A method of designing a curved waveguide

Abstract

The application provides a design method of a curved waveguide, which comprises the following steps: parameterized modeling of the curved waveguide through a first curve and a second curve, wherein the first curve is used to control the change of the curvature radius of the curved waveguide along the arc length of the waveguide center line, and the second curve controls the change of the waveguide width along the arc length of the waveguide center line; taking the control point coordinates of the first curve and the second curve as design variables, in each round of iteration of an optimization algorithm, a geometric model of the curved waveguide is generated through the parameterized modeling according to the design variable values of the current round; and taking the transmittance obtained by optical simulation on the geometric model as an optimization target, the design variables are iteratively optimized to obtain a set of optimal control point coordinates as the structural parameters of the curved waveguide. The application realizes the global optimization of the waveguide geometric shape in a wider search space by decoupling the curvature distribution optimization and the width distribution optimization into two independent design dimensions, and significantly reduces the curved transmission loss.

Description

Technical Field

[0001] This invention relates to the field of optical device design technology, and in particular to a design method for a bent waveguide. Background Technology

[0002] With the rapid development of photonic integrated circuit technology, various material platforms such as silicon-on-insulator (SOI), silicon nitride (Si3N4), indium phosphide (InP), and lithium niobate (LiNbO3) have been widely used in data center interconnects, high-performance computing, optical sensing, and quantum information. Bent waveguides, as key routing structures connecting various functional devices in photonic integrated circuits, directly affect the overall chip performance due to their transmission loss and occupied area. In large-scale photonic integrated systems, the sheer number of bent waveguides means that even small individual device losses can accumulate significantly after cascading.

[0003] The differences in refractive index contrast, mode confinement capability, and fabrication dimensions across different material platforms lead to variations in the design window and dominant loss mechanisms of bent waveguides. The design challenges of bent waveguides essentially stem from two competing loss mechanisms: first, bending radiation loss, where higher curvature (smaller radius) results in higher radiation loss, particularly pronounced on lower refractive index contrast platforms (such as Si3N4); and second, mode conversion loss, where abrupt curvature changes at the junction of the bent section and the straight waveguide, causing mode field mismatch. Furthermore, wide waveguide structures are prone to exciting higher-order modes, increasing intermode crosstalk. These issues exist in both high and medium-to-low refractive index contrast material platforms, albeit to varying degrees and within different design windows.

[0004] Traditional bent waveguides typically employ a circular arc structure with a fixed radius of curvature, maintaining a constant waveguide width. This simple structure exhibits significant mode-field mismatch at the mode-switching interface, leading to high transition losses. In recent years, adiabatic bent waveguides based on Euler spirals have been proposed and applied to silicon-based platforms, reducing mode-switching losses through continuous gradual changes in curvature; Bézier curve bent waveguides have also been proven to effectively reduce bending losses.

[0005] However, all of the above methods suffer from insufficient design freedom: the curvature variation law of the Euler spiral is fixed; and it is difficult to achieve global optimization for a specific material platform and bending radius in traditional Bézier profile curved waveguides. In other words, in existing curved waveguide design methods, the geometry of the curved waveguide is limited by a preset single function form or a simple combination thereof, and the geometric space that can be described is extremely limited, which often leads to the design results deviating from the true optimal geometric profile. Summary of the Invention

[0006] This invention provides a design method for curved waveguides to address the limitations of the design flexibility and freedom of curved waveguides in the prior art. It achieves a universal solution for curved waveguide design that can simultaneously and independently optimize the waveguide curvature radius distribution and waveguide width distribution, can be extended to any bending angle, and is applicable to different material platforms.

[0007] This invention provides a method for designing a curved waveguide, comprising: Based on a predefined first curve and a second curve, a parametric model of a curved waveguide is performed. The first curve is used to control the change of the radius of curvature of the curved waveguide along the arc length of the waveguide centerline, and the second curve is used to control the change of the width of the curved waveguide along the arc length of the waveguide centerline. Both the first curve and the second curve are parametric design curves defined by control points and basis functions. Using the coordinates of the control points of the first and second curves as design variables, in each iteration of the optimization algorithm, the geometric model of the curved waveguide is generated through the parametric modeling based on the design variable values ​​of the current iteration. Using the transmittance obtained from optical simulation of the geometric model as the optimization objective, the design variables are iteratively optimized to obtain a set of optimal control point coordinates as the parameters of the curved waveguide structure, thus completing the design of the curved waveguide.

