data of a VCSEL resonant cavity, and performing adaptive spatial discretization according to the surface relief microstructure data to obtain relief grid data; performing mixed boundary condition setting according to the relief grid data to obtain mixed boundary data; performing in-cavity simulation according to the relief grid data and the mixed boundary data to obtain in-cavity simulation data; performing multimode interference analysis on the in-cavity simulation data to obtain multimode interference data; performing quantitative coupling according to the surface relief microstructure data and the multimode interference data to obtain a relief coupling prediction model; obtaining experimental simulation data, and performing optimization iteration according to the relief coupling prediction model and the experimental simulation data to obtain a relief cavity parameter prediction model. The present application realizes simulation of in-cavity mode distribution and multimode interference, and improves single-mode output stability.

Description

Technical Field

[0001] This invention relates to the field of optical device design technology, and in particular to a method and system for predicting VCSEL resonator parameters for multimode suppression. Background Technology

[0002] Surface-emitting diode (VCSEL) lasers are widely used in high-speed optical communication and micro-optical systems due to their small size, low power consumption, and ease of array integration. However, VCSELs are prone to multimode oscillations within the cavity, leading to unstable output light fields, increased signal interference, and severe mode competition. Traditional methods rely mainly on empirical design or repeated experimental adjustments to control multimode interference, which has drawbacks such as long design cycles, high trial-and-error costs, and the inability to accurately quantify the local effects of the relief microstructure and the intracavity light field. Therefore, accurately predicting cavity mode outputs and guiding relief microstructure optimization during the design phase has become a significant challenge. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a method and system for predicting VCSEL resonator parameters for multimode suppression, thereby resolving at least one of the aforementioned technical issues.

[0004] This application provides a method for predicting VCSEL resonator parameters for multimode suppression, including the following steps: S1: Obtain the surface relief microstructure data of the VCSEL resonant cavity, and perform adaptive spatial discretization based on the surface relief microstructure data to obtain relief mesh data; S2: Set the blending boundary conditions based on the relief mesh data to obtain the blending boundary data; S3: Perform intracavity simulation based on relief mesh data and mixed boundary data to obtain intracavity simulation data; S4: Perform multimode interference analysis on the intracavity simulation data to obtain multimode interference data; S5: Quantitative coupling is performed based on surface relief microstructure data and multimode interference data to obtain a relief coupling prediction model; S6: Obtain experimental simulation data, and optimize and iterate based on the relief coupling prediction model and experimental simulation data to obtain the relief cavity parameter prediction model.

[0005] This invention achieves precise quantification of intracavity mode distribution and multimode interference effects by adaptive spatial discretization of the surface relief microstructure, setting hybrid boundary conditions, and performing full-wave simulation of the intracavity optical field. It can quantitatively couple the characteristics of the relief microstructure with the multimode interference results to form a relief coupling prediction model, and obtain high-precision cavity parameter prediction results through experimental data optimization and iteration. This allows for accurate prediction of cavity mode output and interference loss during the design phase, reducing trial-and-error costs and improving single-mode output stability and optical field uniformity. Simultaneously, it is sensitive to minute changes in the relief structure, enabling refined cavity parameter optimization. This provides reliable engineering guidance and quantifiable reference for high-performance VCSEL design, improving multimode suppression efficiency and optical device reliability.

[0006] Optionally, S1 specifically refers to: Obtain surface relief microstructure data of VCSEL resonant cavity; The relief geometric model is constructed based on the surface relief microstructure data to obtain the relief geometric model; Local geometric features are extracted from the relief geometric model to obtain local geometric feature data; Spatially discretize the surface relief microstructure data based on local geometric feature data to generate relief mesh data.

[0007] This invention acquires surface relief microstructure data of a VCSEL resonant cavity and constructs a relief geometric model. It then performs refined modeling and local feature extraction of the cavity microstructure, followed by adaptive spatial discretization to generate relief mesh data. This achieves high-resolution quantitative representation of the cavity microstructure. It accurately captures local features such as the height, curvature, and concavity / convexity distribution of the relief microstructure, providing a geometric basis. Through local geometric feature extraction and spatial discretization, the sensitivity of the relief mesh data to optical mode distribution and multimode interference is enhanced, facilitating accurate simulation of the local coupling effect of the microstructure on the optical field. This improves the VCSEL cavity mode prediction accuracy and multimode suppression effect.

[0008] Optionally, S2 specifically refers to: Optical attribute matrix is ​​constructed based on relief mesh data to obtain optical attribute data; Local feature data is obtained by extracting local features from the relief mesh data; Local feature data and optical property data are coupled to obtain hybrid boundary data.

[0009] This invention constructs an optical attribute matrix from relief mesh data and extracts local geometric features, finely coupling the geometric information of the microstructure with optical parameters to generate hybrid boundary data. This achieves high-precision characterization of intracavity optical boundary conditions. It accurately reflects the local influence of the relief microstructure on light field propagation, including refractive index changes, reflectivity distribution, and local energy transfer characteristics, providing reliable boundary input for intracavity light field simulation. Through the coupling of local features and optical attributes, the boundary conditions reflect both spatial anisotropy and optical continuity, thereby improving the accuracy of multimode interferometry analysis and mode prediction precision. This provides quantifiable technical basis for the design optimization and multimode suppression of VCSEL resonant cavities.

[0010] Optionally, S3 specifically refers to: Boundary conditions are set based on the relief mesh data and the mixed boundary data to obtain boundary setting data; The cavity excitation source is set according to the boundary setting data to obtain the initial state data of the optical field; Full-wavelength optical field simulation was performed based on the initial state data of the optical field to obtain intracavity simulation data.

[0011] This invention utilizes relief mesh data and hybrid boundary data to precisely define the intracavity boundary conditions, and on this basis, initializes the intracavity excitation source, performs full-wavelength optical field simulation, and generates intracavity simulation data, achieving high-precision simulation of the intracavity optical field. It accurately reflects the influence of relief microstructures and local optical boundaries on light wave propagation, ensuring a high degree of consistency between the initial state of the optical field and the actual cavity conditions. Full-wavelength optical field simulation can capture inter-mode interference, wavefront distortion, and local energy distribution characteristics, providing reliable data support for subsequent mode extraction and multimode interferometry analysis. Through this process, the intracavity optical field response and multimode behavior can be predicted during the design phase, effectively reducing trial-and-error costs and improving single-mode output stability and optical performance.

[0012] Optionally, S4 specifically refers to: The mode electromagnetic field is extracted from the intracavity simulation data to obtain the mode electromagnetic field data; Intermode interference analysis is performed based on the mode electromagnetic field data to obtain mode interference data; Multimode interferometry analysis is performed based on the modal interferometry data to obtain multimode interferometry data.

[0013] This invention extracts the electromagnetic fields of different modes from intracavity simulation data and then performs intermode interference analysis and multimode interference analysis to achieve a systematic quantification of the optical field distribution and mode coupling behavior within the VCSEL resonant cavity. It accurately captures the amplitude, phase, and spatial distribution characteristics of each mode, quantifies the mutual interference and energy transfer laws between modes, and reveals mode competition, interference enhancement and attenuation regions, and wavefront distortion characteristics, providing high-precision data for evaluating intracavity optical performance. This layered analysis allows for the identification of potential multimode interference problems during the design phase, improving single-mode output stability and interference controllability. Simultaneously, it provides reliable and quantifiable technical basis for optimizing relief microstructures and adjusting cavity parameters, thereby enhancing the multimode suppression efficiency and optical field uniformity of the VCSEL cavity.

