Analysis and alignment of the light path of Gauss beam matched to the fundamental mode ofan optical resonator

In order to reduce the influences of misalignment parameter and mismatch parameter on measurement based on optical resonator, the influence on the coupling efficiency of a source laser is stabilized to a fundamental cavity mode, and two limiting cases are analyzed and derived by using conversion of Gaussian beam, mode coupling theory and coordinate transformation theory, including the expression of coupling efficiency of fundamental cavity mode as two limiting cases emerge simultaneously. Analyses show that for mismatch parameter, only even-indexed Hermite-Gaussians beam is excited; for misalignment parameter, there exists an effect on the proportion of Hermite-Gaussians beam, which should bring about serious measurement error. These optical signals provide the error signals which are minimized. By taking the laser line width into account, we propose two methods for real time alignment of a Gaussian beam for an optical resonator perfectly coupled system: Fabry-Perot electro-optic sensors of a misadjusted system and control loops system depends on detecting emergent light of cavity via multi-dimensional quadrant detector. All of these will provide a theoretical direction for analyzing the measurement error and improving the measurement accuracy.