Stochastic Model on the Post-Fabrication Error for a Bragg Reflectors Based Photonic Allpass Filter

This paper presents an analysis of the post fabrication performance for a Bragg-mirrors-based photonic allpass filter. The development subsequently leads to a first definition of the stochastic measures in a realistic system implementation. A Digital Signal Processing (DSP) approach to examining photonic integrated circuitry is explored in depth. The physical origins of error that manifests in an unbalanced phase error is mathematically described in detail. We describe the details of error analysis and demonstrate a stochastic measure for the expected behavior of first-order allpass filter as well as high complexity systems. Our findings show that the frequency performance under error can be characterized by a convolution of the ideal response with a probability function based kernel.