Beam waist dependence in mode projection of Hermite-Gaussian beams

Abstract

We report a significant factor that affects the mode spectrum in the projection of Hermite-Gaussian (HG) beams: the beam waist. In this study, we show analytically that beam waist mismatch invalidates the orthogonality condition in the coupling coefficient of HG modes, signifying a distortion in the mode spectrum of the beam. We demonstrate experimentally the beam waist dependence using spatial mode projection. Initially, we projected a series of rotating beams to optimize optical alignment, ensuring that any substantial distortion in the mode spectrum is solely due to beam waist mismatch. Subsequently, we projected higher-order HG modes onto a purely Gaussian mode, and recorded the resulting intensity of the projections. Results show that even modes in the spectrum have gained significant intensity weights due to the beam waist mismatch. Furthermore, the dependence of the coupling coefficient on the increasing ratio of the beam waists reveals a substantial decrease in intensity. These findings underscore the importance of precise beam waist matching to minimize power or information loss in mode coupling applications.