A cascaded low-loss bending waveguide design method based on vector synthesis and application thereof

Abstract

This invention discloses a cascaded low-loss bent waveguide design method based on vector synthesis. The steps are as follows: S1, the bent waveguide is regarded as a curve, and four control vectors are defined to describe the curve: the curve start point, the curve end point, a fixed distance point in the tangent direction of the curve start point, and a fixed distance point in the tangent direction of the curve end point, and the parameter vector of the curve is constructed; S2, based on the connection requirements and curvature smoothing characteristics of the bent waveguide to be designed, boundary condition constraint equations are established, and the algebraic relationship between the four control vectors is solved; S3, the structural parameters of the bent waveguide are defined, and the four control vectors are transformed into expressions related to the design parameters to be determined, namely the structural parameters and length; S4, following the order of length first and then structural parameters, with the goal of obtaining the minimum transmission loss, the unknowns in the design parameters to be determined are determined sequentially; this method has the characteristics of achieving ultra-low transmission loss and ultra-small structural size, which greatly simplifies the design process and reduces the difficulty.

Description

Technical Field

[0001] This invention relates to the fields of optical integration technology, such as optical communication, lidar, optical computing, and optical chips, and particularly to a design method and application of cascaded low-loss bent waveguides based on vector synthesis. Background Technology

[0002] In optical integration fields such as optical communication, lidar, optical computing, and optical chips, the cascading of multiple unit components is often involved. Cascading waveguides, as key components for optical signal transmission and functional implementation, play a crucial role in constructing complex optical communication systems and integrated optical devices. They enable the connection and collaborative operation of multiple optical functional modules, providing fundamental support for the expansion of optical communication networks and the diversification of optical signal processing.

[0003] Cascaded waveguides are essentially structures used to connect various optical modules to achieve optical signal transmission and processing. Their working principle is based on the transmission characteristics of light within a waveguide. By designing the waveguide's material properties, geometry, and coupling methods, they guide optical signals accurately from one optical module to another, performing processing such as transmission, splitting, multiplexing, and modulation during transmission. In optical communication systems, cascaded waveguides achieve stable and efficient connections between optical transmitting, receiving, and relay modules, ensuring reliable transmission of optical signals over long distances and in complex network architectures. In lidar, cascaded waveguides precisely connect laser transmitting, scanning, and detection modules, enabling optical signals to accurately complete target detection and data acquisition tasks. In optical computing, they build information bridges between optical computing units, facilitating the rapid flow of optical signals between functional modules such as logic operations and data storage, promoting efficient optical computing operations. Inside optical chips, cascaded waveguides act like a network, enabling tight interconnection between different functional units, such as photodetectors, modulators, and amplifiers, ensuring high integration and functional realization of the optical chip.

[0004] However, current cascaded waveguides face a series of pressing problems. During optical signal transmission, factors such as discontinuities in waveguide connections, scattering at waveguide bends, and absorption by the materials themselves lead to significant transmission losses, severely limiting the effective transmission distance and intensity of optical signals. Simultaneously, existing cascaded waveguide designs are not simple enough, involving numerous parameters and complex calculations, increasing design costs and difficulty, and limiting their widespread application in practical engineering. Furthermore, as integrated optics technology develops towards miniaturization and multifunctionality, cascaded waveguides perform poorly in terms of integration, making efficient integration with other optical modules within limited space difficult, and failing to meet the ever-increasing integration demands.

[0005] Gao Mingyang et al. (Gao Mingyang. Silicon-based Bending Waveguide Based on Germanium Metal and Etching Groove [D]. Jiangnan University, 2024.) proposed a single-mode bending waveguide structure with a mismatch structure based on a germanium arc and etching. The mismatch structure reduces the loss caused by the refractive index mismatch at the contact surface between the straight waveguide and the bending waveguide. The introduced germanium arc and external etching groove are used to increase the effective refractive index on the inner side of the bending waveguide and reduce the radiation loss caused by the outer bending waveguide. This successfully realizes a single-mode bending waveguide with ultra-small size (bending radius 500nm, device size 0.75μm×0.75μm) and low insertion loss (IL=0.131dB / 90°). However, this bending waveguide design process requires the introduction of multiple mismatch structures, which increases the processing and design cost and difficulty.

[0006] The published patent CN202210822722.X discloses a single-mode 90° bent waveguide based on a silicon-based platform and its fabrication method. The waveguide is divided into three segments along its propagation direction: a first transmission segment with a tapered structure, a second transmission segment connecting the first and third transmission segments (which is a bent waveguide), and a third transmission segment with a tapered structure. The device loss is no higher than 0.15 dB / bend, and the device size is 0.95 × 0.95 μm. 2 However, this scheme involves tapered waveguides, which have high requirements for the manufacturing process and increase the difficulty of manufacturing design.

[0007] The published patent CN202210642501.4 provides a waveguide device in which at least one segment of the waveguide layer is one of the following waveguides: a bent waveguide based on Hermite curves, a bent waveguide based on B-spline curves, and a tapered waveguide based on Hermite curves. The transmittance of the three types of bent waveguides reaches 0.99992, 0.999902, and 0.996, respectively. However, the design process of this device involves a relatively complex derivation process, which increases the design difficulty, design complexity and design cycle, and is not conducive to rapid promotion and application in actual engineering.

