Micro-ring filter and design method thereof

Abstract

This invention belongs to the field of optical device technology and discloses a microring filter and its design method. The invention utilizes a three-dimensional finite-difference time-domain algorithm to establish a simulation model of the microring filter, which includes a microring region and a coupled waveguide region. Based on a set free spectral range and a set coupling coefficient, with the fundamental mode transmittance as the optimization objective, a first curve is used as the waveguide center curve, and a second curve is used to adjust the waveguide width. The microring region and the coupled waveguide region are then designed in reverse, and iterative optimization yields a set of optimal microring structure parameters and a set of optimal coupled waveguide structure parameters, thus completing the design of the microring filter. This invention can significantly improve the free spectral range and enhance the loss performance of the microring filter.

Description

Technical Field

[0001] This invention belongs to the field of optical device technology, and more specifically, relates to a micro-ring filter and its design method. Background Technology

[0002] Microring filters, as a key optical device, have wide applications in optical communication, wavelength division multiplexing (WDM) systems, and integrated quantum photonics. With their compact size, high channel isolation, and tunable bandwidth, they have become an important functional module in silicon photonic integrated circuits.

[0003] However, with the continuous improvement of communication speeds and integration levels, traditional microring filters face numerous challenges in design and performance. For example, insufficient Free Spectral Range (FSR). Due to the limitation of the FSR, the number of channels that a microring filter can achieve is limited, and the bandwidth of each channel is also restricted. The size of the FSR is negatively correlated with the physical size of the microring; that is, the smaller the microring size, the larger the FSR. However, to ensure that the microring loss remains within a reasonable range, the reduction in microring size must be carefully controlled. For example, a large microring loss means an increase in loss as the microring size decreases. When the microring size is reduced to a FSR of 37 nm, its half-ring loss is 0.018 dB / 180°. Under this design, if the microring size is further reduced to a FSR of 55 nm, its half-ring loss will exceed 0.036 dB / 180°, which means the loss increases by two times, limiting the performance of the microring filter. Furthermore, traditional microring filters may suffer from problems such as excessive coupling loss between the curved directional coupler and the microring (in existing technologies, the coupling loss between the curved directional coupler and the microring is typically 0.07 dB; this high coupling loss not only reduces the transmission efficiency of optical signals but also affects the isolation between channels and increases crosstalk), insufficient flat-top effect in the output spectrum, increased loss over long wavelengths, and bandwidth variations. These issues significantly affect the performance consistency and applicability of the filter. Therefore, there is an urgent need for an improved microring filter design method to increase the free spectral range while reducing loss and improving the performance of the microring filter, thereby meeting the needs of next-generation high-speed optical communication and integrated photonics systems. Summary of the Invention

[0004] This invention provides a microring filter and its design method, which solves the problems of insufficient free spectral range and the need to improve the loss performance of microring filters in the prior art.

[0005] This invention provides a design method for a micro-ring filter, comprising the following steps:

[0006] A simulation model of a microring filter is established using a three-dimensional time-domain finite-difference algorithm. The microring filter includes a microring region and a coupled waveguide region.

[0007] Based on the set free spectral range and the set coupling coefficient, with the fundamental mode transmittance as the optimization target, the first curve is used as the waveguide center curve, and the width of the waveguide is adjusted using the second curve. The micro-ring region and the coupled waveguide region are designed in reverse, and a set of optimal micro-ring structure parameters and a set of optimal coupled waveguide structure parameters are obtained through iterative optimization, thus completing the design of the micro-ring filter.

[0008] Preferably, multiple microrings with identical structures are arranged in the microring region. The structure of each microring is divided into four quarter-microring curved waveguides. The center curve of the quarter-microring curved waveguide is the first curve. The quarter-microring curved waveguide is used as the target for reverse design.

[0009] The coupled waveguide region is provided with a first coupled waveguide and a second coupled waveguide located on the upper and lower sides of the micro-ring region, respectively. The first coupled waveguide includes an input port straight waveguide, a first curved coupled waveguide unit, and an output port straight waveguide. The second coupled waveguide includes a first transmission unit, a second curved coupled waveguide unit, and a second transmission unit. The structure of the second curved coupled waveguide unit is symmetrical to that of the first curved coupled waveguide unit. The first curved coupled waveguide unit is divided into four curved coupled waveguide segments, which are respectively denoted as the first curved coupled waveguide, the second curved coupled waveguide, the third curved coupled waveguide, and the fourth curved coupled waveguide. The center curve of the third curved coupled waveguide is the first curve, and the center curve of the fourth curved coupled waveguide is the antisymmetric curve of the center curve of the third curved coupled waveguide. The second curved coupled waveguide and the third curved coupled waveguide are horizontally mirror-symmetrical, and the first curved coupled waveguide and the fourth curved coupled waveguide are horizontally mirror-symmetrical. The third curved coupled waveguide and the fourth curved coupled waveguide are used as targets for reverse engineering.

[0010] Preferably, the transmittance of the TE fundamental mode light at the working wavelength through the microring is recorded as the first TE fundamental mode transmittance; the transmittance of the TE fundamental mode light at the working wavelength through the first bent coupled waveguide unit is recorded as the second TE fundamental mode transmittance; and the transmittance of the TE fundamental mode light at the working wavelength through the junction of two adjacent quarter-wave bend waveguide segments in the structure of a certain microring is recorded as the third TE fundamental mode transmittance.

[0011] The micro-ring region is reverse-designed using one of the following algorithms: particle swarm optimization, gradient algorithm, swarm intelligence algorithm, or neural network algorithm, with the first TE fundamental mode transmittance as the optimization objective; the coupled waveguide region is reverse-designed using the particle swarm optimization algorithm, with the sum of the absolute values ​​of the second and third TE fundamental mode transmittance as the optimization objective.

[0012] Preferably, the first curve is one of Euler curve, Archimedean spiral, logarithmic spiral, and B-spline curve, and the second curve is one of Bézier curve, spline interpolation curve, and B-spline curve.

[0013] Preferably, when the first curve is an Euler curve and the second curve is a Bezier curve, the initial waveguide width W0 of the microring is set, and the perimeter L of the central Euler curve of the quarter-microring curved waveguide is determined according to the set free spectrum range. The range of the maximum radius of curvature Rmax of the central Euler curve of the quarter-microring curved waveguide and the range of the arc length proportionality coefficient A of the central Euler curve of the quarter-microring curved waveguide are also determined.

[0014] The maximum value of the abscissa of the center Euler curve of the quarter-ring curved waveguide is denoted as Xmax. The width of the quarter-ring curved waveguide is adjusted using a third-order Bézier curve. The Bézier control points are denoted as P0 = [0, W0], P1 = [xx1, yy1], P2 = [xx2, yy2], and P3 = [Xmax, yy3]. Among them, the values ​​of xx1 and xx2 are both in the range of [Xmax / 3, 2Xmax], the values ​​of yy1 and yy2 are both in the range of [-W0 / 2, 3W0], and the value of yy3 is in the range of [W0 / 2, 3W0].

[0015] Using Rmax, A, xx1, yy1, xx2, yy2, and yy3 as variables, the microring region is reverse-designed using a particle swarm optimization algorithm, and a set of optimal microring structure parameters is obtained through iterative optimization.

