Nonreciprocity in synthetic photonic materials with nonlinearity
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troduction Photonic devices in which the flow of light is nonreciprocal, such as optical isolators and circulators, are highly desirable for applications ranging from communications to sensing and metrology. For many years, nonreciprocal photonic devices have been predominantly based on magneto-optical materials, which break Lorentz reciprocity when subjected to a magnetic field. However, magneto-optical devices have several disadvantages—they tend to be bulky, are subject to high losses, and are difficult to integrate into current semiconductor fabrication techniques. An alternative approach to breaking Lorentz reciprocity is to exploit optical nonlinearities, such as the thermo-optic effect, Kerr effect, and two-photon absorption.1–3 For instance, Fan et al. have demonstrated an all-silicon optical isolator with a nonreciprocal transmission ratio of more than 28 dB, based on coupled microrings with thermo-optic nonlinearity.2 This article discusses two recent directions in designing structured nonlinear optical media for nonreciprocal wave transport. The first explores non-Hermitian effects found in open systems with dissipation or amplification, and involves judiciously tailoring the distribution of optical loss or gain.4–7 This includes “parity-time-reversal (PT) symmetric” structures that contain balanced amounts of gain and loss, as well
as structures exhibiting non-Hermitian degeneracies known as exceptional points (EPs). The second direction consists of photonic structures with “topologically nontrivial” photonic bands.8–11 Such structures support an unusual class of electromagnetic modes known as topological edge states, analogous to electronic topological edge states in topological insulators, which are robust to defects or perturbations. In the absence of optical nonlinearity (and the absence of magneto-optical effects and time modulation), synthetic photonic materials cannot break Lorentz reciprocity, even if loss or gain are present.12 Both effects we focus on—nonHermiticity and band topology—do not lead to nonreciprocity by themselves. When combined with optical nonlinearity, however, they can be used to achieve highly nonreciprocal behaviors.
Nonlinear and non-Hermitian photonics The time evolution of a physical system, such as the classical electromagnetic field in a photonic device, can be described by a Hamiltonian that is Hermitian (i.e., H = H†, where † denotes the conjugate transpose operation). Hermiticity guarantees a real energy spectrum and unitary (probability-conserving) time evolution. In practice, however, physical systems often experience loss or gain—in other words, energy enters or
Weijian Chen, Department of Electrical and Systems Engineering, Washington University in St. Louis, USA; [email protected] Daniel Leykam, Institute for Basic Science, South Korea; [email protected] Y.D. Chong, Nanyang Technological University, Singapore; [email protected] Lan Yang, Department of Electrical and Systems Engineering, Washington University in St. Louis, USA; [email protected] doi:10.1557/mr
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