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1. Inverse-Designed Metastructures Together with Reconfigurable Couplers to Compute Forward Scattering

   https://doi.org/10.1021/acsphotonics.2c00373  

   Nikkhah, Vahid; Tzarouchis, Dimitrios C.; Hoorfar, Ahmad; Engheta, Nader (September 2022, ACS Photonics)

   Wave-based analog computing in the forms of inversedesigned metastructures and the meshes of Mach−Zehnder interferometers (MZI) have recently received considerable attention due to their capability in emulating linear operators, performing vector-matrix multiplication, inverting matrices, and solving integral and differential equations via electromagnetic wave interaction and manipulation in such structures. Here, we combine these two platforms to propose a wave-based metadevice that can compute scattered fields in electromagnetic forward scattering problems. The proposed device consists of two subsystems: a set of reconfigurable couplers with a proper feedback system and an inverse-designed inhomogeneous material block. The first subsystem computes the magnitude and phase of the dipole polarization induced in the scatterers when illuminated with a given incident wave (matrix inversion). The second subsystem computes the magnitude and phase of the scattered fields at given detection points (vector-matrix multiplication). We discuss the functionality of this metadevice, and through several examples, we theoretically evaluate its performance by comparing the simulation results of this device with fullwave numerical simulations and numerically evaluated matrix inversion. We also highlight that since the first section is reconfigurable, the proposed device can be used for different permittivity distributions of the scatterer and incident excitations without changing the inverse-designed section. Our proposed device may provide a versatile platform for rapid computation in various scattering scenarios. 

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2. Averaged null energy and the renormalization group

   https://doi.org/10.1007/JHEP12(2023)139  

   Hartman, Thomas; Mathys, Grégoire (December 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We establish a connection between the averaged null energy condition (ANEC) and the monotonicity of the renormalization group, by studying the light-ray operator ∫duT_uuin quantum field theories that flow between two conformal fixed points. In four dimensions, we derive an exact sum rule relating this operator to the Euler coefficient in the trace anomaly, and show that the ANEC implies thea-theorem. The argument is based on matching anomalies in the stress tensor 3-point function, and relies on special properties of contact terms involving light-ray operators. We also illustrate the sum rule for the example of a free massive scalar field. Averaged null energy appears in a variety of other applications to quantum field theory, including causality constraints, Lorentzian inversion, and quantum information. The quantum information perspective provides a new derivation of thea-theorem from the monotonicity of relative entropy. The equation relating our sum rule to the dilaton scattering amplitude in the forward limit suggests an inversion formula for non-conformal theories. 

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3. Norm-dependent convergence and stability of the inverse scattering series for diffuse and scalar waves

   https://doi.org/10.1088/1361-6420/acc682  

   Mahankali, Srinath; Yang, Yunan (April 2023, Inverse Problems)

   Abstract This work analyzes the forward and inverse scattering series for scalar waves based on the Helmholtz equation and the diffuse waves from the time-independent diffusion equation, which are important partial differential equations (PDEs) in various applications. Different from previous works, which study the radius of convergence for the forward and inverse scattering series, the stability, and the approximation error of the series under theL^pnorms, we study these quantities under the SobolevH^snorm, which associates with a general class ofL²-based function spaces. TheH^snorm has a natural spectral bias based on its definition in the Fourier domain: the cases < 0 biases towards the lower frequencies, while the cases > 0 biases towards the higher frequencies. We compare the stability estimates using differentH^snorms for both the parameter and data domains and provide a theoretical justification for the frequency weighting techniques in practical inversion procedures. We also provide numerical inversion examples to demonstrate the differences in the inverse scattering radius of convergence under different metric spaces. 

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4. Inverse design and flexible parameterization of meta-optics using algorithmic differentiation

   https://doi.org/10.1038/s42005-021-00568-6  

   Colburn, Shane; Majumdar, Arka (March 2021, Communications Physics)

   Abstract Ultrathin meta-optics offer unmatched, multifunctional control of light. Next-generation optical technologies, however, demand unprecedented performance. This will likely require design algorithms surpassing the capability of human intuition. For the adjoint method, this requires explicitly deriving gradients, which is sometimes challenging for certain photonics problems. Existing techniques also comprise a patchwork of application-specific algorithms, each focused in scope and scatterer type. Here, we leverage algorithmic differentiation as used in artificial neural networks, treating photonic design parameters as trainable weights, optical sources as inputs, and encapsulating device performance in the loss function. By solving a complex, degenerate eigenproblem and formulating rigorous coupled-wave analysis as a computational graph, we support both arbitrary, parameterized scatterers and topology optimization. With iteration times below the cost of two forward simulations typical of adjoint methods, we generate multilayer, multifunctional, and aperiodic meta-optics. As an open-source platform adaptable to other algorithms and problems, we enable fast and flexible meta-optical design. 

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5. On the Two-sided Permutation Inversion Problem

   https://doi.org/10.62056/a0qj89n4e  

   Alagic, Gorjan; Bai, Chen; Poremba, Alexander; Shi, Kaiyan (April 2024, IACR Communications in Cryptology)

   In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This fundamental problem in query complexity appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation—except that the challenge value cannot be submitted to the latter. Within that setting, we consider three options for the inversion algorithm: whether it can get quantum advice about the permutation, whether the query algorithm can restrict the distribution with which the challenge input is sampled, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the permutation inversion problem and establish lower bounds for them. Our results show that, perhaps surprisingly, the permutation inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse—provided it cannot query the challenge itself. 

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