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Optical microresonators possessing Kerr-type nonlinearity have emerged over the past decade as reliable and versatile sources of optical frequency combs, with varied applications including in the generation of low-phasenoise radio frequency (RF) signals, small-footprint precision timekeeping, and LiDAR. One of the key parameters affecting Kerr microcomb generation in different wavelength ranges is cavity modal dispersion. Dispersion effects such as avoided mode crossings (AMCs) have been shown to greatly limit mode-locked microcomb generation, especially when pumping in close proximity to such disruptions. We present numerical modeling and experimental evidence demonstrating that using an auxiliary laser pump can suppress the detrimental impact of near-pump AMCs. We also report, for the first time to our knowledge, the possibility of the breaking of characteristic soliton steps into two stable branches corresponding to different stable pulse trains arising from the interplay of dichromatic pumping and AMCs. These findings bear significance, particularly for the generation of frequency combs in larger resonators or at smaller wavelengths, such as the visible range, where the cavities become overmoded. 

We study convex empirical risk minimization for high-dimensional inference in binary linear classification under both discriminative binary linear models, as well as generative Gaussian-mixture models. Our first result sharply predicts the statistical performance of such estimators in the proportional asymptotic regime under isotropic Gaussian features. Importantly, the predictions hold for a wide class of convex loss functions, which we exploit to prove bounds on the best achievable performance. Notably, we show that the proposed bounds are tight for popular binary models (such as signed and logistic) and for the Gaussian-mixture model by constructing appropriate loss functions that achieve it. Our numerical simulations suggest that the theory is accurate even for relatively small problem dimensions and that it enjoys a certain universality property. 

Abstract The phase matching between the propagating fundamental and nonlinearly generated waves plays an important role in the efficiency of the nonlinear frequency conversion in macroscopic crystals. However, in nanoscale samples, such as nanoplasmonic structures, the phase-matching condition is often ignored due to the sub-wavelength nature of the materials. Here, we first show that the phase matching of the lattice plasmon modes at the fundamental and second-harmonic frequencies in a plasmonic nanoantenna array can effectively enhance the surface-enhanced second-harmonic generation. Additionally, a significant enhancement of the second-harmonic generation is demonstrated using stationary band-edge lattice plasmon modes with zero phase.