阅读说明：本技术 一种多模波导及其设计方法 (Multimode waveguide and design method thereof ) 是由 朱凝 孙尚森 王娟丽 汪洋 于 2020-06-19 设计创作，主要内容包括：本发明涉及一种多模波导及其设计方法,该多模波导包括波导芯层和覆盖层,该波导芯层由D段圆弧连接而成,D≥3,其相邻圆弧在连接点处有共同切线,所述圆弧的曲率半径在整体上呈由起始段至终段不规则地、跃变型减小的趋势,多模波导所支持的任一模式的传输损耗均不高于5％,任意两个模式间的串扰不高于-20dB。本发明的多模波导能够大幅减小多模波导损耗,大幅减小波导的曲率半径,降低模间串扰,从根本上打破了使用既定数学曲线其曲率半径变化范围较为固定,变化程度难以大幅调节的缺点。(The invention relates to a multimode waveguide and a design method thereof, the multimode waveguide comprises a waveguide core layer and a covering layer, the waveguide core layer is formed by connecting D sections of circular arcs, D is more than or equal to 3, the adjacent circular arcs have a common tangent at the connecting point, the curvature radius of the circular arcs is in the trend of irregularly and suddenly reducing from the initial section to the final section on the whole, the transmission loss of any mode supported by the multimode waveguide is not higher than 5 percent, and the crosstalk between any two modes is not higher than-20 dB. The multimode waveguide can greatly reduce the loss of the multimode waveguide, greatly reduce the curvature radius of the waveguide, reduce the crosstalk between modes, and fundamentally break through the defects that the change range of the curvature radius is relatively fixed and the change degree is difficult to greatly adjust by using a given mathematical curve.)

1. A multimode waveguide comprises a waveguide core layer and a covering layer, wherein the covering layer wraps the waveguide core layer, the refractive index of the waveguide core layer is higher than that of the covering layer, the waveguide core layer has thickness and width, the thickness supports a single mode in the vertical direction, the width supports multiple modes in the horizontal direction, the waveguide core layer is formed by connecting D sections of circular arcs, D is larger than or equal to 3, adjacent circular arcs have a common tangent line at a connecting point, the curvature radius of the circular arcs is in the trend of irregularly and suddenly reducing from an initial section to a final section on the whole, the transmission loss of any mode supported by the multimode waveguide is not higher than 5%, and the crosstalk between any two modes is not higher than-20 dB.

2. The multimode waveguide of claim 1, wherein the circular arc has a radius of curvature R_i，R_i≥R_i+1And at least one i satisfies R_i＞R_i+1，i＝1，……，D-1。

3. The multimode waveguide of claim 1 or 2, wherein said waveguide core layer is selected from Si, Si₃N₄At least one of GaAs and InP; the covering layer is selected from air and SiO₂And a polymer.

4. The multimode waveguide of claim 1 or 2, wherein the number of segments D of the arc in the waveguide core layer is 10 or more.

5. The multimode waveguide of claim 1 or 2, wherein the effective radius of curvature of the waveguide core layer is less than 20 times the multimode waveguide width.

6. The multimode waveguide of claim 5, wherein the multimode waveguide has an effective radius of curvature of less than 15 times the width of the multimode waveguide.

7. A method of designing a multimode waveguide unit, comprising the steps of:

s1, designing multi-mode waveguide parameters to support multi-mode transmission;

s2, setting the deflection angle of a waveguide core layer to be designed to be theta, wherein theta is not equal to 0, equally dividing the deflection angle into D parts, wherein each part corresponds to an arc segment, the corresponding deflection angle of the arc segment is theta/D, and D is more than or equal to 3;

s3, randomly selecting the curvature radius R of each circular arc segment_iSatisfy R_i+1≤R_i≤R_MAX，i＝1，……，D-1，R_MAXConnecting the arc sections to form a waveguide core layer for the maximum curvature radius, wherein a common tangent line is arranged at the connecting point of the two adjacent arc sections;

s4, defining a figure of merit function FOM, wherein the FOM value varies from 0 to 1, and the larger the FOM is, the higher the transmissivity of the multimode waveguide is, and the lower the crosstalk is;

s5, further optimizing the curvature radius of each arc segment through an optimization algorithm to achieve the characteristics of low transmission loss and low inter-mode crosstalk of the multimode waveguide.

