Recent advancements in computational inverse-design approaches — algorithmic techniques for discovering optical structures based on desired functional characteristics — have begun to reshape the landscape of structures available to nanophotonics. Here, we outline a cross-section of key developments in this emerging field of photonic optimization: moving from a recap of foundational results to motivation of applications in nonlinear, topological, near-field and on-chip optics. Starting with a desired optical output it is possible to use computational algorithms to inverse design devices. The approach is reviewed here with an emphasis on nanophotonics.

Inverse design in nanophotonics

We report on the numerical structural optimization of two-dimensional photonic crystal (PhC) power dividers by using two different classes of optimization algorithms, namely, a modified truncated Newton (TN) gradient search as deterministic local optimization scheme and an evolutionary optimization representing the probabilistic global search strategies. Because of the severe accuracy requirements during optimization, the proper PhC device has been simulated by using the multiple-multipole program that is contained in the MaX-1 software package. With both optimizer classes, we found reliable and promising solutions that provide vanishing power reflection and perfect power balance at any specified frequency within the photonic bandgap. This outcome is astonishing in light of the discrete nature inherent in the underlying PhC structure, especially when the optimizer is allowed to intervene only within a very small volume of the device. Even under such limiting constraints structural optimization is not only feasible but has proven to be highly successful.

Optimization of photonic crystal structures

We report on the fabrication of a grating-based add–drop filter in SiON planar waveguide technology. We achieved apodization of the Bragg grating by concatenating subgratings with various duty cycles. We present the theoretical and experimental dependence of the coupling coefficient on the duty cycle, which leads to a minimum coupling coefficient of 30%. With a breeder genetic algorithm we were able to find optimal apodization profiles within this limited coupling coefficient range. The final device is compatible with a 100-GHz channel spacing and has a bandwidth utilization factor of 36%.

Add-drop filter based on apodized surface-corrugated gratings

Nanowire-based solar cells opened a new avenue for increasing conversion efficiency and rationalizing material use by growing different III-V materials on silicon substrates. Here, we propose a multiterminal nanowire solar cell design with a theoretical conversion efficiency of 48.3% utilizing an efficient lateral spectrum splitting between three different III-V material nanowire arrays grown on a flat silicon substrate. This allows choosing an ideal material combination to achieve the proper spectrum splitting as well as fabrication feasibility. The high efficiency is possible due to an enhanced absorption cross-section of standing nanowires and optimization of the geometric parameters. Furthermore, we propose a multiterminal contacting scheme that can be fabricated with a technology close to standard CMOS. As an alternative we also consider a single power source with a module level voltage matching. These new concepts open avenues for next-generation solar cells for terrestrial and space applications.

Efficient Multiterminal Spectrum Splitting via a Nanowire Array Solar Cell

High-efficiency spectrum splitting for solar photovoltaics

This article is a tutorial on using genetic algorithms to optimize antenna and scattering patterns. Genetic algorithms are "global" numerical-optimization methods, patterned after the natural processes of genetic recombination and evolution. The algorithms encode each parameter into binary sequences, called a gene, and a set of genes is a chromosome. These chromosomes undergo natural selection, mating, and mutation, to arrive at the final optimal solution. After providing a detailed explanation of how a genetic algorithm works, and a listing of a MATLAB code, the article presents three examples. These examples demonstrate how to optimize antenna patterns and backscattering radar-cross-section patterns. Finally, additional details about algorithm design are given. >

Introduction to Genetic Algorithms in Electromagnetics

The spatial and spectral treatment of electromagnetic fields express an essential operation regarding, e.g., the functionality of dense integrated optical devices. Such molding of fields can hardly be handled without sophisticated heuristic optimization tools. By means of five design examples we have demonstrated that evolutionary algorithms (EA) are highly qualified to solve "real world" inverse problems considering various applications in the field of planar integrated optics, optical communication technology, and dielectric material modeling as well. In com- parison to other optimization schemes EAs are even able to deliver structural and temporal information of the device under optimization which is an important feature when targeting computer guided engineer- ing and virtual design platforms.

Stephan Hunziker

Papers

Introduction to Genetic Algorithms in Electromagnetics

Application of evolutionary optimization algorithms in computational optics