Design method of integrated multimode curved optical waveguide and integrated multimode curved optical waveguide

Abstract

The application discloses a design method of an integrated multi-mode curved optical waveguide and the integrated multi-mode curved optical waveguide and belongs to the technical field of integrated optics. Aiming at the problem that a traditional multi-mode curved waveguide is difficult to consider low loss and low crosstalk at a compact size, a waveguide model formed by cascading multiple variable-width generalized Euler spiral curve elements is constructed. Through an iterative optimization algorithm based on mode field analysis, the curvature radius and the waveguide width of each curve element are controlled in double degrees of freedom to obtain optimal geometric parameters with the minimum full-mode loss as the target. The waveguide structure breaks through the limitation of the traditional fixed-width design, realizes low-loss and low-crosstalk transmission of multi-mode signals at a very small bending radius, significantly improves the tolerance of the device to manufacturing process deviation, and is suitable for a high-density on-chip optical interconnection system.

Description

Technical Field

[0001] This invention belongs to the field of integrated optics technology, specifically relating to a design method for integrated multimode bent optical waveguides and an integrated multimode bent optical waveguide. Background Technology

[0002] With the explosive growth of big data and communication demands, traditional single-mode transmission systems are facing capacity bottlenecks. Mode Division Multiplexing (MDM) technology utilizes multiple orthogonal modes in an optical waveguide as independent channels to transmit information in parallel, and has become a key technology for improving communication capacity and on-chip interconnect bandwidth density. In MDM integrated photonic systems, curved optical waveguides are an indispensable basic connection unit for realizing optical path turning and compact layout.

[0003] However, the design of multimode bent optical waveguides faces significant challenges: higher-order modes are more prone to radiation leakage at bends, and changes in phase-matching conditions between different modes can easily induce inter-mode coupling (crosstalk), leading to compromised signal integrity. Existing solutions mainly include:

[0004] 1. Traditional circular arc or fixed curve design: Although the structure is simple, due to the sudden change in curvature or insufficient design freedom, it is difficult to suppress radiation loss and inter-mode crosstalk at the same time under small radius bending.

[0005] 2. Introducing auxiliary structures: such as adding a mode converter between a straight waveguide and a curved waveguide, or using subwavelength gratings, sidewall mirrors, etc. These methods often lead to increased device size, more complex manufacturing processes (such as requiring high-precision photolithography), and may introduce additional scattering losses.

[0006] 3. Conventional Free-Form Curve (FCC) Design: Although it introduces gradual curvature, most of them are based on fixed waveguide width or simple mathematical models (such as B-splines and standard Euler spirals). When dealing with the complex boundary conditions of multimode transmission, the design freedom is still limited, and there is a lack of efficient optimization algorithms for all-mode performance, resulting in high optimization costs or difficulty in convergence.

[0007] Therefore, there is an urgent need for a novel multimode bent optical waveguide structure design scheme that can efficiently balance low loss, low crosstalk, compact size, and process tolerance under a large degree of design freedom. Summary of the Invention

[0008] This invention provides a design method and an integrated multimode bent optical waveguide. It addresses the problems of existing multimode bent optical waveguide technologies being limited by fixed waveguide widths or single curvature variation models, resulting in insufficient design freedom, inability to achieve compact bending radii while simultaneously ensuring low loss and low intermode crosstalk for all transmission modes, and often being sensitive to manufacturing process errors.

[0009] The core technology of this invention is to construct a waveguide model using a free-form curve composed of multiple variable-width generalized Euler spiral curve elements. The radius of curvature and waveguide width of each curve element are iteratively optimized with dual degrees of freedom through a directional range bisection search algorithm based on mode field analysis, thereby achieving low-loss and low-crosstalk transmission in all working modes.

[0010] In a first aspect, the present invention provides a design method for an integrated multimode bent optical waveguide, the method comprising the following steps:

[0011] A structural model of the curved optical waveguide to be designed is constructed. The structural model uses a variable-width freeform curve to describe the geometric boundary of the waveguide. The variable-width freeform curve is composed of multiple cascaded curve elements. Each curve element is configured with a curvature radius parameter and a waveguide width parameter that vary independently with the path length.