8. The design method according to claim 7, wherein the optimization algorithm in step S5 is one of a direct range search method, a genetic algorithm, a simulated annealing algorithm, and a particle swarm algorithm.

9. The design method according to claim 8, wherein the S5 includes the steps of:

s5.1, changing R arbitrarily₁Is taken as R₁＇，R₂≤R₁＇≤R_MAXMaintaining the remaining R_iKeeping unchanged, calculating FOM value of the multimode waveguide after changing, and keeping curvature radius value R if FOM value is increased₁' performing S5.2, otherwise repeating the performing step S5.1, and performing S5.2 if the performing is repeated 100 times;

s5.2, optimizing R in sequence_iI 2 … n, optionally changing R_iIs taken as R_i＇，R_i+1≤R_i＇≤R_i-1Keeping the remaining curvature radius unchanged, calculating the FOM value of the multimode waveguide after the change, and keeping the curvature radius value R if the FOM value is increased_iElse continueVarying radius of curvature R_iRepeating step S5.2, and terminating the repetition if the number of repeated execution times reaches 100 times; let i ═ i +1, repeat S5.2 until all R_iAre optimized in turn.

S5.3: and repeating the steps S5.1-S5.2 until the FOM value of the multimode waveguide reaches the design requirement.

10. The design method according to any one of claims 7 to 9, wherein in step S4, the figure of merit function

Where n represents the total number of transmission modes supported by the multimode waveguide, i is 1, … …, n, T_iRepresents the transmission of the i-th mode, X_iRepresenting the total intermodal crosstalk of the ith mode, α is the weight of the intermodal crosstalk in the FOM function, the calculated FOM value varies from 0 to 1, with higher FOM values representing higher transmission and lower crosstalk.

Technical Field

The invention relates to the field of optical communication, in particular to a multimode waveguide and a design method thereof.

Background

Recently, network information has been explosively increased, and it has become increasingly difficult for the original network to meet the current demands. The traditional integrated circuit has the defects of small bandwidth, large transmission power consumption and the like. Compared with electrons, photons are a great advantage as carriers. The transmission of optical information has a larger bandwidth and lower transmission power consumption.

Optical communication technology has developed rapidly over decades, supporting our increasingly informative society and economy. The development of information nowadays has a requirement of rapid expansion on the information capacity expansion of a single optical fiber. Mode multiplexing (MDM) has different modes in the same wavelength, and performs demultiplexing and separation on the different modes, so that the information amount can be further increased, and the MDM technology is provided for solving the problem of single optical fiber capacity. The mode division multiplexing transmission system has a plurality of parallel channels in 1 few-mode optical fiber, so that the transmission capacity is expanded by multiple times. Since different channels belong to different modes, the influence of the nonlinear effect is much smaller under the condition of the same transmission capacity, and the signal-to-noise ratio deterioration caused by the nonlinear effect is reduced. In the MDM system, it is required to support transmission of different modes in the same waveguide, and when transmission light passes through a curved waveguide which is not specially designed, great loss and crosstalk between modes are generated. Therefore, the design of the curved waveguide supporting multi-mode transmission has great significance for the MDM system.

