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

Abstract

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-iondoped 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.

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

“…2(b) of Ref. [8]}, the simulation results in Fig. 2(a) are more in line with the actual situation for the field suffering decreasing instead of increasing at the beginning in absorbing medium.…”

“…Ref. [8]. The first pulse is applied at t = 0 and removed att = t ′ 1 = 500n ′ ∆t; The second pulse is shot into crystal at t = t 2 = 1500n ′ ∆t and removed at t = t ′ 2 = 2000n ′ ∆t; The last pulse is shot into crystal at t = t 3 = 5000n ′ ∆t and removed at t = t ′ 3 = 5500n ′ ∆t.…”

“…The variations of the input pulse and the 3PE over the propagation direction will lead to the variation of 3PE's efficiency which is expressed as [8] η echo α…”

“…The efficiency of 3PE in Ref. [8] | 2 e −α ′ L is only appropriate for the pulse's area being very small. The green line in Fig.…”

“…Our group had directly deduced the analytical solution of the 3PE based on Bloch equations. [8] The methods mentioned above have a flaw in common: the effect of propagation is not taken into consideration and the influence of crystal's thickness on 3PE is ignored. This drawback can be compensated by Maxwell-Bloch (M-B) equations.…”