[0008] According to the present invention, a design method for a curved waveguide is provided, wherein the parametric design curves include Bézier curves, spline interpolation curves, B-spline curves, and non-uniform rational B-spline curves.

[0009] According to the design method of the curved waveguide provided by the present invention, the horizontal axis of the first curve represents the arc length of the center line of the curved waveguide, and the vertical axis represents the radius of curvature at the corresponding arc length position; the horizontal axis of the second curve represents the arc length of the center line of the curved waveguide, and the vertical axis represents the waveguide width at the corresponding arc length position.

[0010] According to a design method for a curved waveguide provided by the present invention, the step of generating a geometric model of the curved waveguide via parametric modeling specifically includes: Based on the design variable values ​​of the current round, integrate along the arc length of the first curve to generate the centerline trajectory of the curved waveguide through integration. Based on the design variable values ​​of the current round and the variation law of the waveguide width along the arc length of the waveguide centerline defined by the second curve, the complete geometric boundary of the curved waveguide is generated along the normal direction of the centerline trajectory, and the geometric model of the curved waveguide is generated.

[0011] According to the present invention, a design method for a curved waveguide includes an optimization algorithm comprising one of particle swarm optimization, gradient descent, and genetic algorithm.

[0012] According to a design method for a curved waveguide provided by the present invention, before the step of iteratively optimizing the design variables with the transmittance obtained by optical simulation of the geometric model as the optimization objective, the method further includes: Set the minimum constraint value for the radius of curvature; Set waveguide width constraints for the start and end segments of the curved waveguide; The minimum constraint value and the waveguide width constraint are used as constraints in the simulation optimization process to constrain the search range of the control points.

[0013] According to the present invention, a design method for a curved waveguide is provided, wherein the curved waveguide has a bending angle range greater than 0° and less than or equal to 360°.

[0014] According to the design method of the curved waveguide provided by the present invention, the optical simulation is realized based on the three-dimensional time-domain finite difference method.

[0015] The present invention also provides a curved waveguide, which is designed by any of the curved waveguide design methods described above.

[0016] The parametric modeling module is used to parametrically model the curved waveguide based on a predefined first curve and a second curve. The first curve is used to control the change of the radius of curvature of the curved waveguide along the arc length of the waveguide centerline, and the second curve is used to control the change of the width of the curved waveguide along the arc length of the waveguide centerline. Both the first curve and the second curve are parametric design curves defined by control points and basis functions. The geometric modeling module is used to generate the geometric model of the curved waveguide in each iteration of the optimization algorithm, using the coordinates of the control points of the first curve and the second curve as design variables, based on the design variable values ​​of the current iteration. The iterative optimization module is used to iteratively optimize the design variables with the transmittance obtained from the optical simulation of the geometric model as the optimization target, so as to obtain a set of optimal control point coordinates as the bending waveguide structure parameters and complete the design of the bending waveguide.

