Design method of silicon-based reticle and silicon-based reticle

Abstract

This invention discloses a design method for a silicon-based mode divider. Based on a silicon-on-insulator (SiI) platform, it defines a bus waveguide, branch waveguides, and a functional region located between the bus and branch waveguides. The number of branch waveguides is n, determined by a linear combination of the input modes and bandwidths of the bus waveguides. The initial structures of the bus waveguides, branch waveguides, and functional regions are defined. Using an FDTD solver, each iteration requires m forward simulations and m adjoint simulations. The gradient field is calculated, and the dielectric constant parameters of the functional region are optimized using the gradient descent method based on the gradient field calculation results, updating the structure. Iteration continues until the design target is reached or further optimization is impossible, at which point it stops. The discrete dielectric constants are binarized, transforming the dielectric constants of the functional regions into a structure defined only by the functional regions. The final structure diagram is output. This invention also discloses a silicon-based mode divider designed using the above method.

Description

Technical Field

[0001] This invention relates to the field of integrated photonics technology, specifically to a design method for a silicon-based mode splitter and the silicon-based mode splitter itself. Background Technology

[0002] With the rapid development of the information age, the demand for data transmission is surging. Based on this, silicon-based photonics has attracted widespread attention due to its high speed, broadband, and efficient integration in the field of information transmission. Multiplexing technology, as an effective means of expanding information transmission capacity, has received unprecedented attention. Among them, mode division multiplexing (MDM), which uses only one light source to transmit multiple modes in a multimode waveguide, and wavelength division multiplexing (WDM), widely used in optical fiber communication systems, have become key technologies for expanding information capacity on silicon-on-insulator (SOI) platforms. However, single mode division multiplexing or single wavelength division multiplexing (WDM) technologies can no longer meet the needs. Seeking a combination of multiple multiplexing technologies can multiply the bandwidth, further improving the capacity of current information and communication systems.

[0003] Silicon-based mode dividers (MDDs) are used to separate modes of different orders into different signals while maintaining the mode order, making them key components for achieving stable on-chip mode-division multiplexing (MDM) systems. Since the effective refractive index of higher-order modes is always lower than that of lower-order modes within the same waveguide, most mode demultiplexing systems involve changes in mode order. The primary mechanism for mode separation is to convert higher-order modes into fundamental modes and map them to specific channels using phase-matching. However, in mode-sensitive systems, mode conversion leads to instability and performance degradation as the mode order changes. Silicon-based MDDs that achieve mode separation without changing the mode order significantly improve the flexibility of MDM systems. However, directly splitting modes with different effective indices within the same waveguide is very challenging, and research reports on MDDs that do not change the mode order are currently scarce. Some researchers have used symmetrical directional couplers (DCs) to separate TE0 / TE1 modes. Others have proposed a mode splitter based on an asymmetric directional coupler (ADC), consisting of two slits and a strip waveguide, capable of separating TE0 and TE1 modes within a 100nm bandwidth with crosstalk (CT) <-8dB and insertion loss (IL) <1dB. By controlling the coupling region size of a tapered directional coupler, researchers have separated the two fundamental modes TE0 / TM0, achieving high extinction ratio (ER <10dB) and low insertion loss (IL <1.6dB) mode separation within a 90nm bandwidth. Furthermore, a dual-mode splitter for separating TM0 and TM1 modes has been developed using a bridged subwavelength grating-assisted (BSWG) DC and a mode filter, achieving CT <-15dB and IL <1.8dB within an 84nm bandwidth. However, these designs consume a large footprint of hundreds of square micrometers and have complex device structures. To achieve a stable and efficient on-chip MDM system, there is an urgent need for an ultra-compact, single-integrated, wide-spectrum mode separation device. In order to be combined with an on-chip WDM system, the designed photonic device also needs to have wavelength separation capabilities, which makes the device design extremely difficult. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is: how to provide a design method for silicon-based splitters that can effectively improve device performance and increase device design efficiency.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A design method for a silicon-based mold splitter includes the following steps:

[0007] (1) Based on the bus waveguide, branch waveguide and functional region located between the bus waveguide and branch waveguide on the silicon-on-insulator platform, the number of branch waveguides is n and is determined according to the linear combination of the input mode and input bandwidth of the bus waveguide. The initial structure of the bus waveguide, branch waveguide and functional region is defined.

