
130 Femtosecond Optics
interfering completely. As a result, the actual shortening factor is
√
1 + u
2
times
smaller than the theoretical one, as can be seen from the first exponential function.
The influence of such a filter can be decreased by using a large beam size.
A measure of this frequency filter, i.e., the magnitude of the quantity (1 + u
2
),
can be derived from the second exponent. Obviously the quantity (1 + u
2
)is
responsible for a certain ellipticity of the output beam which can be measured.
2.7. OPTICAL MATRICES FOR DISPERSIVE
SYSTEMS
In Chapter 1 we pointed out the similarities between Gaussian beam propa-
gation and pulse propagation. Even though ...