Ultrashort pulse

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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" refers to the femtosecond (fs) to picosecond (ps) range, 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.

[edit] Definition

An ultrashort pulse of light in the time domain. In this figure, the amplitude and intensity are Gaussian functions. The phase function is quadratic, resulting in an instantaneous frequency sweep sometimes called chirp, in analogy to the sound of some birds.

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):

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:

The quantity S(ω) is the spectral density (or simply, the spectrum) of the pulse, and φ(ω) is the spectral phase. Example of spectral 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 intensity functions I(t) and S(ω) determine the time duration and spectral 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 φ(ω). High values of the time-bandwidth product, on the other hand, indicate a more complex pulse.

[edit] 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.

[edit] 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 yields the intensity and phase of a pulse. It's just a spectrally resolved autocorrelation. The algorithm that extracts the intensity and phase from a FROG trace is iterative.
• Grating-eliminated no-nonsense observation of ultrafast incident laser light e-fields (GRENOUILLE), a simplified version of FROG.

[edit] Applications of ultrashort pulses

• Micro-machining

• Femtochemistry

• Medical imaging: Ultrashort laser pulses are used in multiphoton fluorescence microscopes

• Terahertz (T-rays) generation and detection.

[edit] External links

• Multiphoton fluorescence microscopy tutorial
• Spectral interferometry (SI) [1]
• The virtual femtosecond laboratory Lab2

[edit] References

• Hirlimann, C. (2004). “Pulsed Optics”, Rullière, Claude Femtosecond Laser Pulses: Principles and Experiments, 2nd ed., New York: Springer. ISBN 0-387-01769-0.