[0008] The published patent CN202110690109.2 provides an S-shaped waveguide structure with offset and groove, which includes an input straight waveguide, two curved waveguides with opposite curvatures and the same radius, an output straight waveguide, offsets at the connection of each waveguide, and grooves filled with a low refractive index medium. The bending loss of the device in the S-shaped waveguide with a bending radius of 1000μm is only 0.11dB. However, the structure of this device is relatively complex and requires high processing precision.

[0009] In summary, existing cascaded waveguides have varying degrees of problems in terms of loss, number of design parameters, and integration. There is an urgent need for a design method for cascaded low-loss waveguide structures to solve these problems and promote the further development of optical integration fields such as optical communication, lidar, optical computing, and optical chips. Summary of the Invention

[0010] The purpose of this invention is to provide a vector synthesis-based cascaded low-loss bent waveguide design method to solve the above-mentioned technical problems.

[0011] Another objective of this invention is to provide an application of the above-mentioned vector synthesis-based cascaded low-loss bent waveguide design method.

[0012] Therefore, the technical solution of the present invention is as follows:

[0013] A method for designing cascaded low-loss bent waveguides based on vector synthesis, comprising the following steps:

[0014] S1. Consider the curved waveguide to be designed as a curve, and define four control vectors to describe the curve as follows: curve starting point Curve termination point The tangent direction of the curve's starting point is at a fixed distance from the point. and the fixed distance point of the tangent direction at the end of the curve. The coordinate positions of the four elements in the coordinate system constructed by the plane of the curved waveguide are expressed as follows: , , , ,in, and These are unit vectors in the x and y directions; therefore, the parameter vector of the curve is constructed as follows:

[0015] ,

[0016] In the formula, The weight of the starting point of the curve. Weights of points at fixed distances along the tangent direction from the starting point of the curve. Weights are assigned to points at fixed distances along the tangent direction at the endpoint of the curve. Weights for the endpoints of the curve;

[0017] S2. Based on the connection requirements and curvature smoothing characteristics of the curved waveguide to be designed, boundary condition constraint equations are established to solve the algebraic relationship between the four control vectors.

[0018] S3. Define the structural parameter m of the curved waveguide, with a range of values. Transform the four control vectors into expressions related to the design parameters to be determined, which are the structural parameter m and the length.

[0019] S4. Following the order of length first, then structural parameter m, with the goal of minimizing transmission loss, determine the unknowns in the design parameters to be determined in turn, and complete the design of the curved waveguide.

[0020] Furthermore, in step S1, the weight of the curve starting point... Weights of points with fixed distances from the tangent direction at the starting point of the curve Weight of points with fixed distance from the tangent direction at the end of the curve Weight of curve termination point Construct a function with the same weight parameter t. Its expression is:

[0021] ,

[0022] Furthermore, as the parameter t changes from 0 to 1, its parameter vector is substituted into the curve. That is, to form a curve starting from the curve's starting point To the end point of the curve A smooth curve, and the distance can be fixed by controlling the tangent direction at the starting point of the curve. And the fixed distance point of the tangent direction at the end of the curve Change the shape of the curve.

[0023] Furthermore, the specific operation of step S2 is as follows:

[0024] parameter vector Mapped to the coordinate system described in step S1, i.e. ;

[0025] Based on the tangential connection between the input end of the curved waveguide and the output end of the preceding device, the tangential connection between the output end of the curved waveguide and the input end of the following device, and the requirement for a smooth transition of bidirectional curvature at the midpoint of the curved waveguide, boundary condition constraint equations are constructed, yielding the following expression:

[0026] ,

[0027] Assuming the starting point of the curve and curve termination point Given the vectors, the algebraic relationship between the four control vectors can be obtained by solving the problem as follows:

[0028] .

[0029] Furthermore, the specific operation of step S3 is as follows:

[0030] By decoupling and mapping the lateral and longitudinal components of the four control vectors, a parameterized coordinate matrix controlled by the structural parameter m is constructed, resulting in the vector composition expression:

[0031] ,

[0032] In the formula, The lateral length of the curved waveguide. The longitudinal length of the curved waveguide.

[0033] Furthermore, the specific operation steps of step S4 are as follows:

[0034] S401. Obtain a reasonable design range for the length among the design parameters to be determined, where the length is specifically at least one of the horizontal length and the vertical length;

[0035] S402. When there is only one type of length among the design parameters to be determined, the other length is set to a known value, and the structural parameter m is 0.5. Then, the transmission loss change curve corresponding to the length to be determined changing within its reasonable design range is obtained through simulation, so as to obtain the value range corresponding to the length to be determined in the set low transmission loss range, or the value corresponding to the length to be determined under the minimum transmission loss.

