94 Femtosecond Optics
2.5. ELEMENTS WITH ANGULAR DISPERSION
2.5.1. Introduction
Besides focusing elements there are various other optical components which
modify the temporal characteristics of ultrashort light pulses through a change
of their spatial propagation characteristics.
Even a simple prism can provide food for thought in fs experiments. Let us
consider an expanded parallel beam of short light pulses incident on a prism,
and diffracted by the angle β = β(), as sketched in Figure 2.17. As discussed
in Chapter 1, a Gaussian beam with beam waist w
0
self-diffracts by an angle
of approximately θ = λ/πw
0
. In the case of a short pulse (or white light), this
diffraction has to be combined with a spectral diffraction, because the light is
no longer monochromatic, and different spectral components will be deflected
by the prism with a different angle β = β(). If the pulse is sufficiently short,
both effects are of the same order of magnitude, resulting in a complex space–
time problem that can no longer be separated. Throughout this section, whether
considering group delays or GVD, we will consider sufficiently broad beams
and sufficiently short propagation distances L
p
behind the prism. This will allow
us to neglect the change in beam diameter because of propagation and spectral
diffraction after the prism. In most cases we will also approximate the beam with
a flat profile. At the end of this chapter the interplay of propagation and spectral
diffraction effects will be discussed for Gaussian beams.
D
A
EA
B
a
B
O
Figure 2.17 Pulse front tilt introduced by a prism. The position of the (plane) wavefronts is
indicated by the dashed lines
AB and A
B
.
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