Based on the transfer-matrix method, we theoretically explore the transmission and reflection properties of light waves in a one-dimensional defective photonic crystal composed of superconductor (HgBa₂Ca₂Cu₃O_8+δ) and semiconductor (GaAs) layers. The whole system is centrosymmetric and can generate a defect transmission peak in the photonic band gap. We study the effect of the temperature on the defect mode. Results obtained show that the defect mode shifts to the lower frequency regions as the value of the environmental temperature increases, and the resonance of the defect mode can be strengthened further as the number of periods increases. In addition, our findings reveal that the central wavelength of the defect mode increases with the increase in the environmental temperature and it presents a nearly linear relationship between the central wavelength of the defect mode and the temperature in cryogenic environments. Therefore, we can use the temperature response of the defect mode to detect the temperature. It is hoped that this study has potential applications for the development of cryogenic sensors with high sensitivity.

We theoretically investigate the tunable dual- and multi-channel filter in one-dimensional aperiodic photonic crystals (PCs) embedded with graphene. The dielectrics slabs arrayed alternately submit to the Cantor sequence rule and graphene sheets are local at the interfaces of dielectrics layers. Cantor PCs are fractal structures and support a series of discrete resonant channels in transmission spectra, viz . fractal states. Consequently, dual- and multi-filtering channels could be achieved in the compound systems. The central wavelength of each channel and its value of transmission could be modulating by the chemical potential of graphene and the incident angle as well. It shows that the dual-channel amplitude of transmission can be varied by over 100% and the multiple channels could be switched on and off by the chemical potential of graphene. This study will be very helpful in designing tunable optical filters.

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.

We theoretically investigate the defect mode transmittance of light waves in superconductor–semiconductor photonic crystals and its pressure-sensing dependence. The photonic crystal is composed of alternating superconducting and semiconducting slabs and a defect locates at the center of this structure. Two trapezoid waveguides are fixed at both sides of the crystal, which induces the hydrostatic pressure applied and beams transmitted simultaneously. The resonant wavelength variation in the defect mode is directly proportional to the pressure applied on the system in the near-IR region, which can be utilized for linear pressure sensors in the cryogenic environment. Pressure sensitivity reaches a high value of 2.6 nm/GPa, which is higher than that in the study based on the reflection spectra. The sensitivity coefficient may be modulated by the environment temperature as well. This study has potential regarding pressure-light-wave sensors.