[0014] Optionally, intermodal interferometry specifically includes: Extract mode amplitude data, mode phase data, and spatial characteristic data from the mode electromagnetic field data; Paired calculations are performed on the mode amplitude data and mode phase data to obtain paired data; Local interferometric analysis is performed on spatial feature data to obtain local interferometric data; By integrating local interferometric data and paired data, mode interferometric data is obtained.

[0015] This invention extracts amplitude, phase, and spatial features from mode electromagnetic field data, and combines this with paired amplitude and phase calculations and local interferometry analysis to achieve precise quantification of the interference behavior of each mode within the cavity. It can accurately capture the local interference effects of each mode in its spatial distribution, quantify the interactions and energy transfer patterns between modes, and thus reveal the local enhancement and attenuation regions of multimode interference within the cavity. By integrating local interference data with paired calculation results to form mode interference data, it provides high-precision input for multimode interference analysis and relief coupling prediction. This improves the spatial resolution and pattern recognition accuracy of interference analysis, helps optimize the structural design of the VCSEL resonant cavity, and enhances single-mode output stability and multimode suppression efficiency.

[0016] Optionally, intermodal interferometry specifically includes: Effective interference pattern pairs are selected from the pattern interference data to obtain effective interference pair data. Based on the effective interferometric data, the corresponding mode field distribution is extracted from the mode electromagnetic field data to obtain the mode data to be superimposed; Modal phase correlation and spatial overlap integral are performed on the superimposed modal data to obtain the first modal interferometric data and the second modal interferometric data, respectively; Multimode interferometric data is obtained by superimposing the light fields of the modes to be superimposed using the first and second mode interferometric data.

[0017] This invention first filters effective interference mode pairs from the modal interferometric data, excluding mode combinations with weak or non-critical interference contributions. Then, it extracts the mode data to be superimposed from the corresponding mode electromagnetic field data. This reduces the redundancy of full-mode calculations and improves the specificity of subsequent interferometric analysis. By calculating modal phase correlation and spatial overlap integration for the mode data to be superimposed, the interference relationship between modes can be quantified from two dimensions: phase consistency and spatial coupling strength, avoiding judgment bias caused by relying solely on a single energy index. Combining the first and second modal interferometric data for full-mode optical field superposition can more accurately reflect the characteristics of intracavity multimode competition, local enhancement, destructive loss, and energy transfer, providing high-quality input for the relief coupling prediction model, thereby improving the accuracy and engineering usability of VCSEL multimode suppression analysis.

[0018] Optionally, the modal phase correlation calculation is specifically as follows: Phase gradient data is obtained by extracting the phase gradient from the modal data to be superimposed. Phase jump analysis is performed based on the phase gradient data to obtain phase jump data; Electromagnetic field subdomains are identified based on phase transition data to obtain electromagnetic field subdomain data; Based on the phase jump data and electromagnetic field subdomain data, overlapping interference mapping is performed to obtain self-coherent destructive loss data. The modal loss discrimination rate is calculated based on the self-coherent destructive loss data to obtain the first mode interference data.

[0019] This invention utilizes phase gradient extraction and phase jump analysis on the modal data to be superimposed to identify phase abrupt change regions within the cavity caused by relief microstructures, local scattering, or wavefront distortion. By dividing the electromagnetic field subdomains based on the phase jump data, interferometric analysis moves beyond global averaging and can pinpoint phase mismatches and local destructive phenomena within specific spatial regions. Self-coherent destructive loss data is generated through overlapping interferometric mapping, quantifying the degree of energy cancellation caused by phase reversal or mismatch in different modes within the overlapping region. Furthermore, the modal loss discrimination rate is used to calculate the first-mode interferometric data, providing more accurate loss weights and interference judgment criteria for subsequent full-mode optical field superposition, thereby improving the accuracy of multimode interferometric analysis and the reliability of VCSEL multimode suppression design.

[0020] Optionally, S5 specifically refers to: Geometric feature extraction is performed on the surface relief microstructure data to obtain geometric feature data; Feature extraction is performed on multimode interferometric data to obtain interferometric feature data; Relief pattern data is obtained by coupling the geometric feature data and the interference feature data; A neural network is trained based on the relief pattern data to obtain a relief coupling prediction model.

[0021] This invention extracts geometric features from surface relief microstructure data and combines this with multimode interferometry data for interference feature extraction, achieving relief mode coupling. A relief coupling prediction model is then generated through neural network training, constructing a quantitative mapping relationship between the relief microstructure and the intracavity optical modes. This allows for precise correlation between the geometric characteristics of the relief microstructure and the intracavity multimode interferometry effect, forming a mathematical model that can be used to predict mode output behavior under different relief designs. Through neural network training, high-precision fitting of complex nonlinear coupling relationships is achieved, improving the accuracy of mode interference and loss prediction, and enhancing single-mode output stability and overall optical performance.

[0022] Optionally, this application also provides a VCSEL resonator parameter prediction system for multimode suppression, used to perform the VCSEL resonator parameter prediction method for multimode suppression as described above. The VCSEL resonator parameter prediction system for multimode suppression includes: The relief data meshing module is used to acquire the surface relief microstructure data of the VCSEL resonant cavity, and to perform adaptive spatial discretization based on the surface relief microstructure data to obtain relief mesh data. The mixed boundary condition setting module is used to set mixed boundary conditions based on the relief mesh data to obtain mixed boundary data. The intracavity light field simulation module is used to perform intracavity simulation based on relief mesh data and mixed boundary data to obtain intracavity simulation data. The multimode interference analysis module is used to perform multimode interference analysis on intracavity simulation data to obtain multimode interference data. The relief-mode quantitative coupling module is used to perform quantitative coupling based on surface relief microstructure data and multimode interference data to obtain a relief coupling prediction model. The prediction model generation module is used to acquire experimental simulation data and perform optimization iterations based on the relief coupling prediction model and experimental simulation data to obtain the relief cavity parameter prediction model.

[0023] This invention provides a method for predicting VCSEL resonant cavity parameters for multimode suppression. It generates relief mesh data by adaptively spatial discretizing surface relief microstructure data and sets refined hybrid boundary conditions to provide accurate input for intracavity optical field simulation. After obtaining intracavity simulation data through full-wave optical field simulation, mode electromagnetic fields are extracted and multimode interference analysis is performed to quantify the interaction of mode amplitude, phase, and energy distribution. The relief microstructure features and multimode interference features are quantitatively coupled, and a relief coupling prediction model is generated through neural network training to achieve accurate mapping between the microstructure and mode output. Iterative optimization based on experimental simulation data yields a high-precision relief cavity parameter prediction model. This invention can accurately predict intracavity mode distribution and multimode interference behavior during the design phase, effectively quantify self-coherence loss and local interference effects, and achieve fine control over single-mode output stability and optical field uniformity. Simultaneously, it provides quantifiable and engineering-grade technical basis for relief microstructure optimization, cavity parameter adjustment, and multimode suppression, reducing experimental trial-and-error costs and improving the overall performance and reliability of VCSEL devices. Attached Figure Description

[0024] Other features, objects, and advantages of this application will become more apparent from the following detailed description of the non-limiting embodiments, taken with reference to the accompanying drawings: Figure 1 A flowchart illustrating the steps of a VCSEL resonator parameter prediction method for multimode suppression according to one embodiment is shown. Figure 2 A flowchart illustrating the steps of an adaptive spatial discretization method according to one embodiment is shown. Figure 3 A flowchart illustrating the steps of a hybrid boundary condition setting method according to an embodiment is shown. Figure 4 A flowchart illustrating the steps of an intracavitary simulation method according to one embodiment is shown. Figure 5 A flowchart illustrating the steps of a multimode interferometry analysis method according to one embodiment is shown. Figure 6 A flowchart illustrating the steps of a relief coupling prediction model construction method according to an embodiment is shown. Detailed Implementation

[0025] The technical method of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0026] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. Functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor methods and / or microcontroller methods.

