Bloch transient solution

The Bloch equations (Eq. 5) can be solved under different conditions. The transient solution yields an expression for 0-22 (0> time-dependent population of the excited singlet state S. It will be discussed in detail in Section 1.2.4.3 in connection with the fluorescence intensity autocorrelation function. Here we are interested in the steady state solution (an = 0-22 = < 33 = di2 = 0) which allows to compute the line-shape and saturation effects. A detailed description of the steady state solution for a three level system can be found in [35]. From those the appropriate equations for the intensity dependence of the excitation linewidth Avfwhm (FWHM full width at half maximum) and the fluorescence emission rate R for a single absorber can be easily derived [10] ... 

At this point we have arrived at the connection between the correlation function and the density matrix elements described in Section 1.2.2.3, because the conditional probability is just proportional to the matrix element (J22 x) corresponding to the transient solution of the optical Bloch equations for our model three-level system in Fig. 6. Then it follows,... 

Faced with a broad range of prospective spin-lattice relaxation times, the investigator needs two types of spectrometers, a situation that is further complicated if multi-frequency measmements are required. Furthermore, the phenomenological descriptions of measurements made by cw and transient spectrometers differ, as they correspond to separate solutions to Bloch s equations. This chapter describes refinements of both instrumental and theoretical/computational techniques that facilitate the measurement of spin-lattice relaxation times. 

One thus obtains the transient and steady-state solutions of Bloch s equations in the time domain as follows ... 

---