Deterministic construction method of photonic device based on envelope reverse mapping under transmission efficiency
By deterministically constructing the geometry of the adiabatic waveguide using the inverse mapping method, the ill-conditioned and phase-sensitive optimization problems in the prior art are solved, and device size reduction and broadband robustness are achieved, while reducing computational complexity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANTONG UNIV
- Filing Date
- 2026-02-09
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies suffer from ill-conditioned optimization problems, excessive sensitivity to phase, and geometric redundancy when designing adiabatic mode evolution devices, resulting in suboptimal design outcomes and a lack of broadband robustness.
By employing a method based on inverse envelope mapping under transmission efficiency, the global shortest adiabatic waveguide geometry is deterministically constructed by establishing an adiabatic hierarchy, discretizing the geometric space, constructing a phase-insensitive inverse envelope function, and performing inverse solution based on constraint boundaries.
It achieves a significant reduction in device size (over 80%), reduced computational complexity, and the generated device is insensitive to wavelength drift and has broadband robustness.
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Figure CN122194376A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of integrated optoelectronics technology, specifically relating to a deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency. Background Technology
[0002] Thermally adiabatic mode evolution devices (such as mode converters, waveguide tapers, and thermally adiabatic couplers) are core components in photonic integrated circuits (PICs) for realizing broadband, high-tolerance optical interconnects. Traditional design methods mainly follow two paths:
[0003] (1) Analytical shape parameterization: The waveguide width variation profile is defined using global analytic functions such as linear, exponential, sine, or cubic polynomials. Designers use several key parameters of the sweep function (such as total length and curvature coefficient) to find solutions that meet efficiency requirements.
[0004] (2) Gradient-based black-box optimization: Using the adjoint method, particle swarm optimization (PSO) or genetic algorithm (GA), the boundary of the device is free-deformed or optimized at the pixel level with the objective function of maximizing transmission efficiency.
[0005] 2. Deep-seated defects in existing technologies
[0006] Despite the widespread use of the above methods, they suffer from fundamental structural deficiencies at the physical and mathematical levels, resulting in suboptimal design outcomes.
[0007] (1) Ill-posedness of optimization problems: The adiabatic theorem states that the transmission efficiency η of mode evolution only asymptotically approaches 1 as the device length L→∞. This means that in an unconstrained optimization objective function, there is no finite extreme point. Optimization algorithms either drive the length to increase infinitely in pursuit of high efficiency, or get trapped in local optima due to the lack of a natural stopping criterion.
[0008] (2) Excessive sensitivity to phase: In adiabatic devices of finite length, there is a continuous energy exchange between the main mode and higher-order modes, which causes the transmission efficiency to oscillate violently with the length. Existing optimization algorithms are easily misled by the peaks and troughs of these coherent oscillations, resulting in the designed device size being extremely sensitive to the operating wavelength and lacking broadband robustness.
[0009] (3) Geometric redundancy: Global parameterization methods force the device to maintain smooth characteristics along its entire length. However, the inter-mode coupling strength (determined by the supermode spectrum) varies greatly in different regions of the waveguide. Using the same smoothness in non-sensitive regions as in sensitive regions inevitably leads to a large amount of wasted length.
[0010] Therefore, the problem that existing technologies need to solve is: what is the physical limit of the device length while ensuring a certain level of efficiency? Summary of the Invention
[0011] This invention aims to overcome the blindness of the "efficiency-length" trade-off in existing thermal insulation designs and provides a deterministic construction method for photonic devices based on inverse mapping of the envelope under transmission efficiency. This invention utilizes the oscillating envelope of inter-mode transmission efficiency for inverse solution, thereby deterministically constructing the global shortest thermal insulation waveguide geometry.
[0012] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:
[0013] A deterministic construction method for photonic devices based on inverse envelope mapping under transmission efficiency includes the following steps: Step S1: Establishing a quantitative mapping between the thermal insulation level (Tier) and local loss constraints; Step S2: Discretizing and slicing the global geometric space; Step S3: Constructing a phase-insensitive inverse envelope function; Step S4: Inverse solution based on constraint boundary saturation; Step S5: Non-uniform stitching and structure generation.
[0014] Further, as a preferred technical solution of the present invention, step S1 differs from the traditional approach of only setting a "total efficiency target." This method first defines discretized adiabatic performance levels (e.g., Tier I: η ≥ 90%, Tier II: η ≥ 95%, Tier III: η ≥ 99%). Subsequently, the Maximum Mode-Connection Loss Fraction (MMCLF) is introduced as a local process control variable. It should be noted that MMCLF is not a simple equal distribution of total losses, but rather, based on the reversibility characteristics of the adiabatic process, nonlinearly maps the global efficiency target to an upper limit δ of the allowable modal deviation for a single segment. limit This step transforms an unexecutable global vision into an executable local hard constraint.