[0012] All operating modes of curved optical waveguide transmission are determined, and full-mode loss evaluation metrics are defined for all operating modes.

[0013] Based on the model field analysis, the full-mode loss of the structural model under the current geometric parameters is calculated. With the goal of satisfying the preset threshold for the full-mode loss, the geometric parameters of each curve element are iteratively optimized until the optimal geometric parameter sequence is obtained.

[0014] The layout structure of the integrated multimode bent optical waveguide is generated based on the optimal geometric parameter sequence.

[0015] Furthermore, the curve element is a variable-width generalized Euler spiral curve element;

[0016] The curvature radius parameter, which varies independently with path length, is characterized by the curvature of a curve element changing linearly with its path length.

[0017] The waveguide width parameter, which varies independently with the path length, is characterized by the fact that the width of the curve element changes linearly with its path length.

[0018] Furthermore, the geometric parameters of each curve element include: starting radius of curvature, ending radius of curvature, starting width, ending width, curve element angle, and curve element length;

[0019] During the iterative optimization process, the length of the curve element is set to a fixed value, and at least one of the starting radius of curvature, the ending radius of curvature, the starting width, and the ending width is used as an adjustable optimization variable.

[0020] Furthermore, the full-mode loss evaluation indicators include full-mode mismatch loss and full-mode radiation loss;

[0021] The full-mode mismatch loss is defined as the maximum value of the mode mismatch loss of each order mode in all operating modes;

[0022] Full-mode radiation loss is defined as the maximum radiation loss of each mode across all operating modes.

[0023] Furthermore, the iterative optimization process employs a directional range binary search algorithm;

[0024] The algorithm constructs a merit function, which is configured as a logical function, to determine whether the current full-mode mismatch loss and full-mode radiation loss are lower than the set mismatch loss threshold and radiation loss threshold, respectively. If the conditions are met, the current geometric parameters are determined to be valid and the search for a better solution continues or the iteration is terminated.

[0025] Furthermore, the mode polarization ratio is introduced as a constraint during the iterative optimization process;

[0026] The mode polarization ratio of each working mode under the current geometric parameters is calculated. The optimization result under the geometric parameters is only accepted if the mode polarization ratio meets the preset polarization purity requirement, so as to suppress modal hybridization.

[0027] Furthermore, in the structural model, the width of the input port and the width of the output port are equal when the curved optical waveguide is connected to the external straight waveguide;

[0028] Furthermore, iterative optimization involves optimizing multiple cascaded curve elements segment by segment, with the endpoint geometric parameters of the previous curve element serving as constraints on the starting point geometric parameters of the next curve element, in order to maintain the continuity of the waveguide boundary.

[0029] Furthermore, the material of the bent optical waveguide includes one of silicon, silicon nitride, silicon dioxide, indium phosphide, gallium arsenide, silicon carbide, lithium niobate, or polymer materials;

[0030] The structural forms of curved optical waveguides include strip waveguides, ridge waveguides, or multilayer waveguides.

[0031] Secondly, the present invention provides an integrated multimode bent optical waveguide, wherein the bent optical waveguide is fabricated using the design method described above.

[0032] The geometry of the curved optical waveguide consists of multiple cascaded variable-width generalized Euler spiral curve elements. The radius of curvature and waveguide width of each curve element change continuously with the optical transmission path, and the overall bending angle of the curved optical waveguide ranges from 0° to 360°.

[0033] Furthermore, the curved optical waveguide is configured to support at least three spatial mode transmissions;

[0034] Within the preset operating wavelength range, the transmission loss of all supported spatial modes and the inter-mode crosstalk between any two spatial modes in the bent optical waveguide are lower than the preset specifications, and the bent optical waveguide has a process tolerance that allows for waveguide width manufacturing deviations within the preset range.