[0036] When there are two lengths among the design parameters to be determined, the first length is designed first, i.e., the second length is set to the median of its reasonable design range, and the structural parameter m is 0.5. Then, the transmission loss variation curve corresponding to the first length changing within its reasonable design range is obtained through simulation, so as to obtain the value range corresponding to the first length in the set low transmission loss range, or the value corresponding to the first length with the lowest transmission loss. Next, for the second length, the first length is set to the value corresponding to the lowest transmission loss obtained through simulation, and the structural parameter m is 0.5. Then, the transmission loss variation curve corresponding to the second length changing within its reasonable design range is obtained through simulation, so as to obtain the value range corresponding to the second length in the set low transmission loss range, or the value corresponding to the second length with the lowest transmission loss.

[0037] S403. For the structural parameter m to be determined, set the longitudinal length and transverse length to known values, or obtain the corresponding values ​​under the minimum transmission loss through simulation; then, simulate to obtain the transmission loss change curve corresponding to the change of structural parameter m in the (0,1) interval, so as to obtain the value range of structural parameter m in the set low transmission loss interval, or obtain the corresponding value of structural parameter m under the minimum transmission loss.

[0038] An application of the above-mentioned vector synthesis-based cascaded low-loss bent waveguide design method is used for the structural design of bent waveguides in cascaded beam splitters of multimode interference couplers, such as 1×8, 1×16, 1×32, and 1×64 beam splitters.

[0039] Compared with existing technologies, this vector synthesis-based cascaded low-loss bent waveguide design method has the advantages of achieving ultra-low transmission loss and ultra-small structural size, and is easy to integrate. In practical operation, it reduces the number of design parameters that need to be determined to three or less, which greatly simplifies the design process and reduces the design difficulty of bent waveguide structures, making it possible to rapidly promote its application in the practical engineering of cascaded beam splitters of multimode interference couplers. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the waveguide structure designed using the vector synthesis-based cascaded low-loss bent waveguide design method in Test Example 1 of the present invention.

[0041] Figure 2 This is a schematic diagram illustrating step S1 of the vector synthesis-based cascaded low-loss bent waveguide design method of the present invention, in which the bent waveguide to be designed is regarded as a curve and four control vectors of the curve are defined.

[0042] Figure 3 This is a graph showing the transmission loss of the waveguide structure in Test Example 1 of the present invention as a function of lateral length.

[0043] Figure 4 This is a graph showing the transmission loss of the waveguide structure in Test Example 1 of the present invention as a function of the structural parameter m.

[0044] Figure 5 This is a cross-sectional view of the optical field transmission obtained from the waveguide structure simulation in Test Example 1 of this invention;

[0045] Figure 6(a) is a top view of the cascaded 1×16 beam splitter with a multimode interference coupler in Test Example 2 of the present invention;

[0046] Figure 6(b) is a side sectional view of the cascaded 1×16 beam splitter of the multimode interference coupler in Test Example 2 of the present invention;

[0047] Figure 7(a) is a schematic diagram of the transmission loss of the cascaded 1×16 beam splitter of the multimode interference coupler in Test Example 2 of the present invention as a function of the transverse length of the bent waveguide between the first-stage multimode interference coupler element and the second-stage multimode interference coupler element.

[0048] Figure 7(b) is a schematic diagram of the transmission loss of the cascaded 1×16 beam splitter of the multimode interference coupler in Test Example 2 of the present invention as a function of the transverse length of the bent waveguide between the second-stage multimode interference coupler element and the third-stage multimode interference coupler element.

[0049] Figure 7(c) is a schematic diagram of the transmission loss of the cascaded 1×16 beam splitter of the multimode interference coupler in Test Example 2 of the present invention as a function of the transverse length of the bent waveguide between the third-stage multimode interference coupler element and the fourth-stage multimode interference coupler element.

[0050] Figure 8 This is a schematic diagram showing the transmission loss of the cascaded 1×16 beam splitter using a multimode interference coupler as a function of the bending waveguide structure parameters between each stage in Test Example 2 of this invention.

[0051] Figure 9 The optical field transmission cross section diagram obtained from the simulation of the multimode interference coupler cascaded with a 1×16 beam splitter in Test Example 2 of the present invention is shown. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention.

[0053] The specific implementation steps of the vector synthesis-based cascaded low-loss bent waveguide structural design method of the present invention are described below.

[0054] S1, see also Figure 1 Based on the curved characteristics of the curved waveguide, the curved waveguide to be designed is regarded as a curve, and a parameter vector is defined to describe the curve of the curved waveguide.

[0055] Specifically, the specific implementation steps of step S1 are described below.

[0056] S101, such as Figure 2 As shown, four control vectors are defined to describe the curved characteristics of a bent waveguide, specifically: the curve starting point... Curve termination point The tangent direction of the curve's starting point is at a fixed distance from the point. and the fixed distance point in the tangent direction of the curve's termination point. .

[0057] The coordinate positions of the four control vectors in the coordinate system constructed by the curved waveguide installation plane are expressed as follows: , , , ,in, and yes and A unit vector in direction.

