Materials for nonreciprocal photonics
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Introduction Reciprocal theorems are a fundamental physical principle for a variety of physical disciplines such as acoustics, mechanics, electronics, and electromagnetic wave theories.1–7 For example, in electric circuit theory, the reciprocal theorem relates the electromotive force and its generated current between two different points.6 The theorem states that in a reciprocal electrical network, current I at a point A generated by electromotive force E at a point B is equal to the current I generated at point B by applying the same electromotive force E at point A.6 In electromagnetic wave and photonic theory, the Lorentz reciprocal theorem7 relates the current sources and their generated electric fields in a volume space by:
∫J V
A
• EB dV = ∫ J B • EA dV , V
where JA and JB are two current sources at two arbitrary points A and B in a background space V, and EA and EB are their generated electric fields, respectively. Such reciprocal theorems form the theoretical basis of modern information technologies. Breaking the reciprocity, or being nonreciprocal, has significant importance and profound impact for information technology, which is also deeply rooted in materials science. For example, the standard electric diode shown in Figure 1a is a nonreciprocal device. Due to the rectifying effect of an electric diode, applying an electric potential at point A
(or a voltage along the forward direction) leads to current flow at point B; but applying the same electric potential at point B results in very low current flow at point A in the backward direction. This violation of reciprocity is due to the Coloumb interaction of carriers in semiconductors subjected to the built-in electric field formed in p–n junctions. Electric diodes have been miniaturized and planarized in integrated circuits, serving as the building blocks for billions of metal oxide semiconductor transistors and bipolar junction transistors on a chip, forming the very backbone of microelectronic technologies today. Unlike electrons, photons do not carry charge, making nonreciprocity far more difficult to realize in photonic materials and systems.8 One kind of nonreciprocal photonic device, the optical isolator, shows similar behavior as an electric diode (Figure 1b). An optical isolator, sometimes called an “optical diode,” is a one-way traffic path for light, which allows light to pass in one direction, but not the opposite direction.9 Rather than relying on Coloumb interactions in semiconductor materials, discrete optical isolators use magneto-optical effects and magneto-optical materials, such as the ferrimagnetic oxide single-crystal material, iron garnet. When magnetized, magneto-optical materials change polarization, absorption, or the phase of light differently when they propagate forward as compared to backward propagation. Optical isolators, for instance, prevent reflected light from entering laser cavities and protect lasers from damage or
Lei Bi, Department of Electronic Engineering, University of Electronic Science and Technology of China,
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