| The frequency measurement of the mercury-ion optical clock requires the high-precision femtosecond optical comb and the theoretically calculated reference frequency of the clock transition.The core component of the femtosecond comb is the mode-locked laser.As a kind of reliable pulse source,the polarization-maintaining mode-locked fiber lasers have been the focus of researchers.They have the advantages of stable operation and compact structure,and have become the ultra-fast laser sources widely used in science,medicine and industry fields.In this thesis,two kinds of passively-mode-locked mechanisms of the polarization-maintaining fiber lasers,namely the real saturable absorber（semiconductor saturable absorber mirror）and the artificial saturable absorber（nonlinear optical loop mirror,nonlinear amplifying loop mirror,and nonlinear polarization rotation）are carefully analyzed from the working principles to numerical simulations and experiments.For the semiconductor saturable absorber mirror（SESAM）,we build a linear mode-locked fiber laser with the SESAM.This simple linear cavity laser is easy to generate high repetition frequency pulses.However,because of the quality problem of the SESAM material,the mode-locking of the laser cannot be achieved.In order to study the mode-locked process of the laser based the real saturable absorber,we numerically simulate a ring fiber laser with the transmission-type saturable absorber,analyze the evolution of the pulses,and achieve the stable mode-locking.For the nonlinear polarization rotation（NPR）lasers,the mode-locking with all polarization-maintaining fiber is still in the research stage,only low-repetition-rate lasers can be implemented,so we only analyze the NPR non-polarization maintaining fiber laser.For the nonlinear optical loop mirror（NOLM）and nonlinear amplifying loop（NALM）schemes,we only perform a theoretical analysis of the NOLM,and mainly discuss the improved NALM.According to the shape of the NALM mode-locked lasers,they can be divided into the figure-8 and the figure-9 lasers.We numerically simulate a complex figure-8 all-normal-dispersion fiber laser,and analyze the pulse evolution processes,the pulse shapes,the spectral shapes and the chirp at different positions.However,the NALM figure-8 lasers have two fiber loops,which make their cavity is too long,the repetition rate is low,and self-starting is not easy to be achieved.For the NALM figure-9 lasers,we build a mode-locked laser with a beam splitter and the other with a polarization beam splitter.The former is an all polarization-maintaining fiber laser with a repetition rate of 99.77 MHz,a pulse width of 514.72 fs,and the output power of 7 m W,which enables self-starting and stable operation of mode-locking.The laser’s NALM is composed of a beam splitter,the passive fiber,a phase shifter,and the gain fiber,but we find that the loop with a phase shifter makes it difficult to further increase the repetition rate.Therefore,we have experimentally studied another NALM laser,and the phase shifter is moved out of the fiber loop and combined with the free-space optical path.The new loop is composed of a polarization beam splitter,the passive fiber,and the gain fiber.This structure increases the laser’s repetition rate to about 150 MHz,and at the same time solves the disadvantage that there is a loss at pulse peak in the previous scheme.In the process of further shortening the length of the fiber to increase the repetition rate,we find that the laser has a high threshold of mode-locked self-starting in the case of a short cavity length.Through theoretical calculation and analysis,it is found that the intra-ring wavelength division multiplexer（WDM）weakens the asymmetry of the loop and increases the loop length,which limits the continuous increase of the repetition rate.The highest repetition rate currently achieved in this scheme is only 250MHz.To solve this problem,we design a novel collimator combining WDM and gain fiber,and make a 5cm long microcavity structure to optimize the free-space optical path.Under the general fusion conditions,the laser can achieve a design repetition rate of 750MHz,which is three times the highest repetition rate of current lasers in the same structure,and exceeds the known maximum repetition rate of 700MHz achieved by the NPR scheme with the non-polarization-maintaining fiber.Besides,this special collimator creates conditions for two-end pumping,simplification in pump control,and high-energy pulse output.In addition,the related experiments of mercury-ion optical clock require theoretical parameters of specific spectral lines in different isotopes.Therefore,we use the GRASP2K program to calculate the isotope shifts of the 5d106s 2S1/2→5d96s2 2D5/2clock transition in mercury ions based on the multi-configuration Dirac-Hartree-Fock method,and obtain the isotope shifts of the transition.And we predict the absolute frequencies of clock lines for the seven natural mercury-isotope ions,which provides important theoretical parameters for experimental line measurements.The accuracy of our theoretical calculation is very high,and the error of the calculated clock transition frequency shift between 199Hg+and 198Hg+ions is only about 2%compared with the existing experimental measurements.Besides,in order to study the variation of mass shift term for heavy element ions in the high-Z range,The isotope shift parameters of the 2s2p 3,1P1→2s2 1S0 transitions in Be-like ions（70≤Z≤92）are calculated by using the multi-configuration Dirac-Hartree-Fock and the relativistic configuration interaction methods with the inclusion of the Breit interaction and the leading QED corrections.We find that the mass shift parameters of these two transitions do not change monotonously along the isoelectronic sequence in the high-Z range due to the relativistic nuclear recoil effects.Especially for the 2s2p 3P1→2s2 1S0 transition,there is a minimum value for the specific mass shift parameters around Z=80.By comparing the trend of the non-relativistic terms and the relativistic correction terms in the mass shift parameters along the isoelectronic sequence,it is found that the relativistic nuclear recoil correction needs to be considered in the calculation of the mass shift of heavy Be-like ions. |
