Silicon Photonic Waveguide Design Using Gröbner Basis Analysis
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current computational geometry software struggles with the design and analysis of silicon photonic layouts, particularly due to the challenges of curvilinear features which are not well-handled by existing CAD tools optimized for rectilinear data, leading to issues such as missed design rule checking errors, false errors, and performance degradation in waveguide manufacturing.
Innovation Solution
The use of Gröbner basis methods for analyzing and optimizing silicon photonic waveguides, employing parametric and algebraic representations to address problems like envelope generation, manufacturability verification, and bend loss minimization, applicable to both silicon photonics and other non-Manhattan structures like MEMS and micro-fluidics layouts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If piecewise linear approximations are used to represent curvilinear features, then the layout can be processed by existing rectilinear CAD tools, but manufacturing precision and accuracy deteriorate due to significant errors when applied to curvilinear surfaces
Solution Approach 1:
The patent applies curvature by representing waveguide centers and edges as parametric curves (e.g., polynomial curves, B-splines, or NURBS) instead of piecewise linear segments. This allows exact representation of curvilinear features while maintaining compatibility with CAD tools through parametric equation-based processing, thereby resolving the contradiction between ease of manufacture and manufacturing precision.
2Device complexity
If piecewise linear approximations are used for non-rectilinear features, then data processing becomes simpler, but data size increases significantly and performance degradation occurs
Solution Approach 1:
The patent changes the parameter representation from piecewise linear coordinates to parametric curve equations with control points and coefficients. This reduces data size by representing complex curves with fewer parameters while maintaining processing simplicity through algebraic operations on polynomial coefficients, thus resolving the contradiction between device complexity and productivity.
3Adaptability or versatility
If existing rectilinear CAD tools are used for curvilinear waveguide design, then tool availability is maintained, but design accuracy deteriorates due to missed design rule checking errors and false errors
Solution Approach 1:
The patent substitutes geometric approximation methods with algebraic geometry-based methods using Gröbner bases. This enables exact mathematical representation and verification of curvilinear features, allowing existing CAD tools to accurately perform design rule checking on parametric curves without the errors associated with piecewise linear approximations, thereby resolving the contradiction between adaptability and measurement precision.
Data Source
AI summary
Methods and apparatus are disclosed for symbolic methods using algebraic geometry (e.g., based on a Gröbner basis of tangent space polynomials of parametric curves). For example, the design, optimization and verification of silicon photonic wave guides using parametric polynomials and/or Gröbner basis functions can be used to perform envelope generation, rectification, manufacturability checking, singularity detection, reticle and etch processing model generation, tapering loss minimization, and bend loss minimization. In one example, a method of analyzing a layout to be manufactured using a photolithographic process includes producing an envelope of a curve representing a layout object based at least in part on a Gröbner basis and performing one or more analysis operations for the envelope to perform verification and manufacturability checks.