The traditional mode multiplexing is generally transverse mode multiplexing, that is, multiple transverse modes are multiplexed and demultiplexed, and the more modes supported by the mode multiplexing, the larger the bending radius of the waveguide is, and the larger the size of the device is. In recent years, many groups of topics both at home and abroad propose various methods for optimizing the bending of the on-chip waveguide. For example, a method of changing a curved shape by using a special curve, and designing a nano-fine structure before and after the curved waveguide or above a waveguide core layer in a curved portion. Most conventional curved waveguides use a circular shape with a constant curvature; the Finland VTT laboratory designs a curved waveguide with gradually changed curvature by adopting an Euler spiral curve; the zinc-wearing subject group at university of Zhejiang optimizes the curve shape of the curved waveguide, and replaces the traditional circular curve with an Euler curve. By changing the curve shape and designing the curve shape of the curved waveguide with gradually changed curvature, the loss of the curved waveguide can be reduced to a certain extent. The method has the advantages that the relaxation curve is adopted, loss caused by mismatching of the central mode field can be reduced, the bending radius can be reduced under the same turning condition, the method is simple in process compared with a method of adding the nano structure on the waveguide core layer, only one-time etching is needed, and exposure and etching steps are not needed. Both of the above-listed problems are problems in designing a curved waveguide having a gradual change in curvature by using a specific mathematical function, and the change of the radius of curvature is limited to a large extent.

Disclosure of Invention

Aiming at the technical problems in the prior art, the primary object of the present invention is to provide a multimode waveguide and a design method thereof, which can greatly reduce the loss of the multimode waveguide, reduce the curvature radius to a large extent, and reduce the crosstalk between modes. Based on the purpose, the invention at least provides the following technical scheme:

a multimode waveguide comprises a waveguide core layer and a covering layer, wherein the covering layer wraps the waveguide core layer, the refractive index of the waveguide core layer is higher than that of the covering layer, the waveguide core layer has thickness and width, the thickness supports a single mode in the vertical direction, the width supports multiple modes in the horizontal direction, the waveguide core layer is formed by connecting D sections of circular arcs, D is larger than or equal to 3, adjacent circular arcs have a common tangent line at a connecting point, the curvature radius of the circular arcs is in a trend of irregularly and gradually decreasing from an initial section to a final section on the whole, the transmission loss of any mode supported by the multimode waveguide is not higher than 5%, and the crosstalk between any two modes is not higher than-20 dB.

In one embodiment, the arc has a radius of curvature R_i，R_i≥R_i+1And at least one i satisfies R_i＞R_i+1，i＝1，……，D-1。

The waveguide core layer is selected from Si and Si₃N₄At least one of GaAs and InP; the covering layer is selected from air and SiO₂And a polymer.

In a specific embodiment, the segment number D of the circular arc in the waveguide core layer is more than or equal to 10.

The effective radius of curvature of the waveguide core layer is less than 20 times the width of the multimode waveguide. In another alternative specific embodiment, the effective radius of curvature of the multimode waveguide is less than 15 times the width of the multimode waveguide.

The invention also provides a design method of the multimode waveguide unit, which comprises the following steps:

s1, designing multi-mode waveguide parameters to support multi-mode transmission;

s2, setting the deflection angle of a waveguide core layer to be designed to be theta, wherein theta is not equal to 0, equally dividing the deflection angle into D parts, wherein each part corresponds to an arc segment, the corresponding deflection angle of the arc segment is theta/D, and D is more than or equal to 3;

s3, randomly selecting the curvature radius R of each circular arc segment_iSatisfy R_i+1≤R_i≤R_MAX，i＝1，……，D-1，R_MAXConnecting the arc sections to form a waveguide core layer for the maximum curvature radius, wherein a common tangent line is arranged at the connecting point of the two adjacent arc sections;

s4, defining a figure of merit function FOM, wherein the FOM value varies from 0 to 1, and the larger the FOM is, the higher the transmissivity of the multimode waveguide is, and the lower the crosstalk is;

s5, further optimizing the curvature radius of each arc segment through an optimization algorithm to achieve the characteristics of low transmission loss and low inter-mode crosstalk of the multimode waveguide.

The optimization algorithm in the step S5 is selected from one of a direct range search method, a genetic algorithm, a simulated annealing algorithm, and a particle swarm algorithm.

