Inverse Design Method Research Articles

Interpretable inverse-designed cavity for on-chip nonlinear photon pair generation

Inverse design is a powerful tool in wave physics for compact, high-performance devices. To date, applications in photonics have mostly been limited to linear systems and it has rarely been investigated or demonstrated in the nonlinear regime. In addition, the “black box” nature of inverse design techniques has hindered the understanding of optimized inverse-designed structures. We propose an inverse design method with interpretable results to enhance the efficiency of on-chip photon generation rate through nonlinear processes by controlling the effective phase-matching conditions. We fabricate and characterize a compact, inverse-designed device using a silicon-on-insulator platform that allows a spontaneous four-wave mixing process to generate photon pairs at a rate of 1.1 MHz with a coincidence to accidental ratio of 162. Our design method accounts for fabrication constraints and can be used for scalable quantum light sources in large-scale communication and computing applications.

Generation of spatiotemporal vortices in nonlinear photonic crystals

Spatiotemporal vortices (STOVs) are a new, to the best of our knowledge, type of structured light in which the optical phase circulates in space–time. In this work, we propose to generate STOVs via second harmonic generation in lithium niobate nonlinear photonic crystals (NPCs) with a linearly chirped Gaussian pulse as the fundamental wave. The structural function of the NPC is derived by the inverse design method. Numerical simulations of the intensity and phase profiles of the generated second harmonic waves are performed with both the amplitude-phase-modulated and the simplified binary-phase-modulated NPCs. We anticipate our study will be valuable for the experimental generation and manipulation of STOVs in NPCs.

Ultra-compact all-optical half-adder based on inverse design

The all-optical half-adder is an important module in integrated photonics, which can be used to realize optical computing and optical communication. At present, the all-optical half-adder implemented by traditional methods cannot easily be further compressed in size, which also limits the development of its integration. In this paper, four optical devices, the power beam splitter, waveguide cross, XOR gate, and AND gate, are designed by the inverse design method. Their footprint is only 2µm×2µm, and they have extremely low insertion loss and high contrast ratio. These devices are further interconnected with waveguides to realize an all-optical half-adder module with a size of only 10µm×4.5µm. When working at 1550 nm, the module exhibits contrast ratios of 14.47 dB and 5.14 dB for SUM and CARRY, respectively. These photonic devices have the characteristics of ultra-compact size and high performance, rendering them highly valuable for photonic integrated circuits.

Multi-objective inverse design of finned heat sink system with physics-informed neural networks

This study proposes a new inverse design method that utilizes a physics-informed neural network (PINN) to parameterize the geometric and operating inputs, enabling the identification of optimal heat sink designs by starting with the desired objectives and working backward. A specialized hybrid PINN is designed to accurately approximate the governing equations of the conjugate heat transfer processes. On this basis, a surrogate model derived from the hybrid PINN is constructed and integrated with multi-objective optimization and decision-making algorithms. The results of an example finned heat sink system are presented, showcasing the accelerated search for Pareto-optimal designs. The proposed method nearly halved the search time to approximately 113.9 h in comparison with the traditional methods. Moreover, three representative scenarios—high-performance design, equilibrium design, and low-cost design —were compared to visualize the real-time changes in the multiphysics field, facilitating improved physical inspection and understanding of the optimal designs.

Rapid inverse design of high Q-factor terahertz filters [Invited

6 G communication technology using terahertz (THz) frequencies has increased the demand for components such as terahertz band filters. A high Q-factor filter capable of transmitting only narrowband frequencies, in particular, has gained significant research attention due to its wide range of applications. Here we obtained an optimal high Q-factor THz filter using an inverse design method that combines a double deep Q-learning model with an analytical solution within eight hours. Further, we confirmed the results of the inverse design using a numerical simulation, experimentally realized the high Q-factor THz filter, and discussed limitations of the spectral resolution of THz spectroscopy.

