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

129
susceptibility element m n Feynman diagram
(2)
X;:zz
r a
1 r b
1
r b
1
A
Pi r c
1
r b
1
A
r~ r b
1
r a
1
B
(2)
r a r~ r b A
Xzxx 1 :I 1
X~~x
Table .5.6: Resonant three photon processes for X~~z(w = 2wo), X~~x(w = 2wo). and
x1~x(w = 2wo) at the r point. The table contains all three photon process in which
the last time ordered photon is the 2wo photon corresponding to a virtual transition
from the GaN conduction band to the valence band.
Thus. the Feynman diagrams graphically display the time ordering of photons in
a three photon process and determine the structure of the energy denominator of
. (- ?)
equatlOn u._ .
\Ve briefly describe Lee's and Gustafson's theory [93] of Feynman diagrams for
second harmonic generation. The process is cast in terms of the perturbation of
the density operator. The density operator is defined as the ensemble average over
product of the ket and bra states
p = Il/I)(¢I· (5.7)
The p can be expanded in a perturbation series as
p = p(O) + p(i) + p(2) + ... (5.8)
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