Measuring the orbital angular momentum (OAM) of vortex beams, including the magnitude and the sign, has great application prospects due to its theoretically unbounded and orthogonal modes. Here, the sign-distinguishable OAM measurement in optomechanics is proposed, which is achieved by monitoring the shift of the transmission spectrum of the probe field in a double Laguerre-Gaussian (LG) rotational-cavity system. Compared with the traditional single LG rotational cavity, an asymmetric optomechanically induced transparency window can occur in our system. Meanwhile, the position of the resonance valley has a strong correlation with the magnitude and sign of OAM. This originally comes from the fact that the effective detuning of the cavity mode from the driving field can vary with the magnitude and sign of OAM, which causes the spectral shift to be directional for different signs of OAM. Our scheme solves the shortcoming of the inability to distinguish the sign of OAM in optomechanics, and works well for high-order vortex beams with topological charge value ±45, which is a significant improvement for measuring OAM based on the cavity optomechanical system.

测量涡旋光束的轨道角动量（OAM），包括幅度和正负号，由于其理论上的无界和正交模式而具有广阔的应用前景。在此，提出了在光力学中可区分符号的OAM测量方法，该方法是通过监视双Laguerre-Gaussian（LG）旋转腔系统中探测场的透射光谱的偏移来实现的。与传统的单个LG旋转腔相比，我们的系统中可能会出现不对称的光机械感应的透明窗口。同时，共振谷的位置与OAM的大小和符号有很强的相关性。这最初是由于这样的事实，即腔模与驱动场的有效失谐会随OAM的大小和符号而变化，这会导致频谱偏移针对OAM的不同符号而定向。我们的方案解决了无法区分光力学中OAM的符号的缺点，并且对于拓扑电荷值为±45的高阶涡旋光束非常适用，这对于基于腔体光力学系统的OAM测量是一个重大改进。