Efficient inverse design method of AWG based on BPNN-PSO algorithm

This paper presents an efficient inverse design method of arrayed waveguide grating (AWG) based on BPNN-PSO. Five important structural parameters of AWG are selected as inputs, and the spectral responses of three output channels are used as outputs. A forward network is trained, and the prediction accuracy of the network is improved by optimizing the number of hidden layer neurons. By combining the forward network with the traditional particle swarm optimization (PSO) algorithm, a series of structure designs targeting the desired performance can be generated. This method significantly improves the efficiency and accuracy of the PSO algorithm by introducing neural networks, making it suitable for efficient inverse design and multi-structure analysis of AWG.

Inverse design of metasurfaces with customized transmission characteristics of frequency band based on generative adversarial networks.

In recent years, deep learning (DL) has demonstrated significant potential in the inverse design of metasurfaces, and the generation of metasurfaces with customized transmission characteristics of frequency band remains a challenging and underexplored area. In this study, we propose a DL-assisted method for the inverse design of transmissive metasurfaces. The method consists of a generative adversarial network (GAN)-based graph generator, an electromagnetic response predictor, and a genetic algorithm optimizer. By integrating these components, we can obtain customized metasurfaces with desired transmission characteristics of frequency band. We demonstrate the effectiveness of the proposed method through examples of inverse-designed three-layer cascaded transmissive metasurfaces with wideband, dual-band, and stopband responses in the 8∼12 GHz frequency range. Specifically, we realize three different types of dual-band metasurfaces, namely double-wide, front-wide and rear-narrow, and front-narrow and rear-wide configurations. Additionally, we analyze the accuracy and reliability of the inverse design method by employing data from the training dataset, self-defined objectives, and bandwidth-reduced target responses scaled from the wideband type as design inputs. Quantitative evaluation is performed using metrics such as mean absolute error and average precision. The proposed method successfully achieves the desired effect as intended.

Tensor completion algorithm-aided structural color design.

In recent years, structural color has developed rapidly due to its distinct advantages, such as low loss, high spatial resolution and environmental friendliness. Various inverse design methods have been extensively investigated to efficiently design optical structures. However, the optimization method for the inverse design of structural color remains a formidable challenge. Traditional optimization approaches, such as genetic algorithms require time-consuming repetitions of structural simulations. Deep learning-assisted design necessitates prior simulations and large amounts of data, making it less efficient for systems with a small number of features. This study proposes a tensor completion algorithm capable of swiftly and accurately predicting missing datasets based on partially obtained datasets to assist in structural color design. Transforming the complex physical problem of structural color design into a spatial structure relationship problem linking geometric parameters and spectral data. The method utilizes tensor multilinear data analysis to effectively capture the complex relationships associated with geometric parameters and spectral data in higher-order data. Numerical and experimental results demonstrate that the algorithm exhibits high reliability in terms of speed and accuracy for diverse structures, datasets of varying sizes, and different materials, significantly enhancing design efficiency. The proposed algorithm offers a viable solution for inverse design problems involving complex physical systems, thereby introducing a novel approach to the design of photonic devices. Additionally, numerical experiments illustrate that the structural color of cruciform resonators with diamond can overcome the high loss issues observed in traditional dielectric materials within the blue wavelength region and enhance the corrosion resistance of the structure. We achieve a wide color gamut and a high-narrow reflection spectrum nearing 1 by this structure, and the theoretical analysis further verifies that diamond holds great promise in the realm of optics.

Ultra-broadband and ultra-compact chip-integrated logic gates based on an inverse design method