[0027] It should be understood that although the terms "first," "second," etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are used merely to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0028] Using a VCSEL resonator with an operating wavelength of 940 nm as an example, the VCSEL resonator employs a GaAs / AlGaAs material system, with a preset equivalent refractive index of 3.4 and an effective aperture diameter of 8 μm. The system acquires surface relief microstructure data for this VCSEL resonator, including the surface height matrix, relief region boundaries, relief depth, periodic dimension or equivalent relief feature spacing, and the effective aperture range of the cavity surface. The initial relief depth is 40 nm, and the periodic dimension or equivalent relief feature spacing is 1.0 μm.

[0029] The system identifies relief boundary regions and regions with abrupt height changes based on the surface height matrix, and performs adaptive spatial discretization on the surface relief microstructure data. In the neighborhood of the relief boundary and regions with large height change rates, the system uses a first discretization step size of 0.03 μm for local refinement; in regions with gentler height changes, the system uses a second discretization step size of 0.10 μm for conventional discretization, generating relief mesh data containing approximately 7800 mesh nodes. Compared to a standard mesh that uniformly uses a 0.10 μm discretization step size, the node density in the relief boundary region is increased by approximately 3 times, allowing for more refined preservation of local phase perturbations at the relief edges.

[0030] The system sets hybrid boundary conditions based on the relief mesh data, designating the relief boundary region as a continuous surface boundary, the outer edge of the effective aperture of the cavity surface as a lateral truncation boundary, and the corresponding periodic region as a periodic boundary, thus obtaining hybrid boundary data. The system uses a normalized value of 1 for the initial light field amplitude and a certain iterative convergence threshold. Under certain conditions, intracavity optical field simulation was performed to obtain intracavity complex optical field distribution, node phase distribution, node light intensity distribution and boundary response data.

[0031] Under unoptimized initial relief parameters, intracavity simulation data shows the existence of three distinct mode candidate regions within the resonant cavity. The normalized peak intensity of the fundamental mode is 1.00, while the normalized peak intensities of the two higher-order modes are 0.46 and 0.38, respectively. The mode phase differences between the fundamental mode and the two higher-order modes are approximately... and This indicates that there is still significant competition for higher-order modes within the cavity. The system performs multimode interferometry analysis on the cavity simulation data, filters effective interferometric mode pairs based on nodal light intensity, mode representative phase, mode spatial adjacency relationship, and boundary response data, and performs phase gradient extraction, phase jump analysis, and electromagnetic field subdomain identification on the modes to be superimposed.

[0032] Analysis results show that both higher-order modes exhibit phase-jump regions near the aperture edge, with these regions spatially adjacent to the lateral cutoff boundary response regions. The system identifies self-coherent destructive regions based on the phase relationship between adjacent electromagnetic field subdomains and calculates the modal loss discrimination rate according to the ratio of the number of nodes in the destructive interference regions to the total number of nodes in the corresponding modes. Initially, the modal loss discrimination rate for the higher-order modes is approximately 18%, indicating some destructive loss in the higher-order modes, but multimode competition is not yet sufficiently weakened.

[0033] The system then establishes a quantitative coupling relationship between relief depth, period size or equivalent relief feature spacing, relief height difference, and boundary response data, and mode phase difference, peak light intensity, spatial overlap, and modal loss discrimination rate, generating a relief coupling prediction model. After optimizing and iterating the relief coupling prediction model based on experimental simulation data, the system outputs candidate relief parameters, where the relief depth is corrected from 40nm to 48nm, and the period size or equivalent relief feature spacing is corrected from 1.0μm to 0.92μm.

[0034] Intracavity simulations were performed again under the corrected candidate relief parameters. The results showed that the normalized peak intensity of the fundamental mode remained above 0.96, while the normalized peak intensities of the two higher-order modes decreased to 0.21 and 0.17, respectively, with an average reduction of approximately 54% in the relative peak intensity of the higher-order modes. Simultaneously, the modal loss discrimination rate, calculated based on the number of nodes in the destructive interference region and the total number of nodes in the corresponding mode, increased from 18% to 31%. These results indicate that the corrected relief parameters can enhance the destructive loss of higher-order modes in the local phase mismatch region while maintaining the stability of the fundamental mode output.

[0035] Therefore, the method described in this embodiment enables the system to predict the impact of different relief depths, periodic dimensions, or equivalent relief feature spacings on the intracavity mode distribution, multimode interference, and higher-order mode losses during the VCSEL resonant cavity design stage, thereby outputting relief cavity parameters that are more conducive to multimode suppression. This method can reduce the number of trial runs, improve the stability of VCSEL single-mode output and the uniformity of the intracavity optical field, and provide quantifiable design basis for optimizing the surface relief microstructure.

[0036] Please see Figures 1 to 6 This application provides a method for predicting VCSEL resonator parameters for multimode suppression, including the following steps: S1: Obtain the surface relief microstructure data of the VCSEL resonant cavity, and perform adaptive spatial discretization based on the surface relief microstructure data to obtain relief mesh data; In one embodiment, the surface relief microstructure data includes the VCSEL resonant cavity surface height matrix H(x,y), relief region boundary B, relief depth d, periodic dimension p, and effective aperture range A of the cavity surface. The system first maps H(x,y) to the cavity surface coordinate system and calculates the height change rate between adjacent sampling points. , The height difference between adjacent sampling points The horizontal sampling interval, The vertical sampling interval is defined. The system extracts the relief boundary contour line based on the relief region boundary B, and searches for the shortest distance between adjacent boundary points along the normal direction of the boundary contour line, obtaining multiple local boundary widths. The minimum value among these is then taken as the minimum feature width of the relief boundary. This is based on the relief depth d, period size p, and the minimum feature width of the relief boundary. and the preset height variation threshold for surface sampling spacing (e.g., 0.08), first step length Second distance from walking length The first one is a long walk Set to no greater than / 5 and not greater than p / 20; second distance from the walk length Set to no greater than p / 8, preferably p / 10, such that the first distance step length ensures at least 5 grid nodes are arranged within a minimum relief boundary width, and is no greater than 1 / 20 of the period size. For example, when , hour, The preferred thickness is between 0.02 μm and 0.04 μm. When Or when the sampling point is located within the neighborhood of boundary B, use Perform local refinement; use other flat areas. Discretization is performed. Then, mesh nodes are generated according to the effective aperture range A of the cavity surface, and the node height is assigned the corresponding H(x,y) value to form a three-dimensional node. Then, based on the node adjacency relationship, mesh cells and boundary markers are generated, such as in a system with three-dimensional nodes. Based on this, mesh elements are generated according to the row and column adjacency relationships of nodes in the cavity surface coordinate system. For any grid cell The system reads the set of nodes it contains. ,in , Let j be the set of nodes of the j-th grid cell. Let j be the first node of the j-th grid cell. For the second node of the j-th grid cell, For the third node of the j-th grid cell, For the fourth node of the j-th grid cell, For the k-th node of the j-th grid cell, Let x be the horizontal coordinate of the k-th node in the j-th grid cell. Let be the vertical coordinate of the k-th node in the j-th grid cell. Let be the relief height value of the k-th node in the j-th mesh cell. If the mesh cell... If at least one node is located within the preset boundary neighborhood of the relief region boundary B, then the mesh cell is marked as a relief boundary cell and assigned a relief boundary identifier. If the grid cell If the node is located at the outer edge of the effective aperture range A of the cavity surface, then an outer edge identifier for the aperture is assigned. If the grid cell If a node is located at the relative boundary position corresponding to the period size p, then a period boundary identifier is assigned. The remaining grid cells located inside the cavity surface and not in contact with the relief boundary are assigned internal area identifiers. The system will use grid cells. Node set With corresponding boundary markers Binding is performed to form embossed mesh data with boundary attributes, where This is the boundary identifier for the j-th mesh cell, used to characterize the boundary properties of this mesh cell in the relief mesh; Indicates an internal region unit. Indicates the relief boundary unit, Indicates the outer edge unit of the effective aperture of the cavity surface. This represents a periodic boundary element.