[0008] (2) Using the FDTD solver, each iteration requires m forward simulations and m adjoint simulations, where m equals n;

[0009] (3) Calculate the gradient field and optimize the dielectric constant parameters of the functional region based on the gradient field calculation results and the gradient descent method, and update the structure;

[0010] (4) Continue iterating until the design goal is achieved or further optimization is no longer possible;

[0011] (5) Binarize the discrete dielectric constants to transform the dielectric constants of the functional regions into structures that only contain the functional regions defined in step (1);

[0012] (6) Output the final structure diagram.

[0013] As an optimization, the initial structure of the bus waveguide, branch waveguide, and functional region is defined, including the width of the bus waveguide and branch waveguide, the spacing between two adjacent branch waveguides, the shape and size of the functional region, and the design material and background material of the functional region.

[0014] As an optimization, the shape of the functional area can be any one of rectangle, Y-shape, triangle or ellipse.

[0015] As an optimization, the design material for the functional area is Si or Si3N4, and the background material is SiO2 or air.

[0016] A silicon-based mold splitter is designed according to the silicon-based mold splitter design method described above.

[0017] Compared with existing technologies, this invention has the following advantages: It employs a reverse design algorithm with adjoint optimization, which broadens the wavelength range of traditional mode splitters and significantly reduces the device area. It can achieve wavelength and mode separation without changing the mode order or the wide-spectrum input light source. This integrated photonic device combining wavelength and mode can serve as the foundation for stable on-chip multiplexing systems and has broad application prospects in optical communication networks. Furthermore, by adjusting design parameters, this design scheme can be used to design integrated hybrid multiplexing devices with more transmission channels and a wider bandwidth range. Attached Figure Description

[0018] Figure 1 This is an initialization structure diagram of the silicon-based splitter in this invention;

[0019] Figure 2 These are the waveguide dispersion curves at 1310nm and 1550nm in this invention;

[0020] Figure 3 This is a flowchart illustrating the design of the dual-wavelength mode splitter in this invention.

[0021] Figure 4 This is a diagram of the output structure of the dual-wavelength silicon-based mode divider in this invention;

[0022] Figure 5 This is a linear graph showing the number of FOM iterations and the quality factor for each channel in this invention.

[0023] Figure 6 This is a diagram showing the transmission efficiency of each channel in this invention;

[0024] Figure 7 This is a performance graph showing the outputs of the present invention with an input light source bandwidth of ±20nm;

[0025] Figure 8 This is a magnetic field transmission diagram of different signals input into the bus waveguide in this invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0027] The design method of the silicon-based splitter in this specific embodiment includes the following steps:

[0028] (1) Based on the bus waveguide 1, branch waveguide 2 and functional region 3 located between the bus waveguide 1 and branch waveguide 2 on the silicon-on-insulator platform, the number of branch waveguide 2 is n and determined according to the linear combination of the input mode and input bandwidth of the bus waveguide 1, the initial structure of the bus waveguide 1, branch waveguide 2 and functional region 3 is defined.

[0029] (2) Using the FDTD solver, each iteration requires m forward simulations and m adjoint simulations, where m equals n;

[0030] (3) Calculate the gradient field and optimize the dielectric constant parameters of functional region 3 based on the gradient field calculation results and the gradient descent method, and update the structure;

[0031] (4) Continue iterating until the design goal is achieved or further optimization is no longer possible;

[0032] (5) Binarize the discrete dielectric constant to transform the dielectric constant of functional region 3 into a structure defined only by functional region 3 in step (1);

[0033] (6) Output the final structure diagram.

