Investigation On Mid-infrared Fiber Optical Parametric Amplification By Vortex Beams Injected

Due to the unique optical properties,vortex beams have been used in many applications,such as optical tweezers,high-resolution imaging,atom manipulation,quantum and classical communications.Unlike ordinary beams,the mode phase distribution of vortex is not uniform,and the special phase distribution causes their isophase surface to be a spiral structure,which makes them have orbital angular momentum.In recent years,there have been many researches about the generation,transmission and detection about vortex beams.Among them,the vortex beams in fibers have higher mode purity and better transmission characteristics,so the vortex beams in fibers is one of the current research hotspots.Four-wave mixing（FWM）in fibers is a nonlinear parametric process,which can realize both wavelength conversion and signal amplification.The main work of this paper is to combine FWM theory with the OAM theory,so as to provide a theoretical basis for the vortex optical parametric amplification or wavelength conversion in the fiber.The main results are as follows:1)We design a photonic crystal fiber with sufficient mode isolation to ensure stable transmission and high mode purity of OAM_1,1 in the mid-infrared waveband（2-6μm）.At the same time,the phase-matching conditions of the FWM are optimized by designing the PCF structure.Finally,The HE₁₁mode in the 2.8-2.89μm is used as the pump wave,and OAM_1,1 in the 1.91μm waveband is used as the signal,and the OAM mode can be generated in the 5-6μm band.We use the finite element method（FEM）to calculate the vector overlap integral,we find that the idler and signal vector mode in the degenerate FWM are consistent.the Runge-Kutta method is used to obtain the FWM characteristics with the participation of the vortex beams,the signal gain spectrum and idler conversion efficiency of different fiber lengths（2.0-2.8 m）or pump wavelengths（2.80-2.89μm）are calculated,respectively.Our work demonstrates that the vortex beam at 5μm could be generated and its conversion efficiency can reach21.96%with appropriate optimization.2)We derive a novel degenerate FWM coupling amplitude equation and give an accurate FWM overlap integral form.We prove that the classic coupling amplitude equation and overlap integral are still useful when the pump is HE₁₁ mode and the signal light is OAM mode.Finally,the more general FWM process is discussed.When the OAM mode participates,the FWM needs to meet the conservation of orbital angular momentum and the conservation of spin angular momentum.This work provides a sufficient theoretical basis for the future experimental research.