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Second-harmonic generation (SHG) plays a significant role in modern photonic technology. Integrated photonic resonators fabricated with thin-film lithium niobate can achieve ultrahigh efficiencies by combining small mode volumes with high material nonlinearity. Cavity-enhanced SHG requires accurate phase and frequency matching conditions, where fundamental and second-harmonic wavelengths are both on resonance. However, this double-resonance condition can typically be realized only at a fixed random wavelength due to the high sensitivity of photonic resonances to the device geometry and fabrication variations. Here, we propose a novel method that can achieve the double-resonance condition over a large wavelength range. We combine thermal-optic and electro-optic (EO) effects to realize the separate tuning of fundamental and second-harmonic resonances. We demonstrated that the optimum SHG efficiency can be maintained over a wavelength range that exceeds the limit achievable with only thermal tuning. With this flexible tuning capability, we further show the precise alignment of SHG wavelengths of two separate thin-film lithium niobate resonators without sacrificing efficiencies. 

Current integrated optical isolators have limited bandwidths due to stringent phase-matching, resonant structures, or absorption. We demonstrate broadband optical isolation in thin-film lithium niobate that simultaneously achieves∼100 nm isolation bandwidth at visible and telecom wavelengths. 

Optical isolators are an essential component of photonic systems. Current integrated optical isolators have limited bandwidths due to stringent phase-matching conditions, resonant structures, or material absorption. Here, we demonstrate a wideband integrated optical isolator in thin-film lithium niobate photonics. We use dynamic standing-wave modulation in a tandem configuration to break Lorentz reciprocity and achieve isolation. We measure an isolation ratio of 15 dB and insertion loss below 0.5 dB for a continuous wave laser input at 1550 nm. In addition, we experimentally show that this isolator can simultaneously operate at visible and telecom wavelengths with comparable performance. Isolation bandwidths up to ∼100 nm can be achieved simultaneously at both visible and telecom wavelengths, limited only by the modulation bandwidth. Our device’s dual-band isolation, high flexibility, and real-time tunability can enable novel non-reciprocal functionality on integrated photonic platforms. 

Automated techniques for rigorous floating-point round-off error analysis are a prerequisite to placing important activities in HPC such as precision allocation, verification, and code optimization on a formal footing. Yet existing techniques cannot provide tight bounds for expressions beyond a few dozen operators—barely enough for HPC. In this work, we offer an approach embedded in a new tool called SATIRE that scales error analysis by four orders of magnitude compared to today’s best-of-class tools. We explain how three key ideas underlying SATIRE helps it attain such scale: path strength reduction, bound optimization, and abstraction. SATIRE provides tight bounds and rigorous guarantees on significantly larger expressions with well over a hundred thousand operators, covering important examples including FFT, matrix multiplication, and PDE stencils.