Controlling the minimal feature sizes in adjoint optimization of nanophotonic devices using b-spline surfaces

Adjoint-Optimized Large Dielectric Metasurface for Enhanced Purcell Factor and Directional Photon Emission

Extracting photons efficiently from quantum sources, such as atoms, molecules, and quantum dots, is crucial for various nanophotonic systems used in quantum communication, sensing, and computation. To improve the performance of these systems, it is not only necessary to provide an environment that maximizes the number of optical modes, but it is also desirable to guide the extracted light toward specific directions. One way to achieve this goal is to use a large area metasurface that can steer the beam. Previous work has used small aperture devices that are fundamentally limited in their ability to achieve high directivity. This work proposes an adjoint-based topology optimization approach to design a large light extractor that can enhance the spontaneous decay rate of the embedded quantum transition and collimate the extracted photons. With the help of this approach, we present all-dielectric metasurfaces for a quantum transition emitting at λ = 600 nm. These metasurfaces achieve a broadband improvement of spontaneous emission compared to that in the vacuum, reaching a 10× enhancement at the design frequency. Furthermore, they can beam the extracted light into a narrow cone (±10°) along a desired direction that is predefined through their respective design process.

Machine learning of all-dielectric core-shell nanostructures: the critical role of the objective function in inverse design

To integrate nanophotonics into light-based technologies, it is critical to elicit a desired optical response from its fundamental component, a nanoresonator. Because the optical resonance of a nanoresonator depends strongly on its base material and structural features, machine learning has been contemplated to enhance the design and optimization processes. However, its accuracy in searching the vast parameter space of nanophotonics still poses unresolved questions. Here, we show how the choice of objective functions, in combination with trained neural networks, can drastically change the optimization process-even for a simple nanophotonic structure. To assess how different objective functions select the correct structural parameters that generate a desired optical Mie response, we use a simple core-shell, all-dielectric nanostructure as the benchmark. By controlling the proportion of training data, which represents the "experience" level, we also quantify how the various objective functions perform in finding the ground-truth parameters. Our findings demonstrate that certain objective functions exhibit improved accuracy when used with highly "experienced" neural networks. Surprisingly, we also find other objective functions that perform better when paired with less "experienced" neural networks. Taken together, our results emphasize that it is critical to understand how neural networks are coupled to optimization schemes, as is evident even when a simple core-shell nanostructure is used.

Topological inverse design of fabrication-constrained nanophotonic devices via an adaptive projection method

Topology optimization has been widely adopted in the inverse design of nanophotonic devices due to low computation cost, which unfortunately produces intermediate relative permittivity values that fail to meet fabrication constraints. Additionally, the postprocessing required inevitably increases the complexity of the inverse design. In this Letter, we propose an adaptive projection method for topology optimization, in which a two-level hierarchical hyperbolic tangent projection function with linear increment and differentiation is constructed and applied to eliminate inherent defects of conventional topology optimization. Two binarized nanophotonic devices have been designed by our adaptive projection method, among which one ultra-compact dual 90°-bend waveguide reduces the average insertion loss to 20.3% of its similar counterpart and shows an 8.1% reduction for the average crosstalk in the O band, the other ultralow-loss waveguide crossing features an average insertion loss as low as 0.09 dB. With the significant advantages of excellent performance guarantee and fabrication-friendly geometry control fully demonstrated, our inverse design solution shows potential to contribute to nanophotonic devices and integrated chips.

Self-adjusting inverse design method for nanophotonic devices

Nanophotonic devices, which consist of multiple cell structures of the same size, are easy to manufacture. To avoid the optical proximity effect in the ultraviolet lithography process, the cell structures must be maintained at a distance from one another. In the inverse design process, the distance is maintained by limiting the optimized range of the location. However, this implementation can weaken the performance of the devices designed during transmission. To solve this problem, a self-adjusting inverse design method based on the adjoint variable method is developed. By introducing artificial potential field method, the location of one cell structure is modified only when the distances between this cell structure and other cell structures are smaller than a threshold. In this case, the range of the location can be expanded, and thus the performance of the designed devices can be improved. A wavelength demultiplexer with a channel spacing of 1.6 nm is designed to verify the performance of the proposed method. The experiment reveals that the transmission of the designed devices can be improved by 20%, and the self-adjusting inverse design process is 100 times faster than the inverse-design process based on the genetic algorithm.

