Transmission characteristics of optical resonator
Authors: Wang Ya-Jun , Wang Jun-Ping , Zhang Wen-Hui , Li Rui-Xin , Tian Long , Zheng Yao-Hui ,   State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China,   Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
Published: August 2021

Quantum noise has become an important limiting factor in the application of precision measurement, and its relevant problems have become a research hotspot. As an important optical device to manipulate quantum noise, the optical resonator possesses the transmission characteristics that determine the evolution characteristics of output signal’s noise. According to their impedance matching factor <i>a</i> values, the resonators can be divided into three categories: over-coupled cavity for <inline-formula><tex-math id="M1">\begin{document}$a \in [ - 1, 0)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20210234_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20210234_M1.png"/></alternatives></inline-formula>, impedance matched cavity for <inline-formula><tex-math id="M2">\begin{document}$a{{ = }}0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20210234_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20210234_M2.png"/></alternatives></inline-formula>, and under-coupled cavity for <inline-formula><tex-math id="M3">\begin{document}$a \in (0, 1]$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20210234_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20210234_M3.png"/></alternatives></inline-formula>. When the resonator fully meets the resonant conditions, its output field can be regarded as a low-pass filter, the high-frequency noise is directly reflected. The high-frequency noise at the output end is greatly suppressed, and the noise at the frequency far larger than the linewidth reaches the shot noise standard. Therefore, the noise of the optical field beyond the linewidth range can be greatly suppressed by the narrow linewidth optical resonator. At the same time, from the three kinds of optical resonator phase diagrams it can be found that the over-coupled cavity is in a state of half a detuning and the sideband frequency phase rotates ± 90° relative to the carrier frequency. In this case, the phase noise of light field can be converted into amplitude noise by an over-coupled cavity, which can be used for the phase noise measurement or squeezing angle rotation of squeezed light and has important applications in analyzing the laser noise component and manipulating the quantum noise. At the same time, the energy loss of the over-coupled cavity is the largest among the three types of cavity structures. Through theoretically analysing the corresponding relation among optical resonator output intensity, phase and frequency, and by making a comparison of comparing transfer function, energy transmission, spectrum characteristics of noise transmission among over-coupled cavity, impedance matched cavity and under-coupled cavity, in this paper the power splitter, frequency filtering, and noise transformation features of the optical resonator are demonstrated. The analysis results in this paper provide a basis for applying various optical resonators to different occasions, and promote the development of using the optical resonators to control the quantum noise of light field and improving the precision of precision measurement.