[0037] S2: Set the blending boundary conditions based on the relief mesh data to obtain the blending boundary data; In one embodiment, the relief mesh data includes mesh nodes. Grid cells Local distance from walking length and embossed boundary markers The system uses the relief boundary markers. Classify the boundaries of the mesh cells: when When characterizing the relief surface, it is set as a continuous surface boundary; when When characterizing the outer edge of the effective aperture of the cavity surface, it is set as a lateral cutoff boundary; when the coordinates of the relative boundary nodes satisfy... or At that time, the boundary is set as the periodic boundary. The system calculates the boundary normal vector based on adjacent grid cells. , Let be the position vector of the first node of the j-th boundary grid cell. Let be the position vector of the second node of the j-th boundary grid cell. Given the position vector of the third node of the j-th boundary mesh element, the boundary type (including continuous surface boundary, lateral truncation boundary and periodic boundary), the boundary node set, the boundary element set (mesh elements corresponding to the boundary type), the normal vector and the corresponding discrete step size are encapsulated to obtain the hybrid boundary data.

[0038] S3: Perform intracavity simulation based on relief mesh data and mixed boundary data to obtain intracavity simulation data; In one embodiment, the system reads the grid nodes from the relief grid data. Grid cells Local distance from walking length and boundary attribute identifier It also reads the boundary type, boundary node set, boundary cell set, and normal vector from the mixed boundary data. The system solves for the intracavity optical field under preset resonant cavity simulation parameters, including the VCSEL operating wavelength. Equivalent refractive index of resonant cavity and iterative convergence threshold The system maps each mesh node to a discrete computation node within the cavity, and determines the node's relief height accordingly. Calculate the local phase correction: ,in Let be the local phase correction amount for the i-th grid node. This is the constant term for pi. Then, based on the grid cells... The node adjacency relationship is used to construct the node light field propagation relationship, and according to... , , Surface continuity boundary conditions, lateral truncation boundary conditions, and periodic boundary conditions are applied respectively. The system iteratively solves for the optical field values ​​at each node. When the change in the nodal light field between two adjacent iterations satisfies ( Let be the intracavity optical field value of the i-th grid node at the (t+1)-th iteration. The calculation stops when the value of the intracavity optical field of the i-th grid node at the t-th iteration is obtained, and the result is calculated according to... Obtain the node phase value ,like ,in Let be the intracavity complex optical field value of the i-th grid node. Let be the real part of the light field at this node. Let j be the imaginary part of the nodal optical field, and j be the imaginary unit. The nodal phase value can be obtained from the argument of the complex optical field: ,in Let i be the node phase value of the i-th grid node. This represents the complex argument extraction operation. This indicates that the phase angle and nodal intensity value are determined based on the imaginary and real parts of the complex optical field. .

[0039] After applying boundary conditions, the system extracts the response from the set of boundary nodes in the mixed boundary data. For boundary nodes corresponding to continuous surface boundary conditions, the system reads the light field values ​​of that boundary node and its adjacent internal nodes, and calculates the continuous deviation of the boundary light field. ,in Let be the continuous response deviation of the i-th surface boundary node. Let be the light field value of the i-th boundary node. This refers to the optical field value of the internal nodes adjacent to this boundary node. For boundary nodes corresponding to lateral truncation boundary conditions, the system uses the optical field value of the boundary node. and normal vector Extract the change in the optical field along the outer normal of the boundary to obtain the attenuation response of the truncated boundary. For boundary nodes corresponding to periodic boundary conditions, the system reads the corresponding periodic node. and The light field value is used to calculate the periodic matching deviation. ,in For periodic boundary response deviation, This represents the nodal optical field value that has a periodic correspondence with the i-th boundary node. The system encapsulates the continuous response deviation, truncated boundary attenuation response, periodic matching response deviation, and corresponding boundary node number to obtain boundary response data. The system also encapsulates the nodal optical field value, nodal phase value, nodal light intensity value, and boundary response data to obtain intracavity simulation data.

[0040] S4: Perform multimode interference analysis on the intracavity simulation data to obtain multimode interference data; In one embodiment, the system reads the node coordinates bound to the mesh node number from the intracavity simulation data. Intracavity complex optical field value Node phase value Node light intensity value and boundary response data. The system uses the maximum node light intensity. Based on the benchmark, select those that satisfy Furthermore, the set of nodes connected to local peak nodes (nodes whose light intensity value is not less than the light intensity values ​​of all their neighboring nodes in the set of neighboring nodes are considered local peak nodes) is merged into the mode candidate region. For any pattern candidate region Select the node with the highest light intensity. The peak light intensity was obtained: and the phase of that node As a phase representing the pattern The system calculates the phase difference between candidate regions of different modes: , Let m be the phase difference between the m-th and n-th mode candidate regions. The mode representative phase of the m-th mode candidate region, Let n be the mode representative phase of the nth mode candidate region. If two mode candidate regions are spatially adjacent and satisfy the following conditions: or , If the term represents the constant value of pi, it is recorded as a multimode interference pair. The system determines the mode candidate region. The spatial adjacency relationship between the middle node and the boundary node set is determined by extracting the boundary response data corresponding to the mode candidate region from the boundary response data in the intracavity simulation data to obtain associated boundary response data. The system encapsulates the mode candidate region, peak light intensity, mode representative phase, phase difference between modes, multimode interference pairs, and associated boundary response data to obtain multimode interference data.

[0041] S5: Quantitative coupling is performed based on surface relief microstructure data and multimode interference data to obtain a relief coupling prediction model; In one embodiment, the system reads the surface height matrix H(x,y), relief depth d, periodic dimension p, relief region boundary B, and effective aperture range A of the cavity surface from the surface relief microstructure data, and reads the mode candidate region from the multimode interferometry data. Peak light intensity The pattern represents the phase. Inter-mode phase difference Multimode interferometric pairs and associated boundary response data. For any multimode interferometric pair... The system extracts the corresponding relief height value from the surface height matrix H(x,y) based on the node coordinates within the pattern candidate area, thus obtaining... and ,in This represents the relief height characteristic value corresponding to the m-th pattern candidate region. This represents the relief height characteristic value corresponding to the nth pattern candidate area. The system combines the relief depth d, period size p, and relief height characteristic value. , Peak light intensity The pattern represents the phase. Inter-mode phase difference Establish a correspondence between the associated boundary response data and form a relief-interference coupling sample. The system generates a relief coupling prediction model based on the variation relationships between relief height, period size, mode phase difference, peak light intensity, and boundary response in multiple relief-interference coupling samples.