In one embodiment, the S5 includes the following steps:

s5.1, changing R arbitrarily₁Is taken as R₁＇，R₂≤R₁＇≤R_MAXMaintaining the remaining R_iKeeping unchanged, calculating FOM value of the multimode waveguide after changing, and keeping curvature radius value R if FOM value is increased₁' performing S5.2, otherwise repeating the performing step S5.1, and performing S5.2 if the performing is repeated 100 times;

s5.2, optimizing R in sequence_iI 2 … n, optionally changing R_iIs taken as R_i＇，R_i+1≤R_i＇≤R_i-1Keeping the remaining curvature radius unchanged, calculating the FOM value of the multimode waveguide after the change, and keeping the curvature radius value R if the FOM value is increased_iElse continue to change the radius of curvature R_iRepeating step S5.2, and terminating the repetition if the number of repeated execution times reaches 100 times; let i ═ i +1, repeat S5.2 until all R_iAre optimized in turn.

S5.3: and repeating the steps S5.1-S5.2 until the FOM of the multimode waveguide reaches the design requirement.

In one embodiment, in the step S4, the quality factor function

Where n represents the total number of transmission modes supported by the multimode waveguide, i is 1, … …, n, T_iRepresents the transmission of the i-th mode, X_iRepresenting the total intermodal crosstalk for the ith mode, α is the weight of intermodal crosstalk in the FOM function, the calculated FOM value varies from 0 to 1, with greater FOM representing higher transmission and lower crosstalk.

Compared with the prior art, the invention has at least the following beneficial effects:

the waveguide core layer in the multimode waveguide provided by the invention is formed by connecting more than three arc sections, the adjacent arc sections have a common tangent line at the connecting point, the curvature radius of the arc sections shows the trend of irregularly and suddenly changing and reducing from the initial section to the final section on the whole, the multimode waveguide adopts the waveguide core layer with larger curvature radius change, the curvature radius is reduced to a larger extent, the multimode waveguide loss is greatly reduced, and the intermode crosstalk is reduced. The use of the waveguide core layer fundamentally breaks through the defects that the change range of the curvature radius of a given mathematical curve is relatively fixed and the change degree is difficult to greatly adjust. The design method of the invention directly optimizes the curvature radius as a variable by utilizing an optimization algorithm, inversely designs the curve shape of the multimode waveguide, realizes the large adjustment of the curvature radius, and can realize the deflection of the multimode waveguide when the curvature radius of the multimode waveguide is less than or equal to 10 mu m. The multimode waveguide is manufactured by only one-time etching, no additional step is needed, and the process is simple and feasible.

Drawings

Fig. 1 is a schematic view of the principle of radius change of a multimode waveguide in an embodiment of the invention.

Fig. 2 is a schematic three-dimensional structure of a multimode waveguide according to an embodiment of the invention.

Fig. 3 is a curvature radius distribution curve of the waveguide core layer formed by connecting 20 circular arcs according to an embodiment of the present invention.

Fig. 4 is a curvature radius distribution curve of the waveguide core layer formed by connecting 26 circular arcs according to an embodiment of the present invention.

Fig. 5 is a curvature radius distribution curve of a waveguide core layer formed by connecting 10 circular arcs according to an embodiment of the present invention.

Fig. 6 is a curvature radius distribution curve of a waveguide core layer formed by connecting 5 circular arcs according to an embodiment of the present invention.

FIG. 7 shows TE in accordance with an embodiment of the present invention₀As an input transmittance curve.

FIG. 8 shows TE in accordance with an embodiment of the present invention₁As an input transmittance curve.

FIG. 9 shows TE in accordance with an embodiment of the present invention₂As an input transmittance curve.

Detailed Description

The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings, and the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, other embodiments obtained by persons of ordinary skill in the art without any creative effort belong to the protection scope of the present invention.

