William Angerer - Department of Physics and Astronomy - University ...

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Emission of a photon on the bra side is represented by
-([I - eTiE*(wdlm)
in
(5.13)
Fig. 5.7 displays the diagrams representing the emission and absorption of a photon
on both the ket and bra side.
3. A propagator takes the state from one vertex to the next and corresponds to an
energy denominator in equation (5.2). Second-harmonic generation involves three
photon interactions (vertices) and therefore two propagators. If the propagator takes
the state from the jth vertex to the {j+1)th vertex when the state is Im)(ll. the
propagator has the form
j
IT j = ±[2)Wi - Wml + irmdr! (5.1.1)
i=!
where '-'.Ji is positive for absorption of a photon on the ket side or emission of a photon
on the bra side. Conversely, Wi is negative for emission of a photon on the ket side or
absorption of a photon on the bra side. The plus (minus) in front of the propagator
corresponds to a {j+ 1 )th vertex on the ket (bra) side.
4. The product of all of the matrix elements and the propagators yields a term in
equation (5.2). In general, there are eight unique ways to arrange the photons in the
Feynman diagrams for a three photon process. For second-harmonic generation. there
are only four unique ways since the two of the photons are indistinguishable. The four
unique photon time orderings correspond to the four unique terms the second-order
susceptibility for SHG.
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