[0042] The system generates a relief coupling prediction model based on multiple relief-interference coupling samples, specifically: using the relief depth d, period size p, and the relief height difference corresponding to the pattern candidate region. and associated boundary response data As a coupling input condition, with peak light intensity Mode phase difference and the multimode interferometry type is used as the coupling output result; if the m-th mode candidate region With the nth pattern candidate region Spatially adjacent and satisfying If the two are in-phase interference, then they are determined to be in-phase interference; if the following conditions are met... If the two signals meet the phase condition or are not spatially adjacent, they are determined to be an antiphase interference pair. If they do not meet the phase condition or are not spatially adjacent, they are not recorded as a valid multimode interference pair. The system classifies samples with the same or similar input conditions (similarity greater than 95%) into intervals and records the corresponding peak light intensity range, phase difference range, and interference type determination conditions within each interval, forming a mapping rule between relief parameters and multimode interference results. The mapping rule, sample number, and interference determination conditions are encapsulated to obtain the relief coupling prediction model.

[0043] S6: Obtain experimental simulation data, and optimize and iterate based on the relief coupling prediction model and experimental simulation data to obtain the relief cavity parameter prediction model.

[0044] In one embodiment, the experimental simulation data includes the measured or high-precision simulated relief depth. Periodic size High characterization value of the candidate region of the model Peak light intensity Mode phase difference and experimental boundary response data The system is based on: The height difference of the experimental relief was obtained, and Input the relief coupling prediction model to obtain the predicted peak light intensity. and predicted phase difference System calculations: , , The allowable deviation threshold for phase difference is set to 0.08. , The threshold value for the allowable deviation of peak light intensity is 8% multiplied by ( + ),when or At that time, the system corrects the relief depth range, period size range, relief height difference range, peak light intensity range, and phase difference range in the relief coupling prediction model based on experimental simulation data; when at least 3 consecutive iterations satisfy and When the iteration stops, the corrected parameter range, prediction output range, and interference type prediction rules are encapsulated to obtain the relief cavity parameter prediction model.

[0045] In one embodiment, if the relief coupling prediction model is constructed using a neural network, the system uses relief depth, period size, relief height difference corresponding to the pattern candidate area, and associated boundary response data as input parameters to the neural network, and peak light intensity, pattern phase difference, and multimode interference type as output parameters. After acquiring experimental simulation data, the system inputs the relief depth, period size, relief height difference, and experimental boundary response data from the experimental simulation data into the neural network to obtain the predicted peak light intensity, predicted pattern phase difference, and predicted multimode interference type. Simultaneously, it reads the corresponding experimental peak light intensity, experimental pattern phase difference, and experimental multimode interference type from the experimental simulation data and calculates the deviation between the prediction result and the experimental simulation result. When the deviation between the predicted pattern phase difference and the experimental pattern phase difference exceeds a preset allowable deviation threshold for phase difference, or when the deviation between the predicted peak light intensity and the experimental peak light intensity exceeds a preset allowable deviation threshold for light intensity, the system uses this set of experimental simulation data as a correction sample to reverse-correct the model parameters of the neural network, so that the updated neural network output gradually approaches the experimental simulation result. The allowable deviation threshold for phase difference is set to... to The allowable deviation threshold for light intensity can be set to 5% to 10% of the experimental peak light intensity. The system recalculates the prediction deviation after each iteration. When the phase difference deviation and peak light intensity deviation requirements are met for 3 to 5 consecutive iterations, the optimization iteration is considered to have reached a stable state. If the continuous convergence condition is not met after 20 to 50 iterations, the currently corrected model parameters are output. The system encapsulates the optimized neural network structure, model parameters, input parameter range, peak light intensity prediction range, mode phase difference prediction range, and multimode interference type prediction rules to obtain the relief cavity parameter prediction model. In this process, the neural network input parameters come from the relief coupling prediction model and experimental simulation data, the output parameters come from multimode interference data and experimental simulation results, and the prediction deviation is calculated from the predicted value and the experimental value.

[0046] Optionally, S1 specifically refers to: S11: Obtain surface relief microstructure data of the VCSEL resonant cavity; In one embodiment, the system acquires the height matrix H(x,y) of the VCSEL resonant cavity surface, the boundary of the relief region B, the relief depth d, the period size p, the effective aperture range A of the cavity surface, and the surface sampling interval. The above data is then mapped to the cavity surface coordinate system to obtain surface relief microstructure data.

[0047] S12: Construct the relief geometric model based on the surface relief microstructure data to obtain the relief geometric model; In one embodiment, the system generates a surface height surface based on the height matrix H(x,y), defines the effective relief area by the relief area boundary B, defines the modeling range by the effective aperture range A of the cavity surface, and calibrates the position of the periodic structure by combining the relief depth d and the periodic dimension p to obtain the relief geometric model.

[0048] S13: Extract local geometric features from the relief geometric model to obtain local geometric feature data; In one embodiment, the system calculates the rate of change of height between adjacent sampling points in the relief geometry model. , The height difference between adjacent sampling points The horizontal sampling interval, This represents the vertical sampling interval. For any grid node... The system calculates the shortest distance from the node to the boundary B of the relief area. .like If the node is located within the neighborhood of the relief region boundary B, then it is determined that the node is within the neighborhood of the relief region boundary B. The radius of the preset boundary neighborhood is set as the first step size. Up to 2 Subsequently, the system marks the mesh cells containing this node as relief boundary neighborhood cells. For the outer edge region of the aperture, the system determines whether the node is close to the effective aperture boundary based on the effective aperture range A of the cavity surface. If the node... Distance to the outer edge of the effective aperture range A of the cavity surface If so, the node is determined to be located in the outer edge neighborhood of the aperture, where Set as the second distance from the walk length Alternatively, the width of a single mesh cell can be used. The system marks the mesh cell containing this node as an aperture outer edge cell. Based on the above identification results, the system generates local geometric feature data: if the mesh cell contains a node located in the B neighborhood of the relief region boundary, it is assigned a relief boundary neighborhood identifier; if it contains a node located in the aperture outer edge neighborhood, it is assigned an aperture outer edge identifier; if it contains a node whose height change rate exceeds a threshold (e.g., 0.08), it is assigned a height abrupt change identifier. After the above identifiers are bound to the corresponding mesh node, mesh cell, and local height change rate, the local geometric feature data is obtained.

[0049] S14: Spatially discretize the surface relief microstructure data based on local geometric feature data to generate relief mesh data.

[0050] In one embodiment, the system sets the discrete step size based on local geometric feature data; when Or, if a node is located in the B-neighborhood of the boundary, the first distance step size is used. The remaining areas adopted the second distance walking length The first one is a long walk Set to no greater than p / 20; second distance from the walk length Set the value to no greater than p / 8, preferably p / 10, and generate mesh nodes, mesh cells, and boundary attribute identifiers. This yields the relief mesh data.

[0051] If grid cells If at least one node is located within the preset boundary neighborhood of the relief region boundary B, then the mesh cell is marked as a relief boundary cell and assigned a relief boundary identifier. If the grid cell If the node is located at the outer edge of the effective aperture range A of the cavity surface, then an outer edge identifier for the aperture is assigned. If the grid cell If a node is located at the relative boundary position corresponding to the period size p, then a period boundary identifier is assigned. The remaining grid cells located inside the cavity surface and not in contact with the relief boundary are assigned internal area identifiers. .