[0034] In this specific embodiment, the initial structure of the bus waveguide 1, branch waveguide 2 and functional region 3 is defined, including the width of the bus waveguide 1 and branch waveguide 2, the spacing between two adjacent branch waveguides 2, the shape and size of the functional region 3, and the design material and background material of the functional region 3.

[0035] In this specific embodiment, the shape of functional area 3 can be any one of rectangle, Y-shape, triangle or ellipse.

[0036] In this specific embodiment, the design material of functional region 3 is Si or Si3N4, and the background material is SiO2 or air.

[0037] A silicon-based mold splitter is designed according to the silicon-based mold splitter design method described above.

[0038] The silicon-based modem in this specific embodiment is designed based on a silicon-on-insulator platform with an etching depth of 220 nm. SiO2 is used to encapsulate the functional regions to protect the etched layer structure. The device design principle is as follows: Figure 1 As shown, the design consists of one bus waveguide, four branch waveguides, and a functional area. Both the bus and branch waveguides are required to support only TE0 and TE1 mode transmissions at 1310nm and 1550nm light source inputs. The optimal waveguide width was determined using the full vector finite element method (FV-FEM), and the results are shown below. Figure 2As shown. Within a width range of 0.75μm to 1.1μm, the waveguide supports TE0 and TE1 mode transmission under input light sources at 1310nm and 1550nm, but does not support higher-order TE modes, thus minimizing the impact of mode crosstalk. Considering that the device area should not be too large, the width of the bus waveguide and branch waveguides was ultimately set to 0.8μm. In the bus waveguide, the bandwidth range of the input signal is 1310±20nm and 1550±20nm, with TE0 and TE1 modes, a linear combination of input mode and input bandwidth. The four branch waveguides form four output channels, from bottom to top: channel 1 (output TE0 / 1310nm), channel 2 (output TE1 / 1310nm), channel 3 (output TE0 / 1550nm), and channel 4 (output TE1 / 1550nm). To minimize crosstalk between channels, the spacing between channels needs to be as large as possible; however, excessive spacing will affect the device's integration density. Considering all factors, the spacing between each branch channel is 1 μm. Therefore, the optimized functional area can be designed as a 6.2 μm × 6.2 μm rectangular structure. Of course, it can also be set to any shape such as Y-shaped, triangular, or elliptical. By using the adjoint method topology optimization algorithm to change the material distribution within the functional area, the effective refractive index of the functional area can be altered, thereby achieving the optimized design of the dual-wavelength mode divider.

[0039] For the designed dual-wavelength silicon-based mode splitter, the optimization space is: Figure 1 The square region is shown. Using the adjoint method, the gradient of the objective function with respect to each point in the optimization space is calculated. Combined with gradient descent, this guides the filling of the design material (Si) and background material (SiO2) within the optimization region. (Alternatively, Si3N4 can be used as the design material and air as the background material, or Si3N4 as the design material and SiO2 as the background material, or Si as the design material and air as the background material). Their dielectric constants are ε0 and ε1 respectively. Si =3.48 and ε SiO2 =1.44, thereby changing the effective refractive index of the optimization region. Through continuous iterative optimization of device performance, the effects of wavelength separation and mode separation are achieved. The optimization goal is to separate light of different wavelengths and modes input in the bus waveguide into different branch waveguides for output, and to require that the transmission efficiency of each channel reaches its maximum.

[0040] The objective function FOM for each channel can be defined as:

[0041]

[0042] In the formula, FOM is the optimization objective function, defined as the average transmittance of the target mode at the output port under the design bandwidth, where λ1 and λ2 represent the minimum and maximum wavelengths of the target bandwidth, respectively, i represents the index of the output waveguide under the current incident light source, and T... cur / T i This represents the normalized transmission efficiency (FOM) when using the light source supported by the current channel as input, and can be given by the Poynting vector. The values ​​in parentheses indicate the distance between the current transmission efficiency and the ideal transmission efficiency for each different input condition. The FOM value for each channel will gradually decrease with reverse engineering and optimization iterations, representing a gradual approach to the optimal transmission efficiency.