[0058] S102. Based on the four control vectors defined above, construct the parameter vector of the curve, the expression of which is:

[0059] ,

[0060] In the formula, The starting point of the curve, The endpoint of the curve. A fixed distance from the starting point of the curve along the tangent direction. A fixed distance from the tangent direction at the end of the curve. The weight of the starting point of the curve. Weights of points at fixed distances along the tangent direction from the starting point of the curve. Weights are assigned to points at fixed distances along the tangent direction at the endpoint of the curve. The weight is the endpoint of the curve.

[0061] In the parameter vector expression of the curve, the four weights are specifically constructed as the same weight parameter t ( The function is expressed as:

[0062] ,

[0063] Based on this, when the parameter t changes from 0 to 1, its substitution The middle is formed as Figure 2 shown arrive A smooth curve, wherein, by controlling and It can change the shape of the curve.

[0064] S2. Based on the connection requirements and curvature smoothing characteristics of the curved waveguide, establish boundary condition constraint equations and solve the algebraic relationship between the control vectors.

[0065] The specific steps for step S2 are as follows:

[0066] S201. In practical applications, the input end of the curved waveguide is tangentially connected to the output end of the preceding device, and the output end of the curved waveguide is tangentially connected to the input end of the following device. Based on this, in order to achieve smooth mode field docking, the curvature of both the input and output ends of the curved waveguide must be controlled to 0. At the same time, a smooth transition of bidirectional curvature is achieved at the midpoint of the curved waveguide, that is, the curvature at the midpoint of the curved waveguide is 0.

[0067] Specifically, in order to quantitatively characterize the connection characteristics and curvature requirements of the curved waveguide, the parameter vector is first... Mapped to the coordinate system described in step S1; specifically,

[0068] make, ,

[0069] In the formula, and They respectively represent the curves at shaft and Component functions in the axial direction;

[0070] According to the principles of differential geometry, the tangential slope of a curve is determined by its first derivative. and The curvature of the curve is determined by both the first and second derivatives.

[0071] Combining the tangential docking requirements and the curvature zeroing constraint described in step S201, the above geometric features can be transformed into boundary condition constraints regarding the component functions:

[0072] ,

[0073] In the formula, express The first derivative, express The second derivative of .

[0074] S202, Assuming the starting point of the curve and curve termination point Given a vector, then:

[0075] ,

[0076] Furthermore, based on the above mathematical operations, the algebraic relationship between the four control vectors can be obtained.

[0077]

[0078] S3. Define the structural parameter m of the curved waveguide, with a range of values. Transform the four control vectors into expressions related to the design parameters to be determined, which are the structural parameter m and the length.

[0079] Specifically, step S3 constructs a parameterized coordinate matrix controlled by the structural parameter m by decoupling and mapping the lateral and longitudinal components of the four control vectors. Its vector synthesis expression is as follows:

[0080]

[0081] Specifically, the physical meaning and calculation logic of the control vector expression are as follows: In the horizontal direction, using the horizontal length... As a scaling reference, through structural parameters The equation is weighted and mapped. Here, the vector... The distribution of the four control points along the horizontal axis was determined. In the vertical direction, the longitudinal length was used... Combined vector Define the vertical displacement of the control points. Through the above vector synthesis operation, the originally independent multiple coordinate degrees of freedom are compressed into only requiring the adjustment of a single variable. This significantly reduces the computational complexity of subsequent simulation optimization.

[0082] In practical applications, the positional relationship between the start and end points of a curved waveguide is usually known or partially known, i.e., the lateral length... and longitudinal length If the structural parameters are known or partially known, then the vector synthesis-based cascaded low-loss bent waveguide structure proposed in this invention only needs to be determined. By considering the positional relationships, the structural design of the bent waveguide can be realized; as mentioned above, the design parameters that need to be determined for the bent waveguide to be designed are the transverse length, longitudinal length, and structural parameters. The maximum number is 3, and the minimum is only 1.

[0083] S4. Following the order of length first, then structural parameter m, with the goal of minimizing transmission loss, determine the unknowns in the design parameters to be determined in turn, and complete the design of the curved waveguide.

[0084] The specific implementation steps of step S4 are as follows:

[0085] S401. Obtain a reasonable design range for the length among the design parameters to be determined, where the length is specifically at least one of the horizontal length and the vertical length;

[0086] S402. When determining the length in the design parameters to be determined.

[0087] When there is only one type of length among the design parameters to be determined, the other length is set to a known value, and the structural parameter m is 0.5. Then, the transmission loss variation curve corresponding to the length to be determined changing within its reasonable design range is obtained through simulation, so as to obtain the value range of the length to be determined in the set low transmission loss range, or the value corresponding to the length to be determined under the minimum transmission loss.

[0088] When there are two lengths among the design parameters to be determined, the first length is designed first, i.e., the second length is set to the median of its reasonable design range, and the structural parameter m is 0.5. Then, the transmission loss variation curve corresponding to the first length changing within its reasonable design range is obtained through simulation, so as to obtain the value range corresponding to the first length in the set low transmission loss range, or the value corresponding to the first length with the lowest transmission loss. Next, for the second length, the first length is set to the value corresponding to the lowest transmission loss obtained through simulation, and the structural parameter m is 0.5. Then, the transmission loss variation curve corresponding to the second length changing within its reasonable design range is obtained through simulation, so as to obtain the value range corresponding to the second length in the set low transmission loss range, or the value corresponding to the second length with the lowest transmission loss.

