Contents I. Introduction
Nonreciprocal optical devices such as isolators are important for optical circuits. With the rapid progress in integrated optical systems [1]–[3], the needs to minimize and to integrate these devices on chip are becoming increasingly urgent [4], [5]. Realizing nonreciprocal optical components requires time-reversal symmetry breaking. This is usually achieved in bulk optical systems using magneto-optical (MO) materials, which can possess permittivity tensor under external magnetic field. The minimization and integration of those traditional nonreciprocal components, which are required by integrated optical systems, encounter a problem that the MO effect is very weak in optical frequencies. This weakness prevents bulk components from being adopted in integrated optical systems. In order to achieve integratable nonreciprocal devices, many new methods and designs have been proposed. Optical isolations by nonreciprocal waveguides [6]–[15], Mach–Zehnder interferometers [16]–[24], photonic crystals [25]–[27], micro-resonators [28]–[30], nonlinear coupler [31], surface plasmon [32]–[34] and interband photonic transitions [35]–[37] have been studied. Meanwhile, waveguides with unidirectional guided modes have also been proposed [38]–[42], which can offer people new approaches to realize electromagnetic isolation. However, realizable on-chip nonreciprocal components with structurally simple configuration have not been reported yet.
