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

210
that propagate through quartz as
(A.l)
where the subscript m denotes either b or f for the bound or free waves. In the time
domain, we can write the field at the beginning of the crystal (y = 0) as
(A.2)
with Tin as the F'VVHM of the pulse duration. The field acquires a phase dJ = k(;..))y
as it traverses the crystal. This phase perturbs the shape of the pulse and leads to
an increase in the width of the pulse at the end of the crystaL Taut, as
1 + _0/_
Tin 48 2 .
To aut =
~'f2
(A.3)
In equation (.-\.3) dJ" is defined as the second derivative of the phase of the wave,
k(uJ )d, with respect to w, i.e.
with
¢" = 8 2 ¢ I
8w 2 w
(A.-1)
3 is defined as
dJ = k(w)d = n(w)wL.
c
2
8 = Tin.
8ln2
(A.5)
(.-\.6 )
It is easy to show that ¢" can be rewritten as
(A.7)
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