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

153
GaN/Ah03 interface, which propagates through the sapphire substrate. E f2 . The
free nonlinear waves have the form
(6.16)
with j = L rl, or 2. The amplitude of the free wave components are
and
kfjz
E/ix = --k Efj.
fj
( 6.17)
Matching boundary conditions at the air/CaN interface determines Ell as
k 10 2 k lIz ) -1(k210
)
Ell = ( k k - k/l (kbl.: - -k)EblX - kblxEblz .
fOz /1
fOz
(6.18)
Similarly, matching boundary conditions at the GaN/A.l 2 0 3 interface determines E frl
and Ef2 as
(
k2 k ) -1 ( k 2
k
k 12z 11
11 bIz k
12z
blx
_ 12 lIz + k (k _ -.E..)E e-i(kbl=+kfl=Jd
(6.19)
-k E e-i(kb1=+kfl=Jd + (k _ kJ2k/lZ)E e-i2k/l=dJ)
blx bIz 11 k k 11
12z 11
and
(
k2 k )-l( k 2
12 bIz - -- blx - -
k /lz kf2
k/lrz
11 12z + k (k Ilr)E e-i(kbl--k/2-Jd
(6.20)
-k E e-i(kbl=-k/ 2=)d+2k E e-i(k fl =-k/2=Jd)
blx bIz 11 fl .
The previous calculations determine the magnitude of the nonlinear waves. The
measured SHG signal also requires inclusion of the phase relationships between the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.