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Register a new userMapping the Design Space of Photonic Topological States via Deep Learning
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Topological states in photonics offer novel prospects for guiding and manipulating photons and facilitate the development of modern optical components for a variety of applications. Over the past few years, photonic topology physics has evolved and unveiled various unconventional optical properties in these topological materials, such as silicon photonic crystals. However, the design of such topological states still poses a significant challenge. Conventional optimization schemes often fail to capture their complex high dimensional design space. In this manuscript, we develop a deep learning framework to map the design space of topological states in the photonic crystals. This framework overcomes the limitations of existing deep learning implementations. Specifically, it reconciles the dimension mismatch between the input (topological properties) and output (design parameters) vector spaces and the non-uniqueness that arises from one-to-many function mappings. We use a fully connected deep neural network (DNN) architecture for the forward model and a cyclic convolutional neural network (cCNN)for the inverse model. The inverse architecture contains the pre-trained forward model in tandem, thereby reducing the prediction error significantly.
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Photonic topological states have revolutionized our understanding on the propagation and scattering of light. Recent discovery of higher-order photonic topological insulators opens an emergent horizon for zero-dimensional topological corner states. However, the previous realizations of higher-order photonic topological insulators suffer from either a limited operational frequency range due to the lumped components involved or a bulky structure with a large footprint, which are unfavorable for future integrated photonics. To overcome these limitations, we hereby experimentally demonstrate a planar surface-wave photonic crystal realization of two-dimensional higher-order topological insulators. The surface-wave photonic crystals exhibit a very large bulk bandgap (a bandwidth of 28%) due to multiple Bragg scatterings and host one-dimensional gapped edge states described by massive Dirac equations. The topology of those higher-dimensional photonic bands leads to the emergence of zero-dimensional corner states, which provide a route toward robust cavity modes for scalable, integrated photonic chips and an interface for the control of light-matter interaction.
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Iterative Greens function, based on cyclic reduction of block tridiagonal matrices, has been the ideal algorithm, through tight-binding models, to compute the surface density-of-states of semi-infinite topological electronic materials. In this paper, we apply this method to photonic and acoustic crystals, using finite-element discretizations and a generalized eigenvalue formulation, to calculate the local density-of-states on a single surface of semi-infinite lattices. The three-dimensional (3D) examples of gapless helicoidal surface states in Weyl and Dirac crystals are shown and the computational cost, convergence and accuracy are analyzed.
Topological photonic systems represent a new class of optical materials supporting boundary modes with unique properties, not found in conventional photonics. While the early research on topological photonics has focused on edge and surface modes in 2D and 3D systems, respectively, recently higher-order topological insulators (HOTIs) supporting lower-dimensional boundary states have been introduced. In this work we design and experimentally realize a photonic kagome metasurface exhibiting a Wannier-type higher-order topological phase. We demonstrate and visualize the emergence of a topological transition and opening of a Dirac cone by directly exciting the bulk modes of the HOTI metasurface via solid-state immersion spectroscopy. The open nature of the metasurface is then utilized to directly image topological boundary states. We show that, while the domain walls host 1D edge states, their bending induces 0D higher-order topological modes confined to the corners. The demonstrated metasurface hosting topological boundary modes of different dimensionality paves the way to a new generation of universal and resilient optical devices which can controllably scatter, trap and guide optical fields in a robust way.
Valley pseudospin, a new degree of freedom in photonic lattices, provides an intriguing way to manipulate photons and enhance the robustness of optical networks. Here we experimentally demonstrated topological waveguiding, refracting, resonating, and routing of valley-polarized photons in integrated circuits. Specifically, we show that at the domain wall between photonic crystals of different topological valley phases, there exists a topologically protected valley kink state that is backscattering-free at sharp bends and terminals. We further harnessed these valley kink states for constructing high-Q topological photonic crystal cavities with tortuously shaped cavity geometries. We also demonstrated a novel optical routing scheme at an intersection of multiple valley kink states, where light splits counterintuitively due to the valley pseudospin of photons. These results will not only lead to robust optical communication and signal processing, but also open the door for fundamental research of topological photonics in areas such as lasing, quantum photon-pair generation, and optomechanics.
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