The present invention will be described in further detail below. The present invention provides a multimode waveguide, as shown in figures 1-2, comprising a waveguide core layer and a cladding layerShown is a waveguide core layer, not shown, the cladding layer surrounding the waveguide core layer, the waveguide core layer being selected from Si, Si₃N₄GaAs and InP, and the cover layer is selected from air and SiO₂And a polymer. The refractive index of the waveguide core layer is higher than that of the cladding layer.

The waveguide core layer has a thickness and a width, and the thickness of the waveguide core layer supports a single mode in a vertical direction, and preferably may be 0.22 to 0.34 μm. The waveguide core has a lateral width sized to support two or more multiple modes in the horizontal direction. Here, the vertical direction means a direction perpendicular to the paper surface in fig. 1, and the horizontal direction means a direction parallel to the paper surface. The multimode waveguide is structurally formed by connecting D sections of circular arcs, D is more than or equal to 3, and adjacent circular arcs have a common tangent at the connecting point, so that the two adjacent circular arcs are smoothly connected.

The waveguide core layer is formed by connecting more than three arc sections. Fig. 3 to 6 show curvature radius distribution curves of waveguide core layers formed by connecting 20 circular arcs, 26 circular arcs, 10 circular arcs and 5 circular arcs in different embodiments of the present invention. The total number of transmission modes supported by the multimode waveguide formed by connecting 26 segments of circular arcs shown in fig. 4 is 4, and the total number of transmission modes in fig. 3, 5 and 6 is 3. The curvature radius of the arc section in the waveguide core layer shows the trend of irregularly and steppingly reducing the arc from the initial arc section to the D section on the whole. The beginning arc segment is the input end, and the D-th arc segment is the final segment, also called the output end. The arc segment has a curvature radius R_i，R_i≥R_i+1And at least one i satisfies R_i＞R_i+1，i＝1，……，D-1。

The multimode waveguide has the characteristics of low transmission loss and low inter-mode crosstalk, specifically, the transmission loss of any mode supported by the multimode waveguide is not higher than 5%, and the crosstalk between any two modes is not higher than-20 dB.

In particular, the effective radius of curvature of the waveguide core in the multimode waveguide of the invention is less than 20 times its width. In one embodiment, the effective radius of curvature of the waveguide core is less than 15 times its width.

Preferably, the number D of the arc sections of the waveguide core layer in the multimode waveguide is more than or equal to 10, and the waveguide core layer is formed by connecting 20 arcs.

FIG. 1 shows a multimode waveguide according to an embodiment of the invention, in which the waveguide core is formed by three circular arcs, the deflection angle is 45 °, where O is the equivalent center of a circle and O is the equivalent center of a circle₁，O₂，O₃Is a segment center of a circle, OA₀Is the effective radius of the waveguide core layer, A₀A₁，A₁A₂，A₂A₃Is a three-segment circular arc, O₁A₁，O₂A₂，O₃A₃Is the radius of three circular arcs. The deflection angles in units of 90 deg. may be combined into other angles such as 180 deg.. Fig. 1 is designed by taking 45 ° as an example, and a multimode waveguide with a deflection angle of 90 ° is a multimode waveguide with a deflection angle of 90 ° that can be realized by mirror symmetry along an output end face of a final section of a waveguide core layer in the multimode waveguide on the basis of the 45 ° multimode waveguide of the present invention. The deflection angle of the multimode waveguide of the present invention is not limited to 45 °, and is applicable to multimode waveguides of any specific angle. The input end and the output end of the multimode waveguide can be respectively adjacent to a straight waveguide or other waveguide structures with different shapes to realize the transmission of light.

