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Chapter VI UV-Vis Spectroscopic….
Considering that the second-harmonic fields from different particles
are correlated provided that the particles are separated by a distance less
l ˆ N . L
than coherence length. Dividing the cell thickness up to N regions
and each contains l rˆ ˆ '.
. particles and treating the non-
c
N c
linear polarization P NLS within each of the N regions by a one-dimensional
random walk model having step length proportional to d 2 , the net
contribution of each region to second-harmonic intensity is,
2
2
2 rˆ 2
. d N'
.. . L d
2
lˆ .
.
total N
c
I .
(6.6)
Now considering the phase matching condition, for certain directions
of light propagation in uniaxial and biaxial crystals, the phase matching can
occur between the polarizing wave, traveling with velocity
transmitted second harmonic wave, traveling with velocity
227
c
ne
c
no
, and the
.
2
For these certain directions the coherence length becomes very
large. However, the angular width over which phase matching takes place
is usually very small and only a small fraction of the particles will have the
correct orientation.
In the vicinity of the phase-matched direction the coherence length is
2
lc . .
m
(6.7)
n
Where, sin
c
o
. . (6.8)
Here, m = angle between phase-matching direction and optic axis,