Casimir Force: Vacuum fluctuation, zero-point energy, and computational electromagnetics

Abstract

The understanding of the Casimir force foretells applications in micro/nanoelectromechanical sensors and quantum friction. We review the history of quantum theory and Casimir force modeling and, using the homomorphism between electromagnetic oscillations and a linear pendulum with simple harmonic oscillation, we explore various concepts needed for Casimir force calculations. Through the argument principle, we simplify the derivation of Casimir energy and, hence, the Casimir force. Then, we discuss the connection between the Casimir force and computational electromagnetics (CEM), focusing on the method of moments (MOM). Finally, we consider the marriage of these concepts with recently developed broadband fast algorithms. The resulting approaches illustrate that the Casimir force calculation is for various highly complex structures.