[0035] The main contributions and innovations of this invention are as follows:

[0036] 1. Extremely high design freedom and transmission performance: This invention breaks through the limitation of constant waveguide width in traditional methods and proposes a variable-width generalized Euler spiral model. This model allows for a high degree of design freedom and transmission performance. S ,R T ) and waveguide width (W S W T The parameters change simultaneously with the transmission path. This dual-parameter control mechanism can more precisely match the evolution of each mode in curved transmission, thereby reducing the full-mode transmission loss to below 0.033dB and suppressing inter-mode crosstalk to below -25dB in a compact size (e.g., equivalent radius 84.9µm), which is significantly better than traditional circular arc or B-spline waveguides.

[0037] 2. Excellent process tolerance (robustness): Thanks to the dynamic optimization of the optical field confinement capability through the variable width design, the structure of this invention has extremely high tolerance to manufacturing deviations. Simulations show that even with waveguide width deviations as high as ±140nm, inter-mode crosstalk can still be kept below -20dB, far exceeding the ±20~30nm tolerance range typically achieved by existing technologies, greatly reducing processing difficulty and improving yield.

[0038] 3. Efficient Optimization Algorithm and Convergence: This invention proposes an optimization strategy that combines full-mode loss calculation with directional range binary search, and constructs a Form of Good Value (FOM) based on a logistic function. This method avoids the problems of large computational cost and easy getting trapped in local optima in traditional global search algorithms (such as genetic algorithms), and can achieve fast and accurate iterative convergence for the "bottleneck" modes (i.e., maximum mismatch loss or maximum radiation loss) in multimode transmission.

[0039] 4. Wide versatility and scalability: This design method supports arbitrary bending angles from 0° to 360° and is applicable to various isotropic or anisotropic material platforms such as silicon, lithium niobate, and silicon nitride. It can be flexibly extended to the design of complex photonic devices such as S-shaped bends and ring resonators.

[0040] Details of one or more embodiments of the present invention are set forth in the following drawings and description, so that other features, objects and advantages of the invention will be more readily understood. Attached Figure Description

[0041] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0042] Figure 1 A schematic diagram of the integrated multimode bent optical waveguide based on variable width FFC design provided by the present invention;

[0043] Figure 2 This is a schematic diagram of the structure of the variable-width generalized Euler spiral curve element used to construct a variable-width FFC structure, provided by the present invention.

[0044] Figure 3 When the working wavelength is 1550nm, At that time, (a) the radius of curvature at the endpoint and Between the variable width generalized Euler elements of 40 μm and 200 μm respectively With the radius of curvature at the starting point and endpoint width A changing two-dimensional mapping, (b) at the end section of the curved waveguide. With the radius of curvature at the endpoint and endpoint width A changing two-dimensional mapping;

[0045] Figure 4 (a) is a curve and width parameter distribution diagram of the integrated three-mode bent optical waveguide based on variable width FFC design optimized in an embodiment of the present invention. Figure 4 (b) is the mode polarization ratio distribution diagram corresponding to the structural parameter set;

[0046] Figure 5 The transmission response spectra of (a) TE0 mode, (b) TE1 mode, and (c) TE2 mode in the wavelength range of 1500~1600nm obtained by numerical simulation of the integrated trimode bent optical waveguide designed in the embodiment of the present invention.

[0047] Figure 6The transmission responses of the integrated tri-mode bent optical waveguide designed in the numerical simulation of this invention, at an operating wavelength of 1550 nm, are shown for (a) TE0 mode, (b) TE1 mode, and (c) TE2 mode, as a function of waveguide width deviation. Trend chart of changes;

[0048] Figure 7 This is a flowchart of the design method for integrating multimode bent optical waveguides in an embodiment of the present invention. Detailed Implementation

[0049] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with one or more embodiments of this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of one or more embodiments of this specification as detailed in the appended claims.

[0050] It should be noted that the steps of the corresponding methods are not necessarily performed in the order shown and described in this specification in other embodiments. In some other embodiments, the methods may include more or fewer steps than described in this specification. Furthermore, a single step described in this specification may be broken down into multiple steps in other embodiments; and multiple steps described in this specification may be combined into a single step in other embodiments.