[0052] Optionally, S2 specifically refers to: S21: Construct an optical attribute matrix based on the relief mesh data to obtain optical attribute data; In one embodiment, the system reads the grid nodes from the relief grid data. ( Let be the horizontal coordinate of the i-th node. Let be the vertical coordinate of the i-th node. (representing the relief height of the i-th node) and mesh cells and boundary attribute identifier And call the preset equivalent refractive index of the resonant cavity. Generate node optical attribute data Optical property data were obtained. The equivalent refractive index of the resonant cavity. The material structure of the VCSEL resonator is predetermined. For example, when the VCSEL resonator uses a GaAs / AlGaAs material system, the refractive index of the active region and adjacent confinement layer within the cavity is in the range of approximately 3.2 to 3.6. The system will then set the equivalent refractive index of the resonator. The default setting is 3.4. If the VCSEL resonator uses a different material system or a different epitaxial layer structure, the system can be reset according to the corresponding material parameter table or device design file. .

[0053] S22: Extract local features from the relief mesh data to obtain local feature data; In one embodiment, the system reads grid cells. Node set Calculate the local height difference based on the node height. And calculate the boundary normal vector based on the node coordinates. Identify relief boundaries by combining boundary attribute identifiers. Local feature data are obtained by analyzing the outer edge of the aperture and the periodic boundary.

[0054] S23: Couple the local feature data and optical property data to obtain mixed boundary data.

[0055] In one embodiment, the system combines the boundary type, boundary node set, boundary cell set, and normal vector from the local feature data. , with node height in optical property data Equivalent refractive index and boundary attribute identifier Bind; when When the values ​​are 1, 2, and 3, respectively, the surface continuous boundary, the lateral truncation boundary, and the periodic boundary are set to obtain the mixed boundary data.

[0056] Optionally, S3 specifically refers to: S31: Set boundary conditions based on relief mesh data and mixed boundary data to obtain boundary setting data; In one embodiment, the system reads the grid nodes from the relief grid data. Grid cells Boundary attribute identifier The effective aperture range A of the cavity surface is determined, and the boundary type, boundary node set, and normal vector in the mixed boundary data are read. The system will =1, 2, and 3 are set as surface continuous boundary, lateral truncation boundary, and periodic boundary, respectively, to obtain boundary setting data.

[0057] S32: Set the intracavity excitation source according to the boundary setting data to obtain the initial state data of the optical field; In one embodiment, the system is based on the VCSEL operating wavelength. Preset resonant cavity equivalent refractive index and initial light field amplitude Take the normalized value of 1, where The design parameters of the VCSEL resonant cavity to be simulated are preset, for example, set to 850nm, 940nm, or 980nm. An intracavity excitation source is set within the effective aperture range A of the cavity surface, and the excitation source is determined according to the node relief height. Calculate the local phase correction amount The initial complex light field of each grid node is assigned the value. j is the imaginary unit. This is the local phase correction for the i-th grid node, thus obtaining the initial state data of the optical field.

[0058] S33: Perform full-wavelength optical field simulation based on the initial state data of the optical field to obtain intracavity simulation data.

[0059] In one embodiment, the system uses initial state data of the light field. Using the initial input, the light field of each grid node is iteratively solved according to the boundary set data to obtain the node complex light field value. When two consecutive iterations satisfy ( The calculation stops when the iterative convergence threshold is reached (taking a value of 10 to the power of -4), and then... Extracting node phase values and node light intensity value After applying boundary conditions, the system extracts the response from the set of boundary nodes in the mixed boundary data. For boundary nodes corresponding to continuous surface boundary conditions, the system reads the light field values ​​of that boundary node and its adjacent internal nodes, and calculates the continuous deviation of the boundary light field: ,in Let be the continuous response deviation of the i-th surface boundary node. Let be the light field value of the i-th boundary node. This refers to the optical field value of the internal nodes adjacent to this boundary node. For boundary nodes corresponding to lateral truncation boundary conditions, the system uses the optical field value of the boundary node. and normal vector Extract the change in the optical field along the outer normal of the boundary to obtain the attenuation response of the truncated boundary. For boundary nodes corresponding to periodic boundary conditions, the system reads the corresponding periodic node. and The light field value is used to calculate the periodic matching deviation. ,in For periodic boundary response deviation, This represents the optical field value of the node that has a periodic correspondence with the i-th boundary node. The system encapsulates the continuous response deviation, the truncated boundary attenuation response, the periodic matching response deviation, and the corresponding boundary node number to obtain the boundary response data. This encapsulation yields the intracavity simulation data.

[0060] Optionally, S4 specifically refers to: S41: Extract the mode electromagnetic field from the intracavity simulation data to obtain the mode electromagnetic field data; In one embodiment, the system reads the grid node coordinates and complex optical field values ​​from the intracavity simulation data. Phase value and light intensity value And calculate the maximum light intensity of all nodes. The system determines the set of adjacent nodes based on node adjacency relationships. ,like Not less than the light intensity of each adjacent node and Then it is determined as a local peak node, and is used as As the light intensity threshold for pattern selection, it will satisfy Furthermore, grid nodes spatially connected to local peak nodes are identified as valid mode nodes, and these valid mode nodes are merged into mode candidate regions. The electromagnetic field data of the mode were obtained.

[0061] S42: Perform intermode interference analysis based on the mode electromagnetic field data to obtain mode interference data; In one embodiment, the system selects any pattern candidate region. Select the node with the highest light intensity. The peak light intensity was obtained. and the phase of that node As a phase representing the pattern The system identifies candidate regions for different modes. Calculate phase difference The resulting mode interferometric data includes mode candidate region numbers, mode candidate region node sets, peak light intensity, mode representative phase, inter-mode phase difference, mode spatial adjacency relationship, and candidate interference pair identifiers. Specifically, the mode candidate region number distinguishes different mode candidate regions; the mode candidate region node set represents the range of grid nodes corresponding to that mode; the peak light intensity characterizes the maximum light intensity within the mode candidate region; the mode representative phase characterizes the phase characteristics of the mode candidate region; the inter-mode phase difference characterizes the phase difference between two mode candidate regions; the mode spatial adjacency relationship characterizes whether two mode candidate regions are adjacent in the cavity surface space; and the candidate interference pair identifier records combinations of mode candidate regions that satisfy the spatial adjacency relationship.

[0062] S43: Perform multimode interferometry analysis based on the modal interferometry data to obtain multimode interferometry data.

[0063] In one embodiment, the system determines the pattern candidate region. Does a node adjacency relationship exist, or is the boundary distance not greater than the local distance step size? If satisfied Recorded as in-phase interference pairs; if the following conditions are met... The data is recorded as antiphase interference pairs. The system encapsulates the interference pairs, peak light intensity, mode representative phase, phase difference, and corresponding associated boundary response data to obtain multimode interferometric data. The system then determines the mode candidate region based on these parameters. The spatial adjacency relationship between the middle node and the boundary node set is determined by extracting the boundary response data corresponding to the candidate region of the mode from the boundary response data in the cavity simulation data to obtain the associated boundary response data.

[0064] Optionally, intermodal interferometry specifically includes: Extract mode amplitude data, mode phase data, and spatial characteristic data from the mode electromagnetic field data; In one embodiment, the system reads the candidate region of the mode. Complex optical field values ​​at each node Phase value Light intensity value and node coordinates, select The node with the highest internal light intensity is designated as the peak node. Extract mode amplitude ( Peak node (corresponding nodal complex field value), mode phase The model candidate region node set is used to obtain model amplitude data, model phase data, and spatial feature data.

[0065] Paired calculations are performed on the mode amplitude data and mode phase data to obtain paired data; In one embodiment, the system considers any two pattern candidate regions. Perform pairing and read the mode amplitude. and mode phase Calculate the phase difference And generate pattern pairing numbers to obtain pairing data.

