This is quite difficult to explain without a figure !!! I suggest that you read Allen's and Eberly's book "Optical resonance and two-level atoms". The basic ingredient is that the dipoles created by light in an inhomogeneously broadened medium get dephased in time due to the difference in their Bohr frequencies. If you are able to reverse this evolution by applying a light pulse, then the atomic dipoles come back in phase after some time and emit light in the form of the so-called "photon echo".

If ensemble of atoms in excited state emits photons spontaneously, than every  photon is produced independently. However, coherent state of excited ensemble can be produced, with nondiagonal element of rho matrix (rho21) that is oscillating in the same way in all atoms. In paricular case, all atoms  emit in the same moment, producing a pulse that is called photon echo

I think that the simplest and most intuitive explanation of photon echo can be found in Hermann Haken's book "Light", I think that in Vol. 1. Take a look.

This is quite difficult to explain without a figure !!! I suggest that you read Allen's and Eberly's book "Optical resonance and two-level atoms". The basic ingredient is that the dipoles created by light in an inhomogeneously broadened medium get dephased in time due to the difference in their Bohr frequencies. If you are able to reverse this evolution by applying a light pulse, then the atomic dipoles come back in phase after some time and emit light in the form of the so-called "photon echo".

 Dear Aleksander, Eugenio and Fabien,

   Thanks all of you ! Definitely I need to read some books and papers about photon echo.

   But in experiments, what kind of things, such as excitation laser pulse and gain medium, are critical for observing photon echo signal ? 

  Here let me introduce my experiment briefly. The excitation pulse I used is at 800 nm with duration of 45 fs, which was split into three replica: one is for first excitation pulse with 1 mJ, another is for second excitation pulse with 4 mJ and the third one (weak) at good emission wavelengh 391 nm as probe beam. These two excitation pulses can generate filamentary plasma (~few cm long, 200 um wide) in 15 mbar nitrogen gas, from where strong 391 nm lasing radiation emits. The emission is from the transition of ionic nitrogen molecules. It has a pulse duration of few ps. With the probe pulse at same wavelength, we can probe the gain dynamics induced by excitation pulses. The spatiotemporal overlap between them are almost good.

 During the measurement, we first separate two excitation pulses by few ps (let's say DL), and then use the probe pulse to probe the gain. Unfortunately, at the delay DL after second excitation pulse, we didn't observe reliable signal.

 If you have some time, please give me some advice or comments about this experiment. 

 Thanks in advance!

 Dear Pengji.

     First of all, the photon echo can exists only on the wavelength of the first two laser pulses (800 nm). Further, atoms or molecules should resonantly absorb laser radiation. Nitrogen does not absorb 800 nm. Only plasma absorbs it. So, it is unlikely that in your experiments a photon echo can be observed.

    I believe, that physical base of a photon echo phenomenon (also as of most other phenomena in nonlinear optics) is inequality of differential cross-sections of forward and reversed transitions in quantum physics ( see, for example, e-print arXiv:physics/0306148). Unfortunately, this fact is not recognized today yet.