[0017] This invention provides a design method for curved waveguides. By decoupling curvature distribution optimization and width distribution optimization into two independent design dimensions, the method achieves parametric modeling of the curved waveguide using a predefined first curve describing the change of the curved waveguide's radius of curvature along the arc length of the waveguide's centerline and a second curve describing the change of the curved waveguide's width along the arc length of the waveguide's centerline. This allows the subsequent iterative optimization process to search for the globally optimal result in a wider geometric space, enabling precise control of the waveguide geometry, significantly reducing bending transmission loss, and extending to a larger angle range. Furthermore, it is applicable to various material platforms, exhibiting broad platform adaptability and design versatility. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 This is one of the flowcharts illustrating the design method for the bent waveguide provided by this invention; Figure 2 This is a schematic diagram of the structure of a 90° bent waveguide in the design method of the bent waveguide provided by the present invention; Figure 3 This is a schematic diagram of the structure of a 180° bent waveguide in the design method of the bent waveguide provided by the present invention; Figure 4 This is the second flowchart illustrating the design method for bent waveguides provided by this invention; Figure 5 This is a schematic diagram showing the variation of the radius of curvature along the arc length of the waveguide centerline of a 90° curved waveguide designed by the curved waveguide design method provided by this invention. Figure 6 This is a schematic diagram showing the variation of the waveguide width along the arc length of the waveguide centerline of a 90° curved waveguide designed by the curved waveguide design method provided by this invention. Figure 7 The present invention provides a mode field diagram of a 90° curved waveguide with an equivalent radius of 15μm, designed using the curved waveguide design method provided in this invention. Figure 8 This is a comparison chart of the transmittance of the curved waveguide design method provided by this invention and a 90° curved waveguide designed using the circular arc method under the same conditions. Figure 9 The present invention provides a mode field diagram of a 180° curved waveguide with an equivalent radius of 12μm, designed using the curved waveguide design method provided in this invention. Figure 10 This is a comparison chart of the transmittance of the curved waveguide design method provided by this invention and a 180° curved waveguide designed using the circular arc method under the same conditions. Figure 11 This is a schematic diagram of the structure of the curved waveguide design device provided by the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0021] The following is combined Figures 1 to 4 This invention introduces a design method for a bent waveguide, such as... Figure 1 As shown, it includes: Step 101: Based on the predefined first curve and second curve, perform parametric modeling of the curved waveguide. The first curve is used to control the change of the radius of curvature of the curved waveguide along the arc length of the waveguide centerline, and the second curve is used to control the change of the width of the curved waveguide along the arc length of the waveguide centerline. Both the first curve and the second curve are parametric design curves defined by control points and basis functions. Step 102: Using the control point coordinates of the first curve and the second curve as design variables, in each iteration of the optimization algorithm, the geometric model of the curved waveguide is generated through the parametric modeling based on the design variable values ​​of the current iteration. Step 103: Using the transmittance obtained from the optical simulation of the geometric model as the optimization objective, iteratively optimize the design variables to obtain a set of optimal control point coordinates as the parameters of the curved waveguide structure, thus completing the design of the curved waveguide.

[0022] Unlike conventional parametric modeling schemes that couple the curvature and width variations of curved waveguides within the same fixed function framework, and unlike some studies that indirectly determine the curvature distribution by directly describing the physical boundary of the curved waveguide using preset curves, this invention predefines a first curve describing the variation of the curvature radius of the curved waveguide along the arc length of the waveguide centerline, and a second curve describing the variation of the width of the curved waveguide along the arc length of the waveguide centerline. Parametric modeling of the curved waveguide is completed using these two independent parametric curves, decoupling curvature distribution optimization from width distribution optimization into two independent design dimensions. This allows subsequent iterative optimization processes to search for the globally optimal result in a wider geometric space, achieving precise control of the waveguide geometry and significantly reducing bending transmission loss.

[0023] In one specific embodiment, an optical waveguide based on silicon nitride (SiN-on-Insulator) material is selected as the design object to illustrate the design method of the present invention in detail. The waveguide core layer is made of Si3N4 (silicon nitride) material with a thickness of 400 nm and a refractive index of approximately 1.98 (1550 nm wavelength); the substrate and upper cladding material are SiO2 with a refractive index of 1.44. The operating wavelength is around 1550 nm, and the operating polarization state is TE (transverse electric mode) polarization. Its refractive index contrast Δn is approximately 0.54, which is about 3.7 times lower than that of the SOI platform (Δn approximately 2.0), thus requiring a larger bending radius and a more refined design method.

[0024] After clarifying the basic design parameters used for simulation based on the design requirements, the first curve and the second curve are first defined to perform parametric modeling of the curved waveguide.

[0025] In some feasible implementations, parametric design curves include Bézier curves, spline interpolation curves, B-spline curves, and non-uniform rational B-spline curves.

[0026] Spline interpolation curves generate smooth interpolation curves through control points, making them suitable for dynamically adjusting waveguide widths, optimizing spectral response characteristics, and reducing optical signal loss. B-splines exhibit local support (moving a single control point only affects the local curve), and their order and number of control points can be set independently, resulting in better convergence optimization. They are suitable for waveguide width and curvature distribution designs requiring high-precision local control. Non-uniform rational B-spline curves have significant advantages when accurately representing the curvature distribution of circular arc segments. Parametric design curves, including the first and second curves, can be flexibly selected according to design requirements.

