distribution of this third order nonlinearity is, IF ROGT G (ω,∆t) =
Z ∞
−∞
E1(t)E2∗(t−∆t)E3(t)e(−iωt)dt
2
. (3.14)
This FROG trace is captured in a single shot by a CCD camera. A schematic illus-tration is shown in Figure 3.10, where all three beams are focused by a cylindrical mirror to form a narrow, elongated focal line in the interaction zone.
Figure 3.10 Setup of a single shot UV FROG with reflecting mirrors. The setup comprises a mask (M), which creates three elongated beams, focused by a curved mirror (CM), via a split mirror (SM) onto the none-linear medium (NLM). The beams are than collimated by (L1) and the signal is selected by a beam block (BB), spectrally resolved by a diffractive grating (DG) and imaged by a second lens (L2) onto a camera (CCD), as taken from [110].
The described setup allows the measurement of single ultrashort UV pulses at λ0 = 248.5 nm, with high single pulse energies also in the presence of pulse to pulse fluctuation, typical for excimer amplifier [88], and pulse durations ranging from 0.1−2 ps. Mathematically a TG trace is very similar to a polarization gating (PG) trace and is retrieved using a similar algorithm [47]. The TG FROG does not have any polarizers or other components in the beam if an all reflective setup is chosen like in the device used here, which was designed and built by T. Nagy [110].
One drawback of the setup is the high complexity resulting from the requirements to the overlapping precision of the three beams. The camera used here is a triggered Lumenera Lu-165M with no cover glass and with a UV sensitive coating on the camera chip. The software used for the image acquisition is MrBeam developed in the LLG e.V. It allows an easy background subtraction and trace recording.
3.2.2 Multi-Shot SD FROG
A self-diffraction (SD) FROG uses a very similar principle than the TG FROG with the difference that the induced grating formed by two beams under a small angle is used for a self-diffraction of the involved beams. The resulting signal intensity distribution is then given by:
IF ROGSD (ω,∆t) =
Z ∞
−∞
E(t)2E(t−∆t)e(−iωt)dt
2
. (3.15)
The power scaling with the third power of the electric field shows that it is also based on a χ(3) nonlinear effect, but in this case an electric field is arriving only from two directions. The two beams from the directions described byk1 andk2 are creating a new vectork3 with a signal in a new direction, as depicted in the inset in the top left in Figure 3.11.
Dt SPEC FS FS
FM1
M1 SM FM2
k2 k1 k3
Figure 3.11 Setup of a multi-shot SD FROG. The incident beam is divided in two parts at a split mirror (SM), directed by (M1) to a focusing mirror (FM1) which overlaps the focus in a fused silica slice (FS). The beams are blocked and the non-collinear signal is focused by (FM2) into a spectrometer (SPEC).
In the multi-shot setup the beam is split up in two by a divided mirror and a variable delay time ∆t is introduced by a nm-precision delay stage for one of the pulses. The beams are focused and overlap inside the medium, where the signal beam is diffracted on its own intensity grating and leaving the medium under an increased angle. The SD signal is then focused on a fiber entrance of a spectrometer.
The beam path is shown schematically in Figure 3.11. The different spectra for each time step are recorded and form a trace which is used for retrieving the complete pulse information, containing the spectrum, the pulse duration and the temporal and spectral phase. In this method not a phase matched nonlinear medium is used, therefore causing more distortions of the beam. This effect is reduced if small angles of the interfering beams (. 2◦) and thin fused silica slices are used (. 200 µm).
However, the distortions limit the well measurable pulse duration to above 20 fs, better above 100 fs. This third order method can reveal asymmetric traces which show a linear chirp directly in the FROG trace and works in the IR and the UV optical range when no polarizers are used and the setup from Figure 3.11 is realized by aluminum mirrors [47]. The device used for this work was home built by T.
Nagy and P. Simon and incorporates a software for an automated multi-shot trace recording.
3.2.3 Multi Shot SHG FROG
The above described SD FROG device can easily be transformed to a setup using the second harmonic generation as a signal with a similar beam path. Therefore in the focus a BBO crystal is inserted creating a SHG signal with 2ω1 = ω1+ω1,
described in Section 2.2.1, given by IF ROGSHG (ω,∆t) =
Z ∞
−∞
E(t)E(t−∆t)e(−iωt)dt
2
. (3.16)
Unlike FROG traces resulting from third order nonlinearities, the SHG traces are not intuitively to understand. They are not unambiguous in the retrieved time direction, a positive or negative chirp can not be distinguished.
SPEC BBO
2w1 w1
Dt BBO
w1
FM1 FM2
M1 SM
Figure 3.12 Setup of a Multi Shot SHG FROG, the incident beam is divided by a split mirror (SM), directed by (M1) to a focusing mirror (FM1) which overlaps the focus in a BBO crystal (BBO), the beams are blocked and the created SHG signal in the center is focused by (FM2) into a fiber entrance of a spectrometer (SPEC).
Due to the frequency doubling and the propagation in a new direction, the spectral and spatial distinction from the fundamental pulse is easier than with other methods.
This leads to a significantly higher signal to noise ratio than with other methods.
Since it is a second order effect, already small pulse energies are sufficient to create a signal [47]. This method allows to measure few fs pulses, if the phase matching bandwidth of the SHG crystal is sufficient, as discussed in Section 2.2.2.
FROG Trace and Pulse Retrieval
In all the described different FROG methods a signal-trace is recorded, shown in Figure 3.13 (top left), from which information about pulse duration, spectrum and the phase information in the temporal and the frequency domain can be retrieved with more or less unambiguities. In this work the retrieval algorithm from the soft-ware FROG 3.2.2 is used, where a trace can be loaded and the different recording methods are included.
The FROG phase-retrieval mechanism can obtain the complex electric fieldE(t) of a pulse from the recorded trace signal IFROG(ω,∆t), since it inherits a gated spec-tral information from which the phase information can be obtained. The retrieval procedure works as follows: with a guessed field E(t) a FROG signal is obtained IFROGretrieved(ω,∆t) by using one of the equations (3.14), (3.15) or (3.16). This delivers the Fourier transform in the time domain. This signal is compared to the measured trace signal IFROG(ω,∆t) and an improved version is created which is than inverse Fourier transformed in the time domain to generate the electric field again. This process is iterated and various methods can be applied to reduce the difference
be-(a) single pulse TG trace (b) double pulse TG trace
Figure 3.13 Experimental FROG traces (top left) shown in (a) and (b) and retrieved traces (top right), respectively. In each plot (bottom left) of (a) and (b) the retrieved spectrum (black) and spectral phase (blue) is shown and in the (bottom right) the retrieved temporal pulse shape and the temporal phase. The pulses are amplified by a KrF excimer and compressed toτ≈150 fs.
In (a) a single pulse and in (b) a double pulse with ∆τ ≈1.3 ps delay between the pulses is shown. The delay is created by an interferometer.
tween the measured and the retrieved pulse, here the software FROG 3.2.2 uses a generalized projections algorithm [49].
In Figure 3.13 two examples of measured FROG traces are shown of a single and double pulse. The trace is obtained by a TG FROG and the retrieved trace and the corresponding spectrum, spectral phase, intensity distribution and temporal phase are shown.