Theoretical Research On Modal Phase Matched One-third Harmonic Generation In Microfibers

Nonlinear optics is a new branch of optics that develops rapidly wit h the emergence of laser technology.It has become the physical foundation of many important technology applications.Among them,the optical parametric down-conversion(OPDC),in which the high-frequency pump light is converted into a low-frequency signal light,can be used to prepare new wavelength laser to meet the requirements of traditional laser technology,such as mid-infrared laser.Furthermore,the OPDC has been the main technical method to prepare the multi-photon entangled state,which is the basis of quantum information science.Recently,the stimulated third-order parametric down-conversion(TOPDC)process with the degenerated frequency has attracted a lot of research attentions,which is also known as the one-third harmonic generation(OTHG)due to the three down-converted photons share the same frequency that equals to the one-third of the pump frequency.Although the phase matching condition of OTHG process has been demonstrated to be satisfied by the modal phase matching technology provided by waveguides,the relevant theoretical exploration is insufficient,especially the influence of attenuation on the intensity and relative phase thresholds to support the OTHG process has not been researched.The variation of phase matching condition alo ng the propagating path is also not fully considered.This thesis aims to establish the OTHG coupling theory in phase matched silica microfibers with attenuation considered,analyze the limitation of attenuation on OTHG conversion,and propose solutions to overcome the restrictions to improve the OTHG conversion efficiency.By doing this,we hope to provide constructive theoretical guidances for the experimental realization of OTHG.Along the line of influence of attenuation on OTHG process,this thesis carries out following studies:The nonlinear coupling transmission theory of OTHG process in silica micro-fibers with attenuation is established.All the third-order nonlinear polarization terms related to the pump and signal frequencies are brought into the Maxwell equations,then the coupled mode differential equations(CMDEs)with attenuation considered can be derived by mode field normalization.The modal dispersion distributions of the two interacting fields with different frequencies in silica microfibers are studied.The phase-matched modes that are most beneficial to the nonlinear energy transfer in OTHG process are selected based on the overlap integrals of the corresponding modes,which lay a foundation for the following researches.The influences of attenuation on the optical field intensity threshold,phase threshold and the phase matching condition during the propagation are discussed.By simplifying and separating the CMDEs expressed by complex amplitudes,the influences of the attenuration on OTHG and its inverse process are systematically analyzed.It turns out that the attenuation increases and decreases the intensity threshold and the effective range of relative phase,respectively.On the basis of the perious analysis,the definition of coherent length describing the phase matching degree for optical parametric processes is optimized.With the help of optimized coherent length,it is demonstrated that the perfect phase matching condition of OTHG process cannot be maintained over the propagating path in the uniform microfiber designed by the traditional modal phase matching technique.The phase mismatch causes periodic changes of relative phase between the effective and ineffective ranges,resulting in round-trip energy transfer between the pump and signal modes,which limites the maximum conversion efficiency of OTHG process.A phase matching scheme based on modulating the modal dispersion to compenstate the evolution of the nonlinear dispersion along the propagating path and improve the OTHG conversion efficiency with serious phase mismatch is proposed and demonstrated.The modulating scheme falls into two categories,modal phase mismatch switching(MPMS)and modal phase mismatch compenstating(MPMC).In the MPMS scheme,the relative phase changes unidirectionally along the propagating path,but with its change rate accelerated when the relative phase within its ineffective range.Accordingly,the propagating length with the nonlinear energy transfered from signal to pump is com-pressed.Comparatively,the relative phase in MPMC scheme is limited within its effective range and changes back and forth.The improvements of OTHG conversion in these schemes at different modulation depths are numerically calculated and compared.At last,it shows that the optimized MPMC scheme can support most efficient OTHG conversion with serious phase mismatch.Using the optimized definition of coherent length,the defects existing in the phase matching schemes based on modulating modal dispersion to pasively compensate the varied nonlinear dispersion is analyzed,and a phase matching scheme based on directly modulating the nonlinear phase mismatch to improve OTHG conversion efficiency is proposed and discussed.It has been demonstrated that this nonlinear phase mismatch modulating(NPMM)scheme can be realized by using the nonlinear positive feedback mechanism provied by silica microfiber ring cavity.The NPMM scheme realized in ring cavity constructed by microfiber is demonstrated by numerical calculation,which shows that the highly efficient OTHG process with an ultra-low intensity threshold can be achieved.Combining the advantages of the modulating modal dispersion and nonlinear dispersion schemes,a cascaded system is proposed to achieve the ultra-highly efficient OTHG conversion with a extremly low intensity threshold,which laid a foundation for the later experimental implementation of the efficient OTHG process.In summary,the results of this work are instructive to improve the theoretical model of TOPDC,and also helpful for designing the highly efficient experiments for producing mid-infrared laser and three photon entangled state.On the other hand,the results can also provide reference for other third-order nonlinear optical parametric processes.