The Si-based chip-integrated OR, XOR, NOR, AND and NAND all-optical logic gates (AO-LGs) with footprints of 2 μm × 2 μm are inversely designed based on an intelligent method, which combines the method of moving asymptotes (MMA) with the finite element method (FEM). In this method, the substrate is divided into many small units, and the refractive index of each unit will be perturbed according to design expectation. Therefore, the optimized refractive index will be gradient, which divorces from fabrication. Binary reconstruction is the process of changing the gradient media into binary media, by filtering out the gradient virtual media, smoothing the boundaries, and refilling Si or air on the substrate to form a new structure. Numerical simulations demonstrate that all the AO-LGs designed by this method work effectively. The contrast ratio (CR) of OR/XOR gate ranges from 23.50 dB to 25.50 dB, NOR gate ranges from 6.33 dB to 7.91 dB, AND gate ranges from 4.44 dB to 6.13 dB, and NAND gate ranges from 8.85 dB to 10.07 dB. And these designed AO-LGs achieve nearly ten times more broad bandwidth than the other reported conventional gates without suffering other performances too much. The OR/XOR, and NOR gate functions well in a broad band range from 800 nm to 1600 nm, and from 850 nm to 1350 nm. AND gate functions well from 1000 nm to 1240 nm and from 1310 nm to 1400 nm. NAND gate functions well from 1360 nm to 1530 nm. It is expected that such a robust method can serve extensive applications in designing photonic devices, and the compact logic gates may contribute to broad applications of future optical computing and signal processing.

Arbitrary Phase Optimization Through Adaptively-Scheduled Nanophotonic Inverse Design

Design of integrated photonic devices continues to drive innovation in electro-optical systems for many applications ranging from communications to sensing and computing. Traditional design methods for integrated photonics involve using fundamental physical principles of guided-wave behavior to engineer optical functionalities for specific application requirements. While these traditional approaches may be sufficient for basic functionalities, the set of physically realizable optical capabilities these methods remains limited. Instead, photonic design can be formulated as an inverse problem where the target device functionality is specified, and a numerical optimizer creates the device with appropriate geometrical features within specified constraints. However, even with inverse design methods, achieving arbitrarily-specified phase offsets on-chip remains an important problem to solve for the reliability of interferometry-based nanophotonic applications. In order to address difficulties in achieving simultaneous phase and power optimization in inverse nanophotonic design, in this paper, we develop a set of optimization approaches that can enable user-specified phase differences in single-wavelength and multi-wavelength nanophotonic devices. By specifying phase offset targets for each output, we prevent convergence failures resulting from the changes in the figure of merit and gradient throughout the iterative optimization process. Additionally, by introducing phase-dependent figure of merit terms through an adaptive scheduling approach during the optimization, we accelerate device convergence up to a factor of 4.4 times. Our results outline a clear path towards the optimization of nanophotonic components with arbitrary phase-handling capabilities, with potential applications in a wide variety of integrated photonic systems and platforms.

An On-Demand Inverse Design Method for Nanophotonic Devices Based on Generative Model and Hybrid Optimization Algorithm

An On-Demand Inverse Design Method for Nanophotonic Devices Based on Generative Model and Hybrid Optimization Algorithm

Diffusion probabilistic model based accurate and high-degree-of-freedom metasurface inverse design

Abstract Conventional meta-atom designs rely heavily on researchers’ prior knowledge and trial-and-error searches using full-wave simulations, resulting in time-consuming and inefficient processes. Inverse design methods based on optimization algorithms, such as evolutionary algorithms, and topological optimizations, have been introduced to design metamaterials. However, none of these algorithms are general enough to fulfill multi-objective tasks. Recently, deep learning methods represented by generative adversarial networks (GANs) have been applied to inverse design of metamaterials, which can directly generate high-degree-of-freedom meta-atoms based on S-parameters requirements. However, the adversarial training process of GANs makes the network unstable and results in high modeling costs. This paper proposes a novel metamaterial inverse design method based on the diffusion probability theory. By learning the Markov process that transforms the original structure into a Gaussian distribution, the proposed method can gradually remove the noise starting from the Gaussian distribution and generate new high-degree-of-freedom meta-atoms that meet S-parameters conditions, which avoids the model instability introduced by the adversarial training process of GANs and ensures more accurate and high-quality generation results. Experiments have proven that our method is superior to representative methods of GANs in terms of model convergence speed, generation accuracy, and quality.