[0016] Preferably, the method of adjusting the width of the quarter-micro-ring curved waveguide using the Bézier curve is as follows: when the abscissa of a point on the Bézier curve is equal to the abscissa of a point on the Euler curve, the ordinate of the Bézier point is taken as the waveguide width of the Euler point, and the waveguide width direction of the Euler point is parallel to the direction of the line connecting the Euler point and the center of curvature of the Euler point, and half of the waveguide width is extended to both sides of the Euler point.

[0017] Preferably, when the first curve is an Euler curve and the second curve is a Bezier curve, the coupled waveguide region is reverse-engineered using a two-step particle swarm optimization algorithm.

[0018] The first step of reverse design includes: determining the maximum radius of curvature Rmax_bend of the central Euler curve of the third curved coupled waveguide, the minimum spacing Wgap between the micro-ring and the coupled waveguide, and the width W_bend of the coupled waveguide based on the set coupling coefficient; determining the range of the perimeter L_bend of the central Euler curve of the third curved coupled waveguide based on the value of Rmax_bend; determining the range of the arc length scaling factor A_bend of the central Euler curve of the third curved coupled waveguide based on the range of L_bend; and determining the range of the arc length scaling factor A_bend of the central Euler curve of the third curved coupled waveguide based on the size of the coupled waveguide region. The range of the actual number of points num for the central Euler curve is determined; the transmittance of the two TE fundamental modes is calculated by simulation, and the coupled waveguide region is reverse-designed using particle swarm optimization algorithm with L_bend, A_bend, and num as variables, and the parameters of the central Euler curve are obtained by iterative optimization; wherein, the starting point of the central Euler curve of the third curved coupled waveguide is its leftmost end, and this point is set as its origin, with the horizontal direction to the right being the positive x-axis; the starting point of the central Euler curve of the fourth curved coupled waveguide is its rightmost end, and this point is set as its origin, with the horizontal direction to the left being the positive x-axis.

[0019] The second step of reverse design includes: adjusting the width of the third curved coupled waveguide using a third-order Bessel function, and adjusting the width of the fourth curved coupled waveguide using a fourth-order Bessel function.

[0020] Preferably, the Bessel control points of the third curved coupled waveguide are denoted as P0_bend1 = [0, W_bend], P1_bend1 = [xx1_bend1, W_bend], P2_bend1 = [xx2_bend1, W_bend], and P3_bend1 = [Xmax_bend, yy3_bend1]; where the values ​​of xx1_bend1 and xx2_bend1 are both in the range of [Xmax × 2 / 3, Xmax_bend], and the range of yy3_bend1 is selected as [W_bend, W1], where W1 is the initial waveguide width of the curved coupled waveguide, Xmax_bend is the maximum value of the abscissa of the center Euler curve of the third curved coupled waveguide, and Xmax is the maximum value of the abscissa of the center Euler curve of the quarter-micro-ring curved waveguide;

[0021] The Bessel control points of the fourth curved coupled waveguide are denoted as P0_bend2 = [0, W1], P1_bend2 = [xx1_bend2, yy1_bend2], P2_bend2 = [xx2_bend2, yy2_bend2], P3_bend2 = [xx3_bend2, yy3_bend2], P4_bend2 = [xx4_bend2, yy4_bend2]; where xx1_bend2, xx2_bend2, and xx3_bend2 are all in the range [0, Xmax_bend], yy1_bend2, yy2_bend2, and yy3_bend2 are all in the range [0, 4W_bend], and P4_bend2 = P3_bend1;

[0022] Using xx1_bend1, xx2_bend1, yy3_bend1, xx1_bend2, xx2_bend2, xx3_bend2, yy1_bend2, yy2_bend2, and yy3_bend2 as variables, the coupled waveguide region is reverse-engineered using a particle swarm optimization algorithm, and a set of optimal coupled waveguide structure parameters is obtained through iterative optimization.

[0023] Preferably, when establishing a simulation model of the microring filter using the three-dimensional finite-difference time-domain algorithm, the basic parameters of the microring filter are used as constraints; the basic parameters include the operating wavelength, waveguide material, and waveguide height of the microring filter.

[0024] On the other hand, the present invention provides a micro-ring filter, which is designed using the micro-ring filter design method described above.

[0025] One or more technical solutions provided in this invention have at least the following technical effects or advantages:

[0026] This invention utilizes a three-dimensional finite-difference time-domain algorithm to establish a simulation model of a microring filter (including a microring region and a coupled waveguide region). Based on a set free spectral range and a set coupling coefficient, and with the fundamental mode transmittance (e.g., TE fundamental mode transmittance, or TM fundamental mode transmittance) as the optimization objective, a first curve is used as the waveguide center curve. A second curve is used to adjust the waveguide width, and the microring region and coupled waveguide region are reverse-engineered (e.g., using a particle swarm optimization algorithm). Iterative optimization yields a set of optimal microring structure parameters and a set of optimal coupled waveguide structure parameters, completing the microring filter design. This invention uses a first curve (e.g., an Euler curve) as the waveguide centerline, combined with a second curve (e.g., a Bezier curve) to adjust the waveguide width. Through reverse design, smooth optical signal transmission is achieved, bending loss is reduced, and the free spectral range and spectral response performance of the microring are significantly improved. This invention employs a two-step optimization strategy. Through reverse design, it first optimizes the geometry of the curved coupled waveguide using a first curve (e.g., an Euler curve), and then precisely controls the waveguide width using a second curve (e.g., two Bezier curves), ensuring high coupling coefficient and low coupling loss. Specifically, addressing the problems of insufficient free spectral range and the need to improve the loss performance of microring filters in existing technologies (high microring loss and high coupling loss between the curved directional coupler and the microring), this invention proposes a reverse design optimization method using multiple curves, achieving a significant performance improvement. Attached Figure Description

[0027] Figure 1 A schematic diagram of a micro-ring filter provided by the present invention;

[0028] Figure 2 A schematic diagram of a microring filter provided by the present invention, wherein each microring structure is divided into four quarter-microring curved waveguide segments;

[0029] Figure 3 A schematic diagram of a curved coupled waveguide and coupling region in a micro-ring filter provided by the present invention;

[0030] Figure 4 This is a schematic diagram of a third-order 16-channel ring filter;

[0031] Figure 5 This is a schematic diagram of a third-order Bézier curve;

[0032] Figure 6 This is a schematic diagram of a fourth-order Bézier curve;

[0033] Figure 7 This is a schematic diagram of the bending radius and waveguide width curves at various angles of a quarter-micro-ring bent waveguide;

[0034] Figure 8This is a schematic diagram of the spectral results of the FDTD simulation of a third-order micro-ring filter. Detailed Implementation

[0035] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0036] In a first aspect, the present invention provides a design method for a micro-ring filter, comprising the following steps:

[0037] A simulation model of a microring filter is established using a three-dimensional time-domain finite-difference algorithm. The microring filter includes a microring region and a coupled waveguide region.

[0038] Based on the set free spectral range and the set coupling coefficient, with the fundamental mode transmittance as the optimization target, the first curve is used as the waveguide center curve, and the width of the waveguide is adjusted using the second curve. The micro-ring region and the coupled waveguide region are designed in reverse, and a set of optimal micro-ring structure parameters and a set of optimal coupled waveguide structure parameters are obtained through iterative optimization, thus completing the design of the micro-ring filter.