[0027] Optionally, the first curve and the second curve can be the same parametric design curve, such as both being Bézier curves, or they can be different parametric design curves, such as the first curve being a Bézier curve and the second curve being a spline interpolation curve.

[0028] In a preferred embodiment, the first curve is a Bézier curve of order 3 or higher, and the second curve is an independent Bézier curve of order 3 or higher.

[0029] Higher-order Bézier curves, through independently adjustable control points, can characterize any continuous and smooth radius of curvature distribution, encompassing all commonly used forms such as Euler spirals, sine variations, and circular arcs as special cases. They can also describe non-monotonic curvature distributions that existing methods cannot achieve. This high degree of freedom in the design space enables optimization algorithms to discover the true globally optimal curvature profile.

[0030] In some feasible implementations, the first curve has the arc length s of the curved waveguide centerline as the abscissa and the radius of curvature R(s) at that point as the ordinate, and the second curve has the arc length s of the curved waveguide centerline as the abscissa and the waveguide width w(s) at that point as the ordinate.

[0031] In a preferred embodiment, the first curve is a 7th-order Bézier curve, corresponding to 8 control points. The curvature radius R(s) along the arc length is defined as the abscissa and the curvature radius R(s) at that point is defined as the ordinate. Thus, the curve is defined by curvature to describe any continuous and smooth curve distribution, breaking through the limitations of fixed curvature functions such as Euler spiral and sine function.

[0032] The second curve is a third-order Bezier curve, corresponding to four control points. The arc length s of the curved waveguide centerline is used as the abscissa, and the waveguide width w(s) at that point is used as the ordinate. The variation law of the waveguide width along the arc length of the waveguide centerline is defined. Thus, the waveguide width profile can be precisely controlled by the position of the control points. The waveguide width is increased in the high curvature region to strengthen the mode field constraint, and the width is reduced in the low curvature region to match the straight waveguide.

[0033] Optionally, in practical applications, the order of the curve (which determines the number of control points) can be flexibly selected according to the design accuracy requirements. The higher the order of the curve and the more control points there are, the greater the degree of freedom in describing the curve shape.

[0034] The design of the first and second curves can be completed in the above manner, and the parametric modeling of the curved waveguide can be realized.

[0035] In a preferred embodiment, in each iteration of the optimization algorithm, the step of generating the geometric model of the curved waveguide via the parametric modeling, based on the design variable values ​​of the current iteration, specifically includes: Based on the design variable values ​​of the current round, integrate along the arc length of the first curve to generate the centerline trajectory of the curved waveguide through integration. Based on the design variable values ​​of the current round and the variation law of the waveguide width along the arc length of the waveguide centerline defined by the second curve, the complete geometric boundary of the curved waveguide is generated along the normal direction of the centerline trajectory, and the geometric model of the curved waveguide is generated.

[0036] Taking the first curve above as a 7th-order Bézier curve and the second curve as a 3rd-order Bézier curve as an example, the two curves have a total of 12 control points. The 24 independent variables corresponding to the horizontal and vertical coordinates of each control point are the design variables of the optimization algorithm.

[0037] In each iteration of the optimization algorithm, the coordinates of a set of 12 control points can be determined based on the design variable values ​​of the current round. Then, the first curve and the second curve are obtained by fitting the control point coordinates and the Bézier curve basis function respectively.

[0038] The optimization algorithm can be particle swarm optimization, gradient descent, or genetic algorithm, or other similar optimization algorithms.

[0039] After determining the first and second curves, the waveguide centerline tangent angle is obtained by integrating 1 / R(s) along the arc length based on the radius of curvature distribution R(s) of the first curve. Then, by integration, we obtain the coordinate parameter equations (x(s), y(s)) of the centerline of the curved waveguide in the Cartesian coordinate system. Taking a 90° curved waveguide and a 180° curved waveguide as examples, for a 90° curve, the integration is as follows: For a 180° bend, integrate to .

