The overall goal of photonics research is to understand and control light in new and richer ways to facilitate new and richer applications. Many major developments to this end have relied on nonlinear optical techniques, such as lasing, mode-locking, and parametric downconversion, to enable applications based on the interactions of coherent light with matter. These processes often involve nonlinear interactions between photonic and material degrees of freedom spanning multiple spatiotemporal scales. While great progress has been made with relatively simple optimizations, such as maximizing single-mode coherence or peak intensity alone, the ultimate achievement of coherent light engineering is complete, multidimensional control of light–light and light–matter interactions through tailored construction of complex optical fields and systems that exploit all of light’s degrees of freedom. This capability is now within sight, due to advances in telecommunications, computing, algorithms, and modeling. Control of highly multimode optical fields and processes also facilitates quantitative and qualitative advances in optical imaging, sensing, communication, and information processing since these applications directly depend on our ability to detect, encode, and manipulate information in as many optical degrees of freedom as possible. Today, these applications are increasingly being enhanced or enabled by both multimode engineering and nonlinearity. Here, we provide a brief overview of multimode nonlinear photonics, focusing primarily on spatiotemporal nonlinear wave propagation and, in particular, on promising future directions and routes to applications. We conclude with an overview of emerging processes and methodologies that will enable complex, coherent nonlinear photonic devices with many degrees of freedom.

中文翻译：

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非线性多模光子学：具有多自由度的非线性光学

光子学研究的总体目标是以新的和更丰富的方式理解和控制光，以促进新的和更丰富的应用。为此目的，许多重大发展都依赖于非线性光学技术，例如激光、锁模和参数下变频，以实现基于相干光与物质相互作用的应用。这些过程通常涉及跨越多个时空尺度的光子和材料自由度之间的非线性相互作用。虽然通过相对简单的优化已经取得了很大进展，例如最大化单模相干或峰值强度，但相干光工程的最终成就已经完成，通过定制构建利用所有光的自由度的复杂光场和系统，对光-光和光-物质相互作用进行多维控制。由于电信、计算、算法和建模方面的进步，这种能力现在已经触手可及。高度多模光场和过程的控制也促进了光学成像、传感、通信和信息处理的定量和定性进步，因为这些应用直接取决于我们在尽可能多的光学自由度中检测、编码和操纵信息的能力. 今天，这些应用正越来越多地通过多模工程和非线性得到增强或启用。在这里，我们简要概述了多模非线性光子学，主要关注时空非线性波传播，特别是有前途的未来应用方向和路线。最后，我们概述了新兴的过程和方法，这些过程和方法将使复杂的、相干的非线性光子器件具有许多自由度。