[0089] In practice, the first length can be either the horizontal length or the vertical length.

[0090] S403. For the structural parameter m to be determined, set the longitudinal length and transverse length to known values, or obtain the corresponding values ​​under the minimum transmission loss through simulation; then, simulate to obtain the transmission loss change curve corresponding to the change of structural parameter m in the (0,1) interval, so as to obtain the value range of structural parameter m in the set low transmission loss interval, or obtain the corresponding value of structural parameter m under the minimum transmission loss.

[0091] The following simulation experiments verify the performance of the vector synthesis cascaded low-loss bent waveguide structure proposed in this invention.

[0092] Test Example 1

[0093] like Figure 1 The diagram shows a waveguide structure based on vector synthesis cascaded low-loss design, which consists of a substrate 1, a waveguide layer 2, and a cladding layer 3. The substrate 1 is a silicon dioxide substrate with a thickness of 2 μm and a cross-sectional width of 30 μm and a length of 50 μm. The waveguide layer 2 is a silicon nitride bent waveguide designed using the method in Example 1, with a thickness of 400 nm and a width of 1.5 μm. The cladding layer 3 is stacked on the top surface of the substrate 1 and completely covers the outside of the waveguide layer 2. It has a thickness of 2 μm and a cross-sectional dimension consistent with that of the substrate 1, with a width of 30 μm and a length of 50 μm.

[0094] According to a pre-set value, the longitudinal length of the curved waveguide Given that the length is 20 μm, the remaining design parameter to be determined is the lateral length. and structural parameters Based on this, the waveguide structure was numerically simulated using the finite-difference time-domain (FDTD) simulation software, and the transmittance of the structure was obtained. Furthermore, transmittance is converted using a numerical formula. The transmission loss can then be obtained. .

[0095] Specifically, first, set the structural parameters. The value is 0.5, the longitudinal length is 20μm, and the transverse length is... The variation range was set to 20μm~50μm based on integration density requirements. The loss of the waveguide structure was analyzed using finite-difference time-domain (FDTD) simulation software. With lateral length The changes.

[0096] like Figure 3 As shown, the transmission loss of the waveguide structure as a function of the transverse length is first obtained through simulation. The changes in the horizontal length; among them, when the horizontal length Simulation results show that the transmission loss decreases monotonically with increasing lateral length when the lateral length varies from 20μm to 50μm. However, when the lateral length exceeds 36μm, the transmission loss stabilizes below 0.2dB; and when the lateral length reaches 50μm, the transmission loss drops below 0.01dB, demonstrating that the waveguide structure still exhibits excellent low transmission loss characteristics within a compact size. Therefore, to achieve low transmission loss, the lateral length... The selection range can be 40μm-50μm, in order to further determine the structural parameters. Horizontal length Choose 40μm or 50μm.

[0097] like Figure 4 As shown, the transmission loss of the waveguide structure as a function of the structural parameters is then obtained through simulation. The variation; where the longitudinal length is set to 20μm and the transverse length is... Taking 40μm and 50μm respectively, when the structural parameters When varying within the range of 0 to 1, the simulation results show that: as As the number of transmission losses gradually increases, the transmission loss first decreases and then increases, and consequently, the structural parameters... The selection range can be from 0.4 to 0.7, and all values ​​can achieve a stable transmission loss below 0.2dB. In particular, some values ​​can reduce the loss to below 0.1dB, achieving better design results. This verifies that optimizing the parameters... It can achieve extremely low transmission loss.

[0098] In summary, through coordinated control of lateral length With structural parameters This enables the design of cascaded bent waveguides with losses below 0.1dB.

[0099] like Figure 5 The figure shown is based on the above simulation results, with a lateral length of 50 μm and structural parameters... This is a cross-sectional view of the optical field transmission under condition 0.5. The figure shows that stable mode transmission and low-loss coupling are achieved in this waveguide structure.

[0100] Test Example 2

[0101] Referring to Figures 6(a) and 6(b), the vector synthesis-based cascaded low-loss bent waveguide design method of the present invention is used to design a cascaded 1×16 beam splitter of multimode interference couplers. The design includes a silicon substrate 1, a buried silica layer 2 on the upper surface of the silicon substrate 1, and a multimode interference coupler array 3 centrally located on the upper surface of the buried silica layer 2. In the horizontal direction, the multimode interference coupler elements are connected by bent waveguides 4. The entire multimode interference coupler array 3 and its connecting bent waveguides 4 are completely covered by a silica cladding layer 5. Specifically, the silicon substrate 1 is a rectangular thin layer with a thickness of 4 μm, a cross-sectional width of 90 μm, and a length of 280 μm. The buried silica layer 2 has the same cross-sectional dimensions as the silicon substrate 1, completely covering the upper surface of the silicon substrate 1, and has a thickness of 2 μm. Among them, the multimode interference coupler array 3 and the bent waveguide 4 are integrated on the upper surface of the silicon dioxide buried oxide layer 2 by photolithography and deposition. The bent waveguide 4 has a thickness of 400nm and is made of silicon nitride material.