Accurate inverse design for high-efficiency and broadband terahertz devices by co-simulation with genetic algorithms

In this study, we combined MATLAB with the rigorous electromagnetic field simulation software Computer Simulation Technology to perform a co-simulation method for inverse design of high-efficiency and broadband THz metasurface devices. In the proposed design method, genetic algorithm (GA) is embedded to realize automatic and inverse design. Aiming toward the different requirements of high-efficiency and broadband THz metasurface devices, different objective functions are set to optimize the design of different types of THz metasurface devices. Based on the rigorous electromagnetic simulation and genetic algorithm, the proposed design method can realize automatic and inverse design with high reliability, compared to the theoretical model based on catenary e-field theory. This study provides an important guiding role and an efficient method for designing and optimizing required metasurface devices with practical applied value.

Inverse method for tailoring optical beams

We present an inverse design method for local tailoring of the characteristic properties of optical beams, including the formation of subwavelength features in the transverse plane. Our proposed technique is based on the superposition of paraxial Laguerre–Gaussian beams, that generate the desirable optical fields. Additionally the effect of nonparaxiality is also considered. This versatile method enables the precise control over amplitude and phase profiles, providing thus new potential applications in wavefront shaping and imaging.

Inverse design of all-dielectric metasurfaces with accidental bound states in the continuum

Abstract Metasurfaces with bound states in the continuum (BICs) have proven to be a powerful platform for drastically enhancing light–matter interactions, improving biosensing, and precisely manipulating near- and far-fields. However, engineering metasurfaces to provide an on-demand spectral and angular position for a BIC remains a prime challenge. A conventional solution involves a fine adjustment of geometrical parameters, requiring multiple time-consuming calculations. In this work, to circumvent such tedious processes, we develop a physics-inspired, inverse design method on all-dielectric metasurfaces for an on-demand spectral and angular position of a BIC. Our suggested method predicts the core–shell particles that constitute the unit cell of the metasurface, while considering practical limitations on geometry and available materials. Our method is based on a smart combination of a semi-analytical solution, for predicting the required dipolar Mie coefficients of the meta-atom, and a machine learning algorithm, for finding a practical design of the meta-atom that provides these Mie coefficients. Although our approach is exemplified in designing a metasurface sustaining a BIC, it can, also, be applied to many more objective functions. With that, we pave the way toward a general framework for the inverse design of metasurfaces in specific and nanophotonic structures in general.

Integrated spatial light receivers based on inverse design.

Photonic integrated spatial light receivers play a crucial role in free space optical (FSO) communication systems. In this paper, we propose a 4-channel and 6-channel spatial light receiver based on a silicon-on-insulator (SOI) using an inverse design method, respectively. The 4-channel receiver has a square receiving area of 4.4 µm × 4.4 µm, which enables receiving four Hermite-Gaussian modes (HG00, HG01, HG10, and HG02) and converting them into fundamental transverse electric (TE00) modes with insertion losses (ILs) within 1.6∼2.1 dB and mean cross talks (MCTs) less than -16 dB, at a wavelength of 1550 nm. The 3 dB bandwidths of the four HG modes range from 28 nm to 46 nm. Moreover, we explore the impact of fabrication errors, including under/over etching and oxide thickness errors, on the performance of the designed device. Simulation results show that the 4-channel receiver is robust against fabrication errors. The designed 6-channel receiver, featuring a regular hexagon receiving area, is capable of receiving six modes (HG00, HG01, HG10, HG02, HG20, and HG11) with ILs within 2.3∼4.1 dB and MCTs less than -15 dB, at a wavelength of 1550 nm. Additionally, the receiver offers a minimum optical bandwidth of 26 nm.

Diverse ranking metamaterial inverse design based on contrastive and transfer learning.

Metamaterials, thoughtfully designed, have demonstrated remarkable success in the manipulation of electromagnetic waves. More recently, deep learning can advance the performance in the field of metamaterial inverse design. However, existing inverse design methods based on deep learning often overlook potential trade-offs of optimal design and outcome diversity. To address this issue, in this work we introduce contrastive learning to implement a simple but effective global ranking inverse design framework. Viewing inverse design as spectrum-guided ranking of the candidate structures, our method creates a resemblance relationship of the optical response and metamaterials, enabling the prediction of diverse structures of metamaterials based on the global ranking. Furthermore, we have combined transfer learning to enrich our framework, not limited in prediction of single metamaterial representation. Our work can offer inverse design evaluation and diverse outcomes. The proposed method may shrink the gap between flexibility and accuracy of on-demand design.

