Non-Hermitian skin effect induced by on-site gain and loss in the optically coupled cavity array

The introduction of non-Hermiticity into topological systems has led to a series of novel physical phenomena and produced application prospects. Here, we combine non-Hermitian and topological photonic systems based on a one-dimensional extended Su-Schrieffer-Heeger (SSH) model, which is composed of the optically coupled cavity array. We found that single on-site gain and loss do not induce the non-Hermitian skin effect (NHSE) in this model. Once the complex next-nearest-neighbor coupling is introduced, which is similar to asymmetric coupling, NHSE exists in the system. Adjusting the parameters of the system, we noted that the behavior of in-gap topological edge modes depends on the competition between non-Hermiticity and band topology. NHSE is featured with two edge modes localized at one end of the array, whereas the latter is characterized by two edge modes distributed at the two ends of the array. In addition, we reveal the conditions is that a system with gain and loss produces the non-Hermitian skin effect. Our research enriches the integration of non-Hermitian and topological photonics.