As mentioned in Chapter 2 , the phenomenon of spin echo is widely employed for spectroscopic investigations. The phenomenon of photon echo has a similar area of applications. Let us consider two examples to illustrate photon-echo applications.
As it was emphasized several times above, the phenomenon of the photon echo is an optical analog of the spin echo that has been discovered [ 1 ] about a decade earlier. That is why many ideas from the theory of the spin echo has been transferred to the theory of the photon echo and appeared to be fruitful there. One of these ideas put forward by Fernbach and Proctor [ 2 ] is the idea of the possibility of the use of the phenomenon of the spin echo for writing, storage, and processing of the data. The authors [ 2 ] determined the conditions under which the signals of the spin and stimulated spin echo can reproduce (direct or time-reversed) shape of one of the exciting pulses. The theoretical analysis was proved by the corresponding experiments.
A review of theoretical and experimental works on the polarization photon-echo spectroscopy (PPE spectroscopy) is carded out. The main attention is payed to the following advantages of the PPE spectroscopy. First, the PPE spectroscopy, free of the influence of the inhomogeneous spectral line broadening, allows to make the high precision measurements within the envelope of a inhomogeneously broadened spectral line. Second, the high resolution ability of the PPE spectroscopy, directly in the temporal field, unables to accomplish the investigations of the fast relaxation processes, when ultrashort nano- and picosecond exciting pulse are used. Third, in the PPE spectroscopy the investigated relaxation processes are not subjected to the perturbing action of the intensive laser radiation. Farther, it is necessary to note the flexibility of the PPE spectroscopy consisting in the existence of a great number of various methods used for receiving different spectroscopic information. Finally, as far as the signal intensifies of the photon echo and of its variants are proportional to the squared number of the resonant atoms (molecules), it secures the definite advantages for the PPE spectroscopy as compared to the spectroscopk methods based on the non-coherent phenomena (especially for low pressure a gas considered). The possibilities of new experiments on photon echo and its variants aimed for obtaining a detailed new spectroscopic information are discussed.
The pulse area theorem is a well-known versatile analytical tool for capturing the general nonlinear nature of light propagation in a two-level medium. Here we derive the pulse area theorem for the photon/spin echo signal generated in a one-side cavity. The obtained analytical solutions for primary and secondary echo pulse areas allow us to describe the nonlinear patterns of the photon/spin echo signals in an atomic ensemble in a cavity. The developed approach and the obtained results constitute an important step in the study of the general properties of the photon/spin echo in optical and microwave cavities expanding applications of the photon echo in coherent spectroscopy, quantum memory, and processing.