Artificial neural network-based inverse design of metasurface absorber with tunable absorption window

Although the development of graphene broadband terahertz (THz) absorbers is relatively mature, studies focusing on modulating the absorption window remain limited. Existing research has mainly concentrated on achieving absorption window switching via the phase transition of materials like vanadium dioxide (VO2). However, this method typically allows for switching within two specific windows, lacking the capacity for arbitrary and flexible regulation. This study introduces a novel approach involving a bilayer graphene metasurface absorber (BGMA) to address this limitation, which allows arbitrary manipulation of the absorption windows. To facilitate rapid and accurate selection of the structural parameters, an artificial neural network (ANN)-based inverse design method is employed, which achieves a tunable absorption bandwidth of 6.70 THz with an error amount to 0.59%. Through in-depth mechanistic analyses, it is demonstrated that the BGMA can achieve tunable absorption between a low-frequency broadband absorption (L-FBA) mode and a high-frequency broadband absorption (H-FBA) mode. This tunability arises from the transition between graphene localized surface plasmon resonance and graphene surface plasmon resonance. Overall, the outcomes of this study underscore the remarkable tunable performance of the BGMA achieved through ANN-based inverse design. This innovation holds significant promise for applications in security detection, and object stealth.

Inverse design of a metasurface based on a deep tandem neural network

Compared with traditional optical devices, metasurfaces have attracted extensive attention due to their unique electromagnetic properties as well as their advantages of thinness, ease of integration, and low loss. However, structural modeling, simulation calculations, and parameter optimization processes are often required for metasurface design by traditional methods, which consume time and computing resources. Here, we propose an inverse design method based on deep tandem neural networks to speed up the design process of metasurfaces. This method connects the pretrained forward prediction model and the inverse design model in series, which effectively solves the problem that the model is difficult to converge due to the nonuniqueness problem. A trained inverse design model can design metasurface structures that conform to a given spectral target in a very short time. Therefore, this paper demonstrates the feasibility of using deep tandem neural networks for metasurface inverse design, which greatly shortens the design time of metasurfaces and provides a reference for researchers to design metamaterial structures with specific optical properties.

Curved-creased origami mechanical metamaterials with programmable stabilities and stiffnesses

Curved Crease Origami (CCO) structures exhibit intrinsic elastic behavior, resulting from a combination of crease folding and facet bending. In this work, we introduce a generic theoretical framework for constructing and predicting the mechanical properties of OMMs composed of curved crease unit cells, and an inverse design method that could achieve programmable stiffness and stability of CCO metamaterials, the CCO stacked unit with 2n-stability is first designed. Theoretical models, which could predict the in- and out-of-plane Poisson's ratios, uniaxial forces and stiffnesses of a single CCO tessellation, are constructed and validated by comparing with the finite element numerical method and experiment. Based on the analytical framework, the mechanical properties of the proposed CCO metamaterial with different crucial parameters are investigated, the results show that the combination of the initial folding angle pair could prominently affects the presence of bistability of the CCO unit. Our framework reveals that stacking two distinct layers of CCO units enables unique properties, such as bistability and zero stiffness, expanding the design space for CCO metamaterials. To determine the most suitable parameters for the unit cell to achieve programmable stabilities and targeted stiffness, the genetic algorithm is employed to optimize the basic model parameters and to carry out the inverse design, several case studies are demonstrated to show that the bistability model with specific stiffness, assigned stable locations, zero-stiffness in stable states and multistability model could be achieved. In summary, this work presents a comprehensive framework for designing and analyzing the curved crease origami mechanical metamaterials and proposes the inverse design method that could pave the way for a range of novel applications.