[0051] Example 1: Design Method of Integrated Multimode Bending Optical Waveguide

[0052] This embodiment provides a design method for a high-performance integrated multimode bent optical waveguide. This method breaks through the limitation of the traditional fixed width of bent waveguides. By introducing variable width FFC and combining it with a full-mode loss optimization algorithm, it achieves low-loss and low-crosstalk transmission in a compact size.

[0053] like Figure 1 As shown, the curved optical waveguide structure to be designed is composed of multiple cascaded segments of variable-width generalized Euler spiral curves. Figure 7 As shown, this design method specifically includes the following steps:

[0054] Step S1: Construct the structural model of the freeform curve with variable width

[0055] The core of this step lies in obtaining the waveguide material parameters, cross-sectional structure parameters, and bending angle parameters of the integrated multimode bent optical waveguide to be designed, clarifying all operating modes and wavelengths of the transmitted light, and constructing the structural model of the multimode bent optical waveguide by using the curve trajectory and structural boundary of the flexible waveguide designed with a variable width freeform curve. A merit function is then defined to optimize the constructed structural model. The variable width FFC is composed of multiple cascaded variable width generalized Euler spiral curve elements; the merit function is constructed as a logical function targeting the loss optimization mechanism. The specific steps are as follows:

[0056] First, determine the material parameters (such as refractive index), cross-sectional structural parameters (such as film thickness and etching depth), and target bending angle (e.g., 90°) of the waveguide to be designed.

[0057] In this embodiment, the constructed structural model uses a "variable-width generalized Euler spiral" as the basic curve element. Unlike traditional Euler spirals that only change curvature, the curve element proposed in this invention has two degrees of freedom: both the radius of curvature R and the waveguide width W change linearly with the path length l. The bending angle design parameters of the bent optical waveguide structural model range from 0° to 360°. This invention can meet the layout requirements of different photonic integrated systems and is applicable to the design of composite devices with different bending angles, S-shaped bends, annular bends, and multi-level bending structures, thereby improving the versatility and scalability of bent optical waveguides in photonic integrated systems.

[0058] Specifically, for the i-th curve element, its geometric parameters include: the starting radius of curvature RS. i , endpoint radius of curvature RT i WS starting point width i Endpoint width WT i , curve element angle and fixed curve element length .

[0059] like Figure 2 As shown, the curvature of this curve element The width w is defined by the following formulas:

[0060]

[0061]

[0062] in, The path length variable represents the curve element, and its value range is... ; Indicates the tangential angle; Indicates path length The curvature at the point; RS represents the radius of curvature at the starting point of the curve element; RT represents the radius of curvature at the ending point of the curve element; represents the total length of the curve element (a constant); 'a' represents the curvature variation coefficient, which is determined by the length of the curve element and the difference in curvature radii at the start and end points.

[0063] Secondly, the waveguide width distribution of the curve element is defined. The waveguide width w of the curve element varies linearly with the transmission path, and its functional relationship is as follows:

[0064]

[0065]

[0066] in, Indicates path length The waveguide width at the point; WS represents the starting width of the curve element; WT represents the ending width of the curve element; b represents the width change slope (or width change coefficient), which is determined by the width difference between the starting and ending points of the curve element and its length.

[0067] Equations (1) and (2) establish the linear relationship between curvature and path, while equations (3) and (4) establish the linear relationship between waveguide width and path. This dual-parameter control mechanism allows the waveguide to dynamically adjust its optical field confinement capability during bending to adapt to the evolution of different modes in multimode transmission.

[0068] Step S2: Define full-mode loss evaluation metrics

[0069] The core of this step lies in setting the curve element length parameter in the structural model, the loss threshold parameter in the merit function, and the polarization ratio parameter in the constraints. The specific steps are as follows:

[0070] To ensure high-quality transmission across all operating modes (e.g., TE0, TE1, TE2), this invention does not optimize for a single mode but defines "all-mode loss" as an evaluation metric. The mode characteristics of the waveguide cross-section are calculated using a finite-difference eigenmode (FDE) solver. The all-mode mismatch loss is defined. The maximum value of the mode mismatch loss across all operating modes:

[0071]

[0072] in, This indicates the nth operating mode supported by the waveguide (e.g., TE0, TE1, TE2, etc.); n is a non-negative integer representing the mode order. This represents the mode mismatch loss of the nth-order operating mode; This indicates taking the maximum value of the corresponding loss value among all operating modes.