[0066] Local interferometric analysis is performed on spatial feature data to obtain local interferometric data; In one embodiment, the system determines the pattern candidate region. Node coordinates, node adjacency relationships, and local distance walk lengths Determine the spatial adjacency status; if two candidate regions have adjacent nodes, or the boundary distance is not greater than 1, then... Then, local interference markers are generated. Otherwise generate This yields local interferometric data.

[0067] By integrating local interferometric data and paired data, mode interferometric data is obtained.

[0068] In one embodiment, the system will use the mode pairing number and mode amplitude from the pairing data. Mode phase Phase difference Spatial adjacency status and local interference markers in local interferometric data Binding, forming pattern interference data.

[0069] Optionally, multimodal interferometry specifically includes: Effective interference pattern pairs are selected from the pattern interference data to obtain effective interference pair data. In one embodiment, the system reads the mode pairing number and mode spatial adjacency identifier from the mode interferometry data. and phase difference Filter to meet and or The pattern pair yields effective interference data.

[0070] Based on the effective interferometric data, the corresponding mode field distribution is extracted from the mode electromagnetic field data to obtain the mode data to be superimposed; In one embodiment, the system numbers the pattern candidate regions in the data based on effective interference. Extracting the corresponding node complex optical field values ​​from the mode electromagnetic field data Node phase value and nodal light intensity value To form modal data to be superimposed .

[0071] Modal phase correlation and spatial overlap integral are performed on the superimposed modal data to obtain the first modal interferometric data and the second modal interferometric data, respectively; In one embodiment, the system determines the modal data to be superimposed based on the modal data. The phase difference is calculated by representing the phase. The first modal interferometric data is obtained; and based on the overlapping or adjacent regions of the two modalities... calculate , Let be the spatial overlap integral value between the m-th and n-th modes to be superimposed. For the mode field distribution of the m-th mode to be superimposed, For the mode field distribution of the nth mode to be superimposed, The region representing the overlap or adjacency analysis between the m-th mode and the n-th mode is determined by the node coordinates, node adjacency relationships, or boundary distances of the corresponding mode candidate regions. For spatial integral infinitesimal elements, The amplitude of the product of the two modal field distributions is used to obtain the second modal interferometric data.

[0072] Multimode interferometric data is obtained by superimposing the light fields of the modes to be superimposed based on the first and second mode interferometric data.

[0073] In one embodiment, the system reads the mode field distribution from the modal data to be superimposed. And read the modal phase difference in the first modal interferometry data. And the spatial overlap in the second modal interferometric data The system is based on Determine the coherent phase relationship between the modes to be superimposed, and based on... Determine the degree of spatial overlap between the modes to be superimposed; when the modes to be superimposed meet the preset phase correlation condition and the spatial overlap is... When the value is not zero, the system performs complex optical field superposition on the corresponding mode field distribution to obtain the superimposed optical field of all modes: , This represents the superimposed light field of all modes. Let M be the mode field distribution of the m-th mode to be superimposed, and M be the number of modes to be superimposed. The preset phase correlation conditions include in-phase phase correlation conditions and out-of-phase phase correlation conditions; when the phase difference between the modes to be superimposed... When, it is determined that the two modes to be superimposed satisfy the in-phase phase correlation condition; when When the two modes to be superimposed are satisfied, it is determined that they meet the anti-phase phase correlation condition; when neither condition is met, it is determined that the two modes to be superimposed do not meet the preset phase correlation condition. The system calculates the superposition intensity distribution: The multimode interferometric data is obtained by encapsulating the superimposed light field, superimposed intensity distribution, modal phase difference, spatial overlap, and corresponding effective interference pairs of all modes.

[0074] Optionally, the modal phase correlation calculation is specifically as follows: Phase gradient data is obtained by extracting the phase gradient from the modal data to be superimposed. In one embodiment, the system reads the mode field distribution from the modal data to be superimposed. Node phase and node coordinates Calculate the phase change rate between adjacent nodes: , Let be the phase gradient value of the i-th grid node. The phase difference between adjacent nodes in the horizontal direction. This refers to the horizontal node spacing. The phase difference between adjacent nodes in the longitudinal direction. The longitudinal node spacing is used to obtain the phase gradient data.

[0075] Phase jump analysis is performed based on the phase gradient data to obtain phase jump data; In one embodiment, the system determines whether the phase difference between adjacent nodes exceeds a preset transition threshold. ,like .like Then, node i and its adjacent node r are marked as a phase transition node pair, and phase transition data is obtained.

[0076] Electromagnetic field subdomains are identified based on phase transition data to obtain electromagnetic field subdomain data; In one embodiment, the system uses phase transition node pairs as dividing boundaries to divide the phase region in the modal data to be superimposed into multiple electromagnetic field subdomains. The data of electromagnetic field subdomains are obtained by recording the set of nodes, phase range and corresponding mode field distribution in each subdomain.

[0077] Based on the phase jump data and electromagnetic field subdomain data, overlapping interference mapping is performed to obtain self-coherent destructive loss data. In one embodiment, the system compares adjacent electromagnetic field subdomains. The phase difference between the two is close. (e.g., greater than or equal to 0.95) If the model field distributions at the subdomain boundary have spatial overlap, then this region is marked as a destructive interference region, and self-coherent destructive loss data is obtained.

[0078] The modal loss discrimination rate is calculated based on the self-coherent destructive loss data to obtain the first mode interference data.

[0079] In one embodiment, the system counts the number of nodes in the destructive interference region. The total number of nodes corresponding to the modes to be superimposed Calculate the modal loss discrimination rate: And the phase gradient, phase jump position, destructive interference region and It is encapsulated as first-mode interferometric data.

[0080] Optionally, S5 specifically refers to: S51: Extract geometric features from the surface relief microstructure data to obtain geometric feature data; In one embodiment, the system reads the surface height matrix H(x,y), relief depth d, periodic dimension p, relief region boundary B, and effective aperture range A of the cavity surface, and extracts the minimum feature width of the relief boundary based on B. The relative position of the period is determined based on the node coordinates and the period dimension p, thus obtaining the geometric feature data. Specifically, the minimum feature width of the relief boundary is extracted based on B. The system extracts the relief boundary outline based on the relief region boundary B, and searches for the shortest distance between adjacent boundary points along the normal direction of the boundary outline to obtain multiple local boundary widths. The minimum value among these is then taken as the minimum feature width of the relief boundary. The system determines the relative position of the period based on the node coordinates and the period size p by reading the coordinates of the i-th grid node. Given the period size p, calculate the remainders of the node's horizontal and vertical coordinates with respect to the period size p to obtain the relative position of the horizontal period. Relative position of longitudinal period And combine the two into the relative position of the node period. The relative position of the node period is used to characterize the relative distribution of mesh nodes within a single relief period cell.

[0081] S52: Extract features from multimode interferometric data to obtain interferometric feature data; In one embodiment, the system reads the effective interference pairs, the set of mode candidate region nodes, and the superimposed light field from the multimode interferometric data. Superposition strength Phase difference Spatial overlap and modal loss discrimination rate Interference characteristic data were obtained.

[0082] S53: Couple relief patterns based on geometric feature data and interference feature data to obtain relief pattern data; In one embodiment, the system extracts the corresponding relief height value from H(x,y) based on the coordinates of the corresponding pattern candidate region nodes of the effective interference pair, and combines it with the relief depth d, period size p, and boundary width. The relief pattern data is obtained by binding it with phase difference, superposition intensity, spatial overlap and modal loss discrimination rate.

[0083] S54: Train a neural network based on the relief pattern data to obtain a relief coupling prediction model.

