Giant Gating Tunability of Optical Refractive Index in Transition Metal Dichalcogenide Monolayers

We report that the refractive index of transition metal dichacolgenide (TMDC) monolayers, such as MoS2, WS2, and WSe2, can be substantially tuned by > 60% in the imaginary part and > 20% in the real part around exciton resonances using CMOS-compatible electrical gating. This giant tunablility is rooted in the dominance of excitonic effects in the refractive index of the monolayers and the strong susceptibility of the excitons to the influence of injected charge carriers. The tunability mainly results from the effects of injected charge carriers to broaden the spectral width of excitonic interband transitions and to facilitate the interconversion of neutral and charged excitons. The other effects of the injected charge carriers, such as renormalizing bandgap and changing exciton binding energy, only play negligible roles. We also demonstrate that the atomically thin monolayers, when combined with photonic structures, can enable the efficiencies of optical absorption (reflection) tuned from 40% (60%) to 80% (20%) due to the giant tunability of refractive index. This work may pave the way towards the development of field-effect photonics in which the optical functionality can be controlled with CMOS circuits

Optimal Scoring Rule Design

This paper introduces an optimization problem for proper scoring rule design. Consider a principal who wants to collect an agent's prediction about an unknown state. The agent can either report his prior prediction or access a costly signal and report the posterior prediction. Given a collection of possible distributions containing the agent's posterior prediction distribution, the principal's objective is to design a bounded scoring rule to maximize the agent's worst-case payoff increment between reporting his posterior prediction and reporting his prior prediction. We study two settings of such optimization for proper scoring rules: static and asymptotic settings. In the static setting, where the agent can access one signal, we propose an efficient algorithm to compute an optimal scoring rule when the collection of distributions is finite. The agent can adaptively and indefinitely refine his prediction in the asymptotic setting. We first consider a sequence of collections of posterior distributions with vanishing covariance, which emulates general estimators with large samples, and show the optimality of the quadratic scoring rule. Then, when the agent's posterior distribution is a Beta-Bernoulli process, we find that the log scoring rule is optimal. We also prove the optimality of the log scoring rule over a smaller set of functions for categorical distributions with Dirichlet priors