[0073] Define full-mode radiation loss The maximum radiation loss across all operating modes:

[0074]

[0075] in, This represents the radiation loss in the nth-order operating mode.

[0076] Step S3: Oriented Range Binary Search Optimization Based on Model Field Analysis

[0077] The core of this step lies in using a directional range binary search algorithm based on mode field analysis to iteratively optimize the curve elements in the curved optical waveguide structure model segment by segment. Each optimization focuses on only one segment of curve elements, performing multiple search iterations until the algorithm converges, at which point the iteration terminates, yielding the optimal geometric parameters of the curve element. The optimization then proceeds to the next segment, continuing until all curve elements have been optimized, at which point the optimization process terminates. The specific steps are as follows:

[0078] Traditional traversal algorithms are computationally intensive, while this embodiment employs a directional range binary search algorithm to rapidly iterate the geometric parameters of each curve element. The Form of Merit (FOM) is constructed as a logical function:

[0079]

[0080] in, and These are the preset mismatch loss threshold and radiation loss threshold, respectively. Expression and This is a Boolean logic judgment; the value is 1 if the condition is met, and 0 otherwise. Preferably, the full-mode mismatch loss threshold... The full-mode radiation loss threshold is 500 dB / m. It is 150dB / m.

[0081] Therefore, when both types of losses are below the threshold, the FOM value is... If any loss exceeds the threshold, the FOM value is -0.5. This FOM constructs a symmetrical numerical interval [-0.5, 0.5] centered at 0, which facilitates the binary search algorithm to quickly determine the convergence direction.

[0082] The optimization process is as follows:

[0083] 1. Segment-by-segment optimization: Starting from the beginning of the curved waveguide, optimize the first segment of the curve.

[0084] 2. Parameter search: While maintaining the curve element length With (e.g., 3 µm) remaining constant, adjust the endpoint radius of curvature RT. i and endpoint width WT iSince the waveguide mainly undergoes continuous bending, the starting parameter (RS) of the i-th segment... i WS i The boundary is usually determined by the endpoint parameter of the (i-1)th segment to maintain boundary continuity.

[0085] 3. Constraint Judgment: In the search process, in addition to satisfying the loss threshold, the mode polarization ratio γ is also introduced as a constraint condition:

[0086]

[0087] in, This represents the radial component (r component) of the electric field on the waveguide cross section. This represents the transverse component (x-component) of the electric field on the waveguide cross section. The square of the modulus represents the electric field strength; This represents the double integral over the waveguide cross section.

[0088] Note: For TE-dominated modes, γ should be close to 1; for TM-dominated modes, γ should be close to 0. The geometric parameter is considered valid only when γ is greater than a preset value (e.g., 0.98) to avoid modal hybridization.

[0089] 4. Binary Iteration: The binary search algorithm is used to quickly locate the parameter combination that satisfies the FOM logic condition in the parameter space.

[0090] Specifically, in order to intuitively verify the effectiveness of the above-mentioned directional range binary search algorithm and to demonstrate the influence of geometric parameters on loss, this embodiment records and analyzes the data during the optimization process.

[0091] Select the i-th curve element, and fix the length of the curve element. In the case of scanning starting point radius of curvature RS i and endpoint width WT i To clearly demonstrate the full-mode mismatch loss. Based on the changing trends of the two parameters and to highlight the optimal parameter region, this embodiment uses the following normalization formula to process the loss data in order to plot the normalized full-mode mismatch loss. Two-dimensional mapping diagram:

[0092]

[0093] in, This represents the normalized full-mode mismatch loss value, which ranges from [0, 1]. This represents the minimum full-mode mismatch loss value measured within the scanning range; This represents the natural logarithm operation, used to compress the dynamic range of data and enhance detail contrast.

