Transform Limit

The minimum pulse duration possible for a given optical spectrum.

In ultrafast optics, the transform limit (or Fourier limit, Fourier transform limit) is usually understood as the lower limit for the pulse duration which is possible for a given optical Spectrum of a pulse. A pulse at this limit is called transform-limited. The condition of being at the transform limit is essentially equivalent to the condition of a frequency-independent Spectral Phase (which leads to the maximum possible peak power), and basically implies that the time-bandwidth product is at its minimum and that there is no chirp.

For a given pulse duration, transform-limited Pulses are those with the minimum possible spectral width. This is important e.g. in optical Fiber communications: a Transmitter emitting close to transform-limited pulses can minimize the effect of Chromatic Dispersion during propagation in the Transmission fiber, and thus maximize the possible transmission distance.

Many mode-locked lasers, particularly Soliton lasers, are able to generate close to transform-limited pulses. Processes such as Dispersion or optical nonlinearities can cause chirp and thus can lead away from the transform limit. Non-transform-limited pulses may be brought to the transform limit (and thus temporally compressed) by modifying their spectral phase, e.g. by applying a proper amount of dispersion or a pulse shaper. This is called dispersion compensation. For not too broad spectra, compensation of second-order dispersion is often sufficient, while very broad spectra may require compensation also of higher-order dispersion in order to get close to the transform limit.

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