Four-wave mixing photon echoes

The three-pulse experiments contain more information than two-pulse methods when the direction and timing of all three pulses is controlled. We have seen that this additional information cannot be interpreted within a Bloch picture. We will therefore outline in the following a more detailed theory, which includes spectral diffusion and which simultaneously explains the linear response (absorption spectrum) and the nonlinear response (four wave mixing, photon echo, transient grating, pump-probe) of vibrational transitions. 

Photon Echo (PE) and Reverse Transient Grating (RTG) measurements of the loss of electronic coherence between the X( 2g+) and B(3FIou+) states of molecular iodine are measured by three pulse four wave mixing (FWM). Two cases are considered, relatively low pressure isolated iodine (1-2 Torr), and iodine at high pressure (>10torr) or in the presence of several hundred Torr of buffer gas. 

There are several classes of optical effects induced by an internal perturbation, such as saturation of absorption, coherent Raman spectroscopy, multi-photon absorption processes, coherent transient spectroscopy (see Table 0.3). Section 5.1 of this chapter deals with saturation of absorption and multi-photon absorption processes. Section 5.2 outlines the principles of coherent anti-Stokes Raman spectroscopy (CARS), Raman-induced Kerr effect spectroscopy (RIKES), four-wave mixing (FWM), and photon echo. 

Due to the stationarity of the process, T2, T3) does not depend on the time elapsing between start of observation t = 0 and tj. It has a similar mathematical structure to that of the nonlinear response function used to describe four-wave mixing spectroscopies such as photon echo or hole burning [62]. 

We have reviewed the EOM-PMA method for the calculation of two-pulse-induced (spontaneous emission, pump-probe, photon echo) and three-pulse-induced (transient grating, photon echo, coherent anti-Stokes-Raman scattering, four-wave-mixing) optical signals. In the EOM-PMA, the interactions of the system with the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. 

---