1. Ultrashort pulse characterisation
UNIVERSITA’ DI NAPOLI
“FEDERICO II”
Ultrashort pulse characterisation
and shaping
Carlo Altucci
Consorzio Nazionale Interuniversitario di Struttura della Materia – CNISM
Dipartimento di Scienze Fisiche, Università “Federico II”, Napoli, Italy
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2. OUTLINE
Characterization of Ultrashort pulses. Measurement of pulse duration
Streak camera
First-order autocorrelator: Fourier limit
Second-order autocorrelator: Pulse duration
Collinear second-order autocorrelator
Noncollinear (background-free) second-order autocorrelator
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3. Pulse duration Electronics is not fast enough to measure from few
ps down to the fs regime
An optoelectronic device carries on a direct measurement:
the streak camera
The streak camera is based on the photoelectric effect:
the radiation pulse is essentially transformed into an electron
bunch by photoelectric effect into some photocathode material.
The electron bunch passes through an intense rump-like electric
field stage which spatially broadens the bunch. Spatial extension
and temporal duration of the electron bunch result proportional,
what makes easy then measuring the temporal duration by
measuring the size of the bunch which hit a fluorescent screen
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4. Streak Camera
Typical time-resolution limit is around 100 fs. Below such limit it is
hard to properly streak electrons as the voltage sweep is not
fast enough. This apparatus is also quite expensive (> 100 k€)
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5. First-order autocorrelator
C. Rullière “Femtosecond Laser Pulses”, 2nd edition, Springer, cap.7
The signal is given by
Contrast ratio 2:1
background
The width of the function I1(t) is related to the coherence length of the pulse. Its inverse is thus being strictly related to the light spectrum. Can be an alternative method to measure the spectrum. Thus not provide information on the actual pulse duration
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6. Second-order autocorrelator (I)
It is based on the second harmonic generation in
nonlinear crystals
In the case of collinear beams with type-I phase-matching (ordinary-ordinary -> parallel polarization beams), by imposing E2(t)=E1(t-) (autocorrelation), the SHG measured signal is proportional to I2() which is given by
Lez.4 - Fisica At. Mol. Spec

7. Second-order autocorrelator (II)
The signal is:
The second order autocorrelation function is always symmetric and therefore can only give limited information concerning the pulse shape and chirp.
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8. Second-order autocorrelator (III)
The interferometric second order autocorrelator
The maximum corresponds to  = 0
The background corresponds to  = 
Contrast ratio 8:1
It selects only a “single point” of the wavefront
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9. Second-order autocorrelator (IV)
The intensity second order autocorrelator
By averaging out the cos(0t) carrier fringes, what is usually done because of the integration of the detector over its response time and because of possible mechanical instabilities, we end up with the intensity autocorrelator.
Advantage: much simpler and more stable signal
Disadvantage: lower signal-to-noise ratio
It is immediately seen that peak-to-background contrast ratio for the autocorrelation measurement is 3:1
The signal is proportional to the 2nd order correlation functionn defined as
Interferometric
Intensity
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10. Second-order collinear autocorrelator: the setup
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11. The background-free second-order autocorrelator: noncollinear setup
Since the two beams are non-collinear, second harmonic is generated along the bisecting line, only when both pulses coincide in time and space. The spatial distribution of the second harmonic signal along the vertical direction, S(x), is imaged by means of a linear CCD array, and turns out to be equivalent to the second order autocorrelation function
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12. The background-free second-order autocorrelator:
the signal
In fact, if the two beams are uniform, with I1(t) and I2(t) and their intensities, respectively, the radiated field at the harmonic frequency at a given distance x0 from the centre of the crystal is proportional to
Where n is the crystal refractive index
The result is:
Which is directly proportional to the 2nd order autocorrelation function
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13. The background-free second-order autocorrelator:
the setup
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14. Second-order autocorrelator: pulse duration retrieval
The second order autocorrelation function is always symmetric and therefore can only give limited information concerning the pulse shape and chirp. It does not measute any asymmetry in the temporal shape. A temporal shape needs to be assumed (the equivalent mathematical problem is a nonlinear integral equation …)
See also J.C. Diels and W. Rudolph “Ultrafast Laser Pulse Phenomena”
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15. The background-free second-order autocorrelator: an example
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16. The signal in the UV (257 nm) for a single delay
Data analysis
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17. Autocorrelation curve
Duration retrieval
Thus
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18. Final result. Pulse duration, t = 134.9  0.3 fs
The best-fit
Final result. Pulse duration, t =  0.3 fs
Lez.4 - Fisica At. Mol. Spec