Precision measurement plays a very important role in many field including optics, astronomy, biochemistry, atmospheric science, environmental engineering, dusty plasma, etc. Here, we propose an efficient scheme to investigate the relationship between linewidth and radius of the metal nanoparticle (MNP) in a hybrid optical microcavity system that included a quantum emitters interacting with a MNP. By using detailed numerical simulations and analytical modeling, we find that the linewidth of the amplification window is sensitive to the radius of MNP. Subsequently, we discuss the application of such a hybrid optical microcavity system as a family of high-sensitivity sensor for measuring the tiny radius of the MNP. Using experimentally achievable parameters, we identify the detection sensitivity of the sensor can arrive at approximately 2.6 GHz nm⁻¹. The present investigation provides a route toward guiding the design of sensitive devices.

精密测量在光学，天文学，生物化学，大气科学，环境工程，多尘等离子体等许多领域中都扮演着非常重要的角色。在这里，我们提出一种有效的方案来研究金属纳米粒子（MNP）的线宽和半径之间的关系在混合光学微腔系统中，该系统包括与MNP相互作用的量子发射器。通过使用详细的数值模拟和分析模型，我们发现放大窗口的线宽对MNP的半径敏感。随后，我们讨论了这种混合光学微腔系统作为高灵敏度传感器系列在测量MNP微小半径方面的应用。使用实验可达到的参数，我们确定传感器的检测灵敏度可以达到大约2.6 GHz nm^-1。本研究提供了指导敏感设备设计的途径。