to refer to E(ω-ω0) by writing just E(ω), which we will do in the rest of this article. Just as in the time domain, an intensity and a phase function can be defined in the frequency domain: The quantity is the power spectral density (or simply, the spectrum) of the pulse, and is the phase spectral density (or simply spectral phase). Example of spectral phase functions include the case where is a constant, in which case the pulse is called a bandwidth-limited pulse, or where is a quadratic function, in which case the pulse is called a chirped pulse because of the presence of an instantaneous frequency sweep. Such a chirp may be acquired as a pulse propagates through materials (like glass) and is due to their dispersion. It results in a temporal broadening of the pulse. The intensity functions—temporal and spectral —determine the time duration and spectrum bandwidth of the pulse. As stated by the uncertainty principle, their product (sometimes called the time-bandwidth product) has a lower bound. This minimum value depends on the definition used for the duration and on the shape of the pulse. For a given spectrum, the minimum time-bandwidth product, and therefore the shortest pulse, is obtained by a transform-limited pulse, i.e., for a constant spectral phase . High values of the time-bandwidth product, on the other hand, indicate a more complex pulse. Pulse shape control Although optical devices also used for continuous light, like beam expanders and spatial filters, may be used for ultrashort pulses, several optical devices have been specifically designed for ultrashort pulses. One of them is the pulse compressor, a device that can be used to control the spectral phase of ultrashort pulses. It is composed of a sequence of prisms, or gratings. When properly adjusted it can alter the spectral phase φ(ω) of the input pulse so that the output pulse is a bandwidth-limited pulse with the shortest possible duration. A pulse shaper can be used to make more complicated alterations on both the phase and the amplitude of ultrashort pulses. To accurately control the pulse, a full characterization of the pulse spectral phase is a must in order to get certain pulse spectral phase (such as transform-limited). Then, a spatial light modulator can be used in the 4f plane to control the pulse. Multiphoton intrapulse interference phase scan (MIIPS) is a technique based on this concept. Through the phase