Femtosecond laser pulses, uncertainty principle

For studies in molecular physics, several characteristics of ultrafast laser pulses are of crucial importance. A fundamental consequence of the short duration of femtosecond laser pulses is that they are not truly monochromatic. This is usually considered one of the defining characteristics of laser radiation, but it is only true for laser radiation with pulse durations of a nanosecond (0.000 000 001s, or a million femtoseconds) or longer. Because the duration of a femtosecond pulse is so precisely known, the time-energy uncertainty principle of quantum mechanics imposes an inherent imprecision in its frequency, or colour. Femtosecond pulses must also be coherent, that is the peaks of the waves at different frequencies must come into periodic alignment to construct the overall pulse shape and intensity. The result is that femtosecond laser pulses are built from a range of frequencies the shorter the pulse, the greater the number of frequencies that it supports, and vice versa. 

The flash lamp teclmology first used to photolyse samples has since been superseded by successive generations of increasingly faster pulsed laser teclmologies, leading to a time resolution for optical perturbation metliods tliat now extends to femtoseconds. This time scale approaches tlie ultimate limit on time resolution (At) available to flash photolysis studies, tlie limit imposed by chemical bond energies (AA) tlirough tlie uncertainty principle, AAAt > 2/j. 

For a time there was concern over just how the uncertainty principle would limit what could be achieved with ultrafast laser pulses. The potential problem turned out to be chimerical, not a problem, once coherence came to be appreciated. This conceptual advance was essential to the successful development of experimental femtosecond chemistry it did not progress through better lasers and nonlinear optical tricks and faster computers alone. 

The shortest laser pulse created to date has a duration (full width at half maximum) of 3.5 femtoseconds, and a center wavelength of approximately 800 nm (v 375 THz). However, because of the uncertainty principle, such a pulse has a very large range of frequencies Av. Use the uncertainty principle to determine... 

In conclusion, it is worth reiterating that the anomalous absorption effects described here may be manifest in any experiments that employ sufficiently high-intensity broadband radiation. To this extent, anomalies may be observable in experiments not specifically involving USES light. In particular, the continued advances in techniques of laser pulse compression have now resulted in the production of femtosecond pulses only a few optical cycles in duration (Knox et al. 1985 Brito Cruz et al. 1987 Fork et al. 1987) which necessarily have a very broad frequency spread, as the time/energy uncertainty principle shows. Thus, mean-frequency absorption may have a wider role to play in the absorption of femtosecond pulses. If this is correct, it raises further questions over the suitablity of absorption-based techniques for their characterization. 

Owing to the short pulse width of a femtosecond laser the energy/firequency spread is large, as required by the uncertainty principle, i.e. 

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