[0094] like Figure 3 As shown in (a), this figure is a two-dimensional mapping generated based on the above formula (9). The closer the color in the figure is to black (the closer the value is to 0), the smaller the full-mode mismatch loss produced by the geometric parameter combination corresponding to that region. The position marked by the black dashed circle in the figure is the optimal parameter combination of that curve element under the current conditions (e.g., when the waveguide width shrinks to about 3.19µm). This result verifies that by jointly optimizing the radius of curvature and the waveguide width, the loss minimum point can be effectively found.

[0095] like Figure 3 (b) shows the logarithm of the full-mode radiation loss, ln(Rloss). i ) with RT i and WT i A changing two-dimensional mapping. As shown in the figure, Rloss... i With RT i and WT i Both show a negative correlation, that is, when RT i or WT i When Rloss decreases, i The corresponding increase.

[0096] As can be seen Figure 3 As shown in (a) and 3(b), by jointly optimizing the radius of curvature and waveguide width, the balance point between full-mode mismatch loss and radiation loss can be found (the location indicated by the black dashed circle in the figure). For example, in Under the condition of 40μm, if The micrometer size was optimized from 3.3μm to 3.19μm, which can effectively reduce... However, at the same time it will make The loss has increased slightly. Therefore, in practical design, a trade-off must be made between the two types of losses, taking into account their combined impact on the performance of the multimode bent waveguide, in order to determine the optimal parameter combination and achieve the best transmission performance of the device.

[0097] Step S4: Cascade to generate layout

[0098] The core of this step lies in cascading the obtained optimized curve elements sequentially to obtain a high-performance integrated multimode bent optical waveguide structure of this size, with an equivalent size of 84.9μm × 83.7μm. The specific steps are as follows:

[0099] After optimizing a curve element, its determined endpoint geometric parameters are used as the starting point parameters for the next curve element. Step S3 is repeated until all curve elements are optimized (covering angles from 0° to 90° or other target angles). Finally, all optimized curve elements are cascaded sequentially to generate a curve element as shown in the image. Figure 1 The complete integrated multimode bent optical waveguide layout is shown.

[0100] Example 2: Integrated Multimode Bending Optical Waveguide Based on Lithium Niobate Platform

[0101] This embodiment is based on the design method described in Embodiment 1, and specifically demonstrates a high-performance integrated trimode bent optical waveguide fabricated on an insulator-on-insulator (LNOI) platform.

[0102] 1. Structural parameters and materials

[0103] The waveguide adopts a ridge structure based on a Z-cut lithium niobate film. The total thickness of the lithium niobate film is 400 nm, the etching depth is 200 nm, a 200 nm plate layer is retained, and the buried oxide layer thickness is 4.7 µm.

[0104] The input and output ports of the waveguide are both set to 3.3µm to support the transmission of the three fundamental modes TE0, TE1 and TE2 as well as higher-order modes, and to achieve low-loss coupling with the external straight waveguide.

[0105] 2. Geometric morphology

[0106] like Figure 4 As shown in (a), the final optimized waveguide structure exhibits a non-monotonic, continuous variation in both curvature and width with the angle (or path length) within a 90° bending range. Figure 4 (b) shows the mode polarization ratios corresponding to each set of structural parameters. The results show that the mode polarization ratios of the optimized parameter combinations are all greater than 0.98, which fully meets the design requirements for avoiding modal hybridization.

[0107] Curvature variation: The waveguide smoothly transitions from a straight waveguide to a curved one, with the curvature gradually increasing and then decreasing, exhibiting a smooth transition characteristic similar to that of an Euler spiral.

[0108] Width Variation: Unlike traditional constant-width waveguides, the waveguide width in this embodiment is not constant at 3.3µm during bending. Instead, it is finely adjusted locally based on optimization results (e.g., the width decreases to approximately 3.19µm in certain high-curvature regions), and then returns to 3.3µm at the output. This dynamic adjustment of the width effectively suppresses mode field distortion of higher-order modes at abrupt bends. The equivalent bending radius of this waveguide structure is extremely compact, at only 84.9µm.

