The refractive index is one of the most basic optical properties of a material and its interaction with light. Modern materials engineering—particularly the concept of metamaterials—has made it necessary to consider its subtleties, including anisotropy and complex values. Here we re-examine the refractive index and find a general way to calculate the direction-dependent refractive index and the condition for zero index in a given direction. By analogy with linear versus circular polarization, we show that when the zero-index direction is complex-valued, a material supports waves that can propagate in only one sense, for example, clockwise. We show that there is an infinite family of both time-reversible and time-irreversible homogeneous electromagnetic media that support unidirectional propagation for a particular polarization. As well as extending the concept of the refractive index, shedding new light on our understanding of topological photonics and providing new sets of material parameters, our simple picture also reproduces many of the findings derived using topology.

折射率是材料及其与光的相互作用的最基本光学特性之一。现代材料工程，尤其是超材料的概念，使得必须考虑其微妙之处，包括各向异性和复杂值。在这里，我们重新检查折射率，并找到一种通常的方法来计算与方向相关的折射率以及在给定方向上零折射率的条件。通过线性极化和圆极化的类比，我们表明，当零折射率方向为复数值时，材料支持的波只能沿一种方向传播，例如顺时针方向。我们表明，存在无限的时间可逆和时间不可逆的均匀电磁介质族，它们支持特定极化的单向传播。