Ultrashort Laser Pulse Phenomena, 2nd Edition

Coherent Interactions with Two-Level Systems 229

A similar representation can be made for the system of Eqs. (4.6)–(4.7).

The pseudo-polarization vector is then the vector



Q(Q

i

, Q

r

, w) rotating around

a pseudo-electric field vector



E(κ

˜

E

r

, κ

˜

E

i

, −ω) [Fig. 4.2(b)]. Physically, the

first two components of the pseudo-polarization vector



Q represent the dipolar

resonant field that opposes the applied external field (and is thus responsible

for absorption).

4.2.2. Rate Equations

If the light field envelope is slowly varying with respect to T

2

, Bloch’s

equations reduce to the standard rate equations. For pulses longer than the dephas-

ing time T

2

, the two first ...