[0043] The gradient of the FOM with respect to the dielectric constant can be efficiently calculated using the adjoint method. The forward-propagating field E is obtained through forward simulation. forward Then, the adjoint field E is obtained by adjusting the reverse field through the phase factor. adjoint The phase factor A is given by the following formula:

[0044]

[0045] Where * denotes conjugate operation, ε0 represents the dielectric constant in vacuum, and E m and H m Let ΔV represent the electric and magnetic fields of the desired output mode m. ΔV represents the volume of the divided pixel. S represents the output waveguide cross section. Integrating over the output cross section S yields the adjoint field E via the phase factor. adjoint At this point, the gradient of FOM relative to the dielectric constant distribution can be expressed as:

[0046]

[0047] Here, the subscript x represents the x-th element of the calculated functional region. The forward and adjoint fields can be obtained using the finite-difference time-domain method. Furthermore, for broadband input light sources, a wavelength scaling factor C(λ) is needed to adjust the gradient field, as shown in the following formula:

[0048]

[0049] Where ω(λ) represents the angular frequency at that wavelength, P source (λ) represents the input source power, j is the imaginary unit, and A(λ) represents the phase factor at this wavelength. In this case, the FOM gradient affected by the wavelength can be expressed as:

[0050]

[0051] Here, Ω represents the design space. The influence of each point within the functional area on the final result is calculated according to equation (5), which guides the dielectric constant of each point based on the gradient in ε.Si and ε SiO2 The structure is updated by considering the changes between these parameters. FDTD is used to calculate the FOM value and continuous iterative optimization is performed until the design goal is achieved and the final device structure diagram is generated.

[0052] The overall reverse design process of the dual-wavelength mode divider in this specific embodiment is as follows: Figure 3 As shown, in the specific design process:

[0053] 1. Determine the initial structure and the initial dielectric constant ε of the functional regions. old ;

[0054] 2. Four forward simulations were performed to obtain the electric field within the functional region.

[0055] 3. Four adjoint simulations (the light source in the adjoint simulation is the same size as the light source in the forward simulation, but its position is changed to four branch waveguides propagating back) to obtain the reverse electric field in the functional region.

[0056] 4. Calculate formula (2) to obtain A0, A1, A2, and A3 respectively;

[0057] 5. Adjust the reverse electric field using A to obtain the adjoint field. Similarly;

[0058] 6. The FOM value is obtained from formula (1), and the gradient is obtained from formula (3).

[0059] 7. Sum the gradients to obtain the overall gradient. Here, a, b, c, and d are the weights of the gradient of each branch waveguide. In this embodiment, the default value is 1. The weight ratio can be changed arbitrarily to achieve arbitrary output ratio of branch waveguides.

[0060] 8. The above steps are for single-wavelength light sources. Using formulas (4) and (5), we can calculate the input of multi-wavelength light sources, such as 1550±20nm (the band can be expanded). The specific idea is to divide the input wideband light source into 10 points (for example), calculate the gradient and gradient scaling factor C(λ) of each point, and use formula (5) to obtain the gradient under the new wideband light source input condition.

[0061] 9. Update the gradient using the gradient descent algorithm: α is the step size, which controls the structure update speed. It is a value between 0 and 1, with a default value of 1. It is usually between 0.9 and 0.99. In this embodiment, the default value is used.

[0062] 10. Repeat steps (2), (3), (4), (5), and (6) to obtain new FOM values ​​(which can be broadband inputs), and compare the FOM values. new Check if the performance meets the requirements. If it does not meet the requirements, continue with steps (7), (8), and (9) until the maximum number of iterations is reached or the requirements are met, then stop iterating and enter the binarization stage. Finally, the output structure refractive index is only Si and SiO2.