[0102] The multimode interference coupler array 3 consists of four 1×2 multimode interference couplers. According to the design, the fourth-stage multimode interference coupler array has 8 multimode interference coupler elements with an element spacing of 10μm; the third-stage multimode interference coupler array has 4 multimode interference coupler elements, with the element position being the middle position between adjacent elements of the fourth-stage multimode interference coupler array and an element spacing of 20μm; the second-stage multimode interference coupler array has 2 multimode interference coupler elements, with the element position being the middle position between adjacent elements of the third-stage multimode interference coupler array and an element spacing of 40μm; and the first-stage multimode interference coupler array has 1 multimode interference coupler element, with the element position being the middle position between adjacent elements of the second-stage multimode interference coupler array and also the middle position of the entire multimode interference coupler array system. Each multimode interference coupler element has the same specifications, including an input waveguide 301, a multimode interference region 302, and output waveguides 303 and 304. The input waveguide 301 and the output waveguides 303 and 304 are all rectangular thin layers with a width of 1.5 μm and a length of 5 μm, and the spacing between them is 4.1 μm. The multimode interference region 302 is a rectangular thin layer with a width of 8 μm and a length of 36.7 μm to meet the multimode interference condition.

[0103] In this test case, since the spacing between the elements of each stage of the multimode interferometric coupler array is determined, the longitudinal length of the curved waveguide connecting adjacent stages of the multimode interferometric coupler array elements is known. Specifically, the longitudinal length of the curved waveguide between the first and second stage multimode interferometric coupler array elements is 17.95 μm, the longitudinal length between the second and third stage multimode interferometric coupler array elements is 7.95 μm, and the longitudinal length between the third and fourth stage multimode interferometric coupler array elements is 2.95 μm. Therefore, in the design of the curved waveguide, the unknown design parameters to be determined are the lateral length and structural parameters. Specifically, in the parameterized coordinate matrix constructed in step S3, , and Given quantities and unknown.

[0104] The first step involves pre-setting reasonable design ranges for the lateral lengths of the curved waveguides at each stage based on the differences in longitudinal offset between the beam splitter elements and the optimization requirements for layout compactness while meeting the minimum bending radius constraint of the waveguide. This aims to minimize device size while ensuring low loss. The second step involves designing the curved waveguide between the first-stage and second-stage multimode interference coupler elements, setting the longitudinal length to 17.95 μm, and setting structural parameters... The value is 0.5. Using the Finite-Difference Time-Domain (FDTD) simulation software, the transmission loss of a 1×16 optical splitter as a function of lateral length is simulated. The variation within the 35μm-45μm range is shown in Figure 7(a). For the curved waveguide design between the second-stage and third-stage multimode interferometric coupler elements, based on the design results of the curved waveguide between the first-stage and second-stage multimode interferometric coupler elements, the longitudinal length is set to 7.95μm, and the structural parameters are... The value is 0.5. Using the Finite-Difference Time-Domain (FDTD) simulation software, the transmission loss of a 1×16 optical splitter as a function of lateral length is simulated. The variation in the 20μm-30μm range is shown in Figure 7(b). For the curved waveguide design between the third-stage and fourth-stage multimode interferometric coupler elements, based on the curved waveguide design results between the first-stage and second-stage multimode interferometric coupler elements, and the curved waveguide design results between the second-stage and third-stage multimode interferometric coupler elements, the longitudinal length is set to 2.95μm, and the structural parameters are... Given a value of 0.5, simulation software using the Finite-Difference Time-Domain (FDTD) method yielded the transmission loss of a 1×16 optical splitter as a function of lateral length. The variation in the 15μm-30μm range is shown in Figure 7(c).

[0105] As can be seen from Figures 7(a) to 7(c), the overall transmission loss of the 1×16 beam splitter exhibits a trend of first decreasing sharply and then increasing slowly with the increase of the lateral length of the curved waveguides at each stage. In the specific optimization process, this invention adopts a step-by-step variable control method: First, based on the variation curve shown in Figure 7(a), the preferred lateral length of the waveguide connecting the first and second stage multimode interference coupler elements is determined to be 41 μm; then, based on the variation curve shown in Figure 7(b), the preferred lateral length of the waveguide connecting the second and third stage multimode interference coupler elements is determined to be 25 μm; finally, based on the variation curve shown in Figure 7(c), the preferred lateral length of the waveguide connecting the third and fourth stage multimode interference coupler elements is determined to be 24 μm. Thus, as shown in Figure 7(c), by combining the lateral length parameters obtained from the above optimization at each stage and performing overall layout, the overall transmission loss of the 1×16 beam splitter is successfully reduced to below 0.55 dB, achieving the best balance between device compactness and high transmission efficiency.