[0109] 3. Performance

[0110] (1) Transmission loss and crosstalk

[0111] The structure was simulated across the entire wavelength range of 1500 nm to 1600 nm using the finite-difference time-domain (FDTD) method. Figure 5 As shown in (a)-(c):

[0112] Transmission loss: The insertion loss of all three modes, TE0, TE1, and TE2, is extremely low across the entire broadband range. Specifically, TE0 loss is <0.014dB, TE1 loss is <0.019dB, and TE2 loss is <0.033dB.

[0113] Inter-mode crosstalk: Crosstalk between any two modes (e.g., TE0-TE1, TE1-TE2, etc.) is significantly suppressed, with the maximum inter-mode crosstalk below -25.287dB. This indicates that the structure can independently and clearly transmit multi-mode signals.

[0114] (2) Process tolerance (robustness)

[0115] In actual manufacturing, etching errors inevitably lead to linewidth deviations. This waveguide requires width deviation measurement. Scanning simulation, setting waveguide width deviation The range of W is -160nm to +160nm, with a step size of 20nm. During the simulation, three modes, TE0, TE1, and TE2, were excited as input optical signals, with the operating wavelength set to 1550nm. The transmission spectrum components of each mode at the output port were extracted using a mode extension monitor. The results are as follows: Figure 6 As shown in (a)-(c).

[0116] When the waveguide width deviation varies within a wide range of ±140 nm, this structure still maintains intermode crosstalk below -20 dB for all modes, with negligible increase in transmission loss (<0.088 dB). Compared to existing technologies that typically have a tolerance range of only around ±20 nm, the structure of this invention exhibits superior process robustness, significantly reducing reliance on high-precision photolithography processes and improving device yield.

[0117] To further verify the advantages of this invention, the theoretical performance of integrated three-mode bent optical waveguides on a lithium niobate platform reported in existing studies was compared and analyzed, and the results are shown in Table 1. The compared metrics include equivalent radius, transmission loss, inter-mode crosstalk, and line tolerance. The results show that, compared to the etched grooved circular arc structure and optimized B-spline curve structure used in existing literature, the embodiments of this invention achieve a smaller bending radius while ensuring low loss and low crosstalk, and exhibit superior robustness and robustness.

[0118] Table 1

[0119]

[0120] Example 3: Application of Other Material Platforms

[0121] Although Example 2 uses lithium niobate anisotropic material as an example, those skilled in the art should understand that the "variable width generalized Euler spiral" design method described in this invention is also applicable to isotropic material platforms.

[0122] For example, the waveguide structure can be fabricated based on silicon-on-insulator (SOI), silicon nitride (SiN), indium phosphide (InP), gallium arsenide (GaAs), or polymer materials.

[0123] For the SOI platform, simply replace the material refractive index parameter with the silicon parameter in step 1, and adjust the initial width and cross-sectional dimensions of the waveguide according to the high refractive index contrast of silicon (e.g., using a top silicon thickness of 220 nm or 340 nm). Then, perform the same full-mode loss optimization process to obtain a variable-width multimode bent waveguide suitable for the silicon photonics platform. Due to the high refractive index contrast of silicon, a smaller equivalent bending radius than in Example 2 is expected to be achieved.

[0124] In summary, this invention introduces waveguide width as a second degree of design freedom besides curvature in multimode curved waveguide design and utilizes an efficient binary search algorithm for full-mode optimization, successfully resolving the contradiction between multimode waveguide size, loss, crosstalk, and process tolerance, thus providing an ideal connection scheme for high-density on-chip mode division multiplexing systems.