[0015] Furthermore, as a preferred embodiment of the present invention, in step S2, based on the geometric parameter space of the device to be designed (e.g., waveguide width W from W...), min To W max The evolution path is discretized into N tiny geometric slices. Each slice represents a perturbation jump (W). i → W i+1 ).
[0016] The slicing here is not intended to approximate a known curve, but rather to resolve the spatial inhomogeneities of the supermode spectrum. The slice density should be sufficient to capture rapid spectral changes in the avoided crossing region.
[0017] Furthermore, as a preferred embodiment of the present invention, in step S3, for each geometric slice, the following sub-steps are performed to establish a deterministic relationship between geometric length and thermal loss:
[0018] (1) Full-wave scanning: Using the characteristic mode expansion (EME) or finite-difference time domain (FDTD) solver, scan the inter-mode conversion transmission efficiency (MCTE) of the slice at different physical lengths L.
[0019] (2) Oscillation phenomenon capture: The MCTE(L) curve obtained at this time will show significant periodic oscillations due to intermodal interference. Directly using this curve for design will result in the results being highly sensitive to wavelength.
[0020] (3) Lower Envelope Extraction: The lower envelope of the MCTE(L) oscillation curve is extracted using a numerical algorithm. The lower envelope is defined as 1 - MMCLF(L).
[0021] Technical essence: The lower envelope represents the transmission efficiency under the "worst-case phase-matching condition". The process of extracting the lower envelope is essentially to mathematically remove the phase-sensitive term and extract the inherent adiabatic cost that is only related to the geometric gradient rate.
[0022] (4) Function monotonicity: The extracted lower envelope MMCLF(L) is a monotonically decreasing function with respect to length L, thus enabling the construction of the inverse function L = f -1 The mathematical foundation of (MMCLF).
[0023] Furthermore, as a preferred embodiment of the present invention, step S4 utilizes the inverse function library established in step S3 to directly calculate the constraint threshold δ satisfying in step S1 for each slice. limit The minimum required length;
[0024] (1) Calculation formula: .
[0025] (2) Boundary Saturation Principle: This step forces each infinitesimal element to operate at the "cliff edge" where leakage is permissible. Any L > L min, i The values of are all considered physical redundancy and are eliminated. Mathematically, this is equivalent to the application of the Pontryagin minimum principle in optimal control theory in the discrete domain.
[0026] Furthermore, as a preferred embodiment of the present invention, step S5 calculates L for all slices. min, i By splicing along the light propagation axis, the total length L is obtained. total = ∑L min, iBased on this length sequence, the function W(z) representing the waveguide width as a function of longitudinal position is reconstructed. This function represents the global shortest geometric solution at a given efficiency level.
[0027] The deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency described in this invention has the following technical advantages compared with the prior art:
[0028] (1) Determinism and uniqueness: This invention eliminates the randomness in traditional optimization algorithms (such as the random seed of particle swarm optimization). As long as the physical parameters and target level are determined, the generated structure is unique and deterministic.
[0029] (2) Approximation of physical limits: Experimental verification shows that the 3dB coupler and mode converter designed using this method are more than 80% smaller in size than the traditional global parameterization design, and it can be mathematically proven that there is no shorter solution that satisfies the same adiabatic constraints.
[0030] (3) Leap in computational efficiency: The non-convex optimization problem in high-dimensional space is reduced to the inversion problem of a series of one-dimensional monotonic functions, and the computational complexity is reduced from exponential to linear.
[0031] (4) Broadband robustness: Since the design is based on the elimination of the "lower envelope" of phase interference, the generated device is naturally insensitive to wavelength drift and does not require additional broadband optimization. Attached Figure Description
[0032] Figure 1 This is a flowchart of the method of the present invention in an embodiment of the present invention;
[0033] Figure 2 This is a comparison of the original MCTE(L) oscillation data of a typical waveguide slice in an embodiment of the present invention with the extracted lower envelope curve of MMCLF(L);
[0034] Figure 3 This is a comparison graph showing the minimum constraint conversion efficiency as a function of device length under two design strategies in this embodiment of the invention. Detailed Implementation
[0035] The present invention will be further explained in detail below with reference to the accompanying drawings, so that those skilled in the art can better understand and implement the present invention. However, the following examples are only used to explain the present invention and are not intended to limit the present invention.
[0036] This invention provides a deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency. This method abandons the traditional "forward iteration" approach and adopts a "reverse construction" strategy. For example... Figure 1 As shown, the core steps are detailed below:
[0037] Step S1: Establish a quantitative mapping between the "insulation level (Tier)" and local loss constraints.
