Generation of High-Intensity Laser Pulses and their Applications

The progress in the laser technology makes it possible to produce a laser pulse having a peak power of over PW. Focusing such high-power laser pulses enables ones to have unprecedentedly strong laser intensity. The laser intensity over 1019 W/cm2, which is called the relativistic laser intensity, can accelerate electrons almost to the speed of light. The acceleration of charged particles using such a high-power laser pulse has been successfully demonstrated in many experiments. According to the recent calculation using the vector diffraction theory, it is possible, by employing a tight focusing geometry, to produce a femtosecond (fs) laser focal spot to have an intensity of over 1024 W/cm2 in the focal plane. Over this laser intensity, protons can be directly accelerated almost to the speed of light. Such ultrashort and ultrastrong laser intensities will bring ones many opportunities to experimentally study ultrafast physical phenomena we have never met before. This chapter describes how to generate a high-power laser pulse. And, then the focusing characteristics of a femtosecond high-power laser pulse are discussed in the scalar and the vector diffraction limits. Finally, the applications of ultrashort high-power laser are briefly introduced

Accelerating Value Iteration with Anchoring

Value Iteration (VI) is foundational to the theory and practice of modern reinforcement learning, and it is known to converge at a $\mathcal{O}(\gamma^k)$-rate, where $\gamma$ is the discount factor. Surprisingly, however, the optimal rate for the VI setup was not known, and finding a general acceleration mechanism has been an open problem. In this paper, we present the first accelerated VI for both the Bellman consistency and optimality operators. Our method, called Anc-VI, is based on an \emph{anchoring} mechanism (distinct from Nesterov's acceleration), and it reduces the Bellman error faster than standard VI. In particular, Anc-VI exhibits a $\mathcal{O}(1/k)$-rate for $\gamma\approx 1$ or even $\gamma=1$, while standard VI has rate $\mathcal{O}(1)$ for $\gamma\ge 1-1/k$, where $k$ is the iteration count. We also provide a complexity lower bound matching the upper bound up to a constant factor of $4$, thereby establishing optimality of the accelerated rate of Anc-VI. Finally, we show that the anchoring mechanism provides the same benefit in the approximate VI and Gauss--Seidel VI setups as well