[0039] The microring region contains multiple microrings with identical structures. Each microring is divided into four quarter-microring curved waveguides. The center curve of each quarter-microring curved waveguide is the first curve. The quarter-microring curved waveguide is used as the target for reverse design.

[0040] The coupled waveguide region is provided with a first coupled waveguide and a second coupled waveguide located on the upper and lower sides of the micro-ring region, respectively. The first coupled waveguide includes an input port straight waveguide, a first curved coupled waveguide unit, and an output port straight waveguide. The second coupled waveguide includes a first transmission unit, a second curved coupled waveguide unit, and a second transmission unit. The structure of the second curved coupled waveguide unit is symmetrical to that of the first curved coupled waveguide unit. The first curved coupled waveguide unit is divided into four curved coupled waveguide segments, which are respectively denoted as the first curved coupled waveguide, the second curved coupled waveguide, the third curved coupled waveguide, and the fourth curved coupled waveguide. The center curve of the third curved coupled waveguide is the first curve, and the center curve of the fourth curved coupled waveguide is the antisymmetric curve of the center curve of the third curved coupled waveguide. The second curved coupled waveguide and the third curved coupled waveguide are horizontally mirror-symmetrical, and the first curved coupled waveguide and the fourth curved coupled waveguide are horizontally mirror-symmetrical. The third curved coupled waveguide and the fourth curved coupled waveguide are used as targets for reverse engineering.

[0041] The present invention can use TE (Transverse Electric) fundamental mode transmittance as the optimization target, or TM (Transverse Magnetic Wave) fundamental mode transmittance as the optimization target, with TE fundamental mode transmittance being preferred. The following explanation uses TE fundamental mode transmittance as the optimization target as an example.

[0042] The transmittance of the TE fundamental mode light at the operating wavelength through the microring is denoted as the first TE fundamental mode transmittance; the transmittance of the TE fundamental mode light at the operating wavelength through the first curved coupled waveguide unit is denoted as the second TE fundamental mode transmittance; and the transmittance of the TE fundamental mode light at the operating wavelength through the junction of two adjacent quarter-wavelength curved waveguide segments in a microring structure is denoted as the third TE fundamental mode transmittance. When reverse-engineering the microring region using the particle swarm optimization algorithm, the first TE fundamental mode transmittance is used as the optimization target; when reverse-engineering the coupled waveguide region using algorithms such as particle swarm optimization, gradient algorithm, swarm intelligence algorithm, and neural network algorithm, the sum of the absolute values ​​of the second and third TE fundamental mode transmittances is used as the optimization target.

[0043] That is, the present invention can be reverse engineered using a variety of algorithms including but not limited to particle swarm optimization, gradient algorithm, swarm intelligence algorithm and neural network algorithm. The particle swarm optimization algorithm is used as an example in the embodiments.

[0044] The first curve is one of Euler curve, Archimedean spiral, logarithmic spiral, and B-spline curve, and the second curve is one of Bézier curve, spline interpolation curve, and B-spline curve.

[0045] Furthermore, when establishing a simulation model of the micro-ring filter using the three-dimensional time-domain finite difference algorithm, the basic parameters of the micro-ring filter are used as constraints; the basic parameters include the operating wavelength, waveguide material, and waveguide height of the micro-ring filter.

[0046] Secondly, the present invention provides a micro-ring filter, which is designed using the micro-ring filter design method described above.

[0047] Based on the above, the present invention provides several embodiments for further explanation.

[0048] Example 1:

[0049] Example 1 provides a design method for a micro-ring filter, using an Euler curve as the first curve and a Bezier curve as the second curve.

[0050] Set the initial waveguide width W0 of the microring. Based on the set free spectral range, determine the perimeter L of the central Euler curve of the quarter-ring curved waveguide. Determine the range of the maximum radius of curvature Rmax of the central Euler curve and the range of the arc length scaling factor A of the central Euler curve. Record the maximum value of the abscissa of the central Euler curve of the quarter-ring curved waveguide as Xmax. Adjust the width of the quarter-ring curved waveguide using a third-order Bézier curve. Record each Bézier control point as P0 = [ [0, W0], P1 = [xx1, yy1], P2 = [xx2, yy2], P3 = [Xmax, yy3]; where the values ​​of xx1 and xx2 are both in the range of [Xmax / 3, 2Xmax], the values ​​of yy1 and yy2 are both in the range of [-W0 / 2, 3W0], and the value of yy3 is in the range of [W0 / 2, 3W0]; using Rmax, A, xx1, yy1, xx2, yy2, and yy3 as variables, the microring region is reverse-designed using the particle swarm optimization algorithm, and a set of optimal microring structure parameters is obtained through iterative optimization.

[0051] The method of adjusting the width of the quarter-micro-ring curved waveguide using Bézier curves is as follows: when the abscissa of a point on the Bézier curve is equal to the abscissa of a point on the Euler curve, the ordinate of the Bézier point is taken as the waveguide width of the Euler point, and the waveguide width direction of the Euler point is parallel to the direction of the line connecting the Euler point and the center of curvature of the Euler point, and half the waveguide width is extended to both sides of the Euler point.

[0052] The coupled waveguide region is reverse-engineered using a two-step particle swarm optimization algorithm.

[0053] The first step of reverse design includes: determining the maximum radius of curvature Rmax_bend of the central Euler curve of the third curved coupled waveguide, the minimum spacing Wgap between the micro-ring and the coupled waveguide, and the width W_bend of the coupled waveguide based on the set coupling coefficient; determining the range of the perimeter L_bend of the central Euler curve of the third curved coupled waveguide based on the value of Rmax_bend; determining the range of the arc length scaling factor A_bend of the central Euler curve of the third curved coupled waveguide based on the range of L_bend; and determining the range of the arc length scaling factor A_bend of the central Euler curve of the third curved coupled waveguide based on the size of the coupled waveguide region. The range of the actual number of points num for the central Euler curve is determined; the transmittance of the two TE fundamental modes is calculated by simulation, and the coupled waveguide region is reverse-designed using particle swarm optimization algorithm with L_bend, A_bend, and num as variables, and the parameters of the central Euler curve are obtained by iterative optimization; wherein, the starting point of the central Euler curve of the third curved coupled waveguide is its leftmost end, and this point is set as its origin, with the horizontal direction to the right being the positive x-axis; the starting point of the central Euler curve of the fourth curved coupled waveguide is its rightmost end, and this point is set as its origin, with the horizontal direction to the left being the positive x-axis.

[0054] The second step of reverse design includes: adjusting the width of the third curved coupled waveguide using a third-order Bessel function, and adjusting the width of the fourth curved coupled waveguide using a fourth-order Bessel function.

[0055] Specifically, the Bessel control points of the third curved coupled waveguide are denoted as P0_bend1 = [0, W_bend], P1_bend1 = [xx1_bend1, W_bend], P2_bend1 = [xx2_bend1, W_bend], and P3_bend1 = [Xmax_bend, yy3_bend1]. Among them, the values ​​of xx1_bend1 and xx2_bend1 are both in the range of [Xmax × 2 / 3, Xmax_bend], and the range of yy3_bend1 is selected as [W_bend, W1]. W1 is the initial waveguide width of the curved coupled waveguide, Xmax_bend is the maximum value of the abscissa of the center Euler curve of the third curved coupled waveguide, and Xmax is the maximum value of the abscissa of the center Euler curve of the quarter-micro-ring curved waveguide.