Ultra-compact dual-mode mode-size converter for silicon photonic few-mode fiber interfaces

Fiber couplers usually take a lot of space on photonic integrated circuits due to the large mode-size mismatch between the waveguide and fiber, especially when a fiber with larger core is utilized, such as a few-mode fiber. We demonstrate experimentally that such challenge can be overcome by an ultra-compact mode-size converter with a footprint of only 10 µm. Our device expands TE₀ and TE₁ waveguide modes simultaneously from a 1-µm wide strip waveguide to an 18-µm wide slab on a 220-nm thick silicon-on-insulator, with calculated losses of 0.75 dB and 0.68 dB, respectively. The fabricated device has a measured insertion loss of 1.02 dB for TE₀ mode and 1.59 dB for TE₁ mode. By connecting the ultra-compact converter with diffraction grating couplers, higher-order modes in a few-mode fiber can be generated with a compact footprint on-chip.

Photonic topology optimization with semiconductor-foundry design-rule constraints

We present a unified density-based topology-optimization framework that yields integrated photonic designs optimized for manufacturing constraints including all those of commercial semiconductor foundries. We introduce a new method to impose minimum-area and minimum-enclosed-area constraints, and simultaneously adapt previous techniques for minimum linewidth, linespacing, and curvature, all of which are implemented without any additional re-parameterizations. Furthermore, we show how differentiable morphological transforms can be used to produce devices that are robust to over/under-etching while also satisfying manufacturing constraints. We demonstrate our methodology by designing three broadband silicon-photonics devices for nine different foundry-constraint combinations.

Inverse Design for Silicon Photonics: From Iterative Optimization Algorithms to Deep Neural Networks

Silicon photonics is a low-cost and versatile platform for various applications. For design of silicon photonic devices, the light-material interaction within its complex subwavelength geometry is difficult to investigate analytically and therefore numerical simulations are majorly adopted. To make the design process more time-efficient and to improve the device performance to its physical limits, various methods have been proposed over the past few years to manipulate the geometries of silicon platform for specific applications. In this review paper, we summarize the design methodologies for silicon photonics including iterative optimization algorithms and deep neural networks. In case of iterative optimization methods, we discuss them in different scenarios in the sequence of increased degrees of freedom: empirical structure, QR-code like structure and irregular structure. We also review inverse design approaches assisted by deep neural networks, which generate multiple devices with similar structure much faster than iterative optimization methods and are thus suitable in situations where piles of optical components are needed. Finally, the applications of inverse design methodology in optical neural networks are also discussed. This review intends to provide the readers with the suggestion for the most suitable design methodology for a specific scenario.

Topological inverse design of nanophotonic devices with energy constraint

In this paper, we introduce an energy constraint to improve topology-based inverse design. Current methods typically place the constraints solely on the device geometry and require many optimization iterations to converge to a manufacturable solution. In our approach the energy constraint directs the optimization process to solutions that best contain the optical field inside the waveguide core medium, leading to more robust designs with relatively larger minimum feature size. To validate our method, we optimize two components: a mode converter (MC) and a wavelength demultiplexer. In the MC, the energy constraint leads to nearly binarized structures without applying independent binarization stage. In the demultiplexer, it also reduces the appearance of small features. Furthermore, the proposed constraint improves the robustness to fabrication imperfections as shown in demultiplexer design. With energy constraint optimization, the corresponding spectrum shifts under ±10 nm dimensional variations are reduced by 17% to 30%. The proposed constraint is unique in simultaneously taking both geometry and electric field into account, opening the door to new ideas and insights to further improve the computationally intensive topology-based optimization process of nanophotonic devices.