[0040] Since both the first and second curves use the arc length s of the curved waveguide centerline as the independent variable, the above integration process and width mapping process can be directly applied to 90°, 180°, 360° and other arbitrary bending angles, without the need for segmentation processing for bends exceeding 90°.

[0041] In implementations that require generating symmetrical curved structures, the symmetry relationship can be satisfied by setting the coordinates of corresponding control points, or symmetry constraints can be added during the optimization process to ensure that the generated centerline trajectory and width distribution meet the device layout requirements.

[0042] Then, based on the width distribution w(s) determined by the second curve and the centerline normal vector, the complete curved waveguide geometric boundary is generated.

[0043] After determining the centerline equation, the arc length s is discretely sampled in its value interval [0, S] to obtain a series of discrete coordinate points of the centerline. For each discrete sampling point on the centerline, the waveguide width value corresponding to that point is determined.

[0044] When the second curve defines the width distribution w(s) with arc length s as the independent variable, the corresponding width can be obtained directly from the second curve using the arc length value of the current sampling point, which is applicable to any bending angle.

[0045] After determining the width *w* at each sampling point, the upper and lower boundary points of the waveguide are obtained by offsetting by a distance *w / 2* along the normal vector direction at that point. The normal vector direction at each sampling point can be determined by the tangent direction of the centerline. The bending waveguide is obtained by rotating it ±90°. Connecting the upper boundary points and the lower boundary points in sequence, and then closing them with straight line segments at the input and output ends, the geometric model of the bending waveguide is obtained.

[0046] Among them, the 90° curved waveguide, such as Figure 2 As shown, it includes a first input structure 1, a first curved waveguide section 2 and a first output structure 3. The TE fundamental mode light is input from the upper left port (first input structure 1), propagates in the horizontal direction, turns after passing through the 90° curved section (first curved waveguide section 2), and is output vertically downward from the lower right port (first output structure 3). At the same time, the optical path is reversible, and the input and output ports can be reversed.

[0047] 180° curved waveguide, such as Figure 3 As shown, it includes a second input structure 4, a second curved waveguide segment 5, and a second output structure 6. The TE fundamental mode light is input from the upper left port (second input structure 4) and propagates to the right. After passing through a complete semi-circular bend (180°) (second curved waveguide segment 5), it is reversed and output to the left from the lower left port (second output structure 6). At the same time, the optical path is reversible, and the input and output ports can be reversed.

[0048] It should be noted that the design method of the present invention can be directly extended to any bending angle by changing the integral termination condition (i.e., the cumulative rotation angle).

[0049] Once the geometric model of the curved waveguide is defined for each iteration, the transmittance of the curved waveguide under this geometry can be determined through optical simulation.

[0050] In a preferred embodiment, optical simulation is performed using a three-dimensional finite-difference time-domain (3D-FDTD) algorithm. The light source is placed at the input end of the curved waveguide. In this embodiment, the TE fundamental mode (1550nm) is injected, and a mode unfolding monitor is set at the output end to calculate the TE fundamental mode transmittance as the optimization objective function (FOM).

[0051] It is understandable that if the injected mode is a TM fundamental mode or other higher-order modes, the objective function is constructed using the corresponding fundamental mode transmittance as the optimization target.

[0052] In this embodiment, a particle swarm optimization (PSO) algorithm is introduced for inverse optimization. The number of iteration rounds is set to 1000, with 32 particles per round. Iteration optimization continues until convergence or the maximum number of iteration rounds is reached. In other feasible embodiments, the number of iteration rounds and the number of particles per round can be adaptively adjusted.

[0053] In a preferred embodiment, before the step of iteratively optimizing the design variables with the transmittance obtained from optical simulation of the geometric model as the optimization objective, the method further includes: Set the minimum constraint value for the radius of curvature; Set waveguide width constraints at the start and end segments of the curved waveguide so that the waveguide widths of the start and end segments match the widths of the corresponding connected straight waveguides or functional device ports, respectively. The minimum constraint value and the waveguide width constraint are used as constraints in the simulation optimization process to constrain the search range of the control points.

[0054] In this embodiment, before iterative optimization, the boundary of the design space is restricted by preset constraints to narrow the search range and avoid the optimization algorithm wasting computing resources in invalid or suboptimal regions.

