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Register a new userInverse design of photonic crystals through automatic differentiation
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Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has played a major role in this success. However, gradient-based optimization has not yet been applied to the mode-expansion methods that are the most common approach to studying periodic optical structures like photonic crystals. This is because, in such simulations, the adjoint variable method cannot be defined as explicitly as in standard finite-difference or finite-element time- or frequency-domain methods. Here, we overcome this through the use of automatic differentiation, which is a generalization of the adjoint variable method to arbitrary computational graphs. We implement the plane-wave expansion and the guided-mode expansion methods using an automatic differentiation library, and show that the gradient of any simulation output can be computed efficiently and in parallel with respect to all input parameters. We then use this implementation to optimize the dispersion of a photonic crystal waveguide, and the quality factor of an ultra-small cavity in a lithium niobate slab. This extends photonic inverse design to a whole new class of simulations, and more broadly highlights the importance that automatic differentiation could play in the future for tracking and optimizing complicated physical models.
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Recent advances in the design and fabrication of on-chip optical microresonators has greatly expanded their applications in photonics, enabling metrology, communications, and on-chip lasers. Designs for these applications require fine control of dispersion, bandwidth and high optical quality factors. Co-engineering these figures of merit remains a significant technological challenge due to design strategies being largely limited to analytical tuning of cross-sectional geometry. Here, we show that photonic inverse-design facilitates and expands the functionality of on-chip microresonators; theoretically and experimentally demonstrating flexible dispersion engineering, quality factor beyond 2 million on the silicon-on-insulator platform with single mode operation, and selective wavelength-band operation.
We introduce a systematic approach for designing 3D nonlinear photonic crystals and pump beams for generating desired quantum correlations between structured photon-pairs. Our model is fully differentiable, allowing accurate and efficient learning and discovery of novel designs.
To be useful for most scientific and medical applications, compact particle accelerators will require much higher average current than enabled by current architectures. For this purpose, we propose a photonic crystal architecture for a dielectric laser accelerator, referred to as a multi-input multi-output silicon accelerator (MIMOSA), that enables simultaneous acceleration of multiple electron beams, increasing the total electron throughput by at least one order of magnitude. To achieve this, we show that the photonic crystal must support a mode at the $Gamma$ point in reciprocal space, with a normalized frequency equal to the normalized speed of the phase matched electron. We show that the figure of merit of the MIMOSA can be inferred from the eigenmodes of the corresponding infinitely periodic structure, which provides a powerful approach to design such devices. Additionally, we extend the MIMOSA architecture to electron deflectors and other electron manipulation functionalities. These additional functionalities, combined with the increased electron throughput of these devices, permit all-optical on-chip manipulation of electron beams in a fully integrated architecture compatible with current fabrication technologies, which opens the way to unconventional electron beam shaping, imaging, and radiation generation.
Photonic band structures are a typical fingerprint of periodic optical structures, and are usually observed in spectroscopic quantities such as transmission, reflection and absorption. Here we show that also the chiro-optical response of a metasurface constituted by a lattice of non-centrosymmetric, L-shaped holes in a dielectric slab shows a band structure, where intrinsic and extrinsic chirality effects are clearly recognized and connected to localized and delocalized resonances. Superchiral near-fields can be excited in correspondence to these resonances, and anomalous behaviors as a function of the incidence polarization occur. Moreover, we introduce a singular value decomposition (SVD) approach to show that the above mentioned effects are connected to specific fingerprints of the SVD spectra. Finally, we demonstrate by means of an inverse design technique that the metasurface based on an L-shaped hole array is a minimal one. Indeed, its unit cell geometry depends on the smallest number of parameters needed to implement arbitrary transmission matrices compliant with the general symmetries for 2d-chiral structures. These observations enable more powerful wave operations in a lossless photonic environment.
Photonic inverse design has emerged as an indispensable engineering tool for complex optical systems. In many instances it is important to optimize for both material and geometry configurations, which results in complex non-smooth search spaces with multiple local minima. Finding solutions approaching global optimum may present a computationally intractable task. Here, we develop a framework that allows expediting the search of solutions close to global optimum on complex optimization spaces. We study the way representative black box optimization algorithms work, including genetic algorithm (GA), particle swarm optimization (PSO), simulated annealing (SA), and mesh adaptive direct search (NOMAD). We then propose and utilize a two-step approach that identifies best performance algorithms on arbitrarily complex search spaces. We reveal a connection between the search space complexity and algorithm performance and find that PSO and NOMAD consistently deliver better performance for mixed integer problems encountered in photonic inverse design, particularly with the account of material combinations. Our results differ from a commonly anticipated advantage of GA. Our findings will foster more efficient design of photonic systems with optimal performance.
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