The Investigation Of Photon Echo Based On Maxwell-bloch Equations

When the optical coherent transient interaction between the pulse and the crystal occurred,the phenomena such as optical nutation,free induction decay and photon echo will be observed.In this paper,we focus our attention on photon echo.The main contents of this paper are as follows:(1)The optical Bloch equations are deduced based on the kinematical equations of density matrix's elements in which the slowly-varying amplitude approximation and the rotating wave approximation are used to simplify.Then,the propagation equation is deduced and the relationship between Maxwell equations and Bloch equations is established based on the polarization.(2)The iteration processes for finite-difference time-domain method to solve Maxwell-Bloch equations are described in detail.Then,this method is used to analyze the response of the crystal and the variation of the field.The Rabi frequency's influences on the nutation signal's fluctuation frequency and the maximum value are analyzed.Meanwhile,the relationship between the maximum value of the induced field and the absorption coefficient is presented.Then,the de-phasing process is displayed based on the rotation of Bloch vectors in free induction decay process and the influence of damping time on Bloch vectors is discussed.(3)We display the values of Bloch vectors for different transition frequencies to explain the formation mechanism of the photon echo.Meanwhile,the effect of population grating is presented.Then,we analyze the difference between the two-pulse photon echo and three-pulse photon echo.(4)The influences of input pulse's parameters on photon echo are analyzed in the generation process of three-pulse photon echo.The time interval's influence on the amplitude of three-pulse photon echo is analyzed with the investigation of population grating.Meanwhile,the optimum value of the first two pulses' interval is proposed.At last,the relationship between the photon echo's temporal width and bandwidth of population grating is presented.(5)The influences of crystal's parameters on photon echo are analyzed.The rotation of Bloch vectors in the formation process of photon echo is presented to investigate the influence of damping time on photon echo's amplitude.At last,the variation of photon echo's amplitude with the increasing the crystal's thickness is presented and optimum thickness to generate photon echo is found.Meanwhile,the relationship between photon echo's efficiency and thickness is proposed.