[0038] Unlike traditional approaches that only set a "total efficiency target," this method first defines discretized adiabatic performance levels (e.g., Tier I: η ≥ 90%, Tier II: η ≥ 95%, Tier III: η ≥ 99%). Then, the Maximum Mode-Connection Loss Fraction (MMCLF) is introduced as a local process control variable. It is important to note that the MMCLF is not a simple equal distribution of total losses, but rather, based on the reversibility of the adiabatic process, nonlinearly maps the global efficiency target to an upper limit δ of allowable modal deviation in a single segment. limit This step transforms an unexecutable global vision into an executable local hard constraint.
[0039] Step S2: Discretization and slicing of the global geometric space
[0040] Based on the geometric parameter space of the device to be designed (e.g., waveguide width W from W...), min To W max The evolution path is discretized into N tiny geometric slices. Each slice represents a perturbation jump (W). i → W i+1 ).
[0041] Innovation: The slicing here is not for approximating a known curve, but for resolving the spatial inhomogeneity of the supermode spectrum. The slice density should be sufficient to capture rapid spectral changes in the avoided crossing region.
[0042] Step S3: Construct the "phase-insensitive" inverse envelope function (core step)
[0043] For each geometric slice, perform the following sub-steps to establish a deterministic relationship between geometric length and adiabatic loss:
[0044] (1) Full-wave scanning: Using the characteristic mode expansion (EME) or finite-difference time domain (FDTD) solver, scan the inter-mode conversion transmission efficiency (MCTE) of the slice at different physical lengths L.
[0045] (2) Oscillation phenomenon capture: The MCTE(L) curve obtained at this time will show significant periodic oscillations due to intermodal interference. Directly using this curve for design will result in the results being highly sensitive to wavelength.
[0046] (3) Lower Envelope Extraction: The lower envelope of the MCTE(L) oscillation curve is extracted using a numerical algorithm. The lower envelope is defined as 1 - MMCLF(L).
[0047] Technical essence: The lower envelope represents the transmission efficiency under the "worst-case phase-matching condition". The process of extracting the lower envelope is essentially to mathematically remove the phase-sensitive term and extract the inherent adiabatic cost that is only related to the geometric gradient rate.
[0048] (4) Function monotonicity: The extracted lower envelope MMCLF(L) is a monotonically decreasing function with respect to length L, thus enabling the construction of the inverse function L = f -1 The mathematical foundation of (MMCLF).
[0049] like Figure 2 The figure shows a comparison between the raw MCTE(L) oscillation data of a typical waveguide slice and the extracted lower envelope curve of MMCLF(L). The figure clearly shows the three syllogistic regions: the non-adiabatic region, the transition region, and the adiabatic plateau region.
[0050] Step S4: Inverse solution based on constraint boundary saturation
[0051] Using the inverse function library established in step S3, the constraint threshold δ in step S1 is directly calculated for each slice. limit The minimum required length.
[0052] (1) Calculation formula: .
[0053] (2) Boundary Saturation Principle: This step forces each infinitesimal element to operate at the "cliff edge" where leakage is permissible. Any L > L min, i The values of are all considered physical redundancy and are eliminated. Mathematically, this is equivalent to the application of the Pontryagin minimum principle in optimal control theory in the discrete domain.
[0054] Step S5: Non-uniform splicing and structure generation
[0055] L calculated from all slices min, i By splicing along the light propagation axis, the total length L is obtained. total = ∑L min, i Based on this length sequence, the function W(z) representing the waveguide width as a function of longitudinal position is reconstructed. This function represents the global shortest geometric solution at a given efficiency level.
[0056] In specific implementation, the example is: Design of TE1-TM0 adiabatic pattern converter based on the SOI platform.
[0057] 1. Initialization settings
[0058] (1) Objective: Design a silicon-based (SOI, 220nm thick) mode converter to achieve efficient conversion from TE1 mode to TM0 mode.
[0059] (2) Geometric boundary: input waveguide width W in = 1.2 μm (supports TE1), output width W out = 0.4 μm (TM0 supported).
[0060] (3) Physical analysis: Preliminary calculations show that strong TE / TM mode hybridization exists at W ≈ 0.65 μm within this width range, which is the point where the supermode spectrum avoids crossover. The adiabatic conditions in this region are extremely harsh.
[0061] 2. Data Generation and Processing
[0062] (1) Discretization: The width range of [0.4, 1.2] μm is divided into 80 equally spaced slices with a step size of 10 μm.
[0063] (2) Envelope extraction (key step):
[0064] (i) For slice number 35 (W ≈ 0.65 μm, sensitive area): EME simulation shows that the MCTE oscillates violently with length, with the trough reaching a depth of 0.8. After extracting the lower envelope, it was found that to achieve 99% efficiency, L > 5 μm is required.
