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

150
wavevector components. The free wavevectors are defined as
k fi -
7rnfiW
c
(6.5 )
k fiz - - cos 8 fi k fi (6.6)
k fix - sin 8 fi k fi, (6.7)
where i is equal to 0, 1, 2 and denotes the air, GaN, and sapphire regions, respectively,
and W is the angular frequency of the second-harmonic fields. The bound wavevectors
are defined similarly with nbL substituted for nfi. The free (bound) wave angle of
incidence in region i is 8 fi (8bi) and is determined from 8 0 and nfi (nbi) by Snell's law.
'-IVe now determine the nonlinear polarization induced in Ga0.' by the applied
fundamental field.
The p-polarized fundamental light field generates a nonlinear
polarization of the form
P
(2) _ 2 2 ( ) (2) E E
x - tpOL Wo Xxzx x z (6.8)
and
P (2) - t2 ( ) ( (2) E E (2) E E )
z - pOL Wo Xzxx x x + X;;zz ;; z . (6.9)
Note that E is the incident fundamental field and tpoL(wo)E is the fundamental field
transmitted into the GaN film. The nonlinear polarization generated by an s-polarized
fundamental field is
P
(2) _ 2 ( ) (2) E E
z - tsOL Wo Xzyy Y y. (6.10)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.