The Building Block (BB) approach has recently emerged in photonic as a suitable strategy for the analysis and design of complex circuits. Each BB can be foundry related and contains a mathematical macro-model of its functionality. As well known, statistical variations in fabrication processes can have a strong effect on their functionality and ultimately affect the yield. In order to predict the statistical behavior of the circuit, proper analysis of the uncertainties effects is crucial. This paper presents a method to build a novel class of Stochastic Process Design Kits for the analysis of photonic circuits. The proposed design kits directly store the information on the stochastic behavior of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using this approach, we demonstrate that the augmented macro-models of the BBs can be calculated once and stored in a BB (foundry dependent) library and then used for the analysis of any desired circuit. The main advantage of this approach, shown here for the first time in photonics, is that the stochastic moments of an arbitrary photonic circuit can be evaluated by a single simulation only, without the need for repeated simulations. The accuracy and the significant speed-up with respect to the classical Monte Carlo analysis are verified by means of classical photonic circuit example with multiple uncertain variables.
Unavoidable statistical variations in fabrication processes have a strong effect on the functionality of fabricated photonic circuits and on fabrication yield. It is hence essential to measure and consider these uncertainties during the design in order to predict the statistical behavior of the realized circuits. Also, during the mass production of photonic integrated circuits, the experimental evaluation of circuits’ desired quantity of interest in the presence of fabrication error can be crucial. In this paper we proposed the use of generalized polynomial chaos method to estimate the statistical properties of a circuit from a reduced number of experimental data whilst achieving good accuracy comparable to those obtained by Monte Carlo.