[0106] The second step involves determining the structural parameters of the curved waveguides connecting the elements of the multimode interferometric coupler at each level, given that the transverse lengths are successively determined to be 41 μm, 25 μm, and 24 μm. Similarly, using the finite-difference time-domain (FDTD) simulation software, the transmission loss of a 1×16 optical splitter varies with the structural parameters of each stage. The changes are determined. For example... Figure 8 As shown, The structural parameters of the waveguide connecting the elements of the first-stage and second-stage multimode interferometric couplers are indicated. The trend of change in the 0-1 interval, and the structural parameters of the waveguide connected at other locations. When the value is 0.5, the overall transmission loss of the 1×16 optical splitter is as follows: The structural parameters of the waveguide connecting the elements of the second- and third-stage multimode interferometric couplers represent the structural parameters of the waveguide. The trend of change in the 0-1 interval, and the structural parameters of the waveguide connected at other locations. When the value is 0.5, the overall transmission loss of the 1×16 optical splitter is as follows: The structural parameters of the waveguide connecting the elements of the third- and fourth-stage multimode interferometric couplers are indicated. The trend of change in the 0-1 interval, and the structural parameters of the waveguide connected at other locations. When the value is 0.5, the overall transmission loss of the 1×16 optical splitter is as follows.

[0107] In addition, from Figure 8It can also be seen that the transmission loss of each level of curved waveguide varies with the structural parameters. The increases in these parameters all show a trend of first decreasing and then increasing, indicating that the 1×16 beam splitter structure, composed of cascaded multimode interference couplers, exhibits changes in its structural parameters. There is a minimum transmission loss point near 0.5, therefore, the structural parameters That is, a value of 0.5 is preferred, and correspondingly, the overall transmission loss of the 1×16 beam splitter is reduced to below 0.55dB. From another perspective, when the multimode interference coupler element specifications in the beam splitter remain unchanged, regardless of the number of cascaded stages, the structural parameter m can be fixed at 0.5, effectively achieving mode field matching at each cascaded stage. In the design of other cascaded beam splitters, this method can reduce the number of design parameters to be determined to one, meaning only the lateral length of the bent waveguide needs to be considered.

[0108] Test Example 3

[0109] This embodiment aims to further qualitatively and quantitatively illustrate the advantages of the design method of the present invention in optimizing efficiency through comparative experiments.

[0110] To ensure the comparative results have systematic reference value, this embodiment constructs a "two-stage cascaded structure" as a standard simulation structure. This structure consists of a "pre-stage multimode interference coupler—intermediate connecting waveguide—post-stage multimode interference coupler." Using this structure, the design method of this invention is compared with three traditional schemes (double-circular-arc S-shaped curved waveguide, Bezier curve curved waveguide, and hybrid Euler curved waveguide). This cascaded structure can realistically simulate the transmission loss of optical signals between multiple stages of devices, thereby comparing the computational overhead of different methods in finding the optimal structure while ensuring design accuracy.

[0111] To quantitatively evaluate the computational overhead of different curved waveguide design schemes, the specific evaluation parameter is the structural optimization convergence time. and computing power enhancement factor Among them, the convergence time of structural optimization Defined as the total absolute time consumed in evolving from the initial structure to the scheme with the lowest transmission loss under specific hardware computing power constraints; computing power enhancement factor. To highlight the efficiency leap brought about by parameter dimensionality reduction, its calculation expression is: , and The figures represent the optimized convergence times of the traditional multi-degree-of-freedom scheme and the design method of this invention, respectively.

[0112] To verify the universality of the method of this invention for different computing resources and to eliminate the random influence of single hardware performance on the optimization efficiency measurement, this embodiment conducted comparative tests in two hardware environments with obvious performance gradients. Hardware environment 1 (basic computing platform): equipped with an Intel(R) Xeon(R) E5-1650 v4 processor with a main frequency of 3.60GHz and a memory capacity of 32GB; Hardware environment 2 (high-performance computing platform): equipped with a 13th generation Intel(R) Core(TM) i7-13700KF processor with a main frequency of 3.40GHz and a memory capacity of 64GB.

[0113] Under the two hardware environments described above, different waveguide structures The results of the comparative tests are shown in Table 1 below.

[0114] Table 1:

[0115]

[0116] As can be seen from the comparative data in Table 1, the traditional double-circular-arc S-shape, Bézier curve, and hybrid Euler curve all involve multiple design degrees of freedom in structural design and are highly dependent on a large global multi-parameter scanning matrix. This leads to the optimization convergence time of the above three conventional schemes on two devices being significantly longer. The computational cost remains high, ranging from 82 to 251 hours; however, the design method of this invention can successfully reduce the core variables to single-parameter control. This mechanism reduces the computational cost of simulation optimization by an order of magnitude, on both hardware environments 1 and 2. It requires only a very low 25.14 h and 22.94 h. Calculations show that, compared to the most time-consuming traditional method, the computational efficiency improvement factor of this invention's design method is significantly higher. Up to 10 times.

[0117] In summary, the present invention achieves a leapfrog improvement in device optimization efficiency while maintaining extremely low loss, greatly shortening the optimization cycle in engineering applications and providing key technical support for the rapid design of large-scale integrated photonic networks.

