Introduction
In optics, an ultrashort pulse of light is an electromagnetic pulse whose time duration is on the order of the femtosecond (10 - 15 second). Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators. They are commonly referred to as ultrafast events.
They are characterized by a high peak power that usually leads to nonlinear interactions in various materials, including air. These processes are studied in the field of nonlinear optics.
In the specialized literature, "ultrashort" means in the range 1 fs -- 1 ps, although such pulses no longer hold the record for the shortest pulses artificially generated. Indeed, pulse durations on the attosecond time scale have been reported.
Definition
The real electric field corresponding to an ultrashort pulse is oscillating at an angular frequency ω0 corresponding to the central wavelength of the pulse. To facilitate calculations, a complex field E(t) is defined. Formally, it is defined as the analytic signal corresponding to the real field.
The central angular frequency ω0 is usually explicitly written in the complex field, which may be separated as an intensity function I(t) and a phase function ψ(t):
The expression of the complex electric field in the frequency domain is obtained from the Fourier transform of E(t):
- E(ω) = FE(t)
Because of the presence of the 
term, E(ω) is centered around ω0, and it is a common practice 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:
Example of phase functions include the case where φ(ω) is a constant, in which case the pulse is called a bandwidth limited pulse, or where φ(ω) 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 width intensity functions I(t) and S(ω) determine the time duration and spectral bandwidth of the pulse. As stated by the incertainty principle, their product (sometimes called the time-bandwidth product) has a lower bound. This minimum value depends on the definition used and on the shape of the pulse. For a given spectrum, the minimum time-bandwidth product is obtained by a transform-limited pulse, i.e., for a constant spectral phase φ(ω). High values of the time-bandwidth product, on the other hand, reveal the pulse complexity.
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.
Measurement techniques
Several techniques are available to measure ultrashort optical pulses:
- intensity autocorrelation: gives the pulse width when a particular pulse shape is assumed;
- spectral interferometry (SI): a linear technique that can be used when a pre-characterized reference pulse is available. Gives the intensity and phase. A self-referenced, nonlinear version is also used with a reference pulse with a frequency shear. The algorithm that extracts the intensity and phase from the SI signal is direct.
- frequency-resolved optical gating (FROG): a nonlinear technique that gives the intensity and phase. It's just a spectrally-resolved autocorrelation. The algorithm that extracts the intensity and phase from the FROG trace is iterative
Applications of ultrashort pulses
Last updated: 05-21-2005 05:12:41
