Fundamental asymmetries between spatial and temporal boundaries in electromagnetics

TL;DR

This paper explores the fundamental physical differences between spatial and temporal boundaries in electromagnetics, revealing how conservation laws and classical optics laws adapt or differ in time-varying materials.

Contribution

It provides a thorough analysis of the physical distinctions between spatial and temporal boundaries, deriving optical laws in a temporal context with novel interpretations.

Findings

Temporal boundaries do not conform to energy conservation.

Reflection and Snell's laws have different interpretations in time-varying media.

Temporal boundaries challenge traditional notions of causality.

Abstract

Time-varying materials bring an extra degree of design freedom compared to their conventional time-invariant counterparts. However, few discussions have focused on the underlying physical difference between spatial and temporal boundaries. In this letter, we thoroughly investigate those differences from the perspective of conservation laws. By doing so, the building blocks of optics and electromagnetics such as the reflection law, Snell's law, and Fresnel's equations can be analogously derived in a temporal context, but with completely different interpretations. Furthermore, we study the unique features of temporal boundaries, such as their nonconformance to energy conservation and causality.