Research On Supercontinuum Generation In Photonic Crystal Fibers Via Manipulating Optical Rogue Wave

When a long pulse?e.g.,subpicosecond,picosecond,nanosecond or even a continuous wave?is pumped in a fiber anomalous dispersion region,the low-amplitude random noise at the input will be amplified by modulation instability,which causes a large fluctuation in the amplitude and pulse width of fundamental solitons generated by high-order soliton fission.Since these fundamental solitons have different peak power and pulse widths,there is a large difference in their group velocity,resulting in the collision between these solitons to occur.Soliton collision leads to the energy of fundamental soliton with the low peak power transferred into the fundamental soliton with the high peak power,which finally helps the formation of the optical rogue wave?RW?with ultra-high intensity and extreme-large red-shift.Optical RW is featured as a low-probability event generated at the long wavelength of SC spectrum,which seriously degrades the SC spectral coherence and stability as well as flatness.Therefore,how to improve the performance of SC sources by effectively regulating the generation of optical RW has gradually become an important research topic in the field of nonlinear optics.Photonic crystal fiber?PCF?with flexibly adjustable dispersion and nonlinear characteristics is regarded as a good transmission platform for studying the controlled generation of Optical RW.Based on the effective manipulation on optical RW,people can determine whether to generate or suppress the RW according to the demand on the SC sources.Moreover,optical RW with the ultra-high intensity and extreme-large red-shift contributes to realize the selective excitation of SC sources,namely generating the high-intensity spectral components at the specific long wavelength or even mid-infrared bands,so as to provide an alternative scheme for the efficient excitation of all-fiber tunable mid-infrared SC sources.In this paper,we numerically studied the controlled generation of optical RW via pumping a subpicosecond optical pulse modulated by a seed pulse with the suitable modulation frequency and modulation depth in the fiber anomalous dispersion region.The main work is summarized as follows:1.According to the quantum theory,the generalized nonlinear schr?dinger equation including spontaneous Raman scattering noise is derived when the random noise is considered,which is used to study the generation of optical RW under the long pulses pumping.At the same time,the split-step Fourier algorithm and the technique based on the short-time Fourier transform algorithm for the SC time-frequency analysis are briefly introduced.At last,the interaction between solitons,between soliton and dispersive waves,and between optical RW and dispersive waves during SC generation in fibers are described in detail.2.We studied the generation of optical RW and SC when a subpicosecond pulse modulated by a seed pulse with different modulation frequencies and modulation depths is pumped in the anomalous dispersion regime of a silica PCF.In contrast with noise-induced modulation instability,modulation instability induced by a seed pulse with the optimum modulation frequency can significantly improve the statistical probability of optical RW generation and contribute to the generated optical RW with a more stable intensity and concentrated time delay as well as red-shift to a longer wavelength.In addition,output optical RW can gain a higher intensity and be produced in the fiber with a shorter transmission distance when the seed have a more suitable modulation depth.These simulation results show that in contrast with noise-induced modulation instability,modulation instability induced by a seed with the suitable modulation frequency and modulation depth can suppress the random noise effect and make the optical RW generated at the long wavelength of SC spectrum in a more controlled manner,which provide a new insight for the generation of tunable long-wavelength spectral components and selective excitation of mid-infrared SC.3.We studied how to harness optical RW by a cascaded PCF to solve the uneven energy distribution of output SC spectrum,which finally helps extend the bandwidth and improve the flatness of output SC spectrum.The cascaded PCF consists of two stages,the first stage of which is a PCF with one zero dispersion wavelength and the second is a PCF with two zero dispersion wavelengths.In the first-stage PCF,a subpicosecond optical pulse modulated by a seed pulse with the optimum modulation frequency is pumped in the anomalous dispersion region,which suppresses the random noise effect and contributes to the optical RW with a high intensity and a large redshift generated in a controlled manner.In the second-stage PCF,optical RW generated in the first-stage PCF is converted into different wave forms by adjusting the position of its second zero dispersion wavelength.When the second zero dispersion wavelength of the second-stage PCF is located at a shorter wavelength,optical RW generated in the first-stage PCF directly enters the normal dispersion region of the second-stage PCF and then is converted into the form of dispersive waves,resulting in the improvement in the output SC spectral flatness.When the second zero dispersion wavelength of the second-stage PCF is located at a longer wavelength,optical RW generated in the first-stage PCF directly enters the anomalous dispersion region of the second-stage PCF and then continues to redshift under the action of Raman effect.When optical RW reaches the second zero dispersion wavelength,it will stop the redshift under the combined action of Raman effect and spectral recoiling effect as well as radiates the red-shift dispersive wave into the normal dispersion region via the cross-phase modulation when meeting the phase matching condition,resulting in the output SC with a broader spectral bandwidth.4.We studied how to enhance the spectral power density at mid-infrared wavelength and further expand the mid-infrared SC to a longer wavelength by effectively regulating the generation of optical RW with a high intensity and a large redshift.Since the PCF made of soft glass material contributes to the SC spectral range extended from visible to ultraviolet and mid-infrared band,we numerically studied the generation of optical RW and mid-infrared SC when a subpicosecond optical pulse modulated by a seed pulse with the suitable modulation frequency and modulation depth is pumped in the anomalous dispersion region of a As₂Se₃chalcogenide PCF.By carrying out multiple simulations in the presence of random noise,we showed that optical RW can be generated in a more controlled manner by providing a seed with an optimum modulation frequency,which improves the spectral stability of the generated mid-infrared SC.In contrast with noise-induced modulation instability,the seed-induced modulation instability can contribute to the generated optical RW with a larger redshift range and a higher intensity,which helps improve the signal to noise ratio of long-wavelength spectral components and extend the mid-infrared SC spectrum to a longer wavelength.Moreover,the increase of pump power can facilitate the redshift of optical RW and expand mid-infrared SC spectral bandwidth.