[0055] Specifically, the smaller the radius of curvature, the greater the radiation loss. Therefore, a minimum constraint value is set for the radius of curvature to limit it within a range that can be compensated for by width optimization. This minimum constraint value is determined based on the bending radius and is typically no less than 60% of the bending radius.

[0056] Furthermore, in order to achieve a smooth mode transition and reduce connection loss, the waveguide width constraints at the start and end segments of the curved waveguide were also limited.

[0057] Optionally, the waveguide widths of the starting and ending segments are matched with the widths of the corresponding connected straight waveguides or functional devices ports, respectively. When both ends are connected to straight waveguides of the same width, the widths of the starting and ending segments can be the same. When both ends are connected to straight waveguides or functional devices of different widths, the widths of the starting and ending segments can also be different.

[0058] The starting segment and the ending segment are preset percentage ranges of arc length starting from the starting position and the ending position, respectively. For example, the bending segment corresponding to the first 5% arc length is determined as the starting segment, and the bending segment corresponding to the last 5% arc length is set as the ending segment.

[0059] Optionally, curvature-width co-constraints, port width matching constraints, or pattern matching constraints can be established based on specific material platforms and device connection relationships to further constrain the search range of control points.

[0060] For example, curvature-width coordination constraints, port width matching constraints, or pattern matching constraints can be set according to the specific material platform and device connection relationship; the constraint does not limit the curvature radius and width to maintain a fixed positive or negative correlation.

[0061] Then, the above constraints are used as constraints in the iterative optimization process to speed up the search and make it easier to find the global optimal solution.

[0062] Based on this, a complete design flow for a bent waveguide is as follows: Figure 4 As shown, this invention addresses the problems in existing curved waveguide designs, such as insufficient design freedom of curvature distribution, failure to independently and collaboratively optimize curvature and width, difficulty in extending the design method to arbitrary angles, and high bending loss at small radii on different material platforms. It proposes a reverse design method that independently controls the changes in waveguide curvature radius and waveguide width, and is applicable to the design of multi-radius and multi-angle curved waveguides on material platforms such as Si3N4, SiO2, SOI, and InP, achieving extremely low bending transmission loss.

[0063] Meanwhile, the design method of this invention is decoupled from specific material systems. By adjusting the control point constraint range and FDTD simulation parameters, it can be directly applied to different photonic integrated material platforms such as SOI silicon-based, Si3N4 silicon nitride, and InP indium phosphide, as well as different device types such as bent waveguides, bent sections of micro-ring resonators, and bent directional couplers. There is no need to redevelop the design framework, which has broad platform adaptability and design versatility.

[0064] The present invention provides a curved waveguide, which is designed based on the curved waveguide method described above.

[0065] Under the material platform and design parameters described above, the Si3N4 platform 90° bent waveguide (equivalent radius R) designed using the bent waveguide design method of this invention is shown below. eff =15 The simulation loss is 0.05 dB / 90°, and the radius of curvature starts from approximately 20. Lower to the middle of the bend, then rise to the end at approximately 35 degrees. It exhibits a non-monotonic distribution that first decreases and then increases, such as Figure 5 As shown; the waveguide width starts at 1.0 at the input end. Increased to a peak of approximately 1.86 It then drops to approximately 1.0 at the output. ,like Figure 6 As shown. Its modulus field diagram is as follows. Figure 7 As shown. This distribution is a specific result obtained through optimization in this embodiment and does not constitute a limitation on the width distribution or radius of curvature distribution of this invention.

[0066] In contrast, under the same material platform and the same bending radius, using a fixed 1 Traditional 90° curved waveguide with a width of (R=15) The simulated loss at 1550nm is 0.26dB / 90°, indicating that the R designed in this invention... eff =15 The 90° bent waveguide has a loss of 0.05dB / 90° at 1550nm, which is more than 5 times lower than that of the traditional structure.

[0067] Another 90° curved waveguide (equivalent radius R) on a Si3N4 platform was designed using the curved waveguide design method of this invention. eff =12 The simulated loss at 1550nm is 0.11dB / 90°. For comparison, a fixed loss of 1... Traditional 90° curved waveguide with a width of (R=12) The simulated loss at 1550nm is 0.54dB / 90°, and the present invention also achieves a 4.9-fold reduction in loss at this radius.

