The Measurement Of Small Displacement Based On High-order Traverse Modes

Precision measurement of transverse position of the laser beam have many important applications,including the atomic force microscope(AFM),satellite alignment,and optical tweezer,gravitational wave detection and so on.In these practical applications,through the interaction of the beam and the object we studied,a movement of the optical beam can reflect the mechanical movement of object we studied,which makes precision measurement of the lateral position of the beam is more meaningful.Therefore how to improve the sensitivity of displacement measurement become the focus of current researches.At present,there are two main research methods proposed to improve the measurement precision,one is to introduce multimode nonclassical light to reduce noise,and the other is to optimize the measurement setups.The high-order mode contains more information and freedom,which provide a new method to improve the precision of small displacement measurement.In this article,we mainly focus on the small displacement measurements of high-order Hermite-Gaussian beams.The main contents of this thesis as follows:1.Propagation and transformation properties of high-order Hermite Gaussian mode.In theory,high-order Hermite Gauss mode generation using a misaligned optical cavity are studied.In experiment,the high-order Hermite Gauss modes are generated using misaligned optical cavity.The Hermite-Gaussian mode propagation characteristics in free space and the imaging transformation of Hermite Gauss modes through the lens are calculated in theory.2.The small displacement measurements using high-order Hermite Gaussian mode.The small displacement of n-order Hermite-Gaussian mode is calculated in theory,the theoretical calculation indicates that the displacement information is related to the n-1 order Hermite-Gaussian mode and n+1 order Hermite-Gaussian mode,and as the order of mode is higher,the higher measurement precision can be obtained.In experiment,the optical small-displacement measurement for TEM10 mode are achieved with balanced homodyne detection,the experimental results demonstrate that the measurement precision using TEM10 signal mode and simple TEM20 mode local oscillator is improved about 3 dB relative to that of using TEM00 signal mode and TEM10 mode local oscillator,the measurement precision of using the superposition-mode local oscillator is improved about 1.7 dB relative to that of using simple TEM20 local oscillator for displacement measurement of TEM10 mode,attaining the quantum Cramer-Rao bound limit.The measurement method using high-order modes is applied to the tilt measurement,which improves the tilt measurement precision and provides theoretical reference for the next experiment.