[0063] The final designed dual-wavelength silicon-based mode splitter structure is as follows: Figure 4 As shown, the TE0 signal with a wavelength of 1310nm in the bus waveguide is output from the branch waveguide channel numbered 1, the TE1 signal with a wavelength of 1310nm in the bus waveguide is output from the branch waveguide channel numbered 2, the TE0 signal with a wavelength of 1550nm in the bus waveguide is output from the branch waveguide channel numbered 3, and the TE1 signal with a wavelength of 1550nm in the bus waveguide is output from the branch waveguide channel numbered 4. The designed structure achieves the separation of the TE0 mode and the TE1 mode without changing the mode order, as well as the recombination effect of separating the 1310nm and 1550nm wavelengths. The input light sources are all broadband light sources, ensuring a bandwidth range of at least ±20nm.

[0064] The linear graph of iteration number versus FOM for each channel is shown below. Figure 5 As shown, after 139 iterations, the optimization objectives for each channel meet the expected results. The subsequent binarization process tends to decrease the performance of the finally converged device.

[0065] When the device operates in mode separation mode, the transmission efficiency of the TE0 channels (channels 1 and 3) is as follows: Figure 6 As shown in (a) and (c), TE1 channels (channels 2 and 4) are as follows: Figure 6 As shown in (b) and (d), they clearly maintain low crosstalk while ensuring low insertion loss. When the device operates with wavelength separation, the transmission efficiency of the 1310nm channels (channel 1 and channel 2) is as follows: Figure 6 As shown in (a) and (b), the transmission efficiency of the 1550nm channels (channels 3 and 4) is as follows: Figure 6 As shown in (c) and (d), the device clearly achieves high transmission efficiency over a wide range of wavelengths centered at 1310 nm and 1550 nm.

[0066] The linear graph of iteration number versus FOM for each channel is shown below. Figure 5 As shown, after 139 iterations, the optimization objectives for each channel meet the expected results. The subsequent binarization process tends to decrease the performance of the finally converged device.

[0067] When the device operates in mode separation mode, the transmission efficiency of the TE0 channels (channels 1 and 3) is as follows: Figure 6 As shown in (a) and (c), (a) is the input in 1310nm TE0 mode, and (c) is the input in 1550nm TE0 mode. TE1 channel (channels 2 and 4) are as follows: Figure 6 As shown in (b) and (d), (b) uses the 1310nm TE1 input, and (d) uses the 1550nm TE1 input. Clearly, they maintain low crosstalk while ensuring low insertion loss. When the device operates with wavelength separation, the transmission efficiency of the 1310nm channels (channel 1 and channel 2) is as follows: Figure 6 As shown in (a) and (b), the transmission efficiency of the 1550nm channels (channels 3 and 4) is as follows: Figure 6 As shown in (c) and (d), the device clearly achieves high transmission efficiency over a wide range of wavelengths centered at 1310 nm and 1550 nm.

[0068] Figure 7 The figures show the performance of each output at an input light source bandwidth of ±20nm: (a) TE0 mode with input at 1310nm; (b) TE1 mode with input at 1310nm; (c) TE0 mode with input at 1550nm; (d) TE1 mode with input at 1550nm. It can be seen that each channel maintains a low IL over a relatively wide wavelength range. At a working wavelength centered at 1310nm, when the input is in TE0 mode, the IL and CT of this structure are 0.15dB and -30.54dB, respectively; when the input is in TE1 mode, the IL and CT are below 0.19dB and -27.67dB, respectively. At a working wavelength centered at 1550nm, when the input is in TE0 mode, the IL and CT are 0.11dB and -26.35dB, respectively; when the input is in TE1 mode, the IL and CT are below 0.11dB and -24.83dB, respectively. When the input light source is broadband, although IL and CT are reduced compared to when the tolerance is 0, the designed dual-wavelength mode divider can still maintain a large operating bandwidth and the performance is still close to the design target.