Fig. 2 is a schematic diagram showing a three-dimensional structure in which waveguide core layers in the multimode waveguide of the present invention are connected by 20 circular arcs having a deflection angle of 45 ° and are mirror-symmetrical along an end face of an output end of a final segment thereof, it can be understood that the deflection angle of the waveguide core layer is 90 °, and fig. 7 to 9 are schematic diagrams showing that the multimode waveguide in fig. 2 is respectively formed by TE₀、TE₁、TE₂Patterns as output results at input, self-versus-self, e.g. TE₀-TE₀By transmission or loss, by itself to other modes by inter-modal crosstalk, e.g. TE₀-TE₁Finger slave TE₀Mode to TE₁Cross talk of the mode. It can be seen that the transmission of each mode is greater than 99% (i.e., the loss is less than 1%) and the crosstalk between any two modes is less than-20 dB.

Based on the multi-mode waveguide structure, the design method of the multi-mode waveguide of the present invention is described next, so that those skilled in the art can more clearly recognize the multi-mode waveguide structure.

Step 1, designing multimode waveguide parameters to support multimode transmission.

In the specific embodiment, the waveguide structure uses silicon dioxide as a substrate, silicon is selected as a material of the waveguide core layer, and the covering layer is air or silicon dioxide. The thickness of the waveguide core layer supports a single mode in the vertical direction and its lateral width supports two or more multiple modes in the horizontal direction. The thickness of the waveguide core layer is 0.22um according to the general value of a conventional vertical single-mode device, and 1550nm is selected as the working wavelength. The equivalent radius of curvature R is selected to be 10 um. The width of the waveguide core layer is 1.3um, TE can be transmitted in the multimode waveguide₀,TE₁,TE₂Three modes.

S2, setting the deflection angle of the waveguide core layer to be designed to be theta, wherein theta is not equal to 0, equally dividing the deflection angle into D parts, wherein each part corresponds to an arc segment, the corresponding deflection angle of the arc segment is theta/D, and D is not less than 3.

In this embodiment, the deflection angle of the waveguide core layer in the multimode waveguide is set to 45 degrees, the deflection angle is equally divided into 20 segments, and the equivalent deflection angle of the arc corresponding to each segment is 20

S3, randomly selecting the curvature radius R of each circular arc segment_iSatisfy R_i≥R_i+1And i is 1, … … and D-1, the connecting circular arc segments form a waveguide core layer, and two adjacent circular arc segments have a common tangent at the connecting point.

And determining an equivalent circle center O corresponding to the equivalent curvature radius R of the multimode waveguide, wherein the curvature radius values refer to the outer diameter of the multimode waveguide, and the radius corresponding to the inner diameter is the outer diameter minus the width of the waveguide. In this embodiment, the maximum radius of curvature R selectable for the multimode waveguide is set_maxFor 5 × R ═ 50um, the multimode waveguide is constructed as shown in fig. 1, and fig. 1 shows the multimode waveguide divided into only 3 segments as an example for the sake of simplicity, showingHow to use the arc with simple and convenient curvature to form the multimode waveguide is described, and the number D of the arc segments of the waveguide core layer in the multimode waveguide is 20 in the present embodiment.

Radius of curvature R of 1 st segment of circular arc₁If the random setting is 25um, the center O of the circle is determined₁Is (0, -15). At this time, since R₁Greater than R, center of circle O₁On line segment A₀On the extension of O; otherwise if R₁The circle center is on the line segment A if less than R₀O, and (3) is added. Passing through the starting point A0 of the outer diameter of the 1 st segment of the circular arc, and taking O as₁As the center of circle, as the radius R₁And the arc of (1) is deviated from the arc passing through O by an angle ofIs intersected with A₁Thereby defining a first arc of a circle constituting the multimode waveguide; the radius of the 2 nd segment arc is randomly selected as R₂，R₂Less than R₁Through A₁The point is taken as the radius R₂Circular arc of (1), center of circle O₂Is located on line segment A₁O₁And is deflected by an angle of OIs intersected with A₂If A is₂If not, give R again₂Taking value until A is found₂(ii) a And so on to find the curvature radius value R of the 20 segments of circular arcs₁、R₂、…、R₂₀。

S4, defining a figure of merit function FOM, wherein the value of FOM varies from 0 to 1, and the higher FOM indicates that the higher the transmissivity of the multimode waveguide is, the lower the crosstalk is.

