Analytical Solution Of Bloch Equations With Phase Term And Study Of Photon Echo

In the research of the interaction between light and matter,the motion state of the atom can be characterized by the Bloch equations.Based on this,the corresponding physical phenomena caused can be studied,such as spectral hole burning,photon echo.The influence of the initial phase of the input pulse on the photon echo has not been considered in the reported literatures on the physical phenomena of the photon echo based on the Bloch equations.Based on this,the main contents of this paper are as follows:1.Based on the rotating wave approximation,the Bloch equations with phase term is derived,and the physical meaning of Bloch vector and its components is analyzed.The geometry model of Bloch with phase term is established,and the influence of phase on Bloch vector on Bloch sphere is analyzed.Based on the Maxwell equation,the electric dipole moment is associated with the macroscopic polarization effect,and the Maxwell-Bloch equation is obtained.2.Based on the et A matrix,the analytical solution of Bloch equation with phase term is derived.Based on the analytical solution,the expressions of signal electric field of two pulse photon echo and three pulse photon echo with phase term are derived,the influence of initial phase of each incident pulse on two pulse photon echo and three pulse photon echo is analyzed in detail,and the Bloch geometric model of two pulse and three pulse considering phase is established.3.Based on the Bloch equation with phase term,the principle of phase modulated photon echo amplitude and the principle of silent echo are given.Then,based on the theory of this paper,two models of controlling photon echo based on modulation phase are given,two pulses form a pulse pair of time-domain overlapping,the theoretical derivation and simulation are given.At the same time,the theory of silenced echo is given,and the principle of suppressing spontaneous gain noise by silenced echo is analyzed.