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 timedomain 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 Tm^（3＋）：YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp（α＇L）,which is previously employed to describe the relationship between echo＇s efficiency and thickness,should be modified as 1.3 · 0.09 exp（2.4 ·α＇L） with the propagation of echo considered.

Characteristics of spectral-hole burning in Tm^(3+):YAG based on the perturbation theory

In this paper, the physical mechanism of the interaction between electromagnetic wave and spectral-hole burning crystal material is investigated in detail. In the small signal regime, a perturbation theory model is used to analyze the mechanism of spectral-hole burning. By solving the Liouville equation, three-order perturbation results are obtained. From the theoretic analysis, spectral-hole burning can be interpreted as a photon echo of the zero-order diffraction echo when the first optical pulse and the second optical pulse are overlapped in time. According to the model, the spectral-hole width is dependent on the chirp rate of the reading laser. When the chirp rate is slow with respect to the spectral features of interest, the spectral hole is closely mapped into time domain. For a fast chirp rate, distortions are observed. The results follow Maxwell-Bloch model and they are also in good agreement with the experimental results.