Frequency chirp

Figure 29. Complete excitation from 11 > to 2 > by one period of frequency chirping in the case of the three-level model. Upper part-time variation of the population. Middle part-time variation of laser frequency. Bottom part-envelope of the laser pulse. Taken from Ref. [42].

SH pulses, although the presumption that the SH pulses have a hyperholie seeant temporal profile is quite approximate. Correct accounting of the SH pulse shape would improve the accuracy of the model even further. Significantly, the model reported in references is not able to descrihe such a dependence for the reasons discussed above. Although our analysis has assumed fundamental pulses with no frequency chirp, it is possible to extend the present model to describe SHG with chirped fundamental pulses. 

Frequency Chirp Fast broadband radiofrequency sweep used to... 

Fig. 7.11. Four excitation-pulse waveforms achieving the highest ion yield ratio of ni29/m3i. Waveforms in a and b were obtained by the self-learning adaptive pulse control. The waveform in c was obtained by applying a linear frequency chirp at 2.2 x 10 2 ps2 by the 4/-pulse shaper. The waveform in d was obtained by applying a linear frequency chirp at 2.2 x 10 2 ps2 by adjusting the pulse compressor...

A periodic frequency chirp imposed on the pulses is accounted for by allowing a complex envelope function A(t). Thus the carrier C(t) is defined to be whatever part of the electric field that is non-periodic with T. The convolution theorem allows us to calculate the Fourier transform of E(t) from A(u>) and... 

So we see that spectral broadening of the comb [29,30] is achieved by imposing a large frequency chirp on each of the pulses. Provided that the coupling efficiency into the fiber is stable, the periodicity of the pulse train is maintained. The discussion of section 3 is thus equally valid if the electric field E(t) as measured for example at the fiber output facet instead of the laser output coupler. As described below we have used a frequency comb widened to more than 45 THz by a conventional single mode fiber to perform the first phase coherent vacuum UV to radio frequency comparison in our Garching laboratory [16,31], In recent experiments we have confirmed that the fiber does not affect the mode spacing constancy within our experimental uncertainty of a few parts in 1018 [13]. 

The results of these experiments were in reasonable agreement although the Stanford group reported rather smaller errors. Subsequent, continuous-wave experiments at both Stanford and Oxford show poor agreement with the Stanford pulsed result. This has led to speculation that the frequency chirp in pulse amplified experiments is so difficult to characterise that pulse amplifiers cannot be used for precision measurements. 

We have undertaken an experiment to try to improve the performance of pulse amplifier experiments. The system is shown schematically in figure 2. It consisted of a continuous-wave C102 dye laser amplified in three stages by a frequency tripled Q-switched NdtYAG laser. The output energy was approximately 2.0 mJ in a 150 MHz linewidth and was up-shifted from the continuous-wave laser by 60 MHz caused by the frequency chirp. This light was then spectrally filtered in a confocal interferometer with a finesse of 40 and a free spectral range of 300 MHz. The linewidth of the filtered radiation was approximately 16 MHz. 

A short, smooth, Fourier-transform-limited pulse of electromagnetic radiation may be thought of as being composed of a sum of many longer pulses, each with its own center frequency, amplitude, and phase. By controlling the amplitudes and phases of each of these component pulses, the original short, smooth pulse can be converted into a series of temporally displaced, frequency-chirped sub-pulses (Kawashima, et al., 1995 Cao and Wilson, 1997). Such crafted pulses have been used to accomplish a variety of control and information storage objectives. 

In Fig. 5, a spectrum is plotted, which exhibits the oscillatory features of the symmetric stretch motion of Naa in its electronically excited B-state, indicating the well-known oscillation time of 320 fe. The pump-probe spectnun was obtained with transform-limited pulses of 80 fs duration at a center wavelength of 620 nm. Then the experiment was repeated by changing one experimental parameter only the duration of the pump pulse. This was accomplished — as indicated in Fig. 11 — by passing the pump beam across a set of two parallel gratings. The assembly creates a linear frequency chirp. Its duration and spectral sequence depends only on the incidence angle... 

Another method uses optical pulse compression in optical fibers, where the intensity-dependent part of the refractive index causes a frequency chirp and increases the spectral profile and the time duration of the pulse. Subsequent pulse compression, achieved with a pair of optical gratings or by using prisms, leads to a drastic shortening of the pulse. 

Fig. 6.77 Information drawn from FROG (a) plot of measured light frequencies versus delay time r in units of pulse length AT (b) frequency spectrum of (a) (c) frequency chirp [777]...

In Fig. 6.77 this two-dimensional function is illustrated for a Gaussian pulse profile without frequency chirp and for a chirped pulse. 

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