Research And Designing Femtosecond Fiber Laser Systems Based On The Principle Of Space-Time Duality In Optics

Mathematically,the space-time duality in optics originates from the wave properties of light,which is derived from the mathematical symmetry of the wave equation.This duality is embodied in the correspondence between the temporal and the spatial properties of optical propagation,and the time domain counterparts of the ordinary spatial optical components and optical systems derived therefrom.Photon chromatography is a time domain correspondence phenomenon of Fraunhofer diffraction,and time lens is a time domain corresponding device of spatial lens,which can be regarded as a derivative of photonic chromatography principle.Rare events contain a wealth of system information.Therefore,observing these rare events is an important method to study the characteristics of the system.Because of the unpredictability of rare events,it is very challenging to observe them.Rare events in optics are often not only difficult to capture,but also extremely fast.Observing them requires the use of photonic chromatography techniques based on optical spatiotemporal symmetry.Based on the principle of photon chromatography,we build a photon chromatography system with a spectral resolution of 0.69 nm,a free spectral range of 69.4nm,and a frame frequency equal to the repetition frequency of the lasers to be observed.We use this system to observe the mode-locking start-up process of a saturable absorber mode-locked Erbium doped femtosecond fiber laser with a repetition frequency of 39.5807 MHz,and analyze the observed phenomena by the mode-locking theory of saturable absorber.We also carry out a numerical simulation of the modelocking start-up process,and the results obtained reflect the characteristics of the key parts of the mode-locking process.Based on the imaging principle of time lens,a design method of chirped pulse amplification system can be proposed,in which the time lens is derived from the selfphase modulation effect,which is the corresponding effect of the self-focusing effect in the time domain.According to this method,an Erbium doped fiber chirped pulse amplification system is designed to realize the amplification of single pulse energy from 46.5 pJ to 2nJ,and the compression of pulse duration from 389 fs to 82 fs is realized.The actual output pulse duration is different from the design value by 12 fs.This verifies the reliability of this design method.