Modeling of intracavity light field for the alignment criterion of cavity ring-down technique based on the angular spectrum propagation theory

In cavity ring-down technique,cavity maladjustment has essential effect on the measurement of intracavity loss.Several adjustment criterions had been introduced to achieve the optimal cavity state.However,experimental study has shown that these criterions may correspond to different cavity state,which means there is discrepancy between different criterions.In view of this problem,a model of intracavity propagation of Gaussian beam is established based on the angular spectrum propagation theory.This model is tested by numerical simulation and experimental research together.In the simulation,the true value of intracavity loss can be known beforehand.The two-dimensional angular scanning is carried out for certain cavity mirror.The two-dimensional distributions of the measure value of intracavity loss and the transmission light intensity are obtained simultaneously.These distribution are both nonlinear and multi-extremum,which will doubtlessly increase the difficulty of cavity adjustment.By comparing the distribution results,we do find the discrepancy between the largest transmission light intensity and the least measured intracavity loss.Meanwhile both of these two states may be not corresponding to the true value in fact.After statistical studies,the relative error of the least measured intracavity loss is-37.01±11.79ppm,whereas the relative error of the largest transmission intensity is-2.70±0.89ppm.The criterion of the largest transmission intensity shows better stability and repeatability.This model is further tested in a folded cavity ring-down setup.The similar scanning procedure in carried out.A major problem in the experiment is that the true value of intracavity loss cannot be known.So only the repeatability precision of the measured intracavity loss can be analyzed.The statistical results of the largest light intensity and the least measured intracavity loss are ±29.32ppm and ±70.71ppm,respectively.The criterion of the largest transmission intensity has better repeatability,which is basically consistent with the simulation result.In this way the rationality of this model can be verified to some degree.In this paper,the criterion of the largest transmission intensity is recommended in the cavity ring-down technique.Furthermore,this model can be a reference to the research of intracavity optical field response,intracavity optical field transmission,and the unstable resonator alignment,etc