Stimulated emission is the process by which an atomic electron (or an excited molecular state) interacts with an electromagnetic wave of a certain frequency may drop to a lower energy level, transferring its energy to that field. A new photon created in this manner has the same phase, frequency, polarization, and direction of travel as the photons of the incident wave. How is it possible to get the newly generated photon to have the same phase, polarization etc.similar to incident wave.?
All is described in Chapter 5 of the book Laser Spectroscopy 1, 5th edition, by Wolfgang Demtröder (Springer, Berlin, 2014).
http://www.springer.com/physics/optics+%26+lasers/book/978-3-642-53858-2
You are right, in reality, neither polarization, nor the phase (and even wavelength) of the emitted photon will repeat exactly those of the exciting wave. What we can read in almost all text-books is no more than a rough approximation. For example, in a solid, the position of every atom is fixed and defines the possible polarization of the emission.
But what is important, the probability of such photon emission increases when polarization etc. of the photon approaches to that of the incident wave. Moreover, the coherent input to the incident wave given by the emitted photon is much more important energetically. This, together with certain symmetry properties, results finally in "exact" reproduction of all the parameters of the incident wave by the collective stimulated emission.
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