Claims

1. A method for designing a cascaded low-loss bending waveguide based on vectorial synthesis, characterized in that, The steps are as follows: S1, the bending waveguide to be designed is regarded as a curve, and four control vectors for describing the curve are defined as: a curve starting point , a curve ending point , a curve starting point tangent direction fixed distance point , and a curve ending point tangent direction fixed distance point ; the coordinate positions of the four in a coordinate system constructed by a bending waveguide setting plane are sequentially represented as: , , , , wherein, and are unit vectors in x and y directions; further, a parameter vector of the curve is constructed as: ， In the formula, The weight of the starting point of the curve. Weights of points at fixed distances along the tangent direction from the starting point of the curve. Weights are assigned to points at fixed distances along the tangent direction at the endpoint of the curve. Weights for the endpoints of the curve; S2. Based on the connection requirements and curvature smoothing characteristics of the curved waveguide to be designed, boundary condition constraint equations are established to solve the algebraic relationship between the four control vectors. S3. Define the structural parameter m of the curved waveguide, with a value range of (0,1). Transform the four control vectors into expressions related to the design parameters to be determined, which are the length and structural parameter m. S4. Following the order of length first, then structural parameter m, with the goal of minimizing transmission loss, determine the unknowns in the design parameters to be determined in turn, and complete the design of the curved waveguide.

2. The cascaded low-loss bent waveguide design method based on vector synthesis according to claim 1, characterized in that, In step S1, the weight of the curve starting point The weight of the point with fixed distance from the tangent direction at the starting point of the curve Weight of points with fixed distance from the tangent direction at the end of the curve Weight of curve termination point Construct a function with the same weight parameter t. Its expression is: ， Furthermore, as the parameter t changes from 0 to 1, its parameter vector is substituted into the curve. That is, to form a curve starting from the curve's starting point To the end point of the curve A smooth curve, and the distance can be fixed by controlling the tangent direction at the starting point of the curve. And the fixed distance point of the tangent direction at the end of the curve Change the shape of the curve.

3. The cascaded low-loss bent waveguide design method based on vector synthesis according to claim 1, characterized in that, The specific operation of step S2 is as follows: parameter vector Mapped to the coordinate system described in step S1, i.e. ; Based on the tangential connection between the input end of the curved waveguide and the output end of the preceding device, the tangential connection between the output end of the curved waveguide and the input end of the following device, and the requirement for a smooth transition of bidirectional curvature at the midpoint of the curved waveguide, boundary condition constraint equations are constructed, the expression of which is: ， Assuming the starting point of the curve and curve termination point Given the vectors, the algebraic relationship between the four control vectors can be obtained by solving the problem as follows: 。 4. The cascaded low-loss bent waveguide design method based on vector synthesis according to claim 3, characterized in that, The specific operation of step S3 is as follows: By decoupling and mapping the lateral and longitudinal components of the four control vectors, a parameterized coordinate matrix controlled by the structural parameter m is constructed, resulting in the vector composition expression: ， In the formula, The lateral length of the curved waveguide. The longitudinal length of the curved waveguide.

5. The cascaded low-loss bent waveguide design method based on vector synthesis according to claim 4, characterized in that, The specific steps for step S4 are as follows: S401. Obtain a reasonable design range for the length among the design parameters to be determined, where the length is specifically at least one of the horizontal length and the vertical length; S402. When there is only one type of length among the design parameters to be determined, the other length is set to a known value, and the structural parameter m is 0.

5. Then, the transmission loss change curve corresponding to the length to be determined changing within its reasonable design range is obtained through simulation, so as to obtain the value range corresponding to the length to be determined in the set low transmission loss range, or the value corresponding to the length to be determined under the minimum transmission loss. When there are two lengths among the design parameters to be determined, the first length is designed first, i.e., the second length is set to the median of its reasonable design range, and the structural parameter m is 0.

5. Then, the transmission loss variation curve corresponding to the first length changing within its reasonable design range is obtained through simulation, so as to obtain the value range corresponding to the first length in the set low transmission loss range, or the value corresponding to the first length with the lowest transmission loss. Next, for the second length, the first length is set to the value corresponding to the lowest transmission loss obtained through simulation, and the structural parameter m is 0.

5. Then, the transmission loss variation curve corresponding to the second length changing within its reasonable design range is obtained through simulation, so as to obtain the value range corresponding to the second length in the set low transmission loss range, or the value corresponding to the second length with the lowest transmission loss. S403. For the structural parameter m to be determined, set the longitudinal length and transverse length to known values, or obtain the corresponding values ​​under the minimum transmission loss through simulation; then, simulate to obtain the transmission loss change curve corresponding to the change of structural parameter m in the (0,1) interval, so as to obtain the value range of structural parameter m in the set low transmission loss interval, or obtain the corresponding value of structural parameter m under the minimum transmission loss.

6. An application of the vector synthesis-based cascaded low-loss bent waveguide design method as described in any one of claims 1-5, characterized in that, Structural design of curved waveguides in cascaded beam splitters for multimode interference couplers.

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