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Chapter VI UV-Vis Spectroscopic….
= angle between direction of fundamental wave and optic axis,
228
o
n =
ordinary refractive index at fundamental frequency, = angular frequency
of fundamental, = angle between ellipse and sphere index surfaces at
matching.
For small birefringence, e o
n n
n
.
.
1 and small dispersion,
2
2
2
n
n n
. . 1.
Where, n
2
2
e = extra-ordinary refractive index,
and
c
o e
tan . . .
. n n
n (6.9)
2
2
e o n n . sin .
l . .
.
2
4 2
The intensity is obtained for phase matchable is
.
2
32
64
I ext
I .
ext .
.
L
2
PM
c
n 1
n2 1
2
m
m
2
2 2
d PM
.
.
4
2
ijk
(6.10)
(6.11)
2
Where, .
PM . sin
m and dPM is that d for which the phase
matching occurs, dijk is the second order polarizability tenser.
When the non linear co-efficients
d , k and coherence length lc are
known, it is possible to evaluate the ratio of second harmonic intensities of
any two materials using above equation.
The schematic representation of different particle size dependences
for phase-matchable and non-phase matchable materials are given in
figure (6.2).
2
ijk