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Theoretical bounds are commonly used to assess the limitations of photonic design. Here we introduce a more active way to use theoretical bounds, integrating them into part of the design process and identifying optimal system parameters that maximize the efficiency limit itself. As an example, we consider wide-field-of-view high-numerical-aperture metalenses, which can be used for high-resolution imaging in microscopy and endoscopy, but no existing design has achieved a high efficiency. By choosing aperture sizes to maximize an efficiency bound, setting the thickness according to a thickness bound, and then performing inverse design, we come up with high-numerical-aperture (NA=0.9) metalens designs with, to our knowledge, record-high 98% transmission efficiency and 92% Strehl ratio across all incident angles within a 60° field of view, reaching the maximized bound. This maximizing-efficiency-limit approach applies to any multi-channel system and can help a wide range of optical devices reach their highest possible performance. 

We realize full-wave single-shot computations of the polarization-resolved scattering matrices of 3D complex media using the “augmented partial factorization” method. Our parallelized solver achieves three orders of magnitude speed-up compared to parallelized iterative FDFD method. 

Topology optimization of nonlocal metasurfaces requires the objective-function gradient considering all angles of interest. We generalize the recent “augmented partial factorization” method to compute such gradient efficiently and inverse design a broad-angle metasurface beam splitter. 

Correlations between entangled photons are a key ingredient for testing fundamental aspects of quantum mechanics and an invaluable resource for quantum technologies. However, scattering from a dynamic medium typically scrambles and averages out such correlations. Here we show that multiply scattered entangled photons reflected from a dynamic complex medium remain partially correlated. In experiments and full-wave simulations we observe enhanced correlations, within an angular range determined by the transport mean free path, which prevail over disorder averaging. Theoretical analysis reveals that this enhancement arises from the interference between scattering trajectories, in which the photons leave the sample and are then virtually reinjected back into it. These paths are the quantum counterpart of the paths that lead to the coherent backscattering of classical light. This work points to opportunities for entanglement transport despite dynamic multiple scattering in complex systems. 

Abstract Numerical solutions of Maxwell’s equations are indispensable for nanophotonics and electromagnetics but are constrained when it comes to large systems, especially multi-channel ones such as disordered media, aperiodic metasurfaces and densely packed photonic circuits where the many inputs require many large-scale simulations. Conventionally, before extracting the quantities of interest, Maxwell’s equations are first solved on every element of a discretization basis set that contains much more information than is typically needed. Furthermore, such simulations are often performed one input at a time, which can be slow and repetitive. Here we propose to bypass the full-basis solutions and directly compute the quantities of interest while also eliminating the repetition over inputs. We do so by augmenting the Maxwell operator with all the input source profiles and all the output projection profiles, followed by a single partial factorization that yields the entire generalized scattering matrix via the Schur complement, with no approximation beyond discretization. This method applies to any linear partial differential equation. Benchmarks show that this approach is 1,000–30,000,000 times faster than existing methods for two-dimensional systems with about 10,000,000 variables. As examples, we demonstrate simulations of entangled photon backscattering from disorder and high-numerical-aperture metalenses that are thousands of wavelengths wide. 

Using the Schur complement scattering analysis (SCSA) method, we accelerate the scattering matrix computation for large-scale disordered media by many orders of magnitude and realize full-wave simulations of classical and quantum coherent backscattering.