[0068] The equivalent radius designed using the method of this invention is 12. and 15 The transmittance comparison chart is shown below for a 90° bent waveguide and a 90° bent waveguide using the traditional circular arc method with the same material platform and bending radius. Figure 8 As shown.

[0069] A 180° curved waveguide (equivalent radius R) designed using the curved waveguide design method of this invention. eff =15 The simulated loss at 1550 nm is 0.04 dB / 180°. For comparison, a 180° bent waveguide (R=15) with a uniform-width circular arc structure... The simulated loss at 1550nm is 0.52dB / 180°. Compared with the traditional structure, the loss of the 180° curved waveguide designed in this invention is reduced by more than an order of magnitude.

[0070] Another 180° curved waveguide (equivalent radius R) designed using the curved waveguide design method of this invention eff =12 ),like Figure 10 As shown, the simulated loss at 1550nm is 0.14dB / 180°, and its mode field diagram is as follows. Figure 9 As shown. In contrast, a 180° bent waveguide (R=12) employing a uniform-width circular arc structure is also shown. The simulated loss at 1550nm is 1.08dB / 180°, and the present invention also achieves a significant loss reduction at this radius.

[0071] The equivalent radius designed using the method of this invention is 12. and 15 The transmittance comparison chart is shown below for a 180° bent waveguide and a 180° bent waveguide using the traditional circular arc method with the same material platform and bending radius. Figure 10 As shown.

[0072] Furthermore, at 1550 nm, the R obtained using the design of this invention... eff =15 The 180° bent waveguide has a total loss (0.04dB) that is significantly lower than the two R-segment waveguides designed in this invention. eff =15 The sum of the losses of the 90° bent waveguide (2 × 0.05 = 0.10 dB); the R obtained by using the design of this invention eff =12 The 180° bent waveguide also has a lower total loss (0.14dB) than the two R-segments designed in this invention. eff =12 The sum of the losses in the 90° bend waveguide is (2 × 0.11 = 0.22 dB). This indicates that, compared to the splicing scheme of "two 90° bends connected to a straight waveguide in the middle", the 180° continuous bend waveguide generated directly using the design method of this invention can eliminate the additional connection loss introduced by mode field mismatch at the splicing interface of the two bends. Therefore, when designing structures that require continuous large-angle bends, such as U-shaped bends, spiral optical paths, and micro-ring resonators, the 180° bend waveguide designed in this invention can bring significant system-level advantages.

[0073] The following describes a design apparatus for a curved waveguide provided by the present invention. The curved waveguide design apparatus described below is based on the curved waveguide method described above.

[0074] like Figure 11 As shown, the design device for the curved waveguide of the present invention includes a parameter modeling module 1101, a geometric modeling module 1102, and an iterative optimization module 1103; The parameter modeling module 1101 is used to perform parameterized modeling of the curved waveguide based on a predefined first curve and a second curve. The first curve is used to control the change of the radius of curvature of the curved waveguide along the arc length of the waveguide centerline, and the second curve is used to control the change of the width of the curved waveguide along the arc length of the waveguide centerline. Both the first curve and the second curve are parameterized design curves defined by control points and basis functions. The geometric modeling module 1102 is used to generate the geometric model of the curved waveguide in each iteration of the optimization algorithm, using the coordinates of the control points of the first curve and the second curve as design variables, based on the design variable values ​​of the current iteration. The iterative optimization module 1103 is used to perform iterative optimization on the design variables with the transmittance obtained by optical simulation of the geometric model as the optimization target, so as to obtain a set of optimal control point coordinates as the bending waveguide structure parameters and complete the design of the bending waveguide.

