Efficient Bloch mode calculation of periodic systems with arbitrary geometry and open boundary conditions in the complex wavevector domain.

We show how existing iterative methods can be used to efficiently and accurately calculate Bloch periodic solutions of Maxwell's equations in arbitrary geometries. This is carried out in the complex-wavevector domain using a commercial frequency-domain finite-element solver that is available to the general user. The method is capable of dealing with leaky Bloch mode solutions, and is extremely efficient even for 3D geometries with non-trivial material distributions. We perform independent finite-difference time-domain simulations of Maxwell's equations to confirm our results. This comparison demonstrates that the iterative mode finder is more accurate, since it provides the true solutions in the complex-wavevector domain and removes the need for additional signal processing and fitting. Due to its efficiency, generality and reliability, this technique is well suited for complex and novel design tasks in integrated photonics, and also for a wider range of photonics problems.

Perfectly vertical surface grating couplers using subwavelength engineering for increased feature sizes.

We present perfectly vertical grating couplers for the 220 nm silicon-on-insulator platform incorporating subwavelength metamaterials to increase the minimum feature sizes and achieve broadband low back-reflection. Our study reveals that devices with high coupling efficiencies are distributed over a wide region of the design space with varied back-reflections, while still maintaining minimum feature sizes larger than 100 nm and even 130 nm. Using 3D-finite-difference time-domain simulations, we demonstrate devices with broadband low back-reflection of less than -20dB over more than 100 nm bandwidth centered around the C-band. Coupling efficiencies of 72% and 67% are achieved for minimum feature sizes of 106 nm and 130 nm, respectively. These gratings are also more fabrication tolerant compared to similar designs not using metamaterials.

Mapping the global design space of nanophotonic components using machine learning pattern recognition.

Nanophotonics finds ever broadening applications requiring complex components with many parameters to be simultaneously designed. Recent methodologies employing optimization algorithms commonly focus on a single performance objective, provide isolated designs, and do not describe how the design parameters influence the device behaviour. Here we propose and demonstrate a machine-learning-based approach to map and characterize the multi-parameter design space of nanophotonic components. Pattern recognition is used to reveal the relationship between an initial sparse set of optimized designs through a significant reduction in the number of characterizing parameters. This defines a design sub-space of lower dimensionality that can be mapped faster by orders of magnitude than the original design space. The behavior for multiple performance criteria is visualized, revealing the interplay of the design parameters, highlighting performance and structural limitations, and inspiring new design ideas. This global perspective on high-dimensional design problems represents a major shift in modern nanophotonic design and provides a powerful tool to explore complexity in next-generation devices.