We theoretically investigate the optical bistability in superconductor–semiconductor photonic crystals composed of graphene. The photonic crystals are symmetric to the center and arranged alternately by the superconductor (HgBa₂Ca₂Cu₃O_8+δ) and semiconductor (GaAs) layers. The system supports a defect mode, and graphene is located at the layer interface where the local electric field is the strongest. Consequently, the optical nonlinearity of graphene has been greatly enhanced, and low-threshold optical bistability can be achieved with an incident wavelength red-detuning to the defect mode. The upper and lower thresholds of bistability increase with the increase in the value of low environmental temperature, while the interval between the upper and lower thresholds decreases. This research has a potential application in temperature-controlled optical switches and temperature-controlled optical memory.

This paper considers the event-triggered distributed fixed-time consensus control problem of leader-following multi-agent systems with nonlinear dynamics and inherent disturbances. First, an event-triggered distributed strategy, that is used to decide when to update states by agents, is proposed. Under the proposed strategy, each agent receives its neighbors’ state to make decisions only if the measurement error exceeds a certain threshold. Second, we design a nonsingular terminal sliding mode consensus protocol so that all followers reach the leader’s state in a fixed-time. Particularly, the gain in the consensus protocol is determined by the settling time, which makes devising and tuning the gain conveniently. Simulation examples are worked out to demonstrate the effectiveness of our theoretical results.

Two slabs of dielectrics with different values of refractive index are synthesized to form a composite structure and the whole system satisfies parity-time-reciprocal scaling symmetry. Four coherent-perfect-absorber-laser points are induced by modulating the incident wavelength of lightwaves and the loss/gain factor of materials. The locations of coherent-perfect-absorber-laser points in parameter space, which manifests the multi-wavelengths of coherent-perfect-absorber-lasers could be regulated by the incidence angle. Especially, a value of π phase shift in the transmitted/reflected light wave has been observed as well. This research has potential applications in multi-wavelength absorbers/lasers and half-wave phase shifters.

We numerically investigate asymmetric light propagation in chirped gratings with embedded graphene arrays (CG-GA). The structure comprises alternating graphene sheets and dielectric layers, featuring a linearly chirped spatial period. Using the forward transmission matrix method (FTMM), we demonstrate that CG-GA support multimode resonance. The transmittance of resonant modes exhibits a significant wavelength-dependent decay, ultimately reaching a cutoff. This phenomenon indicates the structure functions as a tunable optical low-pass filter, whose transmittance, cutoff wavelength, and bandwidth can be modulated by varying the number of grating periods, the chirped period gradient, and the graphene chemical potential. This study may be utilized for spectral scanning and adaptive optics applications.