The typical nonlinear phenomenon in cavity optomechanical system is optomechanically induced transparency (OMIT), which is similar to the electromagnetically induced transparency phenomenon in atomic systems. OMIT is theoretically demonstrated and explained by Agarwal and Huang and experimentally discovered by Weis. Over more than a decade of continuous and in-depth research, a series of important and novel phenomena based on OMIT have been identified, such as ideal OMIT, non-reciprocal OMIT, nonlinear OMIT, vector OMIT, multiple OMIT, higher-order OMIT, non-inverse OMIT, topological OMIT, parity-time (P-T) symmetric OMIT, and dark-mode OMIT. Under the rotating wave approximation, achieving an OMIT transparency window with both depth and narrow width presents a significant technical challenge. Although the depth of the transparent window can be increased by raising the power of the drive field, this approach inevitably results in the simultaneous widening of the transparent window. In addition, the mechanical resonator damping rate fundamentally limits the maximum attainable transparency depth. Fortunately, the recent development of ideal OMIT offers a groundbreaking solution to this long-standing challenge. Even in the presence of mechanical resonator damping, ideal OMIT takes advantage of the unique physical properties of the non-rotating wave approximation effect, enabling the simultaneous realization of a transparency window with large depth and narrow width. Since ideal OMIT shows a significant difference compared to traditional OMIT at the transparent window, it holds an inherent advantage for applications such as optical storage and optical delay. By integrating more mechanical or optical subsystems into cavity optomechanical systems, OMIT has been observed not only in standard systems but also in multi-channel cavity optomechanical systems, such as those containing multi-level atomic ensembles, charged systems, topological systems, P-T symmetric systems, multi-channel mixed cavity photomechanical systems, and other Laguerre-Gaussian (L-G) cavity optomechanical systems. This expansion into a hybrid platform demonstrates the adaptability of OMIT. However, the phenomena of ideal OMIT, optomechanically induced gain, and slow light based on OMIT have yet to be explored in double L-G rotational cavity optomechanical systems. Motivated by the significant advancements in ideal OMIT and L-G cavity optomechanical systems, as well as their potential applications, we investigate the phenomena of ideal OMIT, optomechanically induced gain, and slow light based on OMIT in a double L-G rotational cavity optomechanical system that includes both linear coupling effects and orbital angular momentum exchange.

In this paper, we begin with an introduction to the model of the double L-G cavity optomechanical system model (Fig. 1). The system’s composition is analyzed, consisting of two fixed mirrors and one rotational mirror. The system is driven by both a weak probe field and a strong driving field. The definition of each parameter is then provided. The Hamiltonian equation of the system is derived, and it is solved using the Heisenberg equations of motion, factorization, and both the rotating and non-rotating wave approximation effects. Using the input-output relationship for the cavity, real part (absorption) expressions for the output fields are derived under both the rotating wave approximation and the non-rotating wave approximation. By comparing the two expressions, significant differences are revealed: the expression under the non-rotating wave approximation includes an additional term, denoted as N. This N term introduces distinct physical effects that modify the quantum interference behavior of the system, forming a key mechanism for achieving ideal OMIT. With the help of N, the conditions for ideal OMIT are derived. Notably, ideal OMIT can be realized even when the mechanical resonator damping rate is non-zero or large, provided the conditions are satisfied.

Based on the real part expression, the optical response of the probe field in the double L-G rotational cavity optomechanical system is systematically analyzed. Key conclusions are as follows. First, in both the unresolved and resolved sideband regimes, the effects of the non-rotating wave approximation and rotating wave approximation on OMIT are discussed (Fig. 2). The non-rotating wave approximation method can realize ideal OMIT in both regions. The N term plays a crucial role in achieving the ideal OMIT. It can be seen as a highly controllable optical switch to enable the conversion between OMIT and ideal OMIT. Further analysis is conducted on how the coupling strength between the two cavities affects the ideal OMIT window, particularly its width and position (Fig. 3). Second, when the system is driven by red detuning, the optomechanically induced gain can still be achieved (Fig. 4). The gain increases with enhanced coupling strength between the two cavities. Third, slow light can be realized based on ideal OMIT (Fig. 5). It is found that the slow light phenomenon depends on the coupling strength between the two cavities. Thus, the characteristic variation of slow light at the transparent window with varying coupling strength is further discussed (Fig. 6).

In this paper, we propose a scheme for achieving ideal OMIT, optomechanically induced gain, and slow light phenomena based on OMIT in a double L-G rotational cavity optomechanical system that includes linear coupling effects and orbital angular momentum exchange. These phenomena are of great importance. The proposed scheme provides a reference for experimentally realizing ideal OMIT and slow light, offering new insights for the development of L-G rotational cavity optomechanical systems.