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 Lez.4 - Fisica At. Mol. Spec. 2013-2014

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 Lez.4 - Fisica At. Mol. Spec. 2013-2014

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 Lez.4 - Fisica At. Mol. Spec. 2013-2014

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€) Lez.4 - Fisica At. Mol. Spec. 2013-2014

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 Lez.4 - Fisica At. Mol. Spec. 2013-2014

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. 2013-2014

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. Lez.4 - Fisica At. Mol. Spec. 2013-2014

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 Lez.4 - Fisica At. Mol. Spec. 2013-2014

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 Lez.4 - Fisica At. Mol. Spec. 2013-2014

Second-order collinear autocorrelator: the setup Lez.4 - Fisica At. Mol. Spec. 2013-2014

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 Lez.4 - Fisica At. Mol. Spec. 2013-2014

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 Lez.4 - Fisica At. Mol. Spec. 2013-2014

The background-free second-order autocorrelator: the setup Lez.4 - Fisica At. Mol. Spec. 2013-2014

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” Lez.4 - Fisica At. Mol. Spec. 2013-2014

The background-free second-order autocorrelator: an example Lez.4 - Fisica At. Mol. Spec. 2013-2014

The signal in the UV (257 nm) for a single delay Data analysis Lez.4 - Fisica At. Mol. Spec. 2013-2014

Autocorrelation curve Duration retrieval Thus Lez.4 - Fisica At. Mol. Spec. 2013-2014

Final result. Pulse duration, t = 134.9  0.3 fs The best-fit Final result. Pulse duration, t = 134.9  0.3 fs Lez.4 - Fisica At. Mol. Spec. 2013-2014