The realization of robust coherent energy transfer with a long range from a donor to an acceptor has many important applications in the field of quantum optics. However, it is hard to be realized using conventional schemes. Here, we demonstrate theoretically that robust energy transfer can be achieved using a photonic crystal platform, which includes the topologically protected edge state and zero-dimensional topological corner cavities. When the donor and the acceptor are put into a pair of separated topological cavities, the energy transfer between them can be fulfilled with the assistance of the topologically protected interface state. Such an energy transfer is robust against various kinds of defects, and can also occur over very long distances, which is very beneficial for biological detections, sensors, quantum information science, and so on.

Entangled photons are the fundamental resource in quantum information processing. How to produce them efficiently has always been a matter of concern. Here we propose a new way to produce correlated photons efficiently from monolayer WS2 based on bound states in the continuum (BICs). The BICs of radiation modes in the monolayer WS2 are realized by designing the photonic crystal slab-WS2-slab structure. The generation efficiency of correlated photon pairs from such a structure has been studied by using a rigorous quantum model of spontaneous parametric down-conversion with the plane wave expansion method. It is found that the generation efficiency of correlated photon pairs is greatly improved if the signal and idler fields are located at the BICs determined by the inverse scattering matrix of the structure. This is in contrast to the parametric down-conversion process for the enhanced generation of nonlinear waves if the pump field is located at the BICs determined by the scattering matrix of the structure. The generation rate of the correlated photon pairs can be improved by 7 orders of magnitude in some designed structures. The generated quantum signals are sensitive to the wavelength and exhibit narrowed relative line width, which is very beneficial for quantum information processing.

We present an exact solution to the problem of electromagnetic scattering by nanosphere clusters embedded in a liquid crystal cell, based on the Mie theory. The dependence of the scattering property on the structure parameters is investigated in detail. It is shown that strong transverse light currents at the optical frequency can be obtained from these complex structures. Furthermore, we find that sign reversal of the transverse light current can be realized by changing frequency and voltage. The physical origins of these phenomena have been analyzed. The transverse light current for subwavelength nanoscale dimensions is of practical significance. Thus, the application of these phenomena to optical devices is anticipated.

The scattering matrix theory has been developed to calculate the third-order nonlinear effect in sphere-graphene-slab structures. By designing structural parameters, we have demonstrated that the incident electromagnetic wave can be well confined in the graphene in these structures due to the formation of a bound state in the continuum (BIC) of radiation modes. Based on such a bound state, third-harmonic (TH) generation and four-wave mixing (FWM) have been studied. It is found that the efficiency of TH generation in monolayer graphene can be enhanced about 7 orders of magnitude. It is interesting that we can design structure parameters to make all beams (the pump beam, probe beam, and generated FWM signal) be BICs at the same time. In such a case, the efficiency of FWM in monolayer graphene can be enhanced about 9 orders of magnitude. Both the TH and FWM signals are sensitive to the wavelength, and possess high Q factors, which exhibit very good monochromaticity. By taking suitable BICs, the selective generation of TH and FWM signals for S- and P-polarized waves can also be realized, which is beneficial for the design of optical devices.