3.1 Principle of autocorrelation
Since the pulses from the laser are too short to be measured with a photodiode, an indirect measurement of the duration must be made using an optical autocorrelator (Fig.4).
Figure 4: Schematic diagram of an autocorrector.
The idea is to use frequency doubling in a non-linear crystal (c2) , here a barium beta-borate crystal: BBO). A phase tuning is carried out in order to obtain an efficient frequency doubling: to create one photon at 400 nm, two photons are needed at 800 nm.
The role of the optical autocorrelator is to create two beams of equivalent (ideally equal) intensities I1 and I2 (here thanks to a semi-reflecting plate) from the pulse beam to be measured. A movable cube corner allows an adjustable δ delay between the two beams.
The two beams are then recombined in the frequency doubling crystal (BBO), located at the focus of a lens. The BBO therefore sees the intensities I1(t) and I2(t-δ/c) where c is the speed of light in air. At instant t, the doubled intensity Iblue(t) is proportional to the product of the intensities on the fundamental beams :
)$%&'(+) ∝ )((+) ∗ ))(+ −0 1)
Iblue(t) varies with the pulse rate of the laser, but this intensity cannot be resolved temporally because the detector used here has a too slow response time (typically in the microsecond range). Assuming that the detector has a rectangular pulse response of width τr, the signal is therefore proportional to the average value of Iblue(t) :
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1/#!$)1(+)∗ )2(+ −0 1)'(
"!
τr being sufficiently long in relation to the time variations of the intensities, #
the signal detected in the blue corresponds to the autocorrelation function because I1 and I2 come from the same temporal signal. To access the different values of this function, simply modify the delay δ between the two beams.
Q4: In fig.4, the frequency-doubled beam is the bisector between the two infrared beams: explain why.
3.2 Description of the autocorrector
The autocorrelator is described in Figure 5. The first cube corner is mounted on a vibrating pot. The second is mounted on a micrometric translation plate.
Figure 5: Photo of the autocorrelator.
The signal is detected by a photomultiplier (PM) in front of which a blue filter is placed.
Two external devices are required to use the auto-correlation unit: the vibrating pot power supply, which enables the amplitude and frequency of its movement to be managed, and the PM interface box. These two units will then be connected to the oscilloscope in order to display the autocorrelation signal and the control voltage of the vibrating pot as a function of time.
Q5: The BBO crystal is 200 µm thick. Why is it so thin?
Q6: The pot vibrates with an amplitude of about 1 mm. Is it suitable for viewing the entire autocorrelation function of a 100 fs pulse?
3.3 Adjusting the autocorrector
In order to facilitate the adjustment of the auto-correlation unit, first work with
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collinear and merged I1 and I2 beams on the BBO crystal as shown in figure 6.
This setting simplifies the obtaining of the frequency-doubled signal.
The adjustment of the autocorrelation starts with an alignment of the beam to be measured in the centre of the inlet diaphragm and the BBO. To do this, perform a
"laser alignment" using the two mirrors at the input of the autocorrelator and remove the focusing length in front of the BBO crystal.
Check that the PM is well centred on the beam (it can easily translate into its mechanical support).
Add the lens on the beam axis, without misaligning the beam.
Switch on the vibratory pot and trigger the oscilloscope on the control signal of the vibratory pot (sinusoidal signal). The vibratory frequency will be set to 20 Hz (at higher frequencies the signal will be attenuated by the response time of the PM and its electronics, which react like a low-pass filter).
Observe a signal doubled in frequency with the PM by playing on the orientation of the BBO.
Adjust the orientation of the BBO and the focus of the lens to have a maximum frequency doubled signal.
Figure 6: Autocorrelation set with collinear beams.
Q7: On the oscilloscope, you need to observe an autocorrelation function with a modulation inside: what is the origin of this modulation?
Offset the lens and the adjustable cube corner to find the configuration shown in figure 4.
Retrieve the autocorrelation function on the oscilloscope.
Q8: Compare this autocorrelation function (corresponding to figure 4) with the one you observed previously (corresponding to figure 6) and explain the differences observed.
3.4 Measuring pulse duration
Détecteur
Cristal non linéaire
Lentille
Lame semi-réfléchissante
Coin de cube sur pot vibrant
Impulsion à mesurer
Labwork : Femtosecond laser version 2020 29 The duration of the autocorrelation function is measured by calibration. The adjustable cube wedge is used for this purpose, the translation of which along the beam axis is marked by a micrometer. This micrometer will be used to calibrate the displacement of the vibrating cube corner in order to know the delay it imposes on beam 2. From this, the calibration on the oscilloscope can be deduced.
Q9: It is assumed that the pulse has the form of a hyperbolic secant squared. In this case, the mid-height widths of the pulse Dt and its autocorrelation function Dtautoco are related by Dt = Dtautoco/1.54 (for information, in the case of a Gaussian form Dt = Dtautoco/ √3 ). Measure the pulse duration and determine the measurement uncertainty.