An essential difference between continuous-wave and pulsed lasers
is that the intensity, phase etc. of a continuous-wave laser are
continuously evolving variables, whereas for pulsed lasers we are
dealing with parameters of discrete pulses.
Each pulse can be characterized by a set of parameters such as the pulse energy, peak power, duration, mean optical frequency and arrival time, and their fluctuations need to be described statistically.
For single pulses, possibly emitted on demand, the statistical description is relatively simple. For each pulse parameter, there is a distribution function, which may often be approximated with a Gaussian. It is then often sufficient to specify an r.m.s. value of a quantity like the pulse energy under certain conditions (e.g. pulse emission after some minimum pumping time). It may, however, also be relevant to consider correlations between different parameters, as discussed further below.
Frequently, a laser emits pulses periodically with a certain pulse repetition rate frep. The statistics of the fluctuations of pulse parameters can then be described with a power spectral density (PSD) as for a continuous-wave laser, except that the upper noise frequency is limited to frep / 2. Fluctuations faster than that are meaningless. For example, an oscillation of pulse energy with 0.8 frep could not be distinguished from an oscillation with 0.2 frep. On the other hand, the lowest noise frequency on which information can be obtained is again limited by the measurement time: very slow fluctuations are visible only when data are recorded over long times.
For single pulses, possibly emitted on demand, the statistical description is relatively simple. For each pulse parameter, there is a distribution function, which may often be approximated with a Gaussian. It is then often sufficient to specify an r.m.s. value of a quantity like the pulse energy under certain conditions (e.g. pulse emission after some minimum pumping time). It may, however, also be relevant to consider correlations between different parameters, as discussed further below.
Frequently, a laser emits pulses periodically with a certain pulse repetition rate frep. The statistics of the fluctuations of pulse parameters can then be described with a power spectral density (PSD) as for a continuous-wave laser, except that the upper noise frequency is limited to frep / 2. Fluctuations faster than that are meaningless. For example, an oscillation of pulse energy with 0.8 frep could not be distinguished from an oscillation with 0.2 frep. On the other hand, the lowest noise frequency on which information can be obtained is again limited by the measurement time: very slow fluctuations are visible only when data are recorded over long times.
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