When we measure an ultrashort pulse, we wish to know its intensity and phase profile. In the frequency domain we can use a standard spectrome- ter to measure the spectrum, giving us intensity versus wavelength. In our case, we use an Ocean Optics HR2000CG spectrometer. Or, we can make measurements in the time domain, a technique which has historically been dominated by the autocorrelator which measures intensity versus time, ef- fectively using the pulse to measure itself. Unfortunately, autocorrelators are not without their drawbacks [116]. Specifically, as the pulse becomes more complex, the autocorrelation of the pulse in fact becomes simpler causing the fine structure of the pulse to be lost. Secondly, the autocor- relation does not easily reveal the FWHM of the pulse since this depends on the pulse shape. If one assumes a Gaussian pulse with multiplication
Beam splitter
variable delay,t
E(t- )t
E(t)
BBO crystal Camera and spectrometer
E (t, )sig t
Figure 4.7: Experimental layout of an SHG FROG.
factor 1.41 a longer pulse will be predicted than if one assume a sech2with a multiplication factor of 1.54. This is further complicated by the fact that no pulse exactly fits a Gaussian or sech2 function [116]. Further to this, autocorrelators can be quite tricky to align, and unfortunately, when not aligned correctly they can give misleading results.
FROG and GRENOUILLE
More recently, a series of techniques referred to as Frequency Resolved Op- tical Gating (FROG) have been developed which are able to extract the full intensity and phase data from an ultrashort pulse. In FROG, the incom- ing pulse is split in two and one pulse delayed with respect to the other, in much the same way as in autocorrelation. However, in FROG we then measure the spectrum of the signal pulse with respect to delay. This re- sults in a time-frequency domain measurement where we can generate a two-dimensional trace of intensity versus frequency and delay. It now be- comes possible to extract the full intensity and phase data from an ultra- short pulse [116].
Numerous geometries of FROG exist; figure 4.7 shows a second har- monic generation FROG (SHG FROG). In the SHG FROG, the pulses are
spectrally resolved from an autocorrelator based around a second harmonic generating crystal, resulting in a trace of intensityIversus frequencyωand delayτ related to the spectrum of the pulse [116]
I(ω, τ) = ¯ ¯ ¯ ¯ ¯ Z ∞ −∞ E(t) +E(t−τ) exp(−iωt)dt ¯ ¯ ¯ ¯ ¯ 2 . (4.2)
The SHG FROG is a very sensitive measurement technique frequently used for low input pulse energies such as the unamplified pulses from a Ti:sapphire seed laser. The reason for this sensitivity is in part due to the strength of the second order non-linearity (compared to the weaker third- harmonics used by some FROG systems). Additionally, the SHG FROG gives a relatively high signal to noise ratio since the signal light is of a dif- ferent frequency from the input pulse and hence scattered light may be easily filtered.
Trebino, O’Shea and co-workers have devised a novel SHG FROG (fig- ure 4.8) using a thick non-linear crystal to replace the thin crystal and spec- trograph, and a Fresnel biprism to replace the beam splitter and delay line. These innovations have led to the GRENOUILLE (GRating-Eliminated No- nonsense Observation of Ultrafast Incident Laser Light E-fields) [117]—an extremely compact ultrashort pulse measurement device capable of full in- tensity and phase measurements. The lack of a delay line means that the GRENOUILLE is a single shot device, making it possible to compare indi- vidual pulses from low repetition rate amplifier systems [118].
The Fresnel biprism is a prism with an apex angle approaching 180◦
[119]. When a wide beam is incident on the biprism, the beam is split into two and the resulting rays are overlapped into the SHG crystal with variable delay. The crystal is imaged onto a CCD camera, giving a plot of signal versus position (delay) in the horizontal plane, as in a traditional FROG geometry. However, in contrast to the conventional FROG geome-
Camera f Camera f/2 Top Side Cylindrical lens Fresnel biprism Thick BBO crystal Imaging lens Fourier Transform lens
Figure 4.8: Schematic showing the GRENOUILLE beam geometry. (Adapted from reference [117].)
try, the beams in the GRENOUILLE are automatically aligned in space and time [117]. This greatly simplifies the optical alignment, negating the need to align a delay line.
The other innovation with the GRENOUILLE is in the use of a thick SHG crystal which reduces the phase-matching bandwidth and hence the phase matched wavelength becomes a function of angle. In this way, the thick SHG crystal also acts as a spectrograph. The cylindrical lens maps the wavelengths at different output angles as a linear function of vertical position on the camera. The signal received by the camera is analogous to an SHG FROG experiment where delay is plotted horizontally against wavelength vertically.
The GRENOUILLE was used to monitor the pulse length from the am- plifier and the GRENOUILLE was a useful aid to alignment, compressor optimization and for optimizing the delay settings which control the am- plifier’s Pockel cells. A thin 4%beam splitter (Femtolasers) inserted into the beam after the amplifier allowed live viewing of the FROG trace dur- ing the experiment. Figure 4.9 shows a typical GRENOUILLE trace from the Spitfire CPA system.
Delay / fs W avelength/nm -200 -100 0 100 200 650 700 750 800 850 900 -200 -100 0 100 200 Delay / fs Intensity 33 fs -p 0 p Phase/rad 700 750 800 0 0.5 1 Wavelength / nm Intensity -p 0 p Phase/rad (a) 0 0.5 1 (b) (c)
Figure 4.9: (a) The GRENOUILLE trace of a 33 fs pulse from the Spitfire CPA system. (b) The time domain intensity and phase and (c) the frequency domain intensity and phase.