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

20
nonlinear element of quartz, X~~x{w
= 2wo) = 2.2xlO- 9 esu [40]. There are two
solutions to the nonlinear wave equation (equation (2.5)) : a homogeneous solution
and a particular solution. vVe refer to the particular solution as the "bound wave·'
solution; the bound wave solution exists only in the nonlinear optical crystal. This
field is bound to the linear field and propagates with a wavevector twice that of the
linear field. This field may be written as
E - x~E ei (kbl·r--2wot)
b1 - b1 . (2.13 )
The subscript b designates a bound wave solution. The bound wavevector. k bl , is
(2.1.,1)
The magnitude of this field is calculated directly from equation (2.5) and has a value
of
47rp(2)
Ebl = --­
Ebl - Ef1
(2.15)
(2.16)
where tOl (w o ) is the Fresnel transmission coefficient for light with angular frequency
;,va which propagates from vacuum into quartz. The homogeneous solution to the
wave equation is
E - x~E ei(k/l·r--2wo t)
/1 - f1 • (2.17)
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