[0075] Unlike conventional parametric modeling schemes that couple the curvature and width variations of curved waveguides within the same fixed function framework, and unlike some studies that indirectly determine the curvature distribution by directly describing the physical boundary of the curved waveguide using preset curves, this invention predefines a first curve describing the variation of the curvature radius of the curved waveguide along the arc length of the waveguide centerline, and a second curve describing the variation of the width of the curved waveguide along the arc length of the waveguide centerline. Parametric modeling of the curved waveguide is completed using these two independent parametric curves, decoupling curvature distribution optimization and width distribution optimization into two independent design dimensions. This allows subsequent iterative optimization processes to search for the globally optimal result in a wider geometric space, achieving precise control of the waveguide geometry.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A design method for a bent waveguide, characterized in that, include: Based on a predefined first curve and a second curve, a parametric model of a curved waveguide is performed. The first curve is used to control the change of the radius of curvature of the curved waveguide along the arc length of the waveguide centerline, and the second curve is used to control the change of the width of the curved waveguide along the arc length of the waveguide centerline. Both the first curve and the second curve are parametric design curves defined by control points and basis functions. Using the coordinates of the control points of the first and second curves as design variables, in each iteration of the optimization algorithm, the geometric model of the curved waveguide is generated through the parametric modeling based on the design variable values ​​of the current iteration. Using the transmittance obtained from optical simulation of the geometric model as the optimization objective, the design variables are iteratively optimized to obtain a set of optimal control point coordinates as the parameters of the curved waveguide structure, thus completing the design of the curved waveguide.

2. The design method for a bent waveguide according to claim 1, characterized in that, The parametric design curves include Bézier curves, spline interpolation curves, B-spline curves, and non-uniform rational B-spline curves.

3. The design method for a bent waveguide according to claim 1, characterized in that, The horizontal axis of the first curve represents the arc length of the centerline of the curved waveguide, and the vertical axis represents the radius of curvature at the corresponding arc length position; the horizontal axis of the second curve represents the arc length of the centerline of the curved waveguide, and the vertical axis represents the waveguide width at the corresponding arc length position.

4. The design method for a bent waveguide according to claim 1, characterized in that, The step of generating the geometric model of the curved waveguide via the parametric modeling specifically includes: Based on the design variable values ​​of the current round, integrate along the arc length of the first curve to generate the centerline trajectory of the curved waveguide through integration. Based on the design variable values ​​of the current round and the variation law of the waveguide width along the arc length of the waveguide centerline defined by the second curve, the complete geometric boundary of the curved waveguide is generated along the normal direction of the centerline trajectory, and the geometric model of the curved waveguide is generated.

5. The design method for a bent waveguide according to any one of claims 1-4, characterized in that, The optimization algorithm includes one of the following: particle swarm optimization, gradient descent, and genetic algorithm.

6. The design method for a bent waveguide according to any one of claims 1-4, characterized in that, Before the step of iteratively optimizing the design variables based on the transmittance obtained from the optical simulation of the geometric model, the method further includes: Set the minimum constraint value for the radius of curvature; Set waveguide width constraints at the start and end segments of the curved waveguide so that the waveguide widths of the start and end segments match the widths of the corresponding connected straight waveguides or functional device ports, respectively. The minimum constraint value and the waveguide width constraint are used as constraints in the simulation optimization process to constrain the search range of the control points.

7. The design method for a bent waveguide according to claim 1, characterized in that, The bending angle of the curved waveguide is greater than 0° and less than or equal to 360°.

8. The design method for a bent waveguide according to claim 1, characterized in that, The optical simulation is based on the three-dimensional finite-difference time-domain method.

9. A curved waveguide, characterized in that, The waveguide was designed using the design method described in any one of claims 1-8.

10. A design device for a bent waveguide, characterized in that, include: The parametric modeling module is used to parametrically model the curved waveguide based on a predefined first curve and a second curve. The first curve is used to control the change of the radius of curvature of the curved waveguide along the arc length of the waveguide centerline, and the second curve is used to control the change of the width of the curved waveguide along the arc length of the waveguide centerline. Both the first curve and the second curve are parametric design curves defined by control points and basis functions. The geometric modeling module is used to generate the geometric model of the curved waveguide in each iteration of the optimization algorithm, using the coordinates of the control points of the first curve and the second curve as design variables, based on the design variable values ​​of the current iteration. The iterative optimization module is used to iteratively optimize the design variables with the transmittance obtained from the optical simulation of the geometric model as the optimization target, so as to obtain a set of optimal control point coordinates as the bending waveguide structure parameters and complete the design of the bending waveguide.

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