Theoretical Analysis and Numerical Simulation for Cavity Ring‐Down Spectroscopy

Abstract

To investigate the process of the creation of the ring‐down events in cavity ring‐down spectroscopy, theoretical formulae are derived for the interaction of the field in a cavity with the injection light, and a corresponding program for numerical simulation is developed. Using these theoretical formulas, the effects of the frequency detuning between the injection and the cavity mode, the absorption of the medium in the cavity, the residual injection, and the oscillation of the high‐order transverse modes are analyzed. A specific method for improving the measurement of the ring‐down time is proposed. With numerical simulation, the phenomenon of the intensity modulation during the frequency coupling of the cavity mode with the injection light is investigated. As the coherence of the injection light degrades, the light distribution in the cavity gradually develops from a smooth state to random states. Finally, it converges to a state at which the injection light is incoherent. The simple experimental results confirm that the limited coherence of the injection light causes the randomness of the development of the cavity field, and the results are used for the demonstration of the effectiveness and accuracy of the proposed method in solving for the ring‐down time.