Defining a quality factor equation:

wherein n represents the total number of transmission modes supported by the multimode waveguide, T_iRepresents the transmission of the i-th mode, X_iRepresenting the total intermodal crosstalk of the ith mode, α is the weight of intermodal crosstalk in the FOM function, the calculated value of FOMVarying between 0 and 1, higher FOM values represent higher transmission, lower cross talk and better device performance.

In the specific embodiment, n is 3, and a three-dimensional time domain finite difference method is used for calculating TE in the multimode waveguide₀,TE₁,TE₂The crosstalk and loss for these three transmission modes are then calculated for the multimode waveguide structure according to equation (1).

S5, further optimizing the curvature radius of each arc segment through an optimization algorithm to achieve the characteristics of low transmission loss and low inter-mode crosstalk of the multimode waveguide.

Specifically, the optimization algorithm may be one of a direct range search method, a genetic algorithm, a simulated annealing algorithm, and a particle swarm algorithm. In one embodiment of the present invention, a direct range search method is preferred to further optimize the radius of curvature of each arc segment.

S5.1, setting the curvature radius R₁Maximum value of R_MAXIs 5R, then R is arbitrarily changed₁Is taken as R₁＇，R₂≤R₁＇≤R_MAXMaintaining the remaining R_iUnchanged, i ≠ 1, then redraws R₁Changing the multimode waveguide, calculating the FOM value of the multimode waveguide after changing, comparing with the FOM value before changing, and if the FOM value is increased, retaining the curvature radius value R₁' performing S5.2, otherwise repeatedly performing step S5.1, and if the FOM value has not been improved after repeatedly performing step S5.1 100 times, performing S5.2, sequentially optimizing R₂、…、R₂₀。

S5.2, optimizing R in sequence_iI 2 … 20, R is arbitrarily changed_iIs taken as R_i＇，R_i+1≤R_i＇≤R_i-1Keeping the remaining curvature radius unchanged, calculating the FOM value of the multimode waveguide after the change, and keeping the curvature radius value R if the FOM value is increased_iElse continue to change the radius of curvature R_iRepeating step S5.2, and terminating the repetition if the number of repeated execution times reaches 100 times; let i ═ i +1, repeat S5.2 until all R_iAre optimized in turn.

And S5.3, repeating the steps S5.1-S5.2 until the FOM value of the multimode waveguide reaches the design requirement.

In this embodiment, the last radius value R is reached when the optimization is complete₂₀Thereafter, steps S5-S6 are repeated from R₁And restarting, and sequentially optimizing all radius values until the FOM value reaches over 0.95. The FOM value is preferably 0.995 or more.

After multiple optimizations, the resulting multimode waveguide has a FOM value of 0.997 in this embodiment. The transmittance curves for the three transmission modes correspond to fig. 7-9, where the transmittance (e.g., TE) for one mode versus the other two modes₀→TE₁，TE₀→TE₂) I.e., the inter-mode crosstalk that this mode couples to the remaining modes. The optimized multimode waveguide has an equivalent bending radius of only 10um (the outer diameter is 10um, and the central radius is actually 9.35um), and the transmittance and crosstalk level of the multimode waveguide are better than those of the multimode waveguide with an equivalent central bending radius of 20-30 um obtained by using a specific function such as an Euler curve and the like. In addition, since the normal deflection angle is 90 ° and other angles such as 180 ° can be combined, the present invention is designed by taking 45 ° as an example, and the multimode waveguide with a deflection angle of 90 ° is a multimode waveguide which can realize a deflection angle of 90 ° by forming mirror symmetry along the output end face of the final section of the multimode waveguide on the basis of the 45 ° multimode waveguide of the present invention. The method for designing the multimode waveguide by the sectional optimization can be completely suitable for designing the multimode waveguide at any specific angle.

The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.