Power Broadening: Explained & Resources

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Malamala
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Hello! I have seen mentioned in several papers the concept of power broadening, which (if I understand it right) means that the linewidth of a transition (say, in an atom) get wider with increasing the power of the laser used (even if the linewidth of the laser is kept constant). I am not totally sure I understand the physics behind it. Can someone explain it to me or point me towards some accessible readings on this topics (preferably not actual papers, maybe a book or something easier as a first reading). Thank you!
 
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Power broadening appears when the laser intensity becomes close to the saturation intensity of the transition.

A couple of good references:
C. J. Foot, Atomic Physics (OUP, 2005)
P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010)