[0125] Those skilled in the art should understand that the technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0126] The above embodiments are merely illustrative of several implementations of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims

1. A design method for an integrated multimode bent optical waveguide, characterized in that, Includes the following steps: A structural model of the curved optical waveguide to be designed is constructed. The structural model uses a variable-width freeform curve to describe the geometric boundary of the waveguide. The variable-width freeform curve is composed of multiple cascaded curve elements. Each curve element is configured to have a curvature radius parameter and a waveguide width parameter that vary independently with the path length. All operating modes of the curved optical waveguide transmission are determined, and full-mode loss evaluation metrics are defined for all operating modes. Based on the modal field analysis, the full-mode loss of the structural model under the current geometric parameters is calculated, and the geometric parameters of each curve element are iteratively optimized with the goal of satisfying the preset threshold for the full-mode loss, until the optimal geometric parameter sequence is obtained. The layout structure of the integrated multimode bent optical waveguide is generated based on the optimal geometric parameter sequence.

2. The design method as described in claim 1, characterized in that, The curve element is a variable-width generalized Euler spiral curve element; The curvature radius parameter that varies independently with the path length is expressed as follows: the curvature of the curve element changes linearly with its path length; The waveguide width parameter, which varies independently with the path length, is characterized by the fact that the width of the curve element changes linearly with its path length.

3. The design method as described in claim 2, characterized in that, The geometric parameters of each curve element include: starting radius of curvature, ending radius of curvature, starting width, ending width, curve element angle, and curve element length; During the iterative optimization process, the length of the curve element is set to a fixed value, and at least one of the starting radius of curvature, the ending radius of curvature, the starting width, and the ending width is used as an adjustable optimization variable.

4. The design method as described in claim 1, characterized in that, The full-mode loss evaluation index includes full-mode mismatch loss and full-mode radiation loss. The full-mode mismatch loss is defined as the maximum value of the mode mismatch loss of each order mode in all the operating modes; The full-mode radiation loss is defined as the maximum value of the radiation loss of each mode in all operating modes.

5. The design method as described in claim 4, characterized in that, The iterative optimization process employs a directional range binary search algorithm. The algorithm constructs a merit function, which is configured as a logical function, to determine whether the current full-mode mismatch loss and full-mode radiation loss are lower than the set mismatch loss threshold and radiation loss threshold, respectively. If the conditions are met, the current geometric parameters are determined to be valid and the search for a better solution continues or the iteration is terminated.

6. The design method as described in claim 1, characterized in that, In the iterative optimization process, the mode polarization ratio is also introduced as a constraint. The mode polarization ratio of each working mode under the current geometric parameters is calculated. The optimization result under the geometric parameters is only accepted if the mode polarization ratio meets the preset polarization purity requirement, so as to suppress modal hybridization.

7. The design method as described in claim 1, characterized in that, In the structural model, the width of the input port and the width of the output port are equal when the curved optical waveguide is connected to the external straight waveguide; Furthermore, the iterative optimization involves optimizing each of the multiple cascaded curve elements segment by segment, with the endpoint geometric parameters of the previous curve element serving as constraints on the starting point geometric parameters of the next curve element, in order to maintain the continuity of the waveguide boundary.

8. The design method as described in claim 1, characterized in that, The material of the bent optical waveguide includes one of silicon, silicon nitride, silicon dioxide, indium phosphide, gallium arsenide, silicon carbide, lithium niobate, or polymer materials; The structure of the curved optical waveguide includes strip waveguide, ridge waveguide or multilayer waveguide.

9. An integrated multimode bent optical waveguide, characterized in that, The curved optical waveguide is fabricated using the design method described in any one of claims 1 to 8; The geometry of the curved optical waveguide consists of multiple cascaded variable-width generalized Euler spiral curve elements. The radius of curvature and waveguide width of each curve element change continuously with the optical transmission path, and the overall bending angle of the curved optical waveguide ranges from 0° to 360°.

10. The integrated multimode bent optical waveguide according to claim 9, characterized in that, The curved optical waveguide is configured to support at least three spatial mode transmissions; Within the preset operating wavelength range, the transmission loss of the curved optical waveguide for all supported spatial modes and the inter-mode crosstalk between any two spatial modes are lower than the preset index, and the curved optical waveguide has a process tolerance that allows for waveguide width manufacturing deviations within the preset range.

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