S-matrix absolute optimization method for a perfect vertical waveguide grating coupler.

Anat Demeter-Finzi,S Ruschin

doi:10.1364/oe.27.016713

Abstract

Vertical coupling using a diffraction grating is a convenient way to couple light into an optical waveguide. Several optimization approaches have been suggested in order to design such a coupler; however, most of them are implemented using algorithm-based modelling. In this paper, we suggest an intuitive method based on S-matrix formalism for analytically optimize 3-port vertical grating coupler devices. The suggested method is general and can be applied to any 3-port coupler device in order to achieve an optimal design based on user constrains. The simplicity of the model allows reduction of the optimization to two variables and the location of an absolute optimal operation point in a 2D contour map. Accordingly, in an ideal device near 100% coupling efficiency and insignificant return loss could be achieved. Our model results show good agreement with numerical finite difference time domain (FDTD) simulations and can predict the general tendencies and sensitivities of the device's behavior to changes in design parameters. We further apply our model to a previously reported high contrast uni-directional grating coupler device and show that additional improvement in the coupling efficiency is achievable for that layout.

Highlights

Vertical grating couplers are an attractive option for coupling light into an optical waveguide due to their high performance, their easy fabrication, and their reduction of the system’s tuning complexity [1,2,3,4]
We perform a comprehensive analysis of an absolute optimization method for vertical grating coupling based on S-Matrix formalism and its corresponding constraints of reciprocity and power conservation. In spite of these ideality assumptions, our results are in good agreement with numerical FDTD simulations, and able to predict the general tendencies and optimal parameters of the device
We presented a solvable method based on S-matrix formalism for theoretically determining the absolute optimal coupling conditions for vertical coupling using grating arrangement aided by back-reflection

Summary

Introduction

Vertical grating couplers are an attractive option for coupling light into an optical waveguide due to their high performance, their easy fabrication, and their reduction of the system’s tuning complexity [1,2,3,4]. In these gratings, the ability to couple light into a specific direction is necessary since the coupling is symmetrical, transmitting light both to the left and to the right directions. Most of the methods suggested so far are implemented by complex algorithms and numerical simulations that are difficult for the user to follow and reproduce This problem motivated us to develop a model, which is intuitive, based on basic physical assumptions and easy to implement and realize. For a more general validation of our model accuracy, we compared between the analytical and numerical simulations pattern changes for several grating coupler designs, and received very good correlation between these approaches

S-matrix model

Optimization Results

Conclusions