# Perspective on Some Recent and Future Developments in Casimir Interactions
## 1 Introduction  
The ubiquitous Casimir force originates from the exchange of electromagnetic fluctuations between objects, and it is determined by the material's magnetic and dielectric properties and boundary conditions for the fields. The complicated interplay between such properties and geometry has been shown to yield many different scaling laws and wide variations in magnitude, sign, and characteristic dependences upon fundamental constants (such as, e.g., Plank's constant or the speed of light) [1, 2]. The basic understanding of the Casimir force is important for probing novel physics involving materials at a small relative distance and for better design of micro and nanoscale devices [3]. The closely related van der Waals interaction (corresponding to the Casimir force in the non-retarded regime, where the speed of light can be considered infinite) has also recently received much interest due to its importance for materials science, especially in layered systems [4]. Consequently, advances in first principles simulations have resulted in computational tools for making qualitative and quantitative predictions in materials in which long-ranged collective electronic effects are important [5].  
In the past several years, the discovery of many materials with nontrivial topological properties has given a new direction for the field of Casimir physics [6, 7, 8]. Materials with Dirac-like energy dispersions in 2D and 3D dimensions have a wide variety of optical response properties, which in turn can significantly affect electromagnetic interactions. In this Perspective article, we give an overview of key results regarding the Casimir force involving materials from the graphene family, Weyl semimetals, topological, and Chern insulators. This research has moved forward not only our fundamental understanding of properties of topologically nontrivial materials, but also of electromagnetism in such media.  
Recent theoretical and experimental works have shown that many Weyl semimetals and layered transition metal dichalcogenides can also experience enhanced nonlinear optical properties [9,10]. These, in turn, can result in photogalvanic effects, photocurrents, and nonlinear Hall effect, which is especially encouraging for novel optical effects in the visible and infrared regimes [11,12]. The potential of new and improved optical applications has stimulated much work in calculating the nonlinear optical response in different systems. Nonlinear properties can also affect the Casimir interaction, however, this direction has not been considered much by the scientific community as current research on dispersive forces has been primarily within linear response theories. Here, we show that the limited studies in the nonlinear optical response regime demonstrate even further diversity of dependences in the Casimir interactions. We argue that discoveries of strongly nonlinear materials bring forward the necessity to investigate light-matter fluctuation induced interaction beyond the linear response regime. Such materials can serve as excellent platforms bringing together nonlinear optics and its connection to Casimir phenomena for probing novel properties of Dirac-like systems.  
Other Casimir-related phenomena can also benefit from discoveries of new materials with nontrivial properties. One such phenomenon is the Dynamical Casimir Effect (DCE), which shows how real photons can be generated from the \"empty\" vacuum [13,14]. While most methods of describing DCE rely on treating different boundary conditions, understanding the microscopic and materials-related nature of this effect can also be beneficial. In this Perspective, we give a short overview of recent achievements in this field and demonstrate that experimental observation of the DCE relies on nonlinear optics, and we argue that nonlinear media can give new directions of exploration.