Third-Order Optical Polarization and Non-linear Response Functions

2 Third-Order Optical Polarization and Non-linear Response Functions 

Consider an ensemble of systems with two electronic states (a and b), and an 

The electromagnetic radiation field acts on p for a short interval of time (At) at time t, creating a small increment of an off-diagonal density matrix element 

The increment ofp evolves from time t until time t, undergoing oscillations in the complex plane at frequency ojab and decaying with rate constant Yab as a result of fluctuating interactions with the surroundings. The fraction of the increment remaining at time t is ex [—(ia ab + Ya  

Integrating processes 1 and 2 from t = 0 to t gives the total value of p fj at time t resulting from excitations at aU earlier times. Steps 1-3 together comprise a convolution of the time-dependent excitation with a time-dependent response function. 

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