We suggest a flexible control of the diffraction grating by considering an optomechanical cavity system. The cavity is driven by an external control standing wave and realizes the characteristics of the diffraction grating when the light beam interacts with the cavity, a phenomenon which we name optomechanically induced grating (OMIG). A standing wave consists of nodes and antinodes that lead to gratings or slits in the cavity system. The reflected probe field from a moving mirror is diffracted through a standing wave and comes out through a partially reflected mirror. Effective control of the diffraction grating is achieved with the manipulation of the optomechanical strength g mc ( the so-called mirror-light interaction strength). Fascinatingly, the first, second, and third-order diffraction gratings can be easily achieved via the mirror-light interaction strength g mc . The diffraction grating is found to be influenced by the cavity decay rate. For small values of the decay rate, the diffraction grating becomes maximum and vice versa. The results of our model can bring potential applications in optomechanical systems.

The magnitude enhancement of the Goos-Hänchen shift (GHS) in reflected light (RL) is investigated. We consider a cavity in which a four-level atomic medium with a double lambda (Λ)-type configuration is contained. By changing the relative phase φ of optical fields in the four-level atomic configuration, we obtain normal and anomalous dispersions. Similarly, the manipulation of the positive and negative GHS in the RL is explored via the control of the relative phase. In addition, we investigated the GHS in the RL with and without the Doppler broadening (DB) effect. Interestingly, giant GHS in the RL is revealed for the DB medium. The role of the Doppler width on the magnitude of the GHS in RL is also studied. We find that the magnitude of the negative and positive GHS in the RL increased via increasing the Doppler width.

Nonlinear interactions between optical fields and magnetic modes in cavity magnonics constitute a rich source of various nontrivial effects in optics and quantum information processing. In cavity magnonics, biased ferromagnetic material exhibits both magnetostatic and Kittle modes due to field inhomogeneity. Here, we propose a scheme for the investigation of probe field transmission profiles in cavity magnonic systems composed of a microwave cavity and a ferromagnetic material (yttrium iron garnet sphere). We report single-to-double magnon-induced transparency (MIT) dips and a sharp magnon-induced absorption peak, and demonstrate how nonlinear cross- and self-Kerr interactions can significantly enhance or suppress these phenomena. It is observed that the splitting of the MIT window occurs when we incorporate magnon–magnon mode coupling, which helps to introduce a degree of freedom to light–matter interaction problems. Moreover, we investigate the propagation of group delay in the vicinity of transparency and demonstrate how a sharp dip allows the realization of slow light for a longer period of time. We found that both the cavity–Kittle and magnon–magnon mode coupling parameters influence the propagation of group delay, which demonstrates how subluminal-to-superluminal (and vice versa) propagation phenomena may occur and transform. These findings could pave the way for future research into nonlinear effects with novel applications in cavity magnonics devices, which might be exploited for several applications such as quantum computing devices and quantum memories.