Use conservation of energy and momentum to show that light can excite optical phonons but not...

Use conservation of energy and momentum to show that light can excite optical phonons but not acoustic phonons. Give an estimate of the value of k and the energy at which such an excitation can occur.

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Expert Solution

Let us consider a photon of the energy 100 meV for which the momentum will come out to be approximately . At a value of momentum equivalent to this the acoustic phonon will be approximately 0.004 meV and therefore the photon can't be absorbed by this optical phonon. If we make a plot of the relations for dispersion and portray photons of light, optical phonons and acoustic ones it would be something like the one below.

Now, here we see that the line poltted for light is intersecting with only optical mode of phonons and not the acoustic ones. The acoustic phonons have dispersion relation that looks like in equation form where c is the speed of light. While for the optical ones the relation is different and is governed by when and as .

genius_generous answered 1 year ago

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