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Design and Analysis of Silicon Photonics Wave Guides Using Symbolic Methods

Although the demise of Moore's law has been predicted many times in the recent past, the emergence of silicon photonics has the potential to extend the lifetime of Moore's law significantly. Using conventional CMOS processing for the generation, routing, and processing of light waves, silicon photonics has finally brought the full power of photonics to very large scale integration (VLSI). However, along with these benefits, significant challenges in computer aided design of silicon photonics have also arisen. This paper presents a novel symbolic method based on Gröbner basis of tangent space polynomials of parametric curves to address these challenges. We analyze the design, optimization and verification of silicon photonic wave guides using parametric polynomials, and demonstrate the powerful method of Gröbner basis functions to solve complex problems such as envelope generation, rectification, manufacturability, singularity detection, reticle and etch processing model generation, tapering loss minimization, and bend loss minimization. We present the use of computer algebra systems such as MAXIMA and REDUCE, to analyze waveguide arrays. In addition, the methods presented in this paper can also be used for the analysis of curves arising from micro-electronic mechanical systems and micro-fluidics VLSI layouts.