Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works. The influence of thickness on the three-pulse photon echo's amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference time-domain method. We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm³⁺:YAG when the attenuation of the input pulse is taken into account. Meanwhile, we find the expression 0.09exp(α'L), which is previously employed to describe the relationship between echo's efficiency and thickness, should be modified as 1.3·0.09exp(2.4·α'L ight) with the propagation of echo considered.