Investigations On The Egienmodes And Output Properties In Nonplanar Ring Resonators

As a new generation of inertial navigation device,the ring laser gyro(RLG)with nonplanar structure(a nonplanar ring resonator is a closed polygonal ring,in which all the segments do not lie in a single plane)for establishing and splitting the frequencies of the left-and right-handed circularly polarized modes instead of using quartz crystal,which can induce the effective bias of a gyroscope but also induce backscattering and loss.Furthermore,being fully autonomous,highly accurate and reduced the ellipticity of the eigenmodes,the nonplanar structure RLG are almost ideal navigation devices which are motivating ongoing interest of the people.As the core component of the RLG,the nonplanar structure makes RLG present very interesting particularities different from the ordinary coplanar ring cavity.Because there are mutual orthogonal oppositely traveling wave modes(left-and right-handed circularly polarized modes)of oscillation in it and the evolution of eigenmodes will produce an obvious influence on the precision of the RLG.Therefore,the analysis on the evolution of eigenmodes polarization,axis perturbation,and the relationship between output frequency difference and the eigenmodes polarization is important to improving the precision of the RLG.The analysis in the thesis can provide a theoretical basis and technical guidanceare usefully for designing and arranging the diaphragm in ring resonators with a nonplanar structure,as well as optimizing the structure of the resonators themselves,as well as improving the precision of the nonplanar RLG.In this thesis,we first analyze the evolution of the eigenmode polarization and frequency difference theoretically and numerically based on the transfer matrix and Fresnel-Kirchhoff diffraction integral.Then present the evolution of optical axis perturbation in case that there are multiple parameter errors existed.Finally,we also analyze the influences of the slight nonplanar effect on the magnetic sensitivity by means of theoretical analysis and numerical simulation.The main contents are as follows:(1)Analyzing the propagation properties(the size of the elliptical cross section of the eigenmodes,the azimuths of the beam cross section and the phase contour,the wave-front radius)of the eigenmodes throughout the nonplanar ring resonators with different structures theoretically and numerically.According to the satisfactory cross section size of the laser beam,the beam waist in these nonplanar ring resonators is founded,and the three dimensions stability space of these resonators are also presented.According to the evolution of the beam cross section azimuth,we also present the physical nature of evolution of the azimuth of eigenmode cross section in the resonator by view of the lens imaging.(2)We firstly establish the relationship between the eigenmode polarization and the output Sagnac frequency difference in nonplanar ring resonators based on the optical transform matrix.Then influence of the eigenmode polarization deviation(described with ellipticity parameter)on the output Sagnac frequency difference is analyzed for different incident angles and rotation axes in two resonators.The theoretical and numerical analysis results turn out that,the additional eigenmode polarization deviation in the resonators will induce a drop of the output Sagnac frequency difference.(3)Combining with the self-consistent condition,we present the evolution of the frequency spectrum for different order of eigenmodes in nonplanar ring resonators based on the transfer matrix and Fresnel-Kirchhoff diffraction integral.Taking the modes TEMq0,TEMq10,and TEMq01 with different polarization states as examples,we numerically derive the frequency difference versus the resonator structure parameters by considering the polarization and the light field distribution of the eigenmodes synchronously.Furthermore,we also prove that the method that modulating the beam phase is useful for improving the beam quality by Fast Fourier Transformation.(4)For the case of the reflection error,the position error and the angle error of the mirror,we analyze the evolution of eigenmode polarization and optical perturbation in the resonator by statistical method.According to these analyses,we also provide the method to judge the stability of a resonator from the perspective of eigenmode polarization and optical perturbation besides the beam size quantificationally.(5)Based on the relationship between the slight nonplanar angle and the eigenmode polarization rotation,we analyze the output frequency difference and the magnetic sensitivity in total reflection prisms(TRP)ring resonator with different slight nonplanar angles theoretically and numerically.The results show that the slightly nonplanar effect will bring an additional ellipticity of the eigenmode and the environment magnetic field can produce an additional output frequency difference in a TRP ring laser resonator.