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1. Internalizing Indistinguishability with Dependent Types

   https://doi.org/10.1145/3632886  

   Liu, Yiyun; Chan, Jonathan; Shi, Jessica; Weirich, Stephanie (January 2024, Proceedings of the ACM on Programming Languages)

   In type systems with dependency tracking, programmers can assign an ordered set of levels to computations and prevent information flow from high-level computations to the low-level ones. The key notion in such systems isindistinguishability: a definition of program equivalence that takes into account the parts of the program that an observer may depend on. In this paper, we investigate the use of dependency tracking in the context of dependently-typed languages. We present the Dependent Calculus of Indistinguishability (DCOI), a system that adopts indistinguishability as the definition of equality used by the type checker. DCOI also internalizes that relation as an observer-indexed propositional equality type, so that programmers may reason about indistinguishability within the language. Our design generalizes and extends prior systems that combine dependency tracking with dependent types and is the first to support conversion and propositional equality at arbitrary observer levels. We have proven type soundness and noninterference theorems for DCOI and have developed a prototype implementation of its type checker. 

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2. Kernel Smoothing, Mean Shift, and Their Learning Theory with Directional Data

   Zhang, Yikun; Chen, Yen-Chi (January 2021, Journal of machine learning research)

   null (Ed.)

   Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel smoothing for directional data. We generalize the classical mean shift algorithm to directional data, which allows us to identify local modes of the directional kernel density estimator (KDE). The statistical convergence rates of the directional KDE and its derivatives are derived, and the problem of mode estimation is examined. We also prove the ascending property of the directional mean shift algorithm and investigate a general problem of gradient ascent on the unit hypersphere. To demonstrate the applicability of the algorithm, we evaluate it as a mode clustering method on both simulated and real-world data sets. 

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3. Design of a Modified Coupled Resonators Optical Waveguide Supporting a Frozen Mode

   https://doi.org/10.1109/JLT.2023.3266311  

   Nada, Mohamed Y.; Mealy, Tarek; Islam, Md Shafiqul; Vitebskiy, Ilya; Gibson, Ricky; Bedford, Robert; Boyraz, Ozdal; Capolino, Filippo (April 2023, Journal of Lightwave Technology)

   We design a three-way silicon optical waveguide with the Bloch dispersion relation supporting a stationary inflection point (SIP). The SIP is a third order exceptional point of degeneracy (EPD) where three Bloch modes coalesce forming the frozen mode with greatly enhanced amplitude. The proposed design consists of a coupled resonators optical waveguide (CROW) coupled to a parallel straight waveguide. At any given frequency, this structure supports three pairs of reciprocal Bloch eigenmodes, propagating and/or evanescent. In addition to full-wave simulations, we also employ a so-called “hybrid model” that uses transfer matrices obtained from full-wave simulations of sub-blocks of the unit cell. This allows us to account for radiation losses and enables a design procedure based on minimizing the eigenmodes’ coalescence parameter. The proposed finite-length CROW displays almost unitary transfer function at the SIP resonance, implying a nearly perfect conversion of the input light into the frozen mode. The group delay and the effective quality factor at the SIP resonance show an $N^3$ scaling, where N is the number of unit cells in the cavity. The frozen mode in the CROW can be utilized in various applications like sensors, lasers and optical delay lines. 

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4. Wavelength-scale optical parametric oscillators

   https://doi.org/10.1364/OPTICA.411708  

   Jahani, Saman; Roy, Arkadev; Marandi, Alireza (February 2021, Optica)

   Despite recent progress in nonlinear optics in wavelength-scale resonators, there are still open questions on the possibility of parametric oscillation in such resonators. We present a general approach to predict the behavior and estimate the oscillation threshold of multi-mode subwavelength and wavelength-scale optical parametric oscillators (OPOs). As an example, we propose an OPO based on Mie-type multipolar resonances, and we demonstrate that due to the low- $Q$nature of multipolar modes in wavelength-scale resonators, there is a nonlinear interaction between these modes. As a result, the OPO threshold, compared to the single-mode case, can be reduced by a factor that is significantly larger than the number of interacting modes. The multi-mode interaction can also lead to a phase transition manifested through a sudden change in the parametric gain as well as the oscillation threshold, which can be utilized for enhanced sensing. We establish an explicit connection between the second-harmonic generation efficiency and the OPO threshold. This allows us to estimate the OPO threshold based on measured or simulated second-harmonic generation in different classes of resonators, such as bound states in the continuum and inversely designed resonators. Our approach for analyzing and modeling miniaturized OPOs can open unprecedented opportunities for classical and quantum nonlinear photonics. 

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5. Theoretical formulation of chemical equilibrium under vibrational strong coupling

   https://doi.org/10.1038/s41467-024-46442-1  

   Sun, Kaihong; Ribeiro, Raphael F. (March 2024, Nature Communications)

   Abstract Experiments have suggested that strong interactions between molecular ensembles and infrared microcavities can be employed to control chemical equilibria. Nevertheless, the primary mechanism and key features of the effect remain largely unexplored. In this work, we develop a theory of chemical equilibrium in optical microcavities, which allows us to relate the equilibrium composition of a mixture in different electromagnetic environments. Our theory shows that in planar microcavities under strong coupling with polyatomic molecules, hybrid modes formed between all dipole-active vibrations and cavity resonances contribute to polariton-assisted chemical equilibrium shifts. To illustrate key aspects of our formalism, we explore a model S_N2 reaction within a single-mode infrared resonator. Our findings reveal that chemical equilibria can be shifted towards either direction of a chemical reaction, depending on the oscillator strength and frequencies of reactant and product normal modes. Polariton-induced zero-point energy changes provide the dominant contributions, though the effects in idealized single-mode cavities tend to diminish quickly as the temperature and number of molecules increase. Our approach is valid in generic electromagnetic environments and paves the way for understanding and controlling chemical equilibria with microcavities. 

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