Inverse design of broadband and lossless topological photonic crystal waveguide modes

Inverse design in photonic crystals

Photonic crystals are periodic dielectric structures that possess a wealth of physical characteristics. Owing to the unique way they interact with the light, they provide new degrees of freedom to precisely modulate the electromagnetic fields, and have received extensive research in both academia and industry. At the same time, fueled by the advances in computer science, inverse design strategies are gradually being used to efficiently produce on-demand devices in various domains. As a result, the interdisciplinary area combining photonic crystals and inverse design emerges and flourishes. Here, we review the recent progress for the application of inverse design in photonic crystals. We start with a brief introduction of the background, then mainly discuss the optimizations of various physical properties of photonic crystals, from eigenproperties to response-based properties, and end up with an outlook for the future directions. Throughout the paper, we emphasize some insightful works and their design algorithms, and aim to give a guidance for readers in this emerging field.

Ultra-compact electro-optic phase modulator based on a lithium niobate topological slow light waveguide

Electro-optic modulators (EOMs) are essential devices of optical communications and quantum computing systems. In particular, ultra-compact EOMs are necessary for highly integrated photonic chips. Thin film lithium niobate materials are a promising platform for designing highly efficient EOMs. However, EOMs based on conventional waveguide structures are at a millimeter scale and challenging to scale down further, greatly hindering the capability of on-chip integration. Here, we design an EOM based on lithium niobate valley photonic crystal (VPC) structures for the first time. Due to the high effective refractive index introduced by the strong slow light effect, the EOM can achieve an ultra-compact size of 4 μm×14 μm with a half-wave voltage of 1.4 V. The EOM has a high transmittance of 0.87 in the 1068 nm because of the unique spin-valley locking effect in VPC structures. The design is fully compatible with current nanofabrication technology and immune to fabrication defects. Therefore, it opens a new possibility in designing lithium niobate electro-optic modulators and will find broad applications in optical communication and quantum photonic devices.

Inverse design of a photonic moiré lattice waveguide towards improved slow light performances

Slow light waveguides in photonic crystals are engineered using a conventional method or a deep learning (DL) method, which is data-intensive and suffers from data inconsistency, and both methods result in overlong computation time with low efficiency. In this paper, we overcome these problems by inversely optimizing the dispersion band of a photonic moiré lattice waveguide using automatic differentiation (AD). The AD framework allows the creation of a definite target band to which a selected band is optimized, and a mean square error (MSE) as an objective function between the selected and the target bands is used to efficiently compute gradients using the autograd backend of the AD library. Using a limited-memory Broyden-Fletcher-Goldfarb-Shanno minimizer algorithm, the optimization converges to the target band, with the lowest MSE value of 9.844×10^-7, and a waveguide that produces the exact target band is obtained. The optimized structure supports a slow light mode with a group index of 35.3, a bandwidth of 110 nm, and a normalized-delay-bandwidth-product of 0.805, which is a 140.9% and 178.9% significant improvement if compared to conventional and DL optimization methods, respectively. The waveguide could be utilized in slow light devices for buffering.

Impact of figures of merit in photonic inverse design

The rates of optical processes, such as two-photon absorption and spontaneous photon emission, are strongly dependent on the environment in which they take place, easily varying by orders of magnitude between different settings. Using topology optimization, we design a set of compact wavelength-sized devices, to study the effect of optimizing geometries for enhancing processes that depend differently on the field in the device volume, characterized by different figures of merit. We find that significantly different field distributions lead to maximization of the different processes, and - by extension - that the optimal device geometry is highly dependent on the targeted process, with more than an order of magnitude performance difference between optimized devices. This demonstrates that a univeral measure of field confinement is meaningless when evaluting device performance, and stresses the importance of directly targeting the appropriate metric when designing photonic components for optimal performance.

Non-Hermitian kagome photonic crystal with a totally topological spatial mode selection

Recently, the study of non-Hermitian topological edge and corner states in sonic crystals (SCs) and photonic crystals (PCs) has drawn much attention. In this paper, we propose a Wannier-type higher-order topological insulator (HOTI) model based on the kagome PC containing dimer units and study its non-Hermitian topological corner states. When balanced gain and loss are introduced into the dimer units with a proper parity-time symmetric setting, the system will show asymmetric Wannier bands and can support two Hermitian corner states and two pairs of complex-conjugate or pseudo complex-conjugate non-Hermitian corner states. These topological corner states are solely confined at three corners of the triangular supercell constructed by the trivial and non-trivial kagome PCs, corresponding to a topological spatial mode selection effect. As compared to the non-Hermitian quadrupole-type HOTIs, the non-Hermitian Wannier-type HOTIs can realize totally topological spatial mode selection by using much lower coefficients of gain and loss. Our results pave the way for the development of novel non-Hermitian photonic topological devices based on Wannier-type HOTIs.

Inverse design of photonic and phononic topological insulators: a review

Photonic and phononic topological insulators (TIs) offer numerous opportunities for manipulating light and sound with high efficiency and resiliency. On the other hand, inverse design methodologies, such as gradient-based approaches, evolutionary approaches, and deep-learning methods, provide a cost-effective strategy for developing photonic and phononic structures with unique features in steering light and sound. Here, we discuss recent advances and achievements in the development of photonic and phononic TIs employing inverse design methodologies, including one-dimensional TIs, TIs based on the quantum spin Hall effect (QSHE) and quantum valley Hall effect (QVHE), and high-order TIs in lattices with diverse symmetries. Several inversely designed photonic and phononic TIs with superior performance are exhibited. In addition, we offer our perspectives on the future of this emerging study field.

Extended topological valley-locked surface acoustic waves

Stable and efficient guided waves are essential for information transmission and processing. Recently, topological valley-contrasting materials in condensed matter systems have been revealed as promising infrastructures for guiding classical waves, for they can provide broadband, non-dispersive and reflection-free electromagnetic/mechanical wave transport with a high degree of freedom. In this work, by designing and manufacturing miniaturized phononic crystals on a semi-infinite substrate, we experimentally realized a valley-locked edge transport for surface acoustic waves (SAWs). Critically, original one-dimensional edge transports could be extended to quasi-two-dimensional ones by doping SAW Dirac “semimetal” layers at the boundaries. We demonstrate that SAWs in the extended topological valley-locked edges are robust against bending and wavelength-scaled defects. Also, this mechanism is configurable and robust depending on the doping, offering various on-chip acoustic manipulation, e.g., SAW routing, focusing, splitting, and converging, all flexible and high-flow. This work may promote future hybrid phononic circuits for acoustic information processing, sensing, and manipulation.

Multiband topological states in non-Hermitian photonic crystals

Novel phenomena found in non-Hermitian systems and robust edge states have attracted much attention. When non-Hermitian parameters (gain and loss) are above a critical value, the non-Hermitian photonic crystal (PC) bandgaps close, leading to a mixture of the topological edge state (TES) and topological corner state (TCS) with the bulk state. Meanwhile, new bandgaps also open, in which new TES and TCS can appear. Thus, with appropriate non-Hermitian parameters, TES can emerge in both the original bandgaps and the newly opened bandgaps. The results described here will further enrich understanding of the topological properties of non-Hermitian systems.