Improving the intensity and efficiency of compressed echo in rare-earth-ion-doped crystal

We investigate the intensity and efficiency of a compressed echo, which is important in arbitrary waveform generation (AWG). A new model of compressed echo is proposed based on the optical Bloch equations, which exposes much more detailed parameters than the conventional model, such as the time delay of the chirp lasers, the nature of the rare-earth-ion-doped crystal, etc. According to the novel model of compressed echo, we find that reducing the time delay of the chirp lasers and scanning the lasers around the center frequency of the inhomogeneously broadened spectrum, while utilizing a crystal with larger coherence time and excitation lifetime can improve the compressed echo's intensity and efficiency. The theoretical analysis is validated by numerical simulations.