CHAPTER
5
THEORY
Most techniques for characterizing the phase of short pulses can be divided into three successive
steps: a linear filter, a non linear interaction (e.g. SHG) and a spectral measurement of the
output. In the case of Frequency Resolved Optical Gating (FROG), the linear filtering consists
in generating two time-shifted replica of the original pulse. Since a significant number of CPA
amplifiers now include a pulse shaper in their front-end, it is highly convenient to use such a
device not only to correct but also to characterize the amplified pulses by adding at the back-end
a nonlinear element and a spectral detector.
However, in this case, methods that rely on pulse replicas are not favoured since the corre-
sponding pulse structure will not, in general, propagate in the amplifier without being strongly
distorted (e.g. a train of pulses will be obtained instead of two pulses). On the contrary, techniques
that use phase-only shaping produce only negligible non linear effects in a strongly chirped CPA
amplifier.
In the ChirpScan method, we take advantage of the ability of the AOPDF to program pure
accurate second order phase, to implement phase characterization, using few SHG spectra.
5.1
Principle
Applying the stationary phase theorem to the SHG process, one can show that the SHG spectrum
I
SHG
(2
ω
) exhibits a maximum as a function of pulsation whenever
ϕ
00
(
ω
)
'
0. Furthermore,
the same theorem states that for sufficiently chirped pulses the spectrum of the second harmonic
I
SHG
(2
ω
) can be accurately described by the following expression:
I
SHG
(2
ω
)
∝
I
2
(
ω
)
|
ϕ
00
(
ω
)
|
(5.1)
where
I
(
ω
) stands for the spectrum of the fundamental pulses and
ϕ
00
(
ω
) for the second order
derivative of the spectral phase of the fundamental pulse (i.e. the ”local” chirp of the pulse).
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