Nonlinear Evolution Mechanism Of Optical Field In A Microcavity And Theoretical Research On Kerr Optical Frequency Comb

Microcavity-based optical frequency combs(OFCs)have potential applications in the areas of astronomical spectroscopy,arbitrary optical waveform generation and coherent terabit communications.The thesis involves the nonlinear evolution of the optical field and frequency comb generation in a high Q optical microcavity.The researches present here mainly includes nonlinear evolution of intensity-modulated steady-state continuous light field and frequency comb generation in a microcavity with anomalous dispersion,formation of various dark pulse and their corresponding comb spectra from normally dispersive microcavities and repetition-rate-selectable,low threshold dual-pumped microcavity OFCs generation.The main researches and conclusions obtained are summarized as follows:The nonlinear evolution of intensity-modulated steady-state continuous light field relating to the generation optical frequency combs in a microcavitywith anomalous dispersion are studied theoretically.The research results show that a single-free spectral range(FSR)comb arises when a dissipative soliton pulse or multiple nonequidistant soliton pulses form in the cavity.The comb spectrum of a single soliton is regular and exhibits a triangular profile.The comb structure of the unevenly distributed multiple soliton pulses is complex and the intensity fluctuations of the spectral lines are irregular.When the stable intracavity field consists of a “roll” Turing pattern or N(N>1)evenly distributed soliton pulses,multi-FSR combs can be generated.In the case of “roll” Turing pattern solution,we found that the number of rolls and comb mode spacing decrease with the amplitude increase of the group velocity dispersion.For the situation of multiple soliton pulse generation,the calculation results indicate that the number and locations of thesoliton pulses as well as the comb mode spacing can be controlled by adjusting the modulation frequency.When the frequency of the pump laser is smaller than that of the corresponding microcavity resonance,formation of stable dark soliton and various kinds of dark pulses in normally dispersive microcavities are investigated by numerically solving the normalized Lugiato-Lefever equation.The soliton essence is proved by fitting the calculated field intensity profile to the analytical formula of a dark soliton.Meanwhile,two routes to a stable dark soliton generation are indentified including the nonlinear evolution of an optical shock wave and narrowing of a locally broad dark pulse with smoother fronts.Based on the connections between the optical shock wave and the steady-state continuous wave solutions,explicit analytical expression is derived to describe the oscillatory fronts of the optical shock wave.Furthermore,based on the calculation results and theoretical analyses,we show that for a frequency detuning of ?<3,in addition to the dark soliton formation,various kinds of dark pulses with different intensity profiles can also arise and propagate stably in the microcavity under proper pump detuning and pump strength combination.The existence region together with the field intensity profiles and the corresponding comb spectra of dark soliton and dark pulses are obtained by means of numerical calculation.Repetition-rate-selectable,low-threshold dual-pumped microcavity OFCs are theoretically investigated.OFCs and their temporal characteristics corresponding to different pump power levels are studied by numerically solving the driven and damped nonlinear Schr?dinger equation.The calculation results indicate that an ultralow coupled pump power is required to excite the primary comb modes through non-degenerate four-wave mixing(FWM)process.Because of the high intensity contrast between the pump mode and the sidebands,the temporal intensity profile is dominated by the beating of the two pump fields and thus exhibits a cosine variation manner with the frequency equal to the separation of the two pumps.When the pump power is boosted,both the comb modes intensities and spectral bandwidth increase.Instead a cosine waveform,a “roll” Turing pattern is formed in the microcavity at high pump powers.Meanwhile,the calculation results show that the power difference between the two pump fields can be transferred to the newly generated comb modes which are located symmetrically on both sides of the pump modes through cascaded FWM process.The spectral and temporal characteristics of the dual-pumped OFCs are further proved through comparisons with the experimentally measured results.When the pump powers are below the optical parametric oscillation threshold,the numerically calculated OFCs spectra with 1.47-THz(30 FSR)and 1.96-THz(40 FSR)mode spacings accord well with the experimentally measured ones.In addition,the forming of a “roll” Turing pattern at high pump powers is inferred from the experimentally measured autocorrelation trace of a 10-FSR OFC(mode spacing 0.49 THz).