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I'm told that polarisation happens due to the oscillation of an electric dipole and stimulated emission is due to the excitation of an electron between energy levels but both depend on the incoming light frequeny. Are they the same or if not what's the difference?

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Stimulated photons carry the same polarization as their stimulating counterparts. If the incoming radiation is polarized, the stimulated emission should be as well. If the incoming radiation is randomly polarized (unpolarized), the stimulated emission should be unpolarized as well.

They both depend on the same incoming electrical field but they are not the same thing. The polarization vector depends on the material itself as well as the incoming electromagnetic field. Both these quantities depend on the incoming electrical field and not on the incoming electrical fields frequency. Sure, the frequency is a part of the incoming electrical field, but it's not the correct way of putting it.

They are not the same. Stimulated emission produces an electromagnetic field. Polarization is a parameter of this field, and i'd not put it as being its's own entity but rather a component of the other.

In a liear medium the relationship between electric field and polarization vector is $P=\epsilon_0\chi E$. This electric field $E$ might carry a frequency if it is a time-dependant field, and thus we can see the relationship between polarization and electromagnetic field. This field however may be the result from stimulated emission, i.e the field itself is the stimulated emission, and the polarization is a part of this, but they are not the same. They are connected to each other however. Of course stimulated emission is related to the strength of the incoming field, but the polarization vector is also dependent due to this relation.

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