[0065] (ii) For slice #10 (W ≈ 1.1 μm, non-sensitive region): MCTE oscillations are weak. After extracting the lower envelope, it was found that only L = 0.2 μm is needed to achieve 99% efficiency.
[0066] (iii) Through this process, a complete set of L is established. min = f(W, Tier) database.
[0067] 3. Reverse Construction
[0068] (1) Set Tier III standard: global target η ≥ 99%. Map to local constraints and set MMCLF threshold δ = 0.005.
[0069] (2) Solution: Traverse the 80 slices and find the L corresponding to δ = 0.005 based on their respective lower envelope functions. i .
[0070] The results showed that the slice length was automatically stretched in the sensitive region of 0.6-0.7 μm, while the slice length was extremely short at both ends.
[0071] (3) Splicing: Connect all L i The summation yields a total length of 17.8 μm.
[0072] 4. Verification and Comparison
[0073] (1) Simulation verification shows that the transmission efficiency of the structure at 1550 nm is 99.1%.
[0074] (2) Comparison: Using a cubic polynomial (Cubic Taper) for conventional optimization, the optimal result length is 98 μm to achieve the same 99% efficiency. The method of this invention achieves more than 5 times size compression without any manual parameter tuning. For example... Figure 3 The diagram shows a comparison of the minimum constrained conversion efficiency as a function of device length under two design strategies, including the proposed segmented constraint optimization framework and the globally parameterized cubic width distribution. All designs aim for the same conversion efficiency (η = 95%) and satisfy the same multimode bending loss factor constraint to isolate the influence of the spatial parameterization strategy. The results show that the segmented optimization design achieves the target with a total length of only 17.8 μm, while the globally parameterized cubic width scheme requires 98 μm, approximately 5.5 times the length of the segmented design, a highly significant difference.
[0075] The specific implementation schemes described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific implementation schemes of the present invention and are not intended to limit the scope of the present invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the present invention should fall within the scope of protection of the present invention.
Claims
1. A deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency, characterized in that, Includes the following steps: Step S1: Establish a quantitative mapping between the insulation level (Tier) and local loss constraints; Step S2: Discretization and slicing of the global geometric space; Step S3: Construct the phase-insensitive inverse envelope function; Step S4: Inverse solution based on constraint boundary saturation; Step S5: Non-uniform splicing and structure generation.
2. The deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency according to claim 1, characterized in that, Step S1 specifically includes the following steps: First, define the discretized adiabatic performance hierarchy; then, introduce the maximum intermodal coupling loss fraction (MMCLF) as a local process control variable. The MMCLF is not a simple equal distribution of total loss, but rather, based on the reversibility characteristics of the adiabatic process, nonlinearly maps the global efficiency target to the upper limit of the allowable modal deviation δ for a single segment. limi It transforms an unexecutable global vision into an executable local hard constraint.
3. The deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency according to claim 2, characterized in that, Step S2 specifically includes the following steps: discretizing the evolution path into N tiny geometric slices based on the geometric parameter space of the device to be designed.
4. The deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency according to claim 3, characterized in that, Step S3 specifically includes the following steps: For each geometric slice, perform the following sub-steps to establish a deterministic relationship between geometric length and adiabatic loss: Full-wave scanning: Using the characteristic mode expansion EME or finite-difference time-domain FDTD solver, the inter-mode conversion transmission efficiency (MCTE) of the slice at different physical lengths L is scanned. Oscillation capture: The MCTE(L) curve obtained at this point will exhibit significant periodic oscillations due to intermodal interference. Directly using this curve for design will result in highly sensitive results to wavelength; Lower Envelope Extraction: A numerical algorithm was used to extract the lower envelope of the MCTE(L) oscillation curve. This lower envelope is defined as 1 - MMCLF(L). Function monotonicity: The extracted lower envelope MMCLF(L) is a monotonically decreasing function with respect to length L, thus enabling the construction of the inverse function L = f -1 The mathematical foundation of (MMCLF).
5. The deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency according to claim 4, characterized in that, Step S4 uses the inverse function library established in step S3 to directly calculate the constraint threshold δ in step S1 for each slice. limit The minimum required length; 。 6. The deterministic construction method for photonic devices based on envelope inverse mapping under transmission efficiency according to claim 5, characterized in that, Step S5 calculates L for all slices min, i By splicing along the light propagation axis, the total length L is obtained. total = ∑L min, i Based on this length sequence, the function W(z) that the waveguide width varies with the longitudinal position is reconstructed; this function is the global shortest geometric solution at a given efficiency level.