Black phosphorous (BP), the most thermodynamically stable allotrope of phosphorus, is a high-mobility layered semiconductor with direct band-gap determined by the number of layers from 0.3 eV (bulk) to 2.0 eV (single layer). Therefore, BP is considered as a natural candidate for broadband optical applications, particularly in the infrared (IR) and mid-IR part of the spectrum. The strong light-matter interaction, narrow direct band-gap, and wide range of tunable optical response make BP as a promising nonlinear optical material, particularly with great potentials for infrared and mid-infrared opto-electronics. Herein, we experimentally verified its broadband and enhanced saturable absorption of multi-layer BP (with a thickness of ~10 nm) by wide-band Z-scan measurement technique, and anticipated that multi-layer BPs could be developed as another new type of two-dimensional saturable absorber with operation bandwidth ranging from the visible (400 nm) towards mid-IR (at least 1930 nm). Our results might suggest that ultra-thin multi-layer BP films could be potentially developed as broadband ultra-fast photonics devices, such as passive Q-switcher, mode-locker, optical switcher etc.

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This paper considers a single machine scheduling problem with preventive maintenance. In many cases, a machine must be maintained after it continuously works for a period of time. But most papers in the literature ignore non-availability of the machine. For this reason, this paper studies the problem of scheduling processing of jobs and maintenance of machine simultaneously. The objective is to minimise total completion time of jobs. The problem is proved to be NP-hard in the strong sense. Three heuristic algorithms and a branch and bound algorithm are proposed. Computational experiments are done to evaluate the effectiveness of the algorithms.

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