[0084] In one embodiment, the system uses the relief depth, period size, relief height difference, period relative position, and boundary width from the relief pattern data as input to a neural network, and uses the phase difference, superposition intensity, spatial overlap, and modal loss discrimination rate from the interference feature data as output labels to train the neural network parameters Θ, thereby obtaining a relief coupling prediction model. The neural network includes an input layer, a geometric feature encoding layer, a relief-modal coupling layer, an interference response analysis layer, and an output layer connected in sequence. The input layer receives data on relief depth, period size, relief height difference, minimum feature width of the relief boundary, relative position of the period, and associated boundary response. The geometric feature encoding layer consists of two fully connected layers with 64 and 128 neurons respectively, used to extract the implicit representation of the relief geometry. The relief-modal coupling layer consists of two fully connected layers with 128 and 64 neurons respectively, used to establish the correspondence between relief geometric features and modal interference responses. The interference response analysis layer consists of a 32-neuron fully connected layer used to output the implicit features of the interference response. The output layer outputs the predicted mode phase difference, predicted superposition intensity, predicted spatial overlap, predicted modal loss discrimination rate, and predicted interference type. During training, the neural network parameters include the connection parameters and bias parameters of each layer, and the learning rate can be set to... to The batch sample size is set to 16 to 64, and the training rounds can be set to 100 to 300; when the prediction phase difference deviation is no greater than to If the predicted light intensity deviation is no greater than 5% to 10% of the experimental peak light intensity, the model training is deemed to meet the convergence requirements.

[0085] Optionally, this application also provides a VCSEL resonator parameter prediction system for multimode suppression, used to perform the VCSEL resonator parameter prediction method for multimode suppression as described above. The VCSEL resonator parameter prediction system for multimode suppression includes: The relief data meshing module is used to acquire the surface relief microstructure data of the VCSEL resonant cavity, and to perform adaptive spatial discretization based on the surface relief microstructure data to obtain relief mesh data. The mixed boundary condition setting module is used to set mixed boundary conditions based on the relief mesh data to obtain mixed boundary data. The intracavity light field simulation module is used to perform intracavity simulation based on relief mesh data and mixed boundary data to obtain intracavity simulation data. The multimode interference analysis module is used to perform multimode interference analysis on intracavity simulation data to obtain multimode interference data. The relief-mode quantitative coupling module is used to perform quantitative coupling based on surface relief microstructure data and multimode interference data to obtain a relief coupling prediction model. The prediction model generation module is used to acquire experimental simulation data and perform optimization iterations based on the relief coupling prediction model and experimental simulation data to obtain the relief cavity parameter prediction model.

[0086] Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended application documents rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of the equivalents of the application documents be incorporated into the invention.

[0087] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

Claims

1. A method for predicting VCSEL resonator parameters for multimode suppression, characterized in that, Includes the following steps: S1: Obtain the surface relief microstructure data of the VCSEL resonant cavity, and perform adaptive spatial discretization based on the surface relief microstructure data to obtain relief mesh data; S2: Construct an optical attribute matrix based on the relief mesh data to obtain optical attribute data; extract local features from the relief mesh data to obtain local feature data; couple the local feature data and the optical attribute data to obtain hybrid boundary data; S3: Perform intracavity simulation based on relief mesh data and mixed boundary data to obtain intracavity simulation data; S4: Perform multimode interference analysis on the intracavity simulation data to obtain multimode interference data; S5: Quantitative coupling is performed based on surface relief microstructure data and multimode interference data to obtain a relief coupling prediction model; S6: Obtain experimental simulation data, and optimize and iterate based on the relief coupling prediction model and experimental simulation data to obtain the relief cavity parameter prediction model.

2. The method according to claim 1, characterized in that, S1 specifically refers to: Obtain surface relief microstructure data of VCSEL resonant cavity; The relief geometric model is constructed based on the surface relief microstructure data to obtain the relief geometric model; Local geometric features are extracted from the relief geometric model to obtain local geometric feature data; Spatially discretize the surface relief microstructure data based on local geometric feature data to generate relief mesh data.

3. The method according to claim 1, characterized in that, S3 specifically refers to: Boundary conditions are set based on the relief mesh data and the mixed boundary data to obtain boundary setting data; The cavity excitation source is set according to the boundary setting data to obtain the initial state data of the optical field; Full-wavelength optical field simulation was performed based on the initial state data of the optical field to obtain intracavity simulation data.

4. The method according to claim 1, characterized in that, S4 specifically refers to: The mode electromagnetic field is extracted from the intracavity simulation data to obtain the mode electromagnetic field data; Intermode interference analysis is performed based on the mode electromagnetic field data to obtain mode interference data; Multimode interferometry analysis is performed based on the modal interferometry data to obtain multimode interferometry data.

5. The method according to claim 4, characterized in that, Intermodal interferometry specifically includes: Extract mode amplitude data, mode phase data, and spatial characteristic data from the mode electromagnetic field data; Paired calculations are performed on the mode amplitude data and mode phase data to obtain paired data; Local interferometric analysis is performed on spatial feature data to obtain local interferometric data; By integrating local interferometric data and paired data, mode interferometric data is obtained.

6. The method according to claim 4, characterized in that, Multimodal interferometry analysis specifically includes: Effective interference pattern pairs are selected from the pattern interference data to obtain effective interference pair data. Based on the effective interferometric data, the corresponding mode field distribution is extracted from the mode electromagnetic field data to obtain the mode data to be superimposed; Modal phase correlation and spatial overlap integral are performed on the superimposed modal data to obtain the first modal interferometric data and the second modal interferometric data, respectively; Multimode interferometric data is obtained by superimposing the light fields of the modes to be superimposed based on the first and second mode interferometric data.

7. The method according to claim 6, characterized in that, The modal phase correlation calculation is as follows: Phase gradient data is obtained by extracting the phase gradient from the modal data to be superimposed. Phase jump analysis is performed based on the phase gradient data to obtain phase jump data; Electromagnetic field subdomains are identified based on phase transition data to obtain electromagnetic field subdomain data; Based on the phase jump data and electromagnetic field subdomain data, overlapping interference mapping is performed to obtain self-coherent destructive loss data. The modal loss discrimination rate is calculated based on the self-coherent destructive loss data to obtain the first mode interference data.

8. The method according to claim 1, characterized in that, S5 specifically refers to: Geometric feature extraction is performed on the surface relief microstructure data to obtain geometric feature data; Feature extraction is performed on multimode interferometric data to obtain interferometric feature data; Relief pattern data is obtained by coupling geometric feature data and interference feature data; A neural network is trained based on the relief pattern data to obtain a relief coupling prediction model.

9. A VCSEL resonator parameter prediction system for multimode suppression, characterized in that, For performing the VCSEL resonator parameter prediction method for multimode suppression as described in claim 1, the VCSEL resonator parameter prediction system for multimode suppression includes: The relief data meshing module is used to acquire the surface relief microstructure data of the VCSEL resonant cavity, and to perform adaptive spatial discretization based on the surface relief microstructure data to obtain relief mesh data. The mixed boundary condition setting module is used to set mixed boundary conditions based on the relief mesh data to obtain mixed boundary data. The intracavity light field simulation module is used to perform intracavity simulation based on relief mesh data and mixed boundary data to obtain intracavity simulation data. The multimode interference analysis module is used to perform multimode interference analysis on intracavity simulation data to obtain multimode interference data. The relief-mode quantitative coupling module is used to perform quantitative coupling based on surface relief microstructure data and multimode interference data to obtain a relief coupling prediction model. The prediction model generation module is used to acquire experimental simulation data and perform optimization iterations based on the relief coupling prediction model and experimental simulation data to obtain the relief cavity parameter prediction model.

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