[0069] The magnetic field distributions of the TE0 and TE1 modes of the optimized dual-wavelength silicon-based mode splitter are as follows: Figure 8 As shown, (a) and (b) represent the propagation of the TE1 and TE0 signals with a center wavelength of 1550 nm in the bus waveguide and branch waveguide, respectively; (c) and (d) represent the propagation of the TE1 and TE0 signals with a center wavelength of 1310 nm in the bus waveguide and branch waveguide, respectively. It can be seen that the designed device supports the separation of the TE0 and TE1 modes without changing the mode order in a dual-wavelength range.

[0070] <![CDATA[Occupied area (μm 2 )]]> aisle Loss / dB Crosstalk / dB Modulus change Related References 50×2 1λand 2TE <1 <-8 NO Reference 1 40×12 1λand 2TE <1.47 <-19.6 NO Reference 2 5×3 1λand 2TE <0.54 <-18.06 NO Reference 3 4.8×4.8 2λand 2TE <0.29 <-17.23 YES Reference 4 6.2×6.2 2λand 2TE <0.19 <-24.83 NO This embodiment

[0071] Table 1

[0072] Table 1 shows the development of similar functional devices in recent years. As can be seen from the table, the designed silicon-based mode splitter performs well in terms of compactness, and in terms of performance, both IL and CT reach the best values ​​in this category of literature. The device in Reference 4 can achieve wavelength and mode mixed multiplexing integration, but it cannot achieve mode separation without changing the order. Other works can achieve stable mode separation, but cannot achieve wavelength multiplexing. Finally, the dual-wavelength silicon-based mode splitter designed in this embodiment has a size of only 6.2 × 6.2 μm. 2 It can achieve wavelength separation at 1310nm±20nm and 1550nm±20nm, and mode separation between TE0 and TE1, without changing the mode order and the broadband input light source. Furthermore, electromagnetic simulation experiments showed that the device's IL and CT are less than 0.19dB and -24.83dB, respectively, reaching an advanced level for this type of device.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A design method for a silicon-based mold splitter, characterized in that: Includes the following steps: (1) Based on the bus waveguide, branch waveguide and functional region located between the bus waveguide and branch waveguide on the silicon-on-insulator platform, the number of branch waveguides is n and is determined according to the linear combination of the input mode and input bandwidth of the bus waveguide. The initial structure of the bus waveguide, branch waveguide and functional region is defined. The initial structure of the bus waveguide, branch waveguide and functional region includes the width of the bus waveguide and branch waveguide, the spacing between two adjacent branch waveguides, the shape and size of the functional region, and the design material and background material of the functional region. (2) Using the FDTD solver, each iteration requires m forward simulations and m adjoint simulations, where m equals n; (3) Calculate the gradient field and optimize the dielectric constant parameters of the functional region based on the gradient field calculation results and the gradient descent method, and update the structure; The gradient field calculation includes: calculating the gradient of the objective function FOM with respect to the dielectric constant using the adjoint method. The objective function FOM is defined as: ； In the formula, λ1 and λ2 represent the minimum and maximum wavelengths of the target bandwidth, respectively, i represents the index of the output waveguide under the current incident light source, and T cur / T i This represents the normalized transmission efficiency when the light source supported by the current channel is used as input. The gradient of FOM with respect to the dielectric constant distribution is expressed as: ； In the formula, The adjoint field is obtained by adjusting the reverse field using a phase factor. To obtain the forward-propagating electric field through forward simulation, the subscript x represents the x-th element of the calculated functional region; (4) Continue iterating until the design goal is achieved or optimization can no longer be achieved, then stop iterating; (5) Binarize the discrete dielectric constants to transform the dielectric constants of the functional regions into structures that only contain the functional regions defined in step (1); (6) Output the final structure diagram.

2. The design method of the silicon-based mold splitter according to claim 1, characterized in that: The functional area can be any shape, such as a rectangle, a Y-shape, a triangle, or an ellipse.

3. The design method of the silicon-based splitter according to claim 1, characterized in that: The functional areas are designed with Si or Si3N4 as the material, and the background material is SiO2 or air.

4. A silicon-based mold release device, characterized in that: The design is carried out according to the design method of the silicon-based splitter according to any one of claims 1 to 3.

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