[0056] The Bessel control points of the fourth curved coupled waveguide are denoted as P0_bend2 = [0, W1], P1_bend2 = [xx1_bend2, yy1_bend2], P2_bend2 = [xx2_bend2, yy2_bend2], P3_bend2 = [xx3_bend2, yy3_bend2], P4_bend2 = [xx4_bend2, yy4_bend2]; where xx1_bend2, xx2_bend2, and xx3_bend2 are all in the range of [0, Xmax_bend], yy1_bend2, yy2_bend2, and yy3_bend2 are all in the range of [0, 4W_bend], and P4_bend2 = P3_bend1.

[0057] Using xx1_bend1, xx2_bend1, yy3_bend1, xx1_bend2, xx2_bend2, xx3_bend2, yy1_bend2, yy2_bend2, and yy3_bend2 as variables, the coupled waveguide region is reverse-engineered using a particle swarm optimization algorithm, and a set of optimal coupled waveguide structure parameters is obtained through iterative optimization.

[0058] The following description, in conjunction with the parameters, further illustrates Example 1.

[0059] Euler curves are curves with a smooth curvature transition, used in micro-ring filter design to reduce bending losses. Their equation is as follows:

[0060]

[0061] Where A is the arc length scaling factor of the curve, and R... max Let be the maximum radius of curvature, L be the total curve length (i.e., the circumference of the curve), and t be a parameter representing the position within the curve.

[0062] Bézier curves are used to control the variation of waveguide width. The shape of the curve is adjusted by controlling the position of the control points. The ordinate of the Bézier curve corresponds to the waveguide width at the Euler curve where the abscissa is located. Bézier curves support order-wise definitions. This invention primarily uses third-order and fourth-order Bézier curves, whose equations are as follows:

[0063] Figure 5 This is a schematic diagram of a third-order Bézier curve. The equation of a third-order Bézier curve is as follows:

[0064] W(t)=P0(1-t) 3 +3P1(1-t) 2 ·t+3P2(1-t)·t 2 +P3t 3t∈[0,1] (3)

[0065] Where P0, P1, P2, and P3 are the control point positions, and t is a parameter representing the position on the curve. For example... Figure 5 As shown, P0 is the starting point of the curve, P3 is the ending point of the curve, and P1 and P2 control the shape of the curve. Let P0 = [xx0, yy0], P1 = [xx1, yyl], P2 = [xx2, yy2], and P3 = [xx3, yy3].

[0066] Figure 6 This is a schematic diagram of a fourth-order Bézier curve, and the equation of a fourth-order Bézier curve is as follows:

[0067] W(t)=P0(1-t) 4 +4P1(1-t) 3 ·t+6P2(1-t) 2 ·t 2 +4P3(1-t)·t 3 +P4t 4 t∈[0,1] (4)

[0068] Where P0, P1, P2, P3, and P4 are the control point positions, and t is a parameter representing the position on the curve. For example... Figure 6 As shown, P0 is the starting point of the curve, P4 is the ending point of the curve, and P1, P2, and P3 control the shape of the curve. Let P0 = [xx0, yy0], P1 = [xx1, yy1], P2 = [xx2, yy2], P3 = [xx3, yy3], and P4 = [xx3, yy3].

[0069] A silicon nanowire optical waveguide based on silicon insulator (SOI) material is selected: its core layer is silicon material with a thickness of 220 nm, i.e., the waveguide height is 220 nm, and the refractive index is 3.47; its lower / upper cladding material is SiO2, with the lower cladding SiO2 thickness being 2 μm and the upper cladding SiO2 thickness being 1 μm, and the refractive index being 1.44. The operating wavelength range is around 1550 nm, and the operating polarization state is TE (Transverse Electric) polarization.

[0070] Multiple identical microrings are disposed within the microring region, and a first coupling waveguide and a second coupling waveguide are disposed on the upper and lower sides of the microring region, respectively. For example, see [link to relevant documentation]. Figures 1 to 3 The micro-ring region is provided with a first micro-ring 110, a second micro-ring 120 and a third micro-ring 130, and the coupled waveguide region is provided with a first coupled waveguide 200 and a second coupled waveguide 300.

[0071] The structure of the first microring 110 is divided into four quarter-ring curved waveguides, namely the first curved waveguide 111, the second curved waveguide 112, the third curved waveguide 113, and the fourth curved waveguide 114 of the first microring. The center of the first microring 110 is the origin. The second curved waveguide 112 of the first microring is a vertical mirror symmetric change of the first curved waveguide 111 of the first microring. The fourth curved waveguide 114 of the first microring is a horizontal mirror change of the first curved waveguide 111 of the first microring. The third curved waveguide 113 of the first microring is a central symmetric change of the first curved waveguide 111 of the first microring with the origin as the center.

[0072] The second microring 120 and the third microring 130 are replicas of the first microring 110. The structure of the second microring 120 is divided into four quarter-microring curved waveguides, namely the first curved waveguide 121, the second curved waveguide 122, the third curved waveguide 123, and the fourth curved waveguide 124 of the second microring. The structure of the third microring 130 is divided into four quarter-microring curved waveguides, namely the first curved waveguide 131, the second curved waveguide 132, the third curved waveguide 133, and the fourth curved waveguide 134 of the third microring.

[0073] The first microring 110 is directionally coupled to the second microring 120, and the second microring 120 is directionally coupled to the third microring 130. The entire filtering operating region is denoted as the resonant region 60.

[0074] In this design, the first curved waveguide 121 of the second microring and the first curved waveguide 131 of the third microring are both replicas of the first curved waveguide 111 of the first microring. Therefore, once the first curved waveguide 111 of the first microring is determined, the structure of the entire microring is also determined.

[0075] In the first curved waveguide 111 of the first microring, its waveguide center curve is an Euler curve, and its waveguide width is controlled by a Bézier curve. The length (i.e., circumference) of the central Euler curve of the first curved waveguide 111 of the first microring is a constant L, resulting in a total center curve length of 4L for the microring, thus determining the basic size of the microring. The Bézier curve controls the waveguide width of the first curved waveguide 111 of the first microring as follows: when the abscissa of a point on the Bézier curve is equal to the abscissa of a point on the Euler curve, the waveguide width at that Euler point is equal to the ordinate of that Bézier point. Furthermore, the waveguide width direction at that point is parallel to the direction of the line connecting the Euler point and its center of curvature, extending half the waveguide width to both sides of the Euler point.

[0076] Because the microring is small enough, this invention only uses a third-order Bézier curve to adjust the waveguide width. Let the Bézier control points be P0 = [xx0, yy0], P1 = [xx1, yy1], P2 = [xx2, yy2], and P3 = [xx3, yy3]. The initial waveguide width is determined to be W0 = 0.4 μm, so the control point P0 is determined to be [0, W0]. To ensure the FSR is not less than 55 nm, the circumference L of the center Euler curve of the first curved waveguide 111 of the first microring is determined to be 2.6585 μm. The maximum radius of curvature Rmax of the Euler curve is selected to be between 2.2 μm and 2.5 μm, and the corresponding A value range is between 2.55 μm and 3.45 μm. Furthermore, the abscissa xx3 of the control point P3 is the maximum abscissa value of the center Euler curve of the first curved waveguide 111 of the first microring, denoted as Xmax. Thus, there are seven variables in total: A, Rmax, xx1, yy1, xx2, yy2, and yy3. Once their values ​​are determined, the structure of the microring is also determined. To ensure that the initial waveguide width does not change drastically, the values ​​of xx1 and xx2 are set to be greater than Xmax / 3. Furthermore, to overcome the limitations of the Bezier curve variation, the maximum value of xx1 and xx2 is set to 2Xmax. Therefore, the ranges of xx1 and xx2 are [Xmax / 3, 2Xmax] and [Xmax / 3, 2Xmax], respectively. Simultaneously, to ensure a sufficient range of waveguide width variation, the ranges of yy1, yy2, and yy3 are set to [-W0 / 2, 3W0], [-W0 / 2, 3W0], and [W0 / 2, 3W0], respectively.

[0077] The simulation algorithm employs a high-precision three-dimensional finite-difference time-domain (FDTD) algorithm. The light source is positioned at the center of the top waveguide of the micro-ring, with the input light being the TE fundamental mode at a wavelength of 1550 nm. A monitor is placed at the center of the bottom waveguide of the micro-ring to calculate the transmittance of the TE fundamental mode. The bending radius and bending direction of the light source and monitor are set to the bending radius and bending direction at their respective waveguide locations. A particle swarm optimization (PSO) algorithm is introduced, with seven independent variables: A, Rmax, xx1, yy1, xx2, yy2, and yy3. The number of iterations is set to 200, with each iteration having a size of 32. The size of each iteration is determined by the number of parameters and the number of GPUs. The optimization objective (FOM) is the transmittance of the TE fundamental mode at the semi-ring. This invention uses GPUs to accelerate simulation calculations, reducing the computation time of the reverse design by more than 32 times compared to using only CPUs. The reverse design fully converges around iteration 120. The calculated optimal value is 0.008 dB / 180°, the FSR of the ring is 55.5 nm, and the curves showing the variation of its bending radius and waveguide width with angle are as follows. Figure 7As shown, the Euler curve has Rmax = 2.2 μm and A = 3.05042 μm, which meets the expected design requirements.

[0078] Bending coupled waveguide design method: See Figure 1 , Figure 3 The first coupling waveguide 200 includes an input port straight waveguide (denoted as the first straight waveguide 201, with a width of 500 nm), a first curved coupling waveguide unit (including a first curved coupling waveguide 202, a second curved coupling waveguide 203, a third curved coupling waveguide 204, and a fourth curved coupling waveguide 205, used for directional coupling with the third micro-ring 130, with the coupling region denoted as the second coupling region 50), and an output port straight waveguide (denoted as the second straight waveguide 206); the second coupling waveguide 300 includes a first transmission unit (including a first transmission waveguide 301 and a first curved waveguide 302), a second curved coupling waveguide unit (including a fifth curved coupling waveguide 303, a sixth curved coupling waveguide 304, a seventh curved coupling waveguide 305, and an eighth curved coupling waveguide 306, used for directional coupling with the first micro-ring 110, with the coupling region denoted as the first coupling region 40), and a second transmission unit (including a second curved waveguide 307 and a second transmission waveguide 308). The second bent waveguide 307 and the first bent waveguide 302 are mutually symmetrical 90° bent waveguides with a radius of 3µm and a circular curve at the center. The waveguide width is controlled by a Bessel function to reduce the overall structure size and bending loss. The first transmission waveguide 301 is the download port for outputting filtered light. The second transmission waveguide 308 is the upload port.

[0079] TE-polarized light enters from the first straight waveguide 201, which serves as the input port, and then enters the first curved coupling waveguide 202, the second curved coupling waveguide 203, the third curved coupling waveguide 204, and the fourth curved coupling waveguide 205. A portion of this light is output via the second straight waveguide 206 to the input of the next micro-ring filter or directly output, while the remaining light is directionally coupled into the third micro-ring 130. Of the light entering the third micro-ring 130, some is coupled into the next micro-ring, namely the second micro-ring 120; some circulates within the ring; and some is coupled back into the first curved coupling waveguide 202, the second curved coupling waveguide 203, the third curved coupling waveguide 204, and the fourth curved coupling waveguide 205, and output via the second straight waveguide 206.

[0080] Similarly, the second microring 120 is coupled to the first microring 110 and the third microring 130, respectively. The first microring 110 is coupled to the second microring 120, the eighth curved coupling waveguide 306, the seventh curved coupling waveguide 305, the sixth curved coupling waveguide 304, and the fifth curved coupling waveguide 303, respectively. A resonant region 60 is formed between the microrings and between the microrings and the curved coupling waveguides. Light input from the first straight waveguide 201 is filtered through the resonant region 60, then passes through the first curved waveguide 302 (bent at 90°) and is output from the first transmission waveguide 301, thus completing the filter function.

[0081] The first curved coupling waveguide 202, the second curved coupling waveguide 203, the third curved coupling waveguide 204, and the fourth curved coupling waveguide 205 are all curved coupling waveguides, while the fifth curved coupling waveguide 303, the sixth curved coupling waveguide 304, the seventh curved coupling waveguide 305, and the eighth curved coupling waveguide 306 are symmetrical curved coupling waveguides. The center curve of the seventh curved coupling waveguide 305 is an Euler curve, with its starting point at the leftmost end. The center curve of the eighth curved coupling waveguide 306 is its antisymmetric curve. The sixth curved coupling waveguide 304 and the fifth curved coupling waveguide 303 are horizontally mirror-symmetrical variations of the seventh curved coupling waveguide 305 and the eighth curved coupling waveguide 306, respectively.

[0082] To ensure that the coupling coefficients of the eighth curved coupled waveguide 306, the seventh curved coupled waveguide 305, the sixth curved coupled waveguide 304, the fifth curved coupled waveguide 303, and the first microring 110 remain essentially unchanged during reverse engineering, this invention employs two limiting conditions. Limitation condition 1 is the determination of the maximum radius of curvature Rmax_bend of the central Euler curve of the seventh curved coupled waveguide 305 (i.e., determining the value of the maximum radius of curvature Rmax_bend based on the coupling coefficient); Limitation condition 2 is that the waveguide width change of the portion of the seventh curved coupled waveguide 305 relatively close to the first microring 110 remains essentially unchanged, i.e., the width change of the seventh curved coupled waveguide 305 is slow. Simultaneously, provided that the waveguide of the eighth curved coupled waveguide 306 is smoothly connected to the seventh curved coupled waveguide 305, its waveguide width change can be more drastic.

[0083] To shorten the computation time of reverse design, a two-step particle swarm optimization algorithm is used. The first step aims to determine the center Euler curves of the eighth curved coupled waveguide 306, the seventh curved coupled waveguide 305, the sixth curved coupled waveguide 304, and the fifth curved coupled waveguide 303. At this point, once the center Euler curve of the eighth curved coupled waveguide 306 is determined, the center curves of the other waveguides are also determined.

[0084] Keeping the waveguide widths of the eighth curved coupling waveguide 306, the seventh curved coupling waveguide 305, the sixth curved coupling waveguide 304, and the fifth curved coupling waveguide 303 unchanged, the Rmax_bend value of the Euler curve is determined, as well as the minimum spacing Wgap = 150nm between the microring conforming to the processing technology and the curved coupling waveguide. At this point, the coupling coefficient of the coupling region 40 between the first microring 110 and the eighth curved coupling waveguide 306, the seventh curved coupling waveguide 305, the sixth curved coupling waveguide 304, and the fifth curved coupling waveguide 303 is basically determined. To ensure the coupling coefficient K = 0.25, Rmax_bend = 12µm and the curved coupling waveguide width W_bend = 0.31µm are selected using simulation. Then, the Euler curve length L_bend, the control coefficient (arc length proportional coefficient) A_bend, and the Euler curve truncation coefficient (i.e., the actual number of points taken for the central Euler curve) num still need to be determined. The definition of num is: the Euler curve has a total of 600 points, and num is the first num points of the Euler curve actually taken. Based on the value of Rmax_bend, the range of L_bend is selected as [6um, 20um], and based on the range of L_bend, the range of A_bend is selected as [10um, 120um]. To ensure that the first coupling region 40 has sufficient curved coupling portion, the range of num is selected as [180, 600]. The simulation algorithm uses a high-precision three-dimensional finite-difference time-domain (FDTD) algorithm, shielding other simulation structures, and only calculating the TE fundamental mode transmittance of the TE fundamental mode light through the eighth curved coupling waveguide 306, the seventh curved coupling waveguide 305, the sixth curved coupling waveguide 304, and the fifth curved coupling waveguide 303. A particle swarm optimization (PSO) algorithm is introduced, with the number of iterations set to 40, the size of each iteration being 16, and the independent variables being A_bend, L_bend, and num (a total of 3 variables). The optimization objective value (FOM) is the TE fundamental mode transmittance. Thus, the parameters of the central Euler curve are determined (the parameters of the central Euler curve include Rmax_bend, A_bend, L_bend, and num).

[0085] The second step involves controlling the waveguide width variations of the seventh curved coupled waveguide 305 and the eighth curved coupled waveguide 306 using third-order and fourth-order Bessel functions, respectively. The Bessel control point of the seventh curved coupled waveguide 305 is denoted as:

[0086] P0_bend1=[xx0_bend1,yy0_bend1],

[0087] P1_bend1=[xx1_bend1,yy1_bend1],

[0088] P2_bend1=[xx2_bend1,yy2_bend1],

[0089] P3_bend1=[xx3_bend1,yy3_bend1].

[0090] Let the maximum abscissa of the center Euler curve of the seventh curved coupled waveguide 305 be Xmax_bend, P0_bend1 = [0, W_bend], yy1_bend1 = yy2_bend1 = W_bend, and xx3_bend1 = Xmax_bend. The values ​​of xx1_bend1 and xx2_bend1 are both in the range of [Xmax × 2 / 3, Xmax_bend]. The reason for limiting their minimum value to be greater than Xmax × 2 / 3 is to ensure that the width of the curved waveguide close to the micro-ring remains basically unchanged relative to W_bend, so as to ensure sufficient coupling coefficient. The range of yy3_bend1 is selected as [W_bend, W1], where W1 is the set starting waveguide width of the curved coupled waveguide. According to the result of the first step, the range of yy3_bend1 is selected as [W_bend, 0.5um].

[0091] The width variation of the eighth curved coupled waveguide 306 is controlled using a fourth-order Bézier curve. The Bézier control point of the eighth curved coupled waveguide 306 is denoted as:

[0092] P0_bend2=[xx0_bend2,yy0_bend2],

[0093] P1_bend2=[xx1_bend2,yy1_bend2],

[0094] P2_bend2=[xx2_bend2,yy2_bend2],

[0095] P3_bend2=[xx3_bend2,yy3_bend2],

[0096] P4_bend2=[xx4_bend2,yy4_bend2].

[0097] The starting point of the center Euler curve of the eighth curved coupling waveguide 306 is the rightmost end, and this point is denoted as the origin. The positive x-axis direction is horizontal to the left, and the y-axis direction remains unchanged. The starting waveguide width of the eighth curved coupling waveguide 306 is set to 0.5 μm, so the control point P0_bend2 = [0, 0.5 μm]. To smoothly connect with the seventh curved coupling waveguide 305, the ending control point P4_bend2 = P3_bend1. Therefore, the ranges of xx1_bend2, xx2_bend2, and xx3_bend2 are all set to [0, Xmax_bend], and the ranges of yy1_bend2, yy2_bend2, and yy3_bend2 are all set to [0, 4×W_bend]. The simulation algorithm uses a high-precision three-dimensional finite-difference time-domain (FDTD) algorithm, shielding other simulation structures and retaining only the straight waveguides connected to the left and right sides of the eighth curved coupled waveguide 306, the seventh curved coupled waveguide 305, the sixth curved coupled waveguide 304, the fifth curved coupled waveguide 303, and the first microring 110. The TE fundamental mode light enters from the straight waveguide connected to the left side of the fifth curved coupled waveguide 303. The TE fundamental mode transmittance T_bend of the TE fundamental mode light through the fifth curved coupled waveguide 303, the sixth curved coupled waveguide 304, the seventh curved coupled waveguide 305, and the eighth curved coupled waveguide 306, as well as the TE fundamental mode transmittance T_ring at the junction of the first curved waveguide 111 and the second curved waveguide 112 of the first microring, are calculated. A particle swarm optimization (PSO) algorithm is introduced, with nine independent variables: xx1_bend1, xx2_bend1, yy3_bend1, xx1_bend2, xx2_bend2, xx3_bend2, yy1_bend2, yy2_bend2, and yy3_bend2. The number of iterations is set to 250, with each iteration having a size of 32. The objective function (FOM) is the sum of the absolute values ​​of the TE fundamental mode transmittance T_bend and T_ring. After complete convergence of the PSO algorithm, the coupling coefficient K > 0.25 and the coupling loss is less than 0.019 dB.

[0098] Figure 4This is a schematic diagram of a 16-channel third-order micro-ring filter. Channel 1 is the input port, channels 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17 are the download ports, and channel 18 is the through port. Channels 2 to 17 represent the transition from long-wavelength to short-wavelength channels. Because the input light intensity decreases in the later channels, this helps balance the loss difference between long-wavelength and short-wavelength channels. The spacing between each adjacent channel is 3.2 nm, and the bandwidth of each passband is 2.6 nm, forming a 16-channel filter.

[0099] A third-order micro-loop filter with dimensions of 13.4 μm × 12 μm was simulated and verified using a three-dimensional finite-difference time-domain algorithm. Figure 8 The figure shows the simulation results, where the horizontal axis represents wavelength and the vertical axis represents the transmittance of the TE (Transverse Electric) fundamental mode. As can be seen from the figure, the device of this invention achieves the filtering function of a high-order micro-ring filter. The center wavelengths of the two bands are 1533 nm and 1588.5 nm, respectively, with 3dB bandwidths of 2.6 nm and 3.5 nm, respectively. The channel loss is less than 0.6 dB, the extinction ratio is greater than 60 dB, it has a flattened channel and high kurtosis, exhibits a relatively ideal square spectral response, and has a free spectral range (FSR) of 55.5 nm. Therefore, the device of this invention can provide an on-chip optical multi-channel filter with low loss, a large free spectral range, a high extinction ratio, and a small size.

[0100] In summary, Example 1, by introducing Euler ring curves and combining them with Bessel functions to control the waveguide width, achieved a smooth curvature transition, allowing for further reduction in the size of the microrings while effectively controlling the losses caused by curvature changes. The design achieves an ultra-large free spectral range of 55.5 nm, supporting 16 channels with a 3.2 nm spacing between each channel, significantly expanding the number of filter channels and bandwidth range.

[0101] Example 1 employs a reverse design approach to optimize the geometric parameters and waveguide width of the microring, resulting in smoother optical signal transmission within the microring and significantly reduced loss. When the microring size is reduced to a free spectral range of 55.5 nm, a half-ring loss of less than 0.008 dB / 180° is achieved, a significant reduction compared to existing technologies, providing a more reliable low-loss solution for high-performance optical communication applications.

[0102] Example 1 uses Euler ring curves and Bessel control waveguide width to optimize the design of the directional coupler. While ensuring a sufficiently large coupling coefficient, it achieves a smoother curvature transition, reduces the excitation of higher-order modes, and achieves a coupling loss of less than 0.019 dB (i.e., the coupling loss between the curved directional coupler and the micro-ring in Example 1 is significantly reduced). It also ensures a coupling coefficient of 0.25, which significantly improves the transmission efficiency of optical signals and effectively suppresses inter-channel crosstalk.

[0103] This invention also supports filter designs with different numbers of channels, different passband bandwidths, and different channel spacings. It also supports filters of different orders of micro-rings, enabling the implementation of high-order micro-ring filters.

[0104] In this invention, the design schemes of Euler curves and Bezier curves can be replaced by other curves with control points to achieve similar optical signal transmission and performance optimization effects. Several alternative schemes are described below, with examples 2 to 5 illustrating them respectively.

[0105] Example 2:

[0106] Example 2 provides a design method for a micro-ring filter. The difference between Example 1 and Example 2 is that the centerline of the micro-ring waveguide is designed using an Archimedean spiral instead of an Euler curve.

[0107] Archimedes' spirals have a fixed angular increment, and their regular geometry helps reduce transmission loss and maintain good spectral response characteristics, making them suitable for applications that require high stability of waveguide structures.

[0108] The polar equation of the Archimedean spiral is:

[0109] r(θ) = a + bθ

[0110] Where r is the radial distance, θ is the angle, and a and b are constants.

[0111] Example 2 controls the curve shape by controlling the constants a and b, and then cuts off a portion of the curve as the center curve of the curved waveguide.

[0112] Example 3:

[0113] Example 3 provides a design method for a micro-ring filter. The difference between Example 1 and Example 3 is that a logarithmic spiral is used instead of an Euler curve for the design of the centerline of the micro-ring waveguide.

[0114] Logarithmic spirals have exponentially increasing curvature characteristics, and their smooth curvature changes can effectively reduce bending losses while improving the free spectral range of microrings.

[0115] In the polar coordinate system (r, θ), the curve of the logarithmic spiral can be written as:

[0116] r(θ)=r0e kθ

[0117] Where: r is the radial distance, θ is the angle, r0 is the initial radial distance, and k is a constant.

[0118] Example 3 controls the curve shape by controlling r0 and k, and can take a segment of the curve within a specified range of θ as the center curve of the curved waveguide.

[0119] Example 4:

[0120] Example 4 provides a design method for a micro-ring filter. The difference from Example 1 is that Example 4 uses spline interpolation curves instead of Bezier curves to adjust the waveguide width.

[0121] 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.

[0122] The spline interpolation curve is represented as:

[0123]

[0124] Where C(t) is a point on the curve, a n These are the coordinates of the nth control point, where n is the order of the curve, and t is a parameter representing its position on the curve.

[0125] Example 4 shows that the shape of the spline curve can be controlled by controlling each control point.

[0126] Example 5:

[0127] Example 5 provides a design method for a micro-ring filter. The difference between Example 1 and Example 5 is that B-spline curves are used instead of Euler curves and Bezier curves.

[0128] B-spline curves are defined using multiple control points, enabling smooth curve transitions. Their curvature variations can be effectively controlled, making them suitable for smooth design of waveguide center curves and gradual adjustment of waveguide width, thereby reducing bending loss and optimizing spectral response performance.

[0129] B-spline curves are represented as follows:

[0130]

[0131] Where C(t) is a point on the curve, P i It is a control point. N i,kIt is a B-spline basis function, k is the order of the curve, and n is the number of control points minus 1.

[0132] Similar to Bézier curves, the shape of the curve is defined by defining the order k of the curve and the location of the control points, thereby controlling the width variation of the curved waveguide.

[0133] In summary, this invention, by introducing a design method combining the first and second curves and employing a particle swarm optimization algorithm, enables the realization of an on-chip multi-channel optical filter. This filter exhibits an ultra-wide free spectral range, low loss, and high extinction ratio, while demonstrating excellent flat-top spectral response. The design of this invention not only possesses high flexibility, supporting various channel numbers and bandwidth configurations, but also features low crosstalk and high kurtosis spectral characteristics. This on-chip micro-ring filter has a compact structure, excellent performance, and simple manufacturing process, making it suitable for large-scale integrated photonic applications.

[0134] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A design method for a micro-ring filter, characterized in that, Includes the following steps: A simulation model of a microring filter is established using a three-dimensional time-domain finite-difference algorithm. The microring filter includes a microring region and a coupled waveguide region. Based on the set free spectral range and the set coupling coefficient, with the fundamental mode transmittance as the optimization target, the first curve is used as the waveguide center curve, and the width of the waveguide is adjusted using the second curve. The micro-ring region and the coupled waveguide region are designed in reverse, and a set of optimal micro-ring structure parameters and a set of optimal coupled waveguide structure parameters are obtained through iterative optimization, thus completing the design of the micro-ring filter. The microring region contains multiple microrings with identical structures. Each microring is divided into four quarter-microring curved waveguides, and the center curve of each quarter-microring curved waveguide is the first curve.

2. The design method for a micro-ring filter according to claim 1, characterized in that, The quarter-micro-ring bent waveguide was used as the target for reverse design; The coupled waveguide region is provided with a first coupled waveguide and a second coupled waveguide located on the upper and lower sides of the micro-ring region, respectively. The first coupled waveguide includes an input port straight waveguide, a first curved coupled waveguide unit, and an output port straight waveguide. The second coupled waveguide includes a first transmission unit, a second curved coupled waveguide unit, and a second transmission unit. The structure of the second curved coupled waveguide unit is symmetrical to that of the first curved coupled waveguide unit. The first curved coupled waveguide unit is divided into four curved coupled waveguide segments, which are respectively denoted as the first curved coupled waveguide, the second curved coupled waveguide, the third curved coupled waveguide, and the fourth curved coupled waveguide. The center curve of the third curved coupled waveguide is the first curve, and the center curve of the fourth curved coupled waveguide is the antisymmetric curve of the center curve of the third curved coupled waveguide. The second curved coupled waveguide and the third curved coupled waveguide are horizontally mirror-symmetrical, and the first curved coupled waveguide and the fourth curved coupled waveguide are horizontally mirror-symmetrical. The third curved coupled waveguide and the fourth curved coupled waveguide are used as targets for reverse engineering.

3. The design method for a micro-ring filter according to claim 2, characterized in that, The transmittance of the TE fundamental mode light at the working wavelength through the microring is denoted as the first TE fundamental mode transmittance; the transmittance of the TE fundamental mode light at the working wavelength through the first bent coupled waveguide unit is denoted as the second TE fundamental mode transmittance; the transmittance of the TE fundamental mode light at the working wavelength through the junction of two adjacent quarter-wave bend waveguide segments in the structure of a certain microring is denoted as the third TE fundamental mode transmittance. The micro-ring region is reverse-designed using one of the following algorithms: particle swarm optimization, gradient algorithm, swarm intelligence algorithm, or neural network algorithm, with the first TE fundamental mode transmittance as the optimization objective; the coupled waveguide region is reverse-designed using the particle swarm optimization algorithm, with the sum of the absolute values ​​of the second and third TE fundamental mode transmittance as the optimization objective.

4. The design method of the micro-ring filter according to claim 1, characterized in that, The first curve is one of Euler curve, Archimedean spiral, logarithmic spiral, and B-spline curve, and the second curve is one of Bézier curve, spline interpolation curve, and B-spline curve.

5. The design method for a micro-ring filter according to claim 3, characterized in that, When the first curve is an Euler curve and the second curve is a Bezier curve, the initial waveguide width W0 of the microring is set, and the perimeter L of the central Euler curve of the quarter-microring curved waveguide is determined according to the set free spectrum range. The range of the maximum radius of curvature Rmax of the central Euler curve of the quarter-microring curved waveguide and the range of the arc length proportionality coefficient A of the central Euler curve of the quarter-microring curved waveguide are also determined. The maximum value of the abscissa of the center Euler curve of the quarter-micro-ring curved waveguide is denoted as Xmax. The width of the quarter-micro-ring curved waveguide is adjusted using a third-order Bézier curve. The Bézier control points are denoted as P0 = [0, W0], P1 = [xx1, yy1], P2 = [xx2, yy2], and P3 = [Xmax, yy3]. Among them, the values ​​of xx1 and xx2 are both in the range of [Xmax / 3, 2Xmax], the values ​​of yy1 and yy2 are both in the range of [-W0 / 2, 3W0], and the value of yy3 is in the range of [W0 / 2, 3W0]. Using Rmax, A, xx1, yy1, xx2, yy2, and yy3 as variables, the microring region is reverse-designed using a particle swarm optimization algorithm, and a set of optimal microring structure parameters is obtained through iterative optimization.

6. The design method of the micro-ring filter according to claim 5, characterized in that, The method of adjusting the width of the quarter-micro-ring curved waveguide using Bézier curves is as follows: when the abscissa of a point on the Bézier curve is equal to the abscissa of a point on the Euler curve, the point on the Bézier curve is recorded as the Bézier point, and the corresponding point on the Euler curve is recorded as the Euler point; the ordinate value of the Bézier point is taken as the waveguide width of the Euler point, and the waveguide width direction of the Euler point is parallel to the direction of the line connecting the Euler point and the center of curvature of the Euler point, and half of the waveguide width is extended to both sides of the Euler point.

7. The design method of the micro-ring filter according to claim 3, characterized in that, When the first curve is an Euler curve and the second curve is a Bezier curve, the coupled waveguide region is reverse-engineered using a two-step particle swarm optimization algorithm. The first step of reverse design includes: determining the maximum radius of curvature Rmax_bend of the central Euler curve of the third curved coupled waveguide, the minimum spacing Wgap between the micro-ring and the coupled waveguide, and the width W_bend of the coupled waveguide based on the set coupling coefficient; determining the range of the perimeter L_bend of the central Euler curve of the third curved coupled waveguide based on the value of Rmax_bend; determining the range of the arc length scaling factor A_bend of the central Euler curve of the third curved coupled waveguide based on the range of L_bend; and determining the range of the arc length scaling factor A_bend of the central Euler curve of the third curved coupled waveguide based on the size of the coupled waveguide region. The range of the actual number of points num for the central Euler curve is determined; the transmittance of the two TE fundamental modes is calculated by simulation, and the coupled waveguide region is reverse-designed using particle swarm optimization algorithm with L_bend, A_bend, and num as variables, and the parameters of the central Euler curve are obtained by iterative optimization; wherein, the starting point of the central Euler curve of the third curved coupled waveguide is its leftmost end, and this point is set as its origin, with the horizontal direction to the right being the positive x-axis; the starting point of the central Euler curve of the fourth curved coupled waveguide is its rightmost end, and this point is set as its origin, with the horizontal direction to the left being the positive x-axis. The second step of reverse design includes: adjusting the width of the third curved coupled waveguide using a third-order Bessel function, and adjusting the width of the fourth curved coupled waveguide using a fourth-order Bessel function.

8. The design method of the micro-ring filter according to claim 7, characterized in that, The Bessel control points of the third curved coupled waveguide are denoted as P0_bend1 = [0, W_bend], P1_bend1 = [xx1_bend1, W_bend], P2_bend1 = [xx2_bend1, W_bend], and P3_bend1 = [Xmax_bend, yy3_bend1]; where the values ​​of xx1_bend1 and xx2_bend1 are both in the range of [Xmax×2 / 3, Xmax_bend], and the range of yy3_bend1 is selected as [W_bend, W1], where W1 is the initial waveguide width of the curved coupled waveguide, Xmax_bend is the maximum value of the abscissa of the center Euler curve of the third curved coupled waveguide, and Xmax is the maximum value of the abscissa of the center Euler curve of the quarter-micro-ring curved waveguide; The Bessel control points of the fourth curved coupled waveguide are denoted as P0_bend2 = [0, W1], P1_bend2 = [xx1_bend2, yy1_bend2], P2_bend2 = [xx2_bend2, yy2_bend2], P3_bend2 = [xx3_bend2, yy3_bend2], P4_bend2 = [xx4_bend2, yy4_bend2]; where xx1_bend2, xx2_bend2, and xx3_bend2 are all in the range [0, Xmax_bend], yy1_bend2, yy2_bend2, and yy3_bend2 are all in the range [0, 4W_bend], and P4_bend2 = P3_bend1; Using xx1_bend1, xx2_bend1, yy3_bend1, xx1_bend2, xx2_bend2, xx3_bend2, yy1_bend2, yy2_bend2, and yy3_bend2 as variables, the coupled waveguide region is reverse-engineered using a particle swarm optimization algorithm, and a set of optimal coupled waveguide structure parameters is obtained through iterative optimization.

9. The design method of the micro-ring filter according to claim 1, characterized in that, When establishing a simulation model of a microring filter using a three-dimensional time-domain finite-difference algorithm, the basic parameters of the microring filter are used as constraints; the basic parameters include the operating wavelength, waveguide material, and waveguide height of the microring filter.

10. A micro-ring filter, characterized